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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> if (glob_type_given_pole = 4) then # if number 2
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[2,1],2.0) + expt(array_given_rad_poles[2,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[2,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 3
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 3;
> if (array_poles[2,1] <> glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4, array_poles[2,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 3;
> if ((array_real_poles[2,1] > 0.0) and (array_real_poles[2,1] <> glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4, array_real_poles[2,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 3;
> if ((array_complex_poles[2,1] > 0.0) and (array_complex_poles[2,1] <> glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4, array_complex_poles[2,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[2, 1], 2.0)
+ expt(array_given_rad_poles[2, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_poles[2, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if 0. < array_real_poles[2, 1] and
array_real_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_real_poles[2, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if 0. < array_complex_poles[2, 1] and
array_complex_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_complex_poles[2, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 3;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y1[1]) < min_size) then # if number 3
> min_size := omniabs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (omniabs(array_y2[1]) < min_size) then # if number 3
> min_size := omniabs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < 1.0) then # if number 3
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y1[1]) < min_size then
min_size := omniabs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if omniabs(array_y2[1]) < min_size then
min_size := omniabs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> est_tmp := omniabs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := omniabs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 5
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 6
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 5;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 5
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 6
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 5;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 4
> glob_normmax := tmp;
> fi;# end if 4
> fi;# end if 3;
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 4
> glob_normmax := tmp;
> fi;# end if 4
> fi;# end if 3;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 3
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 4
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 4
> fi;# end if 3;
> if ( not glob_reached_optimal_h) then # if number 3
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 3;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y1_higher[1,n]) = 0.0) or (omniabs(array_y1_higher[1,n+1]) = 0.0)) then # if number 3
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y1_higher[1,n] * glob_h / array_y1_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt = 0) then # if number 5
> if (tmp_rad < rad_c) then # if number 6
> rad_c := tmp_rad;
> fi;# end if 6;
> elif
> (cnt > 0) then # if number 6
> found_sing := 0;
> fi;# end if 6
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_pole[1]) then # if number 6
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM radius ratio test in Henrici1
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> #TOP radius ratio test in Henrici2
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y2_higher[1,n]) = 0.0) or (omniabs(array_y2_higher[1,n+1]) = 0.0)) then # if number 5
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y2_higher[1,n] * glob_h / array_y2_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 6
> if (tmp_rad < rad_c) then # if number 7
> rad_c := tmp_rad;
> fi;# end if 7;
> elif
> (cnt = 0) then # if number 7
> if (tmp_rad < rad_c) then # if number 8
> rad_c := tmp_rad;
> fi;# end if 8;
> elif
> (cnt > 0) then # if number 8
> found_sing := 0;
> fi;# end if 8
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_pole[1]) then # if number 8
> array_pole[1] := rad_c;
> array_poles[2,1] := rad_c;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM radius ratio test in Henrici2
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) = 0.0) or (omniabs(array_y1_higher[1,m-1]) = 0.0) or (omniabs(array_y1_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 7
> rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 8
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 8
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 7;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) = 0.0) or (omniabs(array_y2_higher[1,m-1]) = 0.0) or (omniabs(array_y2_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 7
> rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 8
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[2,1] := rcs;
> array_real_poles[2,2] := ord_no;
> else
> array_real_poles[2,1] := glob_large_float;
> array_real_poles[2,2] := glob_large_float;
> fi;# end if 8
> else
> array_real_poles[2,1] := glob_large_float;
> array_real_poles[2,2] := glob_large_float;
> fi;# end if 7;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y1_higher[1,n]) <> 0.0) then # if number 7
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 7;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 7
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 10
> if (rcs > 0.0) then # if number 11
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 11
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 10
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 9
> fi;# end if 8;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 7;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y2_higher[1,n]) <> 0.0) then # if number 7
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 7;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 7
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 10
> if (rcs > 0.0) then # if number 11
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 11
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 10
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 9
> fi;# end if 8;
> array_complex_poles[2,1] := rad_c;
> array_complex_poles[2,2] := ord_no;
> fi;# end if 7;
> #BOTTOM RADII COMPLEX EQ = 2
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 7
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 7;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 7
> display_poles();
> fi;# end if 7
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y1_higher[1, n]) = 0. or
omniabs(array_y1_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y1_higher[1, n]*glob_h/array_y1_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y2_higher[1, n]) = 0. or
omniabs(array_y2_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y2_higher[1, n]*glob_h/array_y2_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[2, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y1_higher[1, m]) = 0. or
omniabs(array_y1_higher[1, m - 1]) = 0. or
omniabs(array_y1_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y2_higher[1, m]) = 0. or
omniabs(array_y2_higher[1, m - 1]) = 0. or
omniabs(array_y2_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[2, 1] := rcs;
array_real_poles[2, 2] := ord_no
else
array_real_poles[2, 1] := glob_large_float;
array_real_poles[2, 2] := glob_large_float
end if
else
array_real_poles[2, 1] := glob_large_float;
array_real_poles[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y1_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y2_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[2, 1] := rad_c;
array_complex_poles[2, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 7
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 8
> array_norms[iii] := omniabs(array_y1[iii]);
> fi;# end if 8;
> iii := iii + 1;
> od;# end do number 1
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 8
> array_norms[iii] := omniabs(array_y2[iii]);
> fi;# end if 8;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 7;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp1[1] := (array_m1[1] * (array_y2[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y1_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre sub FULL - CONST $eq_no = 2 i = 1
> array_tmp5[1] := array_y1[1] - array_const_1D0[1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y2_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre sub FULL CONST $eq_no = 2 i = 2
> array_tmp5[2] := array_y1[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y1_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre sub FULL CONST $eq_no = 2 i = 3
> array_tmp5[3] := array_y1[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y1_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre sub FULL CONST $eq_no = 2 i = 4
> array_tmp5[4] := array_y1[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y1_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre sub FULL CONST $eq_no = 2 i = 5
> array_tmp5[5] := array_y1[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult FULL FULL $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_m1,array_y2,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y1_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit FULL - NOT FULL sub $eq_no = 2
> array_tmp5[kkk] := array_y1[kkk];
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y2_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_tmp1[1] := array_m1[1]*array_y2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
if not array_y1_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp5[1] := array_y1[1] - array_const_1D0[1];
if not array_y2_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_m1, array_y2, 1);
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
if not array_y1_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5[2] := array_y1[2];
if not array_y2_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_m1, array_y2, 1);
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_tmp2[3];
if not array_y1_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp5[3] := array_y1[3];
if not array_y2_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_m1, array_y2, 1);
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_tmp2[4];
if not array_y1_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp5[4] := array_y1[4];
if not array_y2_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_m1, array_y2, 1);
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_tmp2[5];
if not array_y1_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp5[5] := array_y1[5];
if not array_y2_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := array_tmp3[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y1_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
array_tmp5[kkk] := array_y1[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y2_set_initial[2, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y2_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-42.4g %s
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then printf("%-30s = %-32d %s
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(1.0 + cos(x));
> end;
exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc
> exact_soln_y2 := proc(x)
> return(1.0 + sin(x));
> end;
exact_soln_y2 := proc(x) return 1.0 + sin(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest2postode.ode#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 - 1.0;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 10.0;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y1_init:= Array(0..(max_terms + 1),[]);
> array_y2_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(3 + 1),[]);
> array_last_rel_error:= Array(0..(3 + 1),[]);
> array_type_pole:= Array(0..(3 + 1),[]);
> array_type_real_pole:= Array(0..(3 + 1),[]);
> array_type_complex_pole:= Array(0..(3 + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_y2:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1D0[1] := 1.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 10.0;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y1_set_initial[1,1] := true;
> array_y1_set_initial[1,2] := false;
> array_y1_set_initial[1,3] := false;
> array_y1_set_initial[1,4] := false;
> array_y1_set_initial[1,5] := false;
> array_y1_set_initial[1,6] := false;
> array_y1_set_initial[1,7] := false;
> array_y1_set_initial[1,8] := false;
> array_y1_set_initial[1,9] := false;
> array_y1_set_initial[1,10] := false;
> array_y1_set_initial[1,11] := false;
> array_y1_set_initial[1,12] := false;
> array_y1_set_initial[1,13] := false;
> array_y1_set_initial[1,14] := false;
> array_y1_set_initial[1,15] := false;
> array_y1_set_initial[1,16] := false;
> array_y1_set_initial[1,17] := false;
> array_y1_set_initial[1,18] := false;
> array_y1_set_initial[1,19] := false;
> array_y1_set_initial[1,20] := false;
> array_y1_set_initial[1,21] := false;
> array_y1_set_initial[1,22] := false;
> array_y1_set_initial[1,23] := false;
> array_y1_set_initial[1,24] := false;
> array_y1_set_initial[1,25] := false;
> array_y1_set_initial[1,26] := false;
> array_y1_set_initial[1,27] := false;
> array_y1_set_initial[1,28] := false;
> array_y1_set_initial[1,29] := false;
> array_y1_set_initial[1,30] := false;
> array_y2_set_initial[2,1] := true;
> array_y2_set_initial[2,2] := false;
> array_y2_set_initial[2,3] := false;
> array_y2_set_initial[2,4] := false;
> array_y2_set_initial[2,5] := false;
> array_y2_set_initial[2,6] := false;
> array_y2_set_initial[2,7] := false;
> array_y2_set_initial[2,8] := false;
> array_y2_set_initial[2,9] := false;
> array_y2_set_initial[2,10] := false;
> array_y2_set_initial[2,11] := false;
> array_y2_set_initial[2,12] := false;
> array_y2_set_initial[2,13] := false;
> array_y2_set_initial[2,14] := false;
> array_y2_set_initial[2,15] := false;
> array_y2_set_initial[2,16] := false;
> array_y2_set_initial[2,17] := false;
> array_y2_set_initial[2,18] := false;
> array_y2_set_initial[2,19] := false;
> array_y2_set_initial[2,20] := false;
> array_y2_set_initial[2,21] := false;
> array_y2_set_initial[2,22] := false;
> array_y2_set_initial[2,23] := false;
> array_y2_set_initial[2,24] := false;
> array_y2_set_initial[2,25] := false;
> array_y2_set_initial[2,26] := false;
> array_y2_set_initial[2,27] := false;
> array_y2_set_initial[2,28] := false;
> array_y2_set_initial[2,29] := false;
> array_y2_set_initial[2,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 7
> glob_h := glob_max_h;
> fi;# end if 7;
> if (glob_display_interval < glob_h) then # if number 7
> glob_h := glob_display_interval;
> fi;# end if 7;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> if (glob_subiter_method = 1 ) then # if number 7
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 8
> subiter := 1;
> while (subiter <= 2) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 8;
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 8
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 9
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 9;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 9
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 9;
> if (opt_iter > 100) then # if number 9
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 9;
> if (glob_display_interval < glob_h) then # if number 9
> glob_h := glob_display_interval;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 1;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 10
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 11
> subiter := 1;
> while (subiter <= 2) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 11;
> display_alot(current_iter);
> if (glob_look_poles) then # if number 11
> #left paren 0004C
> check_for_pole();
> fi;# end if 11;#was right paren 0004C
> if (reached_interval()) then # if number 11
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 11;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 2
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y2;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 2
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 11
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 11;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 11
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 11;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 - 1.0;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 11
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T02:58:59-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest2")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 12
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 12;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"mtest2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest2 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 - 1.0;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 12
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 12;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 11;
> if (glob_html_log) then # if number 11
> fclose(html_log_file);
> fi;# end if 11
> ;
> ;;
> fi;# end if 10
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest2postode.ode#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 10.0;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 64;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y1_init := Array(0 .. max_terms + 1, []);
array_y2_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 4, []);
array_last_rel_error := Array(0 .. 4, []);
array_type_pole := Array(0 .. 4, []);
array_type_real_pole := Array(0 .. 4, []);
array_type_complex_pole := Array(0 .. 4, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_y2 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 4, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 4, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 4, 0 .. 4, []);
array_real_poles := Array(0 .. 4, 0 .. 4, []);
array_complex_poles := Array(0 .. 4, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 10.0;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y1_set_initial[1, 1] := true;
array_y1_set_initial[1, 2] := false;
array_y1_set_initial[1, 3] := false;
array_y1_set_initial[1, 4] := false;
array_y1_set_initial[1, 5] := false;
array_y1_set_initial[1, 6] := false;
array_y1_set_initial[1, 7] := false;
array_y1_set_initial[1, 8] := false;
array_y1_set_initial[1, 9] := false;
array_y1_set_initial[1, 10] := false;
array_y1_set_initial[1, 11] := false;
array_y1_set_initial[1, 12] := false;
array_y1_set_initial[1, 13] := false;
array_y1_set_initial[1, 14] := false;
array_y1_set_initial[1, 15] := false;
array_y1_set_initial[1, 16] := false;
array_y1_set_initial[1, 17] := false;
array_y1_set_initial[1, 18] := false;
array_y1_set_initial[1, 19] := false;
array_y1_set_initial[1, 20] := false;
array_y1_set_initial[1, 21] := false;
array_y1_set_initial[1, 22] := false;
array_y1_set_initial[1, 23] := false;
array_y1_set_initial[1, 24] := false;
array_y1_set_initial[1, 25] := false;
array_y1_set_initial[1, 26] := false;
array_y1_set_initial[1, 27] := false;
array_y1_set_initial[1, 28] := false;
array_y1_set_initial[1, 29] := false;
array_y1_set_initial[1, 30] := false;
array_y2_set_initial[2, 1] := true;
array_y2_set_initial[2, 2] := false;
array_y2_set_initial[2, 3] := false;
array_y2_set_initial[2, 4] := false;
array_y2_set_initial[2, 5] := false;
array_y2_set_initial[2, 6] := false;
array_y2_set_initial[2, 7] := false;
array_y2_set_initial[2, 8] := false;
array_y2_set_initial[2, 9] := false;
array_y2_set_initial[2, 10] := false;
array_y2_set_initial[2, 11] := false;
array_y2_set_initial[2, 12] := false;
array_y2_set_initial[2, 13] := false;
array_y2_set_initial[2, 14] := false;
array_y2_set_initial[2, 15] := false;
array_y2_set_initial[2, 16] := false;
array_y2_set_initial[2, 17] := false;
array_y2_set_initial[2, 18] := false;
array_y2_set_initial[2, 19] := false;
array_y2_set_initial[2, 20] := false;
array_y2_set_initial[2, 21] := false;
array_y2_set_initial[2, 22] := false;
array_y2_set_initial[2, 23] := false;
array_y2_set_initial[2, 24] := false;
array_y2_set_initial[2, 25] := false;
array_y2_set_initial[2, 26] := false;
array_y2_set_initial[2, 27] := false;
array_y2_set_initial[2, 28] := false;
array_y2_set_initial[2, 29] := false;
array_y2_set_initial[2, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err,
16, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T02:58:59-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest2");
logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 189 | ");
logitem_str(html_log_file,
"mtest2 diffeq.mxt");
logitem_str(html_log_file,
"mtest2 maple results")
;
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest2postode.ode#################
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
diff ( y2 , x , 1 ) = y1 - 1.0;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 10.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(1.0 + cos(x));
end;
exact_soln_y2 := proc(x)
return(1.0 + sin(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 9.9
estimated_steps = 9900000
step_error = 1.0101010101010101010101010101010e-17
est_needed_step_err = 1.0101010101010101010101010101010e-17
opt_iter = 1
bytes used=4000176, alloc=3276200, time=0.17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.4672086055323049562331277806885e-183
estimated_step_error = 2.4672086055323049562331277806885e-183
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6557156646065677204134289038211e-175
estimated_step_error = 1.6557156646065677204134289038211e-175
best_h = 4.00e-06
opt_iter = 3
bytes used=8001416, alloc=4586680, time=0.38
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1111319694584368636820923174826e-167
estimated_step_error = 1.1111319694584368636820923174826e-167
best_h = 8.000e-06
opt_iter = 4
bytes used=12002188, alloc=4586680, time=0.59
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.4566803670241957246681619817534e-160
estimated_step_error = 7.4566803670241957246681619817534e-160
best_h = 1.60000e-05
opt_iter = 5
bytes used=16003096, alloc=4586680, time=0.79
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.0040934120378230048946847695108e-152
estimated_step_error = 5.0040934120378230048946847695108e-152
best_h = 3.200000e-05
opt_iter = 6
bytes used=20004020, alloc=4586680, time=1.00
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3581901424816281269073121711211e-144
estimated_step_error = 3.3581901424816281269073121711211e-144
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.2536431215809227087580736291233e-136
estimated_step_error = 2.2536431215809227087580736291233e-136
best_h = 0.000128
opt_iter = 8
bytes used=24004848, alloc=4586680, time=1.20
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5123941176543087498746423194481e-128
estimated_step_error = 1.5123941176543087498746423194481e-128
best_h = 0.000256
opt_iter = 9
bytes used=28005744, alloc=4586680, time=1.40
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0149502701580566739311213784161e-120
estimated_step_error = 1.0149502701580566739311213784161e-120
best_h = 0.000512
opt_iter = 10
bytes used=32006408, alloc=4586680, time=1.60
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.8112127244081165253087202414265e-113
estimated_step_error = 6.8112127244081165253087202414265e-113
best_h = 0.001024
opt_iter = 11
bytes used=36007600, alloc=4586680, time=1.80
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.5709231343600303584753702483547e-105
estimated_step_error = 4.5709231343600303584753702483547e-105
best_h = 0.002048
opt_iter = 12
bytes used=40008448, alloc=4586680, time=2.00
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.0674887502340254951354356814935e-97
estimated_step_error = 3.0674887502340254951354356814935e-97
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0585490116180929098885606683401e-89
estimated_step_error = 2.0585490116180929098885606683401e-89
best_h = 0.008192
opt_iter = 14
bytes used=44009252, alloc=4586680, time=2.20
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3814583197402461309888420940035e-81
estimated_step_error = 1.3814583197402461309888420940035e-81
best_h = 0.016384
opt_iter = 15
bytes used=48010588, alloc=4586680, time=2.40
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.2706681184281159182706538798651e-74
estimated_step_error = 9.2706681184281159182706538798651e-74
best_h = 0.032768
opt_iter = 16
bytes used=52011776, alloc=4586680, time=2.60
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.2212490020161221570851682852212e-66
estimated_step_error = 6.2212490020161221570851682852212e-66
best_h = 0.065536
opt_iter = 17
bytes used=56012620, alloc=4586680, time=2.81
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.1747508750792467142506979498164e-58
estimated_step_error = 4.1747508750792467142506979498164e-58
best_h = 0.131072
opt_iter = 18
bytes used=60013704, alloc=4586680, time=3.01
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.8012747543996062244493916551861e-50
estimated_step_error = 2.8012747543996062244493916551861e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0998334166468281523068141984106
y2[1] (numeric) = 1.0998334166468281523068141984106
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09579
Order of pole (three term test) = -1.134
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=64014656, alloc=4586680, time=3.21
x[1] = 0.11
y1[1] (analytic) = 1.9939560979566968503578396114198
y1[1] (numeric) = 1.9939560979566968503578396114198
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1097783008371748086649494900835
y2[1] (numeric) = 1.1097783008371748086649494900835
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1052
Order of pole (three term test) = -1.184
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=68015432, alloc=4652204, time=3.42
x[1] = 0.12
y1[1] (analytic) = 1.9928086358538662522480981678576
y1[1] (numeric) = 1.9928086358538662522480981678576
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.119712207288919359967350614271
y2[1] (numeric) = 1.119712207288919359967350614271
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1146
Order of pole (three term test) = -1.239
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=72016628, alloc=4652204, time=3.63
x[1] = 0.13
y1[1] (analytic) = 1.9915618937147880395945121711518
y1[1] (numeric) = 1.9915618937147880395945121711518
absolute error = 1e-63
relative error = 5.0211846448554824157110355498792e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1296341426196948595412058107083
y2[1] (numeric) = 1.1296341426196948595412058107083
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1239
Order of pole (three term test) = -1.299
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.14
y1[1] (analytic) = 1.9902159962126371718989482270114
y1[1] (numeric) = 1.9902159962126371718989482270114
absolute error = 1e-63
relative error = 5.0245802561279320882102203714577e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1395431146442364817179883517054
y2[1] (numeric) = 1.1395431146442364817179883517054
absolute error = 1e-63
relative error = 8.7754468185453288747766003261556e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1332
Order of pole (three term test) = -1.364
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=76017384, alloc=4652204, time=3.84
x[1] = 0.15
y1[1] (analytic) = 1.9887710779360422867349809986543
y1[1] (numeric) = 1.9887710779360422867349809986543
absolute error = 1e-63
relative error = 5.0282308059196314117533356413880e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1494381324735992214977254386876
y2[1] (numeric) = 1.1494381324735992214977254386876
absolute error = 1e-63
relative error = 8.6999027763938257948745204743366e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1425
Order of pole (three term test) = -1.433
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=80018088, alloc=4652204, time=4.05
x[1] = 0.16
y1[1] (analytic) = 1.9872272833756269490409525240183
y1[1] (numeric) = 1.9872272833756269490409525240183
absolute error = 1e-63
relative error = 5.0321370301505636686694704794452e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.159318206614245963311463159686
y2[1] (numeric) = 1.159318206614245963311463159686
absolute error = 1e-63
relative error = 8.6257594704776525046338123046310e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1517
Order of pole (three term test) = -1.507
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=84018796, alloc=4652204, time=4.26
x[1] = 0.17
y1[1] (analytic) = 1.9855847669095607091719299902125
y1[1] (numeric) = 1.9855847669095607091719299902125
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1691823490669960101576243766709
y2[1] (numeric) = 1.1691823490669960101576243766709
absolute error = 1e-63
relative error = 8.5529857750418229057076547011106e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1608
Order of pole (three term test) = -1.585
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=88019672, alloc=4652204, time=4.47
x[1] = 0.18
y1[1] (analytic) = 1.9838436927881214145927160246115
y1[1] (numeric) = 1.9838436927881214145927160246115
absolute error = 1e-63
relative error = 5.0407197080864074714095761345368e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1790295734258241783418027396992
y2[1] (numeric) = 1.1790295734258241783418027396992
absolute error = 1e-63
relative error = 8.4815514601077358374588506352998e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1698
Order of pole (three term test) = -1.668
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.19
y1[1] (analytic) = 1.9820042351172703189678775041899
y1[1] (numeric) = 1.9820042351172703189678775041899
absolute error = 1e-63
relative error = 5.0453978971484511380378270067106e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1888588949765005779928511529813
y2[1] (numeric) = 1.1888588949765005779928511529813
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1788
Order of pole (three term test) = -1.755
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=92020596, alloc=4652204, time=4.68
x[1] = 0.2
y1[1] (analytic) = 1.9800665778412416311241965167482
y1[1] (numeric) = 1.9800665778412416311241965167482
absolute error = 1e-63
relative error = 5.0503352321124744441427458016855e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1986693307950612154594126271184
y2[1] (numeric) = 1.1986693307950612154594126271184
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1877
Order of pole (three term test) = -1.847
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=96022092, alloc=4652204, time=4.89
x[1] = 0.21
y1[1] (analytic) = 1.9780309147241482449161385680993
y1[1] (numeric) = 1.9780309147241482449161385680993
absolute error = 1e-63
relative error = 5.0555327146616298321218548967033e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2084598998460995706087124262276
y2[1] (numeric) = 1.2084598998460995706087124262276
absolute error = 1e-63
relative error = 8.2749953070627542800285284189374e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1966
Order of pole (three term test) = -1.943
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=100022884, alloc=4652204, time=5.10
x[1] = 0.22
y1[1] (analytic) = 1.9758974493306054894060229810447
y1[1] (numeric) = 1.9758974493306054894060229810447
absolute error = 1e-63
relative error = 5.0609914008380343129064224226209e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.218229623080869319951791005457
y2[1] (numeric) = 1.218229623080869319951791005457
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2054
Order of pole (three term test) = -2.044
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.23
y1[1] (analytic) = 1.9736663950053748369677306480716
y1[1] (numeric) = 1.9736663950053748369677306480716
absolute error = 1e-63
relative error = 5.0667124015012513028472330778856e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2279775235351883954046172123601
y2[1] (numeric) = 1.2279775235351883954046172123601
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.214
Order of pole (three term test) = -2.149
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=104023740, alloc=4652204, time=5.31
x[1] = 0.24
y1[1] (analytic) = 1.9713379748520296049261752469634
y1[1] (numeric) = 1.9713379748520296049261752469634
absolute error = 1e-63
relative error = 5.0726968828115883892711953865451e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2377026264271345883607920844898
y2[1] (numeric) = 1.2377026264271345883607920844898
absolute error = 1e-63
relative error = 8.0794851578096049324790437368210e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2226
Order of pole (three term test) = -2.259
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=108024448, alloc=4652204, time=5.52
x[1] = 0.25
y1[1] (analytic) = 1.9689124217106447841445954494942
y1[1] (numeric) = 1.9689124217106447841445954494942
absolute error = 2e-63
relative error = 1.0157892133477148162823768328465e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2474039592545229295968487048494
y2[1] (numeric) = 1.2474039592545229295968487048494
absolute error = 1e-63
relative error = 8.0166492384521756598648137763580e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2311
Order of pole (three term test) = -2.373
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=112025292, alloc=4652204, time=5.73
x[1] = 0.26
y1[1] (analytic) = 1.9663899781345132255582176464501
y1[1] (numeric) = 1.9663899781345132255582176464501
absolute error = 2e-63
relative error = 1.0170922463189993136027761953899e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2570805518921550973533884643652
y2[1] (numeric) = 1.2570805518921550973533884643652
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2395
Order of pole (three term test) = -2.491
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=116026316, alloc=4652204, time=5.94
x[1] = 0.27
y1[1] (analytic) = 1.9637708963658905130162327094922
y1[1] (numeric) = 1.9637708963658905130162327094922
absolute error = 2e-63
relative error = 1.0184487425193815822387289203730e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2667314366888311287322865210205
y2[1] (numeric) = 1.2667314366888311287322865210205
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2479
Order of pole (three term test) = -2.613
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.28
y1[1] (analytic) = 1.9610554383107709479245900535965
y1[1] (numeric) = 1.9610554383107709479245900535965
absolute error = 2e-63
relative error = 1.0198589804900035966671716237316e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2763556485641137333196695584578
y2[1] (numeric) = 1.2763556485641137333196695584578
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2561
Order of pole (three term test) = -2.739
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=120027016, alloc=4652204, time=6.15
x[1] = 0.29
y1[1] (analytic) = 1.9582438755126971680701247779319
y1[1] (numeric) = 1.9582438755126971680701247779319
absolute error = 2e-63
relative error = 1.0213232503925847651838292289105e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2859522251048355326839402055044
y2[1] (numeric) = 1.2859522251048355326839402055044
absolute error = 1e-63
relative error = 7.7763386576703993762228663985884e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2642
Order of pole (three term test) = -2.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=124027680, alloc=4652204, time=6.37
x[1] = 0.3
y1[1] (analytic) = 1.955336489125606019642310227568
y1[1] (numeric) = 1.955336489125606019642310227568
absolute error = 2e-63
relative error = 1.0228418541375284006057458660780e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.295520206661339575105320745685
y2[1] (numeric) = 1.295520206661339575105320745685
absolute error = 1e-63
relative error = 7.7189070062988900384443781475275e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2722
Order of pole (three term test) = -3.004
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=128028520, alloc=4652204, time=6.58
x[1] = 0.31
y1[1] (analytic) = 1.9523335698857133978428054362022
y1[1] (numeric) = 1.9523335698857133978428054362022
absolute error = 2e-63
relative error = 1.0244151055175867931257817440931e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.305058636443443501565643323959
y2[1] (numeric) = 1.305058636443443501565643323959
absolute error = 1e-63
relative error = 7.6624909569213548956184351464994e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2801
Order of pole (three term test) = -3.143
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.32
y1[1] (analytic) = 1.9492354180824408675753072737661
y1[1] (numeric) = 1.9492354180824408675753072737661
absolute error = 2e-63
relative error = 1.0260433303471874928122818774541e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3145665606161177666617575434171
y2[1] (numeric) = 1.3145665606161177666617575434171
absolute error = 2e-63
relative error = 1.5214140233892985911200315312248e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2879
Order of pole (three term test) = -3.285
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=132029264, alloc=4652204, time=6.78
x[1] = 0.33
y1[1] (analytic) = 1.9460423435283869715294105783662
y1[1] (numeric) = 1.9460423435283869715294105783662
absolute error = 2e-63
relative error = 1.0277268666075281350616725445343e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3240430283948683467001956961702
y2[1] (numeric) = 1.3240430283948683467001956961702
absolute error = 2e-63
relative error = 1.5105249278979939004455728596918e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2956
Order of pole (three term test) = -3.431
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=136030128, alloc=4652204, time=7.00
x[1] = 0.34
y1[1] (analytic) = 1.9427546655283462285026440600266
y1[1] (numeric) = 1.9427546655283462285026440600266
absolute error = 2e-63
relative error = 1.0294660645975519957886314289830e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3334870921408143967817714870308
y2[1] (numeric) = 1.3334870921408143967817714870308
absolute error = 2e-63
relative error = 1.4998270412870278911587530301459e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3031
Order of pole (three term test) = -3.581
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=140031812, alloc=4652204, time=7.20
x[1] = 0.35
y1[1] (analytic) = 1.9393727128473789200350323573037
y1[1] (numeric) = 1.9393727128473789200350323573037
absolute error = 2e-63
relative error = 1.0312612870909214506215850713097e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3428978074554513491896349069176
y2[1] (numeric) = 1.3428978074554513491896349069176
absolute error = 2e-63
relative error = 1.4893166024223679025311041078695e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3106
Order of pole (three term test) = -3.735
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=144032892, alloc=4652204, time=7.42
x[1] = 0.36
y1[1] (analytic) = 1.9358968236779348583509123681247
y1[1] (numeric) = 1.9358968236779348583509123681247
absolute error = 2e-63
relative error = 1.0331129094991116404338563250505e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3522742332750899768499134359207
y2[1] (numeric) = 1.3522742332750899768499134359207
absolute error = 2e-63
relative error = 1.4789899495135501032851987062370e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3179
Order of pole (three term test) = -3.893
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.37
y1[1] (analytic) = 1.9323273456060344232038129044909
y1[1] (numeric) = 1.9323273456060344232038129044909
absolute error = 2e-63
relative error = 1.0350213200407519209978648165456e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3616154319649619780372924691272
y2[1] (numeric) = 1.3616154319649619780372924691272
absolute error = 3e-63
relative error = 2.2032652756224035342138577028514e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.325
Order of pole (three term test) = -4.054
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=148033620, alloc=4652204, time=7.62
x[1] = 0.38
y1[1] (analytic) = 1.9286646355765102494925308077246
y1[1] (numeric) = 1.9286646355765102494925308077246
absolute error = 2e-63
relative error = 1.0369869199173481044712361719667e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3709204694129826718454854663492
y2[1] (numeric) = 1.3709204694129826718454854663492
absolute error = 3e-63
relative error = 2.1883107495539667077660402456053e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3321
Order of pole (three term test) = -4.219
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=152034524, alloc=4717728, time=7.84
x[1] = 0.39
y1[1] (analytic) = 1.9249090598573130414506767528811
y1[1] (numeric) = 1.9249090598573130414506767528811
absolute error = 2e-63
relative error = 1.0390101234955240921477781782336e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3801884151231614282311820978472
y2[1] (numeric) = 1.3801884151231614282311820978472
absolute error = 3e-63
relative error = 2.1736162737841081757625165280629e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.339
Order of pole (three term test) = -4.387
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=156035360, alloc=4717728, time=8.05
x[1] = 0.4
y1[1] (analytic) = 1.9210609940028850827985267320518
y1[1] (numeric) = 1.9210609940028850827985267320518
absolute error = 2e-63
relative error = 1.0410913584959272590539665982747e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3894183423086504916663117567957
y2[1] (numeric) = 1.3894183423086504916663117567957
absolute error = 3e-63
relative error = 2.1591769078096487269562799734596e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3458
Order of pole (three term test) = -4.559
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.41
y1[1] (analytic) = 1.917120822816605105475642058277
y1[1] (numeric) = 1.917120822816605105475642058277
absolute error = 2e-63
relative error = 1.0432310661889478894613496025689e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3986093279844228935937976400511
y2[1] (numeric) = 1.3986093279844228935937976400511
absolute error = 3e-63
relative error = 2.1449878389724372722099303120905e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3524
Order of pole (three term test) = -4.734
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=160036076, alloc=4717728, time=8.26
x[1] = 0.42
y1[1] (analytic) = 1.9130889403123082724360887896657
y1[1] (numeric) = 1.9130889403123082724360887896657
absolute error = 2e-63
relative error = 1.0454297015974090864488178763314e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4077604530595701859727871580863
y2[1] (numeric) = 1.4077604530595701859727871580863
absolute error = 3e-63
relative error = 2.1310443786653618192289435896370e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3589
Order of pole (three term test) = -4.912
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=164036852, alloc=4717728, time=8.47
x[1] = 0.43
y1[1] (analytic) = 1.9089657496748851224759104776634
y1[1] (numeric) = 1.9089657496748851224759104776634
absolute error = 2e-63
relative error = 1.0476877337063898968472555724709e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4168708024292107662169186726246
y2[1] (numeric) = 1.4168708024292107662169186726246
absolute error = 3e-63
relative error = 2.1173419586715529166330801579148e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3653
Order of pole (three term test) = -5.093
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=168037664, alloc=4717728, time=8.68
x[1] = 0.44
y1[1] (analytic) = 1.9047516632199634171655373889984
y1[1] (numeric) = 1.9047516632199634171655373889984
absolute error = 2e-63
relative error = 1.0500056456803509141406868692400e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4259394650659996027697207507799
y2[1] (numeric) = 1.4259394650659996027697207507799
absolute error = 3e-63
relative error = 2.1038761276315085446489287824607e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3715
Order of pole (three term test) = -5.278
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=172038472, alloc=4717728, time=8.89
x[1] = 0.45
y1[1] (analytic) = 1.9004471023526769216688406114864
y1[1] (numeric) = 1.9004471023526769216688406114864
absolute error = 2e-63
relative error = 1.0523839350877383554554287495668e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4349655341112302104208442462319
y2[1] (numeric) = 1.4349655341112302104208442462319
absolute error = 3e-63
relative error = 2.0906425476331039108511438031133e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3776
Order of pole (three term test) = -5.466
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.46
y1[1] (analytic) = 1.8960524975255252425363899035004
y1[1] (numeric) = 1.8960524975255252425363899035004
absolute error = 2e-63
relative error = 1.0548231141332495642983950217470e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4439481069655197652415136439289
y2[1] (numeric) = 1.4439481069655197652415136439289
absolute error = 3e-63
relative error = 2.0776369909196725801655318740957e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3835
Order of pole (three term test) = -5.657
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=176039840, alloc=4717728, time=9.10
x[1] = 0.47
y1[1] (analytic) = 1.8915682881953289364540192765334
y1[1] (numeric) = 1.8915682881953289364540192765334
absolute error = 1e-63
relative error = 5.2866185494897503913377495700579e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4528862853790682907032748003964
y2[1] (numeric) = 1.4528862853790682907032748003964
absolute error = 3e-63
relative error = 2.0648553367115574478447327143951e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3892
Order of pole (three term test) = -5.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=180041028, alloc=4717728, time=9.31
x[1] = 0.48
y1[1] (analytic) = 1.8869949227792841943999548311587
y1[1] (numeric) = 1.8869949227792841943999548311587
absolute error = 2e-63
relative error = 1.0598862645874398310359626801090e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4617791755414828891366429425886
y2[1] (numeric) = 1.4617791755414828891366429425886
absolute error = 3e-63
relative error = 2.0522935681367318352779055472654e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3949
Order of pole (three term test) = -6.047
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=184041692, alloc=4717728, time=9.52
x[1] = 0.49
y1[1] (analytic) = 1.8823328586101214957054681591367
y1[1] (numeric) = 1.8823328586101214957054681591367
absolute error = 1e-63
relative error = 5.3125566789413687071833591327688e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.470625888171158036181358337188
y2[1] (numeric) = 1.470625888171158036181358337188
absolute error = 3e-63
relative error = 2.0399477692662830003845548414891e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4003
Order of pole (three term test) = -6.246
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.5
y1[1] (analytic) = 1.8775825618903727161162815826038
y1[1] (numeric) = 1.8775825618903727161162815826038
absolute error = 2e-63
relative error = 1.0651994967328498908487019298619e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4794255386042030002732879352156
y2[1] (numeric) = 1.4794255386042030002732879352156
absolute error = 3e-63
relative error = 2.0278141222507331243186658844985e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4056
Order of pole (three term test) = -6.448
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=188043324, alloc=4717728, time=9.73
x[1] = 0.51
y1[1] (analytic) = 1.8727445076457512631058084735755
y1[1] (numeric) = 1.8727445076457512631058084735755
absolute error = 1e-63
relative error = 5.3397566828649335759938166413281e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4881772468829074945001302376746
y2[1] (numeric) = 1.4881772468829074945001302376746
absolute error = 2e-63
relative error = 1.3439259363688979012428704319126e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4107
Order of pole (three term test) = -6.653
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=192044056, alloc=4717728, time=9.94
x[1] = 0.52
y1[1] (analytic) = 1.8678191796776499003878475719885
y1[1] (numeric) = 1.8678191796776499003878475719885
absolute error = 1e-63
relative error = 5.3538373033120957608058782225345e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4968801378437367143344589425478
y2[1] (numeric) = 1.4968801378437367143344589425478
absolute error = 2e-63
relative error = 1.3361123241844934559451623257491e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4157
Order of pole (three term test) = -6.86
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=196045072, alloc=4717728, time=10.15
x[1] = 0.53
y1[1] (analytic) = 1.8628070705147610118066950185642
y1[1] (numeric) = 1.8628070705147610118066950185642
absolute error = 2e-63
relative error = 1.0736484908484525005190792269169e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5055333412048469618136610224661
y2[1] (numeric) = 1.5055333412048469618136610224661
absolute error = 2e-63
relative error = 1.3284328850528422535436688681208e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4205
Order of pole (three term test) = -7.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=200046012, alloc=4717728, time=10.37
x[1] = 0.54
y1[1] (analytic) = 1.8577086813638241425379687789178
y1[1] (numeric) = 1.8577086813638241425379687789178
absolute error = 2e-63
relative error = 1.0765950657730218806758766578607e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5141359916531131046772806829582
y2[1] (numeric) = 1.5141359916531131046772806829582
absolute error = 2e-63
relative error = 1.3208853174518539592632826995508e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4251
Order of pole (three term test) = -7.281
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.55
y1[1] (analytic) = 1.8525245220595057428049817976178
y1[1] (numeric) = 1.8525245220595057428049817976178
absolute error = 3e-63
relative error = 1.6194117617751219706707057230078e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5226872289306591677883781077573
y2[1] (numeric) = 1.5226872289306591677883781077573
absolute error = 2e-63
relative error = 1.3134673766224100386001291625475e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4295
Order of pole (three term test) = -7.496
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=204047324, alloc=4717728, time=10.57
x[1] = 0.56
y1[1] (analytic) = 1.8472551110134161260945255038663
y1[1] (numeric) = 1.8472551110134161260945255038663
absolute error = 2e-63
relative error = 1.0826874902529229099584834949339e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.531186197920883403851869441112
y2[1] (numeric) = 1.531186197920883403851869441112
absolute error = 2e-63
relative error = 1.3061768730123704185584278128487e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4338
Order of pole (three term test) = -7.712
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=208048552, alloc=4717728, time=10.78
x[1] = 0.57
y1[1] (analytic) = 1.841900975162268740133756363916
y1[1] (numeric) = 1.841900975162268740133756363916
absolute error = 2e-63
relative error = 1.0858347039117034891643604791244e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5396320487339692409944634930788
y2[1] (numeric) = 1.5396320487339692409944634930788
absolute error = 2e-63
relative error = 1.2990116707719800529642780620819e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4379
Order of pole (three term test) = -7.931
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=212050060, alloc=4717728, time=10.99
x[1] = 0.58
y1[1] (analytic) = 1.83646264991518693465788732805
y1[1] (numeric) = 1.83646264991518693465788732805
absolute error = 2e-63
relative error = 1.0890501911881331673290929365453e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5480239367918735561826960595765
y2[1] (numeric) = 1.5480239367918735561826960595765
absolute error = 3e-63
relative error = 1.9379545294481706612613473985738e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4418
Order of pole (three term test) = -8.151
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.59
y1[1] (analytic) = 1.8309406791001634952479965224907
y1[1] (numeric) = 1.8309406791001634952479965224907
absolute error = 1e-63
relative error = 5.4616733978047902132895212575370e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5563610229127837757225433788758
y2[1] (numeric) = 1.5563610229127837757225433788758
absolute error = 2e-63
relative error = 1.2850488868302101599991556595291e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4456
Order of pole (three term test) = -8.373
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=216050772, alloc=4717728, time=11.21
x[1] = 0.6
y1[1] (analytic) = 1.8253356149096782972409524989554
y1[1] (numeric) = 1.8253356149096782972409524989554
absolute error = 1e-63
relative error = 5.4784445766127356489621396798198e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5646424733950353572009454456587
y2[1] (numeric) = 1.5646424733950353572009454456587
absolute error = 3e-63
relative error = 1.9173709336232307994808196421010e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4492
Order of pole (three term test) = -8.598
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=220051980, alloc=4717728, time=11.42
x[1] = 0.61
y1[1] (analytic) = 1.8196480178454795179007465786548
y1[1] (numeric) = 1.8196480178454795179007465786548
absolute error = 2e-63
relative error = 1.0991136639535721315725263428320e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5728674601004812611909760321627
y2[1] (numeric) = 1.5728674601004812611909760321627
absolute error = 2e-63
relative error = 1.2715629579317711552779454373119e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4526
Order of pole (three term test) = -8.824
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=224052680, alloc=4717728, time=11.63
x[1] = 0.62
y1[1] (analytic) = 1.8138784566625339286839996543607
y1[1] (numeric) = 1.8138784566625339286839996543607
absolute error = 2e-63
relative error = 1.1026097105094475286557172642480e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5810351605373050758429632275822
y2[1] (numeric) = 1.5810351605373050758429632275822
absolute error = 3e-63
relative error = 1.8974910077145080380050596318682e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4558
Order of pole (three term test) = -9.051
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=228053392, alloc=4717728, time=11.84
x[1] = 0.63
y1[1] (analytic) = 1.8080275083121518725237089657771
y1[1] (numeric) = 1.8080275083121518725237089657771
absolute error = 2e-63
relative error = 1.1061778600188778265263196803500e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5891447579422695131181120907946
y2[1] (numeric) = 1.5891447579422695131181120907946
absolute error = 3e-63
relative error = 1.8878078821998568793560236713126e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.58
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.85
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4588
Order of pole (three term test) = -9.281
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.64
y1[1] (analytic) = 1.8020957578842926135861107792603
y1[1] (numeric) = 1.8020957578842926135861107792603
absolute error = 1e-63
relative error = 5.5490946894743599099478432799465e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5971954413623920518835462392079
y2[1] (numeric) = 1.5971954413623920518835462392079
absolute error = 3e-63
relative error = 1.8782923631694249097683450580593e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4617
Order of pole (three term test) = -9.511
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=232054768, alloc=4717728, time=12.05
x[1] = 0.65
y1[1] (analytic) = 1.7960837985490558289176045706799
y1[1] (numeric) = 1.7960837985490558289176045706799
absolute error = 2e-63
relative error = 1.1135337903585987259748653798338e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6051864057360395603725216786059
y2[1] (numeric) = 1.6051864057360395603725216786059
absolute error = 3e-63
relative error = 1.8689418183954684600175006748137e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4643
Order of pole (three term test) = -9.743
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=236055720, alloc=4717728, time=12.27
x[1] = 0.66
y1[1] (analytic) = 1.7899922314973650927838170912302
y1[1] (numeric) = 1.7899922314973650927838170912302
absolute error = 2e-63
relative error = 1.1173232848764707296363091532342e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6131168519734337886151454793963
y2[1] (numeric) = 1.6131168519734337886151454793963
absolute error = 4e-63
relative error = 2.4796715719053658979097023508972e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4668
Order of pole (three term test) = -9.977
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=240056932, alloc=4717728, time=12.48
x[1] = 0.67
y1[1] (analytic) = 1.7838216658808492853029421448381
y1[1] (numeric) = 1.7838216658808492853029421448381
absolute error = 2e-63
relative error = 1.1211883106108603507225653945891e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6209859870365596803574439141266
y2[1] (numeric) = 1.6209859870365596803574439141266
absolute error = 4e-63
relative error = 2.4676339166340887638831083318351e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.05
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4691
Order of pole (three term test) = -10.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.68
y1[1] (analytic) = 1.7775727187509279371823940840443
y1[1] (numeric) = 1.7775727187509279371823940840443
absolute error = 2e-63
relative error = 1.1251297788848650725519883317058e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6287930240184685137041781874202
y2[1] (numeric) = 1.6287930240184685137041781874202
absolute error = 4e-63
relative error = 2.4558061957629337867416766127147e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4712
Order of pole (three term test) = -10.45
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=244057872, alloc=4717728, time=12.69
x[1] = 0.69
y1[1] (analytic) = 1.7712460149971066019735393154978
y1[1] (numeric) = 1.7712460149971066019735393154978
absolute error = 1e-63
relative error = 5.6457431183077836773546196134198e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6365371822219679402374292070087
y2[1] (numeric) = 1.6365371822219679402374292070087
absolute error = 4e-63
relative error = 2.4441852244194652463306224128026e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4731
Order of pole (three term test) = -10.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=248058776, alloc=4717728, time=12.90
x[1] = 0.7
y1[1] (analytic) = 1.7648421872844884262558599901919
y1[1] (numeric) = 1.7648421872844884262558599901919
absolute error = 2e-63
relative error = 1.1332458020381652884961903425722e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6442176872376910536726143513987
y2[1] (numeric) = 1.6442176872376910536726143513987
absolute error = 4e-63
relative error = 2.4327678938426070075304109808511e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4749
Order of pole (three term test) = -10.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=252060088, alloc=4717728, time=13.11
x[1] = 0.71
y1[1] (analytic) = 1.7583618759905081665414579441396
y1[1] (numeric) = 1.7583618759905081665414579441396
absolute error = 2e-63
relative error = 1.1374222947556650864249365164370e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6518337710215366812101279728528
y2[1] (numeric) = 1.6518337710215366812101279728528
absolute error = 4e-63
relative error = 2.4215511694777233274212709492360e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.33
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4764
Order of pole (three term test) = -11.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=256061056, alloc=4717728, time=13.32
x[1] = 0.72
y1[1] (analytic) = 1.7518057291408949794454869622519
y1[1] (numeric) = 1.7518057291408949794454869622519
absolute error = 1e-63
relative error = 5.7083955336212487798204503837468e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6593846719714731536180038326482
y2[1] (numeric) = 1.6593846719714731536180038326482
absolute error = 4e-63
relative error = 2.4105320891313891072301790131004e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4777
Order of pole (three term test) = -11.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.73
y1[1] (analytic) = 1.7451744023448703887901321585503
y1[1] (numeric) = 1.7451744023448703887901321585503
absolute error = 1e-63
relative error = 5.7300863378260019292174571738852e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6668696350036978737325941307615
y2[1] (numeric) = 1.6668696350036978737325941307615
absolute error = 4e-63
relative error = 2.3997077611838109845369017811264e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4789
Order of pole (three term test) = -11.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=260062008, alloc=4717728, time=13.53
x[1] = 0.74
y1[1] (analytic) = 1.7384685587295879097914245606988
y1[1] (numeric) = 1.7384685587295879097914245606988
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6742879116281450674838811576082
y2[1] (numeric) = 1.6742879116281450674838811576082
absolute error = 4e-63
relative error = 2.3890753628569406154985665266923e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.26
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4799
Order of pole (three term test) = -11.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=264062740, alloc=4717728, time=13.74
x[1] = 0.75
y1[1] (analytic) = 1.7316888688738208863118387530001
y1[1] (numeric) = 1.7316888688738208863118387530001
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6816387600233341667332419527799
y2[1] (numeric) = 1.6816387600233341667332419527799
absolute error = 4e-63
relative error = 2.3786321385363980318117452389586e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.63
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4806
Order of pole (three term test) = -12.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=268063468, alloc=4717728, time=13.95
x[1] = 0.76
y1[1] (analytic) = 1.724836010740905172339688366667
y1[1] (numeric) = 1.724836010740905172339688366667
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6889214451105513391477556387697
y2[1] (numeric) = 1.6889214451105513391477556387697
absolute error = 4e-63
relative error = 2.3683753981453962342993563621979e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.01
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.06
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4812
Order of pole (three term test) = -12.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.77
y1[1] (analytic) = 1.7179106696109433633712905653243
y1[1] (numeric) = 1.7179106696109433633712905653243
absolute error = 1e-63
relative error = 5.8210244437591788121453662605430e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6961352386273567470198837344522
y2[1] (numeric) = 1.6961352386273567470198837344522
absolute error = 4e-63
relative error = 2.3583025155689283576713641688268e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.39
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4816
Order of pole (three term test) = -12.6
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=272064784, alloc=4717728, time=14.16
x[1] = 0.78
y1[1] (analytic) = 1.7109135380122773572162650237646
y1[1] (numeric) = 1.7109135380122773572162650237646
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7032794192004101843678973251179
y2[1] (numeric) = 1.7032794192004101843678973251179
absolute error = 4e-63
relative error = 2.3484109271265459546558310381225e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.21
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -12.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=276065464, alloc=4717728, time=14.37
x[1] = 0.79
y1[1] (analytic) = 1.703845315652236096912780861085
y1[1] (numeric) = 1.703845315652236096912780861085
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7103532724176078098140288749692
y2[1] (numeric) = 1.7103532724176078098140288749692
absolute error = 3e-63
relative error = 1.7540235975690910053446831558070e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -13.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=280066244, alloc=4717728, time=14.58
x[1] = 0.8
y1[1] (analytic) = 1.6967067093471654209207499816423
y1[1] (numeric) = 1.6967067093471654209207499816423
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7173560908995227616271746105814
y2[1] (numeric) = 1.7173560908995227616271746105814
absolute error = 3e-63
relative error = 1.7468712609442864811736572666541e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4816
Order of pole (three term test) = -13.33
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=284067316, alloc=4717728, time=14.80
x[1] = 0.81
y1[1] (analytic) = 1.6894984329517470175496392406801
y1[1] (numeric) = 1.6894984329517470175496392406801
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7242871743701425109281768525145
y2[1] (numeric) = 1.7242871743701425109281768525145
absolute error = 3e-63
relative error = 1.7398493966620479980921298643277e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4812
Order of pole (three term test) = -13.57
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.82
y1[1] (analytic) = 1.6822212072876135516665579784369
y1[1] (numeric) = 1.6822212072876135516665579784369
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7311458297268958793813133646877
y2[1] (numeric) = 1.7311458297268958793813133646877
absolute error = 3e-63
relative error = 1.7329562584991915412741808720444e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4806
Order of pole (three term test) = -13.81
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=288068156, alloc=4717728, time=15.01
x[1] = 0.83
y1[1] (analytic) = 1.6748757600712671021124629178645
y1[1] (numeric) = 1.6748757600712671021124629178645
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7379313711099627187285802261381
y2[1] (numeric) = 1.7379313711099627187285802261381
absolute error = 3e-63
relative error = 1.7261901418374151892566788287739e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4799
Order of pole (three term test) = -14.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=292068900, alloc=4717728, time=15.22
x[1] = 0.84
y1[1] (analytic) = 1.6674628258413081179226710368709
y1[1] (numeric) = 1.6674628258413081179226710368709
absolute error = 1e-63
relative error = 5.9971351954755342001502602934721e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7446431199708593212565726706296
y2[1] (numeric) = 1.7446431199708593212565726706296
absolute error = 4e-63
relative error = 2.2927325102837145178016633112267e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.03
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4789
Order of pole (three term test) = -14.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=296070020, alloc=4717728, time=15.43
x[1] = 0.85
y1[1] (analytic) = 1.6599831458849821703954160294615
y1[1] (numeric) = 1.6599831458849821703954160294615
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7512804051402927027120715242355
y2[1] (numeric) = 1.7512804051402927027120715242355
absolute error = 4e-63
relative error = 2.2840431425255200148397261438241e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.69
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4778
Order of pole (three term test) = -14.53
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.86
y1[1] (analytic) = 1.6524374681640518462720306642239
y1[1] (numeric) = 1.6524374681640518462720306642239
absolute error = 1e-63
relative error = 6.0516662159146908088972971737922e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7578425628952769722945887295286
y2[1] (numeric) = 1.7578425628952769722945887295286
absolute error = 4e-63
relative error = 2.2755166386526385366592950065839e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4764
Order of pole (three term test) = -14.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=300071080, alloc=4717728, time=15.64
x[1] = 0.87
y1[1] (analytic) = 1.6448265472400011947776638054828
y1[1] (numeric) = 1.6448265472400011947776638054828
absolute error = 1e-63
relative error = 6.0796684104958529208545021706575e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7643289370255050781448028237229
y2[1] (numeric) = 1.7643289370255050781448028237229
absolute error = 4e-63
relative error = 2.2671509354393001933888010742549e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.03
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4749
Order of pole (three term test) = -15.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=304071888, alloc=4717728, time=15.85
x[1] = 0.88
y1[1] (analytic) = 1.6371511441985802080154986057221
y1[1] (numeric) = 1.6371511441985802080154986057221
absolute error = 1e-63
relative error = 6.1081715243189776179311592162596e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.770738878898969291209645130756
y2[1] (numeric) = 1.770738878898969291209645130756
absolute error = 3e-63
relative error = 1.6942080143772384163768237507404e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.71
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4732
Order of pole (three term test) = -15.24
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=308072676, alloc=4717728, time=16.06
x[1] = 0.89
y1[1] (analytic) = 1.6294120265736968802035530573803
y1[1] (numeric) = 1.6294120265736968802035530573803
absolute error = 1e-63
relative error = 6.1371831291977448468527348948594e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7770717475268238654903337129732
y2[1] (numeric) = 1.7770717475268238654903337129732
absolute error = 4e-63
relative error = 2.2508939245513621695428056430029e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.39
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4712
Order of pole (three term test) = -15.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=312073904, alloc=4717728, time=16.27
x[1] = 0.9
y1[1] (analytic) = 1.6216099682706644564847161514071
y1[1] (numeric) = 1.6216099682706644564847161514071
absolute error = 2e-63
relative error = 1.2333421964178368350698866458395e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7833269096274833884613823157135
y2[1] (numeric) = 1.7833269096274833884613823157135
absolute error = 4e-63
relative error = 2.2429987336621047724498351638413e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4691
Order of pole (three term test) = -15.72
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.91
y1[1] (analytic) = 1.6137457494888115465211782261747
y1[1] (numeric) = 1.6137457494888115465211782261747
absolute error = 2e-63
relative error = 1.2393526059687796184498878045927e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7895037396899504118789575178715
y2[1] (numeric) = 1.7895037396899504118789575178715
absolute error = 4e-63
relative error = 2.2352565749278849679304067104333e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.77
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4668
Order of pole (three term test) = -15.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=316074916, alloc=4717728, time=16.48
x[1] = 0.92
y1[1] (analytic) = 1.6058201566434628417974047066744
y1[1] (numeric) = 1.6058201566434628417974047066744
absolute error = 2e-63
relative error = 1.2454694828220767875399382800796e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7956016200363660302682761024816
y2[1] (numeric) = 1.7956016200363660302682761024816
absolute error = 5e-63
relative error = 2.7845820276653213343043348785655e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4644
Order of pole (three term test) = -16.18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=320075876, alloc=4717728, time=16.69
x[1] = 0.93
y1[1] (analytic) = 1.597833982287298238494907084433
y1[1] (numeric) = 1.597833982287298238494907084433
absolute error = 2e-63
relative error = 1.2516944952797920756527907831158e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8016199408837771520843192159107
y2[1] (numeric) = 1.8016199408837771520843192159107
absolute error = 5e-63
relative error = 2.7752801168193502799048493367323e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4617
Order of pole (three term test) = -16.42
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=324076752, alloc=4717728, time=16.91
x[1] = 0.94
y1[1] (analytic) = 1.589788025031098229960989815224
y1[1] (numeric) = 1.589788025031098229960989815224
absolute error = 2e-63
relative error = 1.2580293526622063428193425676008e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8075581004051142868702197986341
y2[1] (numeric) = 1.8075581004051142868702197986341
absolute error = 5e-63
relative error = 2.7661628131783912918607235777903e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.88
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4589
Order of pole (three term test) = -16.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.95
y1[1] (analytic) = 1.5816830894638834941661809737605
y1[1] (numeric) = 1.5816830894638834941661809737605
absolute error = 2e-63
relative error = 1.2644758063879322064650124534699e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8134155047893737506854221021026
y2[1] (numeric) = 1.8134155047893737506854221021026
absolute error = 5e-63
relative error = 2.7572279970004693389413559113807e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4558
Order of pole (three term test) = -16.88
NO COMPLEX POLE (six term test) for Equation 2
bytes used=328077492, alloc=4717728, time=17.12
TOP MAIN SOLVE Loop
x[1] = 0.96
y1[1] (analytic) = 1.5735199860724566621250508003519
y1[1] (numeric) = 1.5735199860724566621250508003519
absolute error = 2e-63
relative error = 1.2710356510895343653297020475909e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8191915683009982716332221464304
y2[1] (numeric) = 1.8191915683009982716332221464304
absolute error = 6e-63
relative error = 3.2981683207797591528248804525188e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4526
Order of pole (three term test) = -17.1
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=332078220, alloc=4717728, time=17.33
x[1] = 0.97
y1[1] (analytic) = 1.5652995311603543130365277548499
y1[1] (numeric) = 1.5652995311603543130365277548499
absolute error = 2e-63
relative error = 1.2777107257659515482921316588081e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8248857133384500574766200378563
y2[1] (numeric) = 1.8248857133384500574766200378563
absolute error = 6e-63
relative error = 3.2878771290414600318041140668199e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4492
Order of pole (three term test) = -17.33
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=336079144, alloc=4717728, time=17.54
x[1] = 0.98
y1[1] (analytic) = 1.5570225467662173008766582673599
y1[1] (numeric) = 1.5570225467662173008766582673599
absolute error = 2e-63
relative error = 1.2845029149730704307483639366537e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8304973704919704680845332877191
y2[1] (numeric) = 1.8304973704919704680845332877191
absolute error = 6e-63
relative error = 3.2777976612921439763050385756450e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4457
Order of pole (three term test) = -17.55
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=340080124, alloc=4717728, time=17.75
x[1] = 0.99
y1[1] (analytic) = 1.5486898605815875753431264086536
y1[1] (numeric) = 1.5486898605815875753431264086536
absolute error = 2e-63
relative error = 1.2914141500538587988858994933764e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8360259786005205167892594115471
y2[1] (numeric) = 1.8360259786005205167892594115471
absolute error = 6e-63
relative error = 3.2679276164563845942139056185213e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4419
Order of pole (three term test) = -17.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1
y1[1] (analytic) = 1.540302305868139717400936607443
y1[1] (numeric) = 1.540302305868139717400936607443
absolute error = 2e-63
relative error = 1.2984464104095248368837664988544e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8414709848078965066525023216303
y2[1] (numeric) = 1.8414709848078965066525023216303
absolute error = 6e-63
relative error = 3.2582647511146769662190167635487e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.438
Order of pole (three term test) = -18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=344080800, alloc=4717728, time=17.96
x[1] = 1.01
y1[1] (analytic) = 1.5318607213743554662067313557792
y1[1] (numeric) = 1.5318607213743554662067313557792
absolute error = 2e-63
relative error = 1.3056017248132318013964077817385e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.846831844618015190123098784782
y2[1] (numeric) = 1.846831844618015190123098784782
absolute error = 6e-63
relative error = 3.2488068783766260418600614006206e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4339
Order of pole (three term test) = -18.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=348082216, alloc=4717728, time=18.18
x[1] = 1.02
y1[1] (analytic) = 1.5233659512516495698896138080338
y1[1] (numeric) = 1.5233659512516495698896138080338
absolute error = 2e-63
relative error = 1.3128821727679626770830986927370e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8521080219493629236165499854554
y2[1] (numeric) = 1.8521080219493629236165499854554
absolute error = 6e-63
relative error = 3.2395518667884920134138466338583e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4296
Order of pole (three term test) = -18.43
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=352083008, alloc=4717728, time=18.39
x[1] = 1.03
y1[1] (analytic) = 1.5148188449699553475335022998374
y1[1] (numeric) = 1.5148188449699553475335022998374
absolute error = 2e-63
relative error = 1.3202898859101978301419954888288e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8572989891886033721462743852944
y2[1] (numeric) = 1.8572989891886033721462743852944
absolute error = 6e-63
relative error = 3.2304976392741240282462252067411e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4252
Order of pole (three term test) = -18.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.04
y1[1] (analytic) = 1.5062202572327784037344734209922
y1[1] (numeric) = 1.5062202572327784037344734209922
absolute error = 2e-63
relative error = 1.3278270494611403563077827214457e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8624042272433384032807916921162
y2[1] (numeric) = 1.8624042272433384032807916921162
absolute error = 6e-63
relative error = 3.2216421721083490313067748674392e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4205
Order of pole (three term test) = -18.86
NO COMPLEX POLE (six term test) for Equation 2
bytes used=356083744, alloc=4717728, time=18.61
TOP MAIN SOLVE Loop
x[1] = 1.05
y1[1] (analytic) = 1.4975710478917269902908495728121
y1[1] (numeric) = 1.4975710478917269902908495728121
absolute error = 2e-63
relative error = 1.3354959037272989274234396530284e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8674232255940168943814094850003
y2[1] (numeric) = 1.8674232255940168943814094850003
absolute error = 7e-63
relative error = 3.7484807429089027798980785065746e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4158
Order of pole (three term test) = -19.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=360084584, alloc=4717728, time=18.82
x[1] = 1.06
y1[1] (analytic) = 1.4888720818605275619186375399564
y1[1] (numeric) = 1.4888720818605275619186375399564
absolute error = 2e-63
relative error = 1.3432987456523166582740481496900e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8723554823449862622829459219974
y2[1] (numeric) = 1.8723554823449862622829459219974
absolute error = 7e-63
relative error = 3.7386062988599897649183766821830e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4108
Order of pole (three term test) = -19.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=364085452, alloc=4717728, time=19.03
x[1] = 1.07
y1[1] (analytic) = 1.4801242290285341243650930681759
y1[1] (numeric) = 1.4801242290285341243650930681759
absolute error = 2e-63
relative error = 1.3512379304220170351974605718951e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8772005042746816103070632577768
y2[1] (numeric) = 1.8772005042746816103070632577768
absolute error = 7e-63
relative error = 3.7289570208722488606049199034892e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4057
Order of pole (three term test) = -19.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=368086172, alloc=4717728, time=19.24
x[1] = 1.08
y1[1] (analytic) = 1.471328364173740023913524788526
y1[1] (numeric) = 1.471328364173740023913524788526
absolute error = 2e-63
relative error = 1.3593158731247244736031450166152e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8819578068849474737353349876248
y2[1] (numeric) = 1.8819578068849474737353349876248
absolute error = 7e-63
relative error = 3.7195307856484486070138809555319e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4004
Order of pole (three term test) = -19.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.09
y1[1] (analytic) = 1.4624853668753008770278970738751
y1[1] (numeric) = 1.4624853668753008770278970738751
absolute error = 2e-63
relative error = 1.3675350504690078184058136885998e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.886626914449487231608600628636
y2[1] (numeric) = 1.886626914449487231608600628636
absolute error = 7e-63
relative error = 3.7103255266781676213523514696047e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.395
Order of pole (three term test) = -19.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=372086844, alloc=4717728, time=19.45
x[1] = 1.1
y1[1] (analytic) = 1.4535961214255773877713700517847
y1[1] (numeric) = 1.4535961214255773877713700517847
absolute error = 2e-63
relative error = 1.3758980025610902976743740015516e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8912073600614353399518025778717
y2[1] (numeric) = 1.8912073600614353399518025778717
absolute error = 7e-63
relative error = 3.7013392332465367340409222611034e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3894
Order of pole (three term test) = -20.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=376088076, alloc=4717728, time=19.66
x[1] = 1.11
y1[1] (analytic) = 1.4446615167417068486437375119336
y1[1] (numeric) = 1.4446615167417068486437375119336
absolute error = 2e-63
relative error = 1.3844073347442693271740424613815e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8956986856800476292406259593394
y2[1] (numeric) = 1.8956986856800476292406259593394
absolute error = 7e-63
relative error = 3.6925699494742628679171392439037e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3836
Order of pole (three term test) = -20.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=380088888, alloc=4717728, time=19.87
x[1] = 1.12
y1[1] (analytic) = 1.4356824462767121676139887939611
y1[1] (numeric) = 1.4356824462767121676139887939611
absolute error = 2e-63
relative error = 1.3930657195027943979804297604077e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9001004421765049971191032473391
y2[1] (numeric) = 1.9001004421765049971191032473391
absolute error = 7e-63
relative error = 3.6840157733881274506494734253782e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3777
Order of pole (three term test) = -20.46
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=384090224, alloc=4717728, time=20.09
x[1] = 1.13
y1[1] (analytic) = 1.4266598079301573103712158356535
y1[1] (numeric) = 1.4266598079301573103712158356535
absolute error = 2e-63
relative error = 1.4018758984327613323163809928104e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9044121893788259160370815224114
y2[1] (numeric) = 1.9044121893788259160370815224114
absolute error = 7e-63
relative error = 3.6756748560211820328846403857160e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3717
Order of pole (three term test) = -20.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.14
y1[1] (analytic) = 1.4175945039583580921751867408226
y1[1] (numeric) = 1.4175945039583580921751867408226
absolute error = 2e-63
relative error = 1.4108406842826967518564790674677e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9086334961158832645942155781022
y2[1] (numeric) = 1.9086334961158832645942155781022
absolute error = 7e-63
relative error = 3.6675454005418926515254374957299e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3655
Order of pole (three term test) = -20.83
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=388091344, alloc=4717728, time=20.30
x[1] = 1.15
y1[1] (analytic) = 1.4084874408841572981525767188099
y1[1] (numeric) = 1.4084874408841572981525767188099
absolute error = 2e-63
relative error = 1.4199629630666279729823385061214e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9127639402605210809440330497537
y2[1] (numeric) = 1.9127639402605210809440330497537
absolute error = 6e-63
relative error = 3.1368219954955820335072147995743e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3591
Order of pole (three term test) = -21.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=392092100, alloc=4717728, time=20.51
x[1] = 1.16
y1[1] (analytic) = 1.399339529406273154451639623394
y1[1] (numeric) = 1.399339529406273154451639623394
absolute error = 1e-63
relative error = 7.1462284812628052419472603003279e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9168031087717669266186616668743
y2[1] (numeric) = 1.9168031087717669266186616668743
absolute error = 6e-63
relative error = 3.1302119516305614955341979356139e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3526
Order of pole (three term test) = -21.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=396093232, alloc=4717728, time=20.72
x[1] = 1.17
y1[1] (analytic) = 1.3901516843082302153326619350505
y1[1] (numeric) = 1.3901516843082302153326619350505
absolute error = 2e-63
relative error = 1.4386919230294236573160021116968e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.920750597736135639573013008962
y2[1] (numeric) = 1.920750597736135639573013008962
absolute error = 7e-63
relative error = 3.6444086016427363074063562662136e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.346
Order of pole (three term test) = -21.37
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.18
y1[1] (analytic) = 1.3809248243668817730295994667128
y1[1] (numeric) = 1.3809248243668817730295994667128
absolute error = 1e-63
relative error = 7.2415238132783518590352837949841e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9246060124080203461075380258748
y2[1] (numeric) = 1.9246060124080203461075380258748
absolute error = 7e-63
relative error = 3.6371080391886388428364436604749e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3392
Order of pole (three term test) = -21.54
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=400094004, alloc=4717728, time=20.93
x[1] = 1.19
y1[1] (analytic) = 1.3716598722605329380656795583505
y1[1] (numeric) = 1.3716598722605329380656795583505
absolute error = 1e-63
relative error = 7.2904370844644794030990521946104e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9283689672491666926020211116027
y2[1] (numeric) = 1.9283689672491666926020211116027
absolute error = 7e-63
relative error = 3.6300107079536518167735414536791e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3323
Order of pole (three term test) = -21.71
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=404094820, alloc=4717728, time=21.15
x[1] = 1.2
y1[1] (analytic) = 1.3623577544766735776383733556231
y1[1] (numeric) = 1.3623577544766735776383733556231
absolute error = 1e-63
relative error = 7.3402158626397872317740364448208e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9320390859672263496701344354948
y2[1] (numeric) = 1.9320390859672263496701344354948
absolute error = 7e-63
relative error = 3.6231151071644224011454912058230e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3253
Order of pole (three term test) = -21.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=408095640, alloc=4717728, time=21.36
x[1] = 1.21
y1[1] (analytic) = 1.3530194012193303387030107136648
y1[1] (numeric) = 1.3530194012193303387030107136648
absolute error = 1e-63
relative error = 7.3908770199363582074053793168680e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9356160015533859334164648885436
y2[1] (numeric) = 1.9356160015533859334164648885436
absolute error = 7e-63
relative error = 3.6164197828403486951992418383993e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3181
Order of pole (three term test) = -22.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=412096900, alloc=4717728, time=21.57
x[1] = 1.22
y1[1] (analytic) = 1.3436457463160470204755229744352
y1[1] (numeric) = 1.3436457463160470204755229744352
absolute error = 1e-63
relative error = 7.4424378802356135937019274632379e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9390993563190675809352452718884
y2[1] (numeric) = 1.9390993563190675809352452718884
absolute error = 7e-63
relative error = 3.6099233271305312612618645636724e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3108
Order of pole (three term test) = -22.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.23
y1[1] (analytic) = 1.3342377271245025982395472454977
y1[1] (numeric) = 1.3342377271245025982395472454977
absolute error = 1e-63
relative error = 7.4949162332200065688716271307286e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9424888019316975100238235653892
y2[1] (numeric) = 1.9424888019316975100238235653892
absolute error = 7e-63
relative error = 3.6036243776740889124229759653462e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3034
Order of pole (three term test) = -22.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=416098372, alloc=4717728, time=21.78
x[1] = 1.24
y1[1] (analytic) = 1.3247962844387762365776934156974
y1[1] (numeric) = 1.3247962844387762365776934156974
absolute error = 1e-63
relative error = 7.5483303489459153835038413637013e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9457839994495389862847059630818
y2[1] (numeric) = 1.9457839994495389862847059630818
absolute error = 7e-63
relative error = 3.5975216169833318580825665228144e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2959
Order of pole (three term test) = -22.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=420099100, alloc=4717728, time=21.99
x[1] = 1.25
y1[1] (analytic) = 1.315322362395268665447538552438
y1[1] (numeric) = 1.315322362395268665447538552438
absolute error = 1e-63
relative error = 7.6026989929597892104060790066535e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.948984619355586214348490847036
y2[1] (numeric) = 1.948984619355586214348490847036
absolute error = 7e-63
relative error = 3.5916137718493055257231874255241e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2882
Order of pole (three term test) = -22.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=424100316, alloc=4717728, time=22.21
x[1] = 1.26
y1[1] (analytic) = 1.3058169083782893268863424891765
y1[1] (numeric) = 1.3058169083782893268863424891765
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9520903415905157638568162214254
y2[1] (numeric) = 1.9520903415905157638568162214254
absolute error = 7e-63
relative error = 3.5858996127692379945297377638671e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2804
Order of pole (three term test) = -22.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.27
y1[1] (analytic) = 1.296280872925318733551137016088
y1[1] (numeric) = 1.296280872925318733551137016088
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9551008555846922350901817421829
y2[1] (numeric) = 1.9551008555846922350901817421829
absolute error = 7e-63
relative error = 3.5803779533954430253479725766801e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2725
Order of pole (three term test) = -22.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=428101164, alloc=4717728, time=22.41
x[1] = 1.28
y1[1] (analytic) = 1.2867152096319555127793868935926
y1[1] (numeric) = 1.2867152096319555127793868935926
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9580158602892249637007538591603
y2[1] (numeric) = 1.9580158602892249637007538591603
absolute error = 6e-63
relative error = 3.0643265571473564380330401348300e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2645
Order of pole (three term test) = -23.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=432101968, alloc=4717728, time=22.62
x[1] = 1.29
y1[1] (analytic) = 1.2771208750565576413866060900612
y1[1] (numeric) = 1.2771208750565576413866060900612
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9608350642060726589055612912854
y2[1] (numeric) = 1.9608350642060726589055612912854
absolute error = 7e-63
relative error = 3.5699076009915434930311400530652e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2564
Order of pole (three term test) = -23.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=436102916, alloc=4717728, time=22.84
x[1] = 1.3
y1[1] (analytic) = 1.2674988286245874069979841092929
y1[1] (numeric) = 1.2674988286245874069979841092929
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9635581854171929647013486300396
y2[1] (numeric) = 1.9635581854171929647013486300396
absolute error = 7e-63
relative error = 3.5649567463735357177349704320267e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2482
Order of pole (three term test) = -23.31
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=440103804, alloc=4717728, time=23.05
x[1] = 1.31
y1[1] (analytic) = 1.2578500325326696613381769786162
y1[1] (numeric) = 1.2578500325326696613381769786162
absolute error = 1e-63
relative error = 7.9500733325618241351132875727626e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9661849516127340291692578059375
y2[1] (numeric) = 1.9661849516127340291692578059375
absolute error = 7e-63
relative error = 3.5601940673273660634899321296923e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2399
Order of pole (three term test) = -23.43
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.32
y1[1] (analytic) = 1.2481754516523729595739827294274
y1[1] (numeric) = 1.2481754516523729595739827294274
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9687151001182652627358998459728
y2[1] (numeric) = 1.9687151001182652627358998459728
absolute error = 7e-63
relative error = 3.5556185857361960772126246903190e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2315
Order of pole (three term test) = -23.55
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=444104616, alloc=4717728, time=23.26
x[1] = 1.33
y1[1] (analytic) = 1.2384760534337232075157849860106
y1[1] (numeric) = 1.2384760534337232075157849860106
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9711483779210445623376830377638
y2[1] (numeric) = 1.9711483779210445623376830377638
absolute error = 7e-63
relative error = 3.5512293637594383413052722820045e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.223
Order of pole (three term test) = -23.67
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=448105292, alloc=4717728, time=23.47
x[1] = 1.34
y1[1] (analytic) = 1.2287528078084594652326394923001
y1[1] (numeric) = 1.2287528078084594652326394923001
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9734845416953193747878703480896
y2[1] (numeric) = 1.9734845416953193747878703480896
absolute error = 7e-63
relative error = 3.5470255034207964665302238738176e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2145
Order of pole (three term test) = -23.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=452106128, alloc=4717728, time=23.69
x[1] = 1.35
y1[1] (analytic) = 1.2190066870930415814200221730106
y1[1] (numeric) = 1.2190066870930415814200221730106
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9757233578266590692611135392652
y2[1] (numeric) = 1.9757233578266590692611135392652
absolute error = 7e-63
relative error = 3.5430061462148021954997148260026e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2058
Order of pole (three term test) = -23.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.36
y1[1] (analytic) = 1.2092386658914193576759752523919
y1[1] (numeric) = 1.2092386658914193576759752523919
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9778646024353161856784924394266
y2[1] (numeric) = 1.9778646024353161856784924394266
absolute error = 7e-63
relative error = 3.5391704727315514236320581551835e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
bytes used=456106944, alloc=4717728, time=23.90
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.197
Order of pole (three term test) = -23.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.37
y1[1] (analytic) = 1.1994497209975729656881983896453
y1[1] (numeric) = 1.1994497209975729656881983896453
absolute error = 1e-63
relative error = 8.3371564684537823697670409228291e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9799080613986142228876885048919
y2[1] (numeric) = 1.9799080613986142228876885048919
absolute error = 7e-63
relative error = 3.5355177022993555853764849836938e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1882
Order of pole (three term test) = -24.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=460107944, alloc=4717728, time=24.11
x[1] = 1.38
y1[1] (analytic) = 1.1896408312978343632091500735982
y1[1] (numeric) = 1.1896408312978343632091500735982
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.981853530372359727878131085206
y2[1] (numeric) = 1.981853530372359727878131085206
absolute error = 7e-63
relative error = 3.5320470926450391647913300445723e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1793
Order of pole (three term test) = -24.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=464109616, alloc=4717728, time=24.33
x[1] = 1.39
y1[1] (analytic) = 1.1798129776729994765961632178041
y1[1] (numeric) = 1.1798129776729994765961632178041
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9837008148112765448400382244429
y2[1] (numeric) = 1.9837008148112765448400382244429
absolute error = 7e-63
relative error = 3.5287579395716280888754412587327e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1703
Order of pole (three term test) = -24.26
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=468110328, alloc=4717728, time=24.54
x[1] = 1.4
y1[1] (analytic) = 1.1699671429002409386167480352036
y1[1] (numeric) = 1.1699671429002409386167480352036
absolute error = 1e-63
relative error = 8.5472485793155863828236215107456e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9854497299884601806594745788061
y2[1] (numeric) = 1.9854497299884601806594745788061
absolute error = 7e-63
relative error = 3.5256495766531874665860100704788e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1613
Order of pole (three term test) = -24.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.41
y1[1] (analytic) = 1.1601043115548311901635625493609
y1[1] (numeric) = 1.1601043115548311901635625493609
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9871001010138503414290888619422
y2[1] (numeric) = 1.9871001010138503414290888619422
absolute error = 7e-63
relative error = 3.5227213749465805629272827945491e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1522
Order of pole (three term test) = -24.42
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=472110972, alloc=4717728, time=24.75
x[1] = 1.42
y1[1] (analytic) = 1.1502254699116857734869821029759
y1[1] (numeric) = 1.1502254699116857734869821029759
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9886517628517197927362734733357
y2[1] (numeric) = 1.9886517628517197927362734733357
absolute error = 7e-63
relative error = 3.5199727427199340621071723310795e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.143
Order of pole (three term test) = -24.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=476112320, alloc=4717728, time=24.96
x[1] = 1.43
y1[1] (analytic) = 1.1403316058467366625338976245749
y1[1] (numeric) = 1.1403316058467366625338976245749
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9901045603371777948572914954818
y2[1] (numeric) = 1.9901045603371777948572914954818
absolute error = 7e-63
relative error = 3.5174031251976075923476729647418e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1338
Order of pole (three term test) = -24.56
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=480113804, alloc=4717728, time=25.17
x[1] = 1.44
y1[1] (analytic) = 1.1304237087381454929775201561292
y1[1] (numeric) = 1.1304237087381454929775201561292
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.991458348191686462527604463958
y2[1] (numeric) = 1.991458348191686462527604463958
absolute error = 7e-63
relative error = 3.5150120043214781729140895464402e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1245
Order of pole (three term test) = -24.63
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=484115104, alloc=4717728, time=25.38
x[1] = 1.45
y1[1] (analytic) = 1.120502769367366570532866627248
y1[1] (numeric) = 1.120502769367366570532866627248
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.992712991037588497665354134323
y2[1] (numeric) = 1.992712991037588497665354134323
absolute error = 7e-63
relative error = 3.5127988985283627163365083233107e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1152
Order of pole (three term test) = -24.69
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.46
y1[1] (analytic) = 1.1105697798200695511746481091234
y1[1] (numeric) = 1.1105697798200695511746481091234
absolute error = 1e-63
relative error = 9.0043869207571660918496856319543e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.99386836341164484228683230125
y2[1] (numeric) = 1.99386836341164484228683230125
absolute error = 7e-63
relative error = 3.5107633625434139903244090419372e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1058
Order of pole (three term test) = -24.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=488115916, alloc=4717728, time=25.59
x[1] = 1.47
y1[1] (analytic) = 1.1006257333869317009069746014624
y1[1] (numeric) = 1.1006257333869317009069746014624
absolute error = 1e-63
relative error = 9.0857406806464690431127404880792e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9949243497775808978599284627356
y2[1] (numeric) = 1.9949243497775808978599284627356
absolute error = 7e-63
relative error = 3.5089049871893375288869834451719e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09641
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=492116796, alloc=4717728, time=25.81
x[1] = 1.48
y1[1] (analytic) = 1.0906716244643096557762265406478
y1[1] (numeric) = 1.0906716244643096557762265406478
absolute error = 1e-63
relative error = 9.1686624788754029971031479664534e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9958808445376400564840751325627
y2[1] (numeric) = 1.9958808445376400564840751325627
absolute error = 7e-63
relative error = 3.5072233992112888947321209175871e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08695
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=496118092, alloc=4783252, time=26.02
x[1] = 1.49
y1[1] (analytic) = 1.0807084484548006148683184845637
y1[1] (numeric) = 1.0807084484548006148683184845637
absolute error = 1e-63
relative error = 9.2531894372603662245462113142181e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9967377520431433885532007170437
y2[1] (numeric) = 1.9967377520431433885532007170437
absolute error = 7e-63
relative error = 3.5057182611173224489134435858866e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07747
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.5
y1[1] (analytic) = 1.0707372016677029100881898514343
y1[1] (numeric) = 1.0707372016677029100881898514343
absolute error = 1e-63
relative error = 9.3393598209016390280655430800658e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9974949866040544309417233711415
y2[1] (numeric) = 1.9974949866040544309417233711415
absolute error = 7e-63
relative error = 3.5043892710342743924600322342379e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06795
Order of pole (three term test) = -24.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=500119316, alloc=4783252, time=26.23
x[1] = 1.51
y1[1] (analytic) = 1.0607588812193859065815955149162
y1[1] (numeric) = 1.0607588812193859065815955149162
absolute error = 2e-63
relative error = 1.8854426160457104505460527049495e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9981524724975481192427378648367
y2[1] (numeric) = 1.9981524724975481192427378648367
absolute error = 7e-63
relative error = 3.5032361625789743216581147222816e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0584
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=504120012, alloc=4783252, time=26.44
x[1] = 1.52
y1[1] (analytic) = 1.0507744849335791967261292701527
y1[1] (numeric) = 1.0507744849335791967261292701527
absolute error = 2e-63
relative error = 1.9033579789734069969172736881246e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9987101439755830071723123941168
y2[1] (numeric) = 1.9987101439755830071723123941168
absolute error = 7e-63
relative error = 3.5022587047446908968479511565357e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04883
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=508120704, alloc=4783252, time=26.66
x[1] = 1.53
y1[1] (analytic) = 1.0407850112415910586889890070761
y1[1] (numeric) = 1.0407850112415910586889890070761
absolute error = 2e-63
relative error = 1.9216264438840503565027755280618e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.999167945271476015924265068709
y2[1] (numeric) = 1.999167945271476015924265068709
absolute error = 7e-63
relative error = 3.5014567018027284769530845183077e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03924
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=512121524, alloc=4783252, time=26.87
x[1] = 1.54
y1[1] (analytic) = 1.0307914590824661576224768070764
y1[1] (numeric) = 1.0307914590824661576224768070764
absolute error = 2e-63
relative error = 1.9402566662516307170263734648064e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.99952583060547905600596353844
y2[1] (numeric) = 1.99952583060547905600596353844
absolute error = 7e-63
relative error = 3.5008299932191027312051947550516e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02964
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.55
y1[1] (analytic) = 1.0207948278030924736439127746956
y1[1] (numeric) = 1.0207948278030924736439127746956
absolute error = 2e-63
relative error = 1.9592575760834405038747057926026e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9997837641893569638976113476345
y2[1] (numeric) = 1.9997837641893569638976113476345
absolute error = 8e-63
relative error = 4.0004325183842677922859062475749e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02002
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=516122304, alloc=4783252, time=27.08
x[1] = 1.56
y1[1] (analytic) = 1.0107961170582674458239206637609
y1[1] (numeric) = 1.0107961170582674458239206637609
absolute error = 3e-63
relative error = 2.9679575825151935089528063740599e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9999417202299662957451700234135
y2[1] (numeric) = 1.9999417202299662957451700234135
absolute error = 8e-63
relative error = 4.0001165629366979811154428504490e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0104
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=520123424, alloc=4783252, time=27.29
x[1] = 1.57
y1[1] (analytic) = 1.0007963267107333254854085336454
y1[1] (numeric) = 1.0007963267107333254854085336454
absolute error = 3e-63
relative error = 2.9976129207627572768570066594626e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9999996829318346202105299238233
y2[1] (numeric) = 1.9999996829318346202105299238233
absolute error = 8e-63
relative error = 4.0000006341364312918163752439218e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0007668
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=524124092, alloc=4783252, time=27.51
x[1] = 1.58
y1[1] (analytic) = 0.99079645673119173519461094301727
y1[1] (numeric) = 0.99079645673119173519461094301727
absolute error = 3.5e-63
relative error = 3.5325116235751419526302379451603e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9999576464987400525517942322517
y2[1] (numeric) = 1.9999576464987400525517942322517
absolute error = 8e-63
relative error = 4.0000847087963769519363443713385e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008874
Order of pole (three term test) = -0.8949
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.59
y1[1] (analytic) = 0.9807975070983074319049726537566
y1[1] (numeric) = 0.9807975070983074319049726537566
absolute error = 3.6e-63
relative error = 3.6704824124712669158299371358500e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9998156151342908719815843437455
y2[1] (numeric) = 1.9998156151342908719815843437455
absolute error = 8e-63
relative error = 4.0003688037323315855291277708955e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01851
Order of pole (three term test) = -0.9018
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=528124888, alloc=4783252, time=27.72
TOP MAIN SOLVE Loop
x[1] = 1.6
y1[1] (analytic) = 0.9708004776987112737942295370535
y1[1] (numeric) = 0.9708004776987112737942295370535
absolute error = 3.6e-63
relative error = 3.7082800046965602740765802907448e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9995736030415051643421138255462
y2[1] (numeric) = 1.9995736030415051643421138255462
absolute error = 8e-63
relative error = 4.0008529757701266972226707016307e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02814
Order of pole (three term test) = -0.9135
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=532125784, alloc=4783252, time=27.93
x[1] = 1.61
y1[1] (analytic) = 0.96080636822701239041467239039898
y1[1] (numeric) = 0.96080636822701239041467239039898
absolute error = 3.7e-63
relative error = 3.8509320112309983345219346460795e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9992316344213905321324131478443
y2[1] (numeric) = 1.9992316344213905321324131478443
absolute error = 8e-63
relative error = 4.0015373217697845104384333539557e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03776
Order of pole (three term test) = -0.93
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=536126496, alloc=4783252, time=28.15
x[1] = 1.62
y1[1] (analytic) = 0.95081617808582955485625572528767
y1[1] (numeric) = 0.95081617808582955485625572528767
absolute error = 3.7e-63
relative error = 3.8913936103283293299780619023621e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9987897434705240139155188912468
y2[1] (numeric) = 1.9987897434705240139155188912468
absolute error = 8e-63
relative error = 4.0024219786666997846476597091736e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04737
Order of pole (three term test) = -0.9513
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=540127240, alloc=4783252, time=28.36
x[1] = 1.63
y1[1] (analytic) = 0.9408309062858517547020283025802
y1[1] (numeric) = 0.9408309062858517547020283025802
absolute error = 3.7e-63
relative error = 3.9326939360512807576430903440025e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9982479743776324551116699849331
y2[1] (numeric) = 1.9982479743776324551116699849331
absolute error = 8e-63
relative error = 4.0035071235298776666665858212064e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05696
Order of pole (three term test) = -0.9775
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.64
y1[1] (analytic) = 0.93085155134593795563550729254339
y1[1] (numeric) = 0.93085155134593795563550729254339
absolute error = 3.8e-63
relative error = 4.0822835762646574408539572634704e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9976063813191736721375819743679
y2[1] (numeric) = 1.9976063813191736721375819743679
absolute error = 8e-63
relative error = 4.0047929736372700946300221012326e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06652
Order of pole (three term test) = -1.008
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=544128052, alloc=4783252, time=28.57
x[1] = 1.65
y1[1] (analytic) = 0.92087911119326604764038540265872
y1[1] (numeric) = 0.92087911119326604764038540265872
absolute error = 3.9e-63
relative error = 4.2350835767644013109686417967926e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9968650284539188517717030402022
y2[1] (numeric) = 1.9968650284539188517717030402022
absolute error = 7e-63
relative error = 3.5054948132472325613181882075811e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07606
Order of pole (three term test) = -1.044
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=548128728, alloc=4783252, time=28.78
x[1] = 1.66
y1[1] (analytic) = 0.91091458306354095881474206834938
y1[1] (numeric) = 0.91091458306354095881474206834938
absolute error = 4.0e-63
relative error = 4.3911910890123267549723763438759e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.996023989916536727501000590613
y2[1] (numeric) = 1.996023989916536727501000590613
absolute error = 7e-63
relative error = 3.5069718777742262253476211444643e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08556
Order of pole (three term test) = -1.085
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=552129916, alloc=4783252, time=28.99
x[1] = 1.67
y1[1] (analytic) = 0.90095896340127191590521765755139
y1[1] (numeric) = 0.90095896340127191590521765755139
absolute error = 4.1e-63
relative error = 4.5507067097948713118445136812227e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9950833498101801744262972465342
y2[1] (numeric) = 1.9950833498101801744262972465342
absolute error = 7e-63
relative error = 3.5086253417262023916794959746074e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09503
Order of pole (three term test) = -1.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.68
y1[1] (analytic) = 0.89101324776012882375199526582718
y1[1] (numeric) = 0.89101324776012882375199526582718
absolute error = 4.2e-63
relative error = 4.7137346280295588486540677644038e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9940432021980759640604878691936
y2[1] (numeric) = 1.9940432021980759640604878691936
absolute error = 7e-63
relative error = 3.5104555369130177628089706990992e-61 %
Correct digits = 64
h = 0.01
bytes used=556130692, alloc=4783252, time=29.21
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1045
Order of pole (three term test) = -1.18
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.69
y1[1] (analytic) = 0.88107843070338772792360953016691
y1[1] (numeric) = 0.88107843070338772792360953016691
absolute error = 4.2e-63
relative error = 4.7668855048999794892679590205801e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9929036510941185200371492939456
y2[1] (numeric) = 1.9929036510941185200371492939456
absolute error = 6e-63
relative error = 3.0106824264715238989336603016991e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1139
Order of pole (three term test) = -1.235
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=560131356, alloc=4783252, time=29.41
x[1] = 1.7
y1[1] (analytic) = 0.87115550570447531591235714266513
y1[1] (numeric) = 0.87115550570447531591235714266513
absolute error = 4.3e-63
relative error = 4.9359729369129440396906043256506e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9916648104524686153461333986479
y2[1] (numeric) = 1.9916648104524686153461333986479
absolute error = 6e-63
relative error = 3.0125551089276480017787666966715e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1232
Order of pole (three term test) = -1.294
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=564132444, alloc=4783252, time=29.63
x[1] = 1.71
y1[1] (analytic) = 0.86124546504762240235731021694889
y1[1] (numeric) = 0.86124546504762240235731021694889
absolute error = 4.3e-63
relative error = 4.9927693956127041283925567628602e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9903268041561580512177522238611
y2[1] (numeric) = 1.9903268041561580512177522238611
absolute error = 6e-63
relative error = 3.0145803128767234413940842938017e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1325
Order of pole (three term test) = -1.358
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=568133264, alloc=4783252, time=29.84
x[1] = 1.72
y1[1] (analytic) = 0.85134929972863633286362171966881
y1[1] (numeric) = 0.85134929972863633286362171966881
absolute error = 4.4e-63
relative error = 5.1682664229623254864635102582586e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9888897660047014571781706570855
y2[1] (numeric) = 1.9888897660047014571781706570855
absolute error = 5e-63
relative error = 2.5139653717682112601595174976708e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1417
Order of pole (three term test) = -1.427
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.73
y1[1] (analytic) = 0.84146799935580222909505164865743
y1[1] (numeric) = 0.84146799935580222909505164865743
absolute error = 4.5e-63
relative error = 5.3477969494324666821277551076568e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9873538397007164510856776762221
y2[1] (numeric) = 1.9873538397007164510856776762221
absolute error = 5e-63
relative error = 2.5159082897653343713084995835276e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1509
Order of pole (three term test) = -1.5
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=572134040, alloc=4783252, time=30.05
x[1] = 1.74
y1[1] (analytic) = 0.83160255205092298493262268465491
y1[1] (numeric) = 0.83160255205092298493262268465491
absolute error = 4.5e-63
relative error = 5.4112388050060283699873191776570e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9857191788355534971206826956655
y2[1] (numeric) = 1.9857191788355534971206826956655
absolute error = 5e-63
relative error = 2.5179794068021502993051121087842e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1601
Order of pole (three term test) = -1.578
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=576134960, alloc=4783252, time=30.26
x[1] = 1.75
y1[1] (analytic) = 0.82175394435050790961732305605737
y1[1] (numeric) = 0.82175394435050790961732305605737
absolute error = 4.6e-63
relative error = 5.5977826837639526960662185485546e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.983985946873936898731662936968
y2[1] (numeric) = 1.983985946873936898731662936968
absolute error = 5e-63
relative error = 2.5201791413282130462124736332584e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1691
Order of pole (three term test) = -1.661
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=580135648, alloc=4783252, time=30.48
x[1] = 1.76
y1[1] (analytic) = 0.8119231611071198989301998234959
y1[1] (numeric) = 0.8119231611071198989301998234959
absolute error = 4.6e-63
relative error = 5.6655607579017021097525549698803e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.982154317137618462424968099456
y2[1] (numeric) = 1.982154317137618462424968099456
absolute error = 5e-63
relative error = 2.5225079383427523196573065771557e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1781
Order of pole (three term test) = -1.748
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=584136592, alloc=4783252, time=30.69
x[1] = 1.77
y1[1] (analytic) = 0.80211118539089099961051415826961
y1[1] (numeric) = 0.80211118539089099961051415826961
absolute error = 4.6e-63
relative error = 5.7348657938965064764576867455820e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9802244727880454670184814488984
y2[1] (numeric) = 1.9802244727880454670184814488984
absolute error = 5e-63
relative error = 2.5249662695867399505997038216284e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.187
Order of pole (three term test) = -1.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.78
y1[1] (analytic) = 0.79231899839121621537344670968737
y1[1] (numeric) = 0.79231899839121621537344670968737
absolute error = 4.7e-63
relative error = 5.9319541870676226460579378234021e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9781966068080446715477686473056
y2[1] (numeric) = 1.9781966068080446715477686473056
absolute error = 5e-63
relative error = 2.5275546337468657784943005619619e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1959
Order of pole (three term test) = -1.936
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=588137472, alloc=4783252, time=30.90
x[1] = 1.79
y1[1] (analytic) = 0.78254757931863538506482973553539
y1[1] (numeric) = 0.78254757931863538506482973553539
absolute error = 4.8e-63
relative error = 6.1338123417100883300845289748481e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9760709219825241934086604331086
y2[1] (numeric) = 1.9760709219825241934086604331086
absolute error = 5e-63
relative error = 2.5302735566715750555938666458981e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2047
Order of pole (three term test) = -2.036
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=592138912, alloc=4783252, time=31.11
x[1] = 1.8
y1[1] (analytic) = 0.77279790530691294468332569346942
y1[1] (numeric) = 0.77279790530691294468332569346942
absolute error = 4.8e-63
relative error = 6.2111969598231548661516562351643e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9738476308781951865323731788434
y2[1] (numeric) = 1.9738476308781951865323731788434
absolute error = 5e-63
relative error = 2.5331235915993287967044712316726e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2133
Order of pole (three term test) = -2.141
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=596139716, alloc=4783252, time=31.32
x[1] = 1.81
y1[1] (analytic) = 0.76307095131532536521225014915802
y1[1] (numeric) = 0.76307095131532536521225014915802
absolute error = 4.9e-63
relative error = 6.4214212211246435041755094469069e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9715269558223153474084512690904
y2[1] (numeric) = 1.9715269558223153474084512690904
absolute error = 5e-63
relative error = 2.5361053193992580604680486553166e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2219
Order of pole (three term test) = -2.25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.82
y1[1] (analytic) = 0.75336769003116603743582895516913
y1[1] (numeric) = 0.75336769003116603743582895516913
absolute error = 4.9e-63
relative error = 6.5041281499572832737106131870216e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9691091288804563745872153184981
y2[1] (numeric) = 1.9691091288804563745872153184981
absolute error = 4e-63
relative error = 2.0313754790595143238206005052467e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2305
Order of pole (three term test) = -2.363
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=600140432, alloc=4783252, time=31.53
x[1] = 1.83
y1[1] (analytic) = 0.74368909177247735317016241638147
y1[1] (numeric) = 0.74368909177247735317016241638147
absolute error = 4.9e-63
relative error = 6.5887748713935628063580447612017e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9665943918332976048972389297428
y2[1] (numeric) = 1.9665943918332976048972389297428
absolute error = 4e-63
relative error = 2.0339730534221253792632316702739e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2389
Order of pole (three term test) = -2.481
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=604141568, alloc=4783252, time=31.75
x[1] = 1.84
y1[1] (analytic) = 0.7340361243910197096197170167184
y1[1] (numeric) = 0.7340361243910197096197170167184
absolute error = 4.9e-63
relative error = 6.6754207826831406787356070773028e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9639829961524481469948936717271
y2[1] (numeric) = 1.9639829961524481469948936717271
absolute error = 4e-63
relative error = 2.0366775108726614899069575991695e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2472
Order of pole (three term test) = -2.603
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=608142240, alloc=4783252, time=31.96
x[1] = 1.85
y1[1] (analytic) = 0.7244097531754871398780501645252
y1[1] (numeric) = 0.7244097531754871398780501645252
absolute error = 4.9e-63
relative error = 6.7641275928721277099601255224206e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9612752029752999300124591686361
y2[1] (numeric) = 1.9612752029752999300124591686361
absolute error = 4e-63
relative error = 2.0394894066533382521347186879782e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2554
Order of pole (three term test) = -2.729
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=612143028, alloc=4783252, time=32.17
x[1] = 1.86
y1[1] (analytic) = 0.71481094075497924792906451171088
y1[1] (numeric) = 0.71481094075497924792906451171088
absolute error = 4.9e-63
relative error = 6.8549594314052438591572497511380e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9584712830789141819789777659032
y2[1] (numeric) = 1.9584712830789141819789777659032
absolute error = 3e-63
relative error = 1.5318069894206963996010683884395e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2636
Order of pole (three term test) = -2.859
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.87
y1[1] (analytic) = 0.70524064700273910087485193519011
y1[1] (numeric) = 0.70524064700273910087485193519011
absolute error = 4.9e-63
relative error = 6.9479829627304065101459315105464e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9555715168529439493442504921726
y2[1] (numeric) = 1.9555715168529439493442504921726
absolute error = 3e-63
relative error = 1.5340783879015739975727742248052e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2716
Order of pole (three term test) = -2.993
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=616143848, alloc=4783252, time=32.38
x[1] = 1.88
y1[1] (analytic) = 0.69569982894016670452068624047776
y1[1] (numeric) = 0.69569982894016670452068624047776
absolute error = 5.0e-63
relative error = 7.1870076604978184534851416211174e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9525761942715953653314574258151
y2[1] (numeric) = 1.9525761942715953653314574258151
absolute error = 3e-63
relative error = 1.5364317196948844218996088375185e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2795
Order of pole (three term test) = -3.131
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=620145008, alloc=4783252, time=32.60
x[1] = 1.89
y1[1] (analytic) = 0.68618944064111766088961758444877
y1[1] (numeric) = 0.68618944064111766088961758444877
absolute error = 5.1e-63
relative error = 7.4323498700810511400181025003410e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9494856148646304709682016721383
y2[1] (numeric) = 1.9494856148646304709682016721383
absolute error = 2e-63
relative error = 1.0259116480522874628264821518867e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2873
Order of pole (three term test) = -3.273
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=624146088, alloc=4783252, time=32.81
x[1] = 1.9
y1[1] (analytic) = 0.67671043313649657772116630491969
y1[1] (numeric) = 0.67671043313649657772116630491969
absolute error = 5.0e-63
relative error = 7.3886846650574246863411364071032e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.946300087687414488489709611635
y2[1] (numeric) = 1.946300087687414488489709611635
absolute error = 2e-63
relative error = 1.0275907670416803606181490885369e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.295
Order of pole (three term test) = -3.419
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.91
y1[1] (analytic) = 0.66726375431915477053366106060247
y1[1] (numeric) = 0.66726375431915477053366106060247
absolute error = 5.1e-63
relative error = 7.6431545501880366835891849325530e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9430199312900105423618865769482
y2[1] (numeric) = 1.9430199312900105423618865769482
absolute error = 2e-63
relative error = 1.0293255194104772916242601689465e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3025
Order of pole (three term test) = -3.569
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=628147320, alloc=4783252, time=33.02
TOP MAIN SOLVE Loop
x[1] = 1.92
y1[1] (analytic) = 0.65785034884910176740076339684095
y1[1] (numeric) = 0.65785034884910176740076339684095
absolute error = 5.1e-63
relative error = 7.7525230607878601703952462471591e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.939645473685324918426371339687
y2[1] (numeric) = 1.939645473685324918426371339687
absolute error = 2e-63
relative error = 1.0311162669330501556435735647905e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.31
Order of pole (three term test) = -3.723
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=632148076, alloc=4783252, time=33.24
x[1] = 1.93
y1[1] (analytic) = 0.64847115805904009521271093528813
y1[1] (numeric) = 0.64847115805904009521271093528813
absolute error = 5.1e-63
relative error = 7.8646520151566558897139294366726e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9361770523163060466151293727488
y2[1] (numeric) = 1.9361770523163060466151293727488
absolute error = 2e-63
relative error = 1.0329633840083687944185628728597e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3173
Order of pole (three term test) = -3.88
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=636148744, alloc=4783252, time=33.45
x[1] = 1.94
y1[1] (analytic) = 0.63912711986023279386493231415927
y1[1] (numeric) = 0.63912711986023279386493231415927
absolute error = 5.1e-63
relative error = 7.9796332240060334815738784802095e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9326150140222004873089793388657
y2[1] (numeric) = 1.9326150140222004873089793388657
absolute error = 3e-63
relative error = 1.5523008867432601679374818716986e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3245
Order of pole (three term test) = -4.041
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=640149488, alloc=4783252, time=33.67
x[1] = 1.95
y1[1] (analytic) = 0.62981916864871307154417154086931
y1[1] (numeric) = 0.62981916864871307154417154086931
absolute error = 5.2e-63
relative error = 8.2563381028187531275854542979935e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9289597150038692957132970350915
y2[1] (numeric) = 1.9289597150038692957132970350915
absolute error = 2e-63
relative error = 1.0368282885555171922020502309869e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3315
Order of pole (three term test) = -4.205
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.96
y1[1] (analytic) = 0.62054823521184548006843478455255
y1[1] (numeric) = 0.62054823521184548006843478455255
absolute error = 5.2e-63
relative error = 8.3796870330713311555156802603665e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.92521152078816823258555628949
y2[1] (numeric) = 1.92521152078816823258555628949
absolute error = 3e-63
relative error = 1.5582703342497248430987418613528e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3385
Order of pole (three term test) = -4.373
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=644150336, alloc=4783252, time=33.87
x[1] = 1.97
y1[1] (analytic) = 0.61131524663524795408536018612069
y1[1] (numeric) = 0.61131524663524795408536018612069
absolute error = 5.3e-63
relative error = 8.6698312027580405972445469623524e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9213708061913953832639509971532
y2[1] (numeric) = 1.9213708061913953832639509971532
absolute error = 2e-63
relative error = 1.0409234873118874952852244284339e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3453
Order of pole (three term test) = -4.545
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=648151032, alloc=4783252, time=34.09
x[1] = 1.98
y1[1] (analytic) = 0.60212112621008402184752614009281
y1[1] (numeric) = 0.60212112621008402184752614009281
absolute error = 5.3e-63
relative error = 8.8022156494651794283516316159777e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.917437955281809840204735217402
y2[1] (numeric) = 1.917437955281809840204735217402
absolute error = 3e-63
relative error = 1.5645877832636747648046754747626e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3519
Order of pole (three term test) = -4.719
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=652152396, alloc=4783252, time=34.30
x[1] = 1.99
y1[1] (analytic) = 0.59296679334073445826636428386971
y1[1] (numeric) = 0.59296679334073445826636428386971
absolute error = 5.3e-63
relative error = 8.9381059100125347572785412561887e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9134133613412251971287932710576
y2[1] (numeric) = 1.9134133613412251971287932710576
absolute error = 2e-63
relative error = 1.0452524480115896542952443510556e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3584
Order of pole (three term test) = -4.898
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=656153156, alloc=4783252, time=34.51
x[1] = 2
y1[1] (analytic) = 0.58385316345285761300243177049924
y1[1] (numeric) = 0.58385316345285761300243177049924
absolute error = 5.3e-63
relative error = 9.0776248751591133664954491738840e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9092974268256816953960198659117
y2[1] (numeric) = 1.9092974268256816953960198659117
absolute error = 2e-63
relative error = 1.0475057326846748133100283768061e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3648
Order of pole (three term test) = -5.079
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.01
y1[1] (analytic) = 0.57478114790184760748261765983457
y1[1] (numeric) = 0.57478114790184760748261765983457
absolute error = 5.3e-63
relative error = 9.2209008930561749805669183972543e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9050905633252009553600997102737
y2[1] (numeric) = 1.9050905633252009553600997102737
absolute error = 3e-63
relative error = 1.5747282873333391534555748591616e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.371
Order of pole (three term test) = -5.263
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=660154176, alloc=4783252, time=34.73
x[1] = 2.02
y1[1] (analytic) = 0.5657516538816995549482971259098
y1[1] (numeric) = 0.5657516538816995549482971259098
absolute error = 5.3e-63
relative error = 9.3680680624368914722800405442350e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9007931915226273171970135245537
y2[1] (numeric) = 1.9007931915226273171970135245537
absolute error = 2e-63
relative error = 1.0521923210372524688200032422639e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3771
Order of pole (three term test) = -5.451
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=664155644, alloc=4783252, time=34.94
x[1] = 2.03
y1[1] (analytic) = 0.5567655843342909169364832683039
y1[1] (numeric) = 0.5567655843342909169364832683039
absolute error = 5.4e-63
relative error = 9.6988753470756088741531163037910e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8964057411515599070388888319676
y2[1] (numeric) = 1.8964057411515599070388888319676
absolute error = 3e-63
relative error = 1.5819399482403493359302101185576e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.383
Order of pole (three term test) = -5.641
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=668156432, alloc=4783252, time=35.15
x[1] = 2.04
y1[1] (analytic) = 0.54782383785908806798272979470864
y1[1] (numeric) = 0.54782383785908806798272979470864
absolute error = 5.4e-63
relative error = 9.8571833257628244112328323711866e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8919286509533796351715256485842
y2[1] (numeric) = 1.8919286509533796351715256485842
absolute error = 3e-63
relative error = 1.5856834762179015926133685921299e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3888
Order of pole (three term test) = -5.835
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.05
y1[1] (analytic) = 0.5389273086232870978140700058326
y1[1] (numeric) = 0.5389273086232870978140700058326
absolute error = 5.5e-63
relative error = 1.0205457975492067135317802628524e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8873623686333754235599666046803
y2[1] (numeric) = 1.8873623686333754235599666046803
absolute error = 3e-63
relative error = 1.5895198769763948025602945222711e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3944
Order of pole (three term test) = -6.031
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=672158132, alloc=4783252, time=35.36
x[1] = 2.06
y1[1] (analytic) = 0.5300768862723978368768903735121
y1[1] (numeric) = 0.5300768862723978368768903735121
absolute error = 5.5e-63
relative error = 1.0375853281732491935715312450161e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8827073508159740500427975851999
y2[1] (numeric) = 1.8827073508159740500427975851999
absolute error = 2e-63
relative error = 1.0622999900293536192841255089695e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3999
Order of pole (three term test) = -6.23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=676159132, alloc=4783252, time=35.58
x[1] = 2.07
y1[1] (analytic) = 0.52127345584128004672267286098827
y1[1] (numeric) = 0.52127345584128004672267286098827
absolute error = 5.6e-63
relative error = 1.0742921852719690477632235271204e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8779640629990780861734511204438
y2[1] (numeric) = 1.8779640629990780861734511204438
absolute error = 2e-63
relative error = 1.0649831055904405890913391735797e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4052
Order of pole (three term test) = -6.432
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=680160500, alloc=4783252, time=35.80
x[1] = 2.08
y1[1] (analytic) = 0.51251789766564067155843115022765
y1[1] (numeric) = 0.51251789766564067155843115022765
absolute error = 5.5e-63
relative error = 1.0731332554532800230552597426901e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8731329795075164948766768050246
y2[1] (numeric) = 1.8731329795075164948766768050246
absolute error = 2e-63
relative error = 1.0677298525414033019184784801202e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4103
Order of pole (three term test) = -6.636
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=684161652, alloc=4783252, time=36.01
x[1] = 2.09
y1[1] (analytic) = 0.50381108729400100116293368812955
y1[1] (numeric) = 0.50381108729400100116293368812955
absolute error = 5.5e-63
relative error = 1.0916790318253660656236416421027e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8682145834456125428216220587275
y2[1] (numeric) = 1.8682145834456125428216220587275
absolute error = 2e-63
relative error = 1.0705408349352091404535081101385e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4153
Order of pole (three term test) = -6.843
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.1
y1[1] (analytic) = 0.49515389540014254837906147628083
y1[1] (numeric) = 0.49515389540014254837906147628083
absolute error = 5.6e-63
relative error = 1.1309615156060807661156278215892e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.863209366648873770680759313269
y2[1] (numeric) = 1.863209366648873770680759313269
absolute error = 1e-63
relative error = 5.3670833664741466195688589559232e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4201
Order of pole (three term test) = -7.053
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=688162368, alloc=4783252, time=36.22
x[1] = 2.11
y1[1] (analytic) = 0.48654718769604039652158984292831
y1[1] (numeric) = 0.48654718769604039652158984292831
absolute error = 5.6e-63
relative error = 1.1509674994768392839987337850326e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8581178296348088522373755083107
y2[1] (numeric) = 1.8581178296348088522373755083107
absolute error = 2e-63
relative error = 1.0763580049135400714699908513894e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4247
Order of pole (three term test) = -7.265
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=692163184, alloc=4783252, time=36.44
x[1] = 2.12
y1[1] (analytic) = 0.47799182484529272329309811701611
y1[1] (numeric) = 0.47799182484529272329309811701611
absolute error = 5.6e-63
relative error = 1.1715681542906097162369496086887e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8529404815528762606147273336542
y2[1] (numeric) = 1.8529404815528762606147273336542
absolute error = 1e-63
relative error = 5.3968274208243293468159819123349e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4292
Order of pole (three term test) = -7.479
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=696163956, alloc=4783252, time=36.65
x[1] = 2.13
y1[1] (analytic) = 0.46948866237705515818347379039028
y1[1] (numeric) = 0.46948866237705515818347379039028
absolute error = 5.6e-63
relative error = 1.1927870572309017495647256670424e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8476778401335697467185299963159
y2[1] (numeric) = 1.8476778401335697467185299963159
absolute error = 2e-63
relative error = 1.0824397828224312049823291963519e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4335
Order of pole (three term test) = -7.695
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.14
y1[1] (analytic) = 0.4610385506004885798455500879914
y1[1] (numeric) = 0.4610385506004885798455500879914
absolute error = 5.6e-63
relative error = 1.2146489686613346450046163915088e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8423304316366457213025066370689
y2[1] (numeric) = 1.8423304316366457213025066370689
absolute error = 1e-63
relative error = 5.4279079519499863413845924845851e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4376
Order of pole (three term test) = -7.913
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=700164860, alloc=4783252, time=36.86
x[1] = 2.15
y1[1] (analytic) = 0.45264233451972890859584611773597
y1[1] (numeric) = 0.45264233451972890859584611773597
absolute error = 5.5e-63
relative error = 1.2150874057849037795542428479975e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8368987907984977178756481370438
y2[1] (numeric) = 1.8368987907984977178756481370438
absolute error = 1e-63
relative error = 5.4439580722098531640546833609282e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4415
Order of pole (three term test) = -8.133
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=704165560, alloc=4783252, time=37.07
x[1] = 2.16
y1[1] (analytic) = 0.44430085374938739699030125601663
y1[1] (numeric) = 0.44430085374938739699030125601663
absolute error = 5.5e-63
relative error = 1.2378999395536460664041126813432e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8313834607786831989610381203463
y2[1] (numeric) = 1.8313834607786831989610381203463
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4453
Order of pole (three term test) = -8.356
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=708166264, alloc=4783252, time=37.29
x[1] = 2.17
y1[1] (analytic) = 0.43601494243058986837553000558349
y1[1] (numeric) = 0.43601494243058986837553000558349
absolute error = 5.5e-63
relative error = 1.2614246588293373720871881891887e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8257849931056080529810564239434
y2[1] (numeric) = 1.8257849931056080529810564239434
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4489
Order of pole (three term test) = -8.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=712167380, alloc=4783252, time=37.50
x[1] = 2.18
y1[1] (analytic) = 0.42778542914756329942177513233751
y1[1] (numeric) = 0.42778542914756329942177513233751
absolute error = 5.5e-63
relative error = 1.2856912894297742695997858922121e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8201039476213742132740097460839
y2[1] (numeric) = 1.8201039476213742132740097460839
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4523
Order of pole (three term test) = -8.806
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.19
y1[1] (analytic) = 0.41961313684477808790979483620305
y1[1] (numeric) = 0.41961313684477808790979483620305
absolute error = 5.5e-63
relative error = 1.3107311275706179615097750170375e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.814340892425795914434327645905
y2[1] (numeric) = 1.814340892425795914434327645905
absolute error = 1e-63
relative error = 5.5116433971952635456861645933305e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4555
Order of pole (three term test) = -9.033
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=716168948, alloc=4783252, time=37.71
x[1] = 2.2
y1[1] (analytic) = 0.41149888274465429147585738734507
y1[1] (numeric) = 0.41149888274465429147585738734507
absolute error = 5.5e-63
relative error = 1.3365771404567560804948840144753e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8084964038195901843040369104161
y2[1] (numeric) = 1.8084964038195901843040369104161
absolute error = 1e-63
relative error = 5.5294552861038301567256314290128e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.83
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4586
Order of pole (three term test) = -9.262
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=720169684, alloc=4783252, time=37.92
x[1] = 2.21
y1[1] (analytic) = 0.40344347826584006662239082248137
y1[1] (numeric) = 0.40344347826584006662239082248137
absolute error = 5.5e-63
relative error = 1.3632640744723844256031060701646e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.802571066246747252518974042556
y2[1] (numeric) = 1.802571066246747252518974042556
absolute error = 1e-63
relative error = 5.5476314844116870858691896016498e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = -9.493
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=724170596, alloc=4783252, time=38.14
x[1] = 2.22
y1[1] (analytic) = 0.39544772894207048008228556249985
y1[1] (numeric) = 0.39544772894207048008228556249985
absolute error = 5.5e-63
relative error = 1.3908285716329655074148578475296e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7965654722360866385208567496092
y2[1] (numeric) = 1.7965654722360866385208567496092
absolute error = 1e-63
relative error = 5.5661762148604290709750739383975e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4641
Order of pole (three term test) = -9.725
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.23
y1[1] (analytic) = 0.38751243434161480658809608931437
y1[1] (numeric) = 0.38751243434161480658809608931437
absolute error = 5.5e-63
relative error = 1.4193092950280478734014155923465e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7904802223420047633777101271885
y2[1] (numeric) = 1.7904802223420047633777101271885
absolute error = 1e-63
relative error = 5.5850938062413689785812703547247e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4666
Order of pole (three term test) = -9.958
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=728171468, alloc=4783252, time=38.35
TOP MAIN SOLVE Loop
x[1] = 2.24
y1[1] (analytic) = 0.37963838798732036824923773368956
y1[1] (numeric) = 0.37963838798732036824923773368956
absolute error = 5.4e-63
relative error = 1.4224062083469693452650462730837e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7843159250844200106020886706045
y2[1] (numeric) = 1.7843159250844200106020886706045
absolute error = 1e-63
relative error = 5.6043886956436133623004795320692e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4689
Order of pole (three term test) = -10.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=732172476, alloc=4783252, time=38.56
x[1] = 2.25
y1[1] (analytic) = 0.3718263772772609110866109426036
y1[1] (numeric) = 0.3718263772772609110866109426036
absolute error = 5.5e-63
relative error = 1.4791850003419198502411526971053e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7780731968879212414109666755878
y2[1] (numeric) = 1.7780731968879212414109666755878
absolute error = 1e-63
relative error = 5.6240654307722171190821043758261e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4711
Order of pole (three term test) = -10.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=736173168, alloc=4783252, time=38.77
x[1] = 2.26
y1[1] (analytic) = 0.36407718340599745382087343125516
y1[1] (numeric) = 0.36407718340599745382087343125516
absolute error = 5.5e-63
relative error = 1.5106686852899330420422441886633e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7717526620201258495250616377403
y2[1] (numeric) = 1.7717526620201258495250616377403
absolute error = 1e-63
relative error = 5.6441286723385812616549226848790e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.473
Order of pole (three term test) = -10.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=740173864, alloc=4783252, time=38.98
x[1] = 2.27
y1[1] (analytic) = 0.3563915812864594827638656518757
y1[1] (numeric) = 0.3563915812864594827638656518757
absolute error = 5.6e-63
relative error = 1.5713053545725724673194465012849e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7653549525292535196507426019347
y2[1] (numeric) = 1.7653549525292535196507426019347
absolute error = 1e-63
relative error = 5.6645831965253407043347446034605e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = -10.9
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.28
y1[1] (analytic) = 0.3487703394724543046286016495393
y1[1] (numeric) = 0.3487703394724543046286016495393
absolute error = 5.5e-63
relative error = 1.5769689613856590767245556249137e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7588807081809219322166535763009
y2[1] (numeric) = 1.7588807081809219322166535763009
absolute error = 1e-63
relative error = 5.6854338975280751750499960730519e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = -11.14
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=744174952, alloc=4783252, time=39.19
x[1] = 2.29
y1[1] (analytic) = 0.34121422008181230625796898181105
y1[1] (numeric) = 0.34121422008181230625796898181105
absolute error = 5.5e-63
relative error = 1.6118906177712274451063426395539e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7523305763941707347419082779737
y2[1] (numeric) = 1.7523305763941707347419082779737
absolute error = 1e-63
relative error = 5.7066857901762660729518730860283e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4776
Order of pole (three term test) = -11.38
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=748175616, alloc=4783252, time=39.41
x[1] = 2.3
y1[1] (analytic) = 0.33372397872017580668211942883398
y1[1] (numeric) = 0.33372397872017580668211942883398
absolute error = 5.6e-63
relative error = 1.6780334519191213318347935078453e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7457052121767201773854062116435
y2[1] (numeric) = 1.7457052121767201773854062116435
absolute error = 2e-63
relative error = 1.1456688025272030899982595398474e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4788
Order of pole (three term test) = -11.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=752176452, alloc=4783252, time=39.62
x[1] = 2.31
y1[1] (analytic) = 0.32630036440543912255583567652897
y1[1] (numeric) = 0.32630036440543912255583567652897
absolute error = 5.6e-63
relative error = 1.7162101581479733174893844671213e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7390052780594708867587641920983
y2[1] (numeric) = 1.7390052780594708867587641920983
absolute error = 2e-63
relative error = 1.1500827658394280952087812218684e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = -11.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=756177272, alloc=4783252, time=39.83
x[1] = 2.32
y1[1] (analytic) = 0.31894411949284740290636383399177
y1[1] (numeric) = 0.31894411949284740290636383399177
absolute error = 5.6e-63
relative error = 1.7557934627873221635583658418973e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7322314440302513279708986777247
y2[1] (numeric) = 1.7322314440302513279708986777247
absolute error = 1e-63
relative error = 5.7729006331473579286921492026411e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -12.1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.33
y1[1] (analytic) = 0.311655979600761723245819572184
y1[1] (numeric) = 0.311655979600761723245819572184
absolute error = 5.6e-63
relative error = 1.7968530580333241751680930437250e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7253843874668195801028441924754
y2[1] (numeric) = 1.7253843874668195801028441924754
absolute error = 1e-63
relative error = 5.7958099497363786177046107865009e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -12.34
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=760178344, alloc=4783252, time=40.04
x[1] = 2.34
y1[1] (analytic) = 0.30443667353709786247689442793865
y1[1] (numeric) = 0.30443667353709786247689442793865
absolute error = 5.7e-63
relative error = 1.8723105642216304146237143207234e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.718464793069126124879428686794
y2[1] (numeric) = 1.718464793069126124879428686794
absolute error = 1e-63
relative error = 5.8191474392328414070824568526825e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=764179332, alloc=4783252, time=40.25
x[1] = 2.35
y1[1] (analytic) = 0.29728692322644611865287088774108
y1[1] (numeric) = 0.29728692322644611865287088774108
absolute error = 5.7e-63
relative error = 1.9173396320759991255217993203138e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7114733527908444222024911820132
y2[1] (numeric) = 1.7114733527908444222024911820132
absolute error = 1e-63
relative error = 5.8429189000771308407099791936325e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=768180392, alloc=4783252, time=40.47
x[1] = 2.36
y1[1] (analytic) = 0.2902074436378794515496369653549
y1[1] (numeric) = 0.2902074436378794515496369653549
absolute error = 5.6e-63
relative error = 1.9296541569718226167973807332896e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7044107657701761194310307129327
y2[1] (numeric) = 1.7044107657701761194310307129327
absolute error = 1e-63
relative error = 5.8671302721332415280843951046881e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.07
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.86
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.37
y1[1] (analytic) = 0.28319894271345717117528339117765
y1[1] (numeric) = 0.28319894271345717117528339117765
absolute error = 5.6e-63
relative error = 1.9774085123142999473010532185220e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6972777382599378138296964202892
y2[1] (numeric) = 1.6972777382599378138296964202892
absolute error = 1e-63
relative error = 5.8917876400429766323243923406338e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.48
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=772181116, alloc=4783252, time=40.68
x[1] = 2.38
y1[1] (analytic) = 0.27626212129743132178885239263247
y1[1] (numeric) = 0.27626212129743132178885239263247
absolute error = 5.6e-63
relative error = 2.0270603779122102391002806259789e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6900749835569363594511131070202
y2[1] (numeric) = 1.6900749835569363594511131070202
absolute error = 2e-63
relative error = 1.1833794473371794526768408186209e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -13.55
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.12
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=776182060, alloc=4783252, time=40.89
x[1] = 2.39
y1[1] (analytic) = 0.26939767306616284073084170738194
y1[1] (numeric) = 0.26939767306616284073084170738194
absolute error = 5.6e-63
relative error = 2.0787113475269942372077509898234e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.682803221930639780862500311013
y2[1] (numeric) = 1.682803221930639780862500311013
absolute error = 1e-63
relative error = 5.9424654467485745672071818273848e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -13.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=780183200, alloc=4783252, time=41.10
x[1] = 2.4
y1[1] (analytic) = 0.26260628445875450039117777266522
y1[1] (numeric) = 0.26260628445875450039117777266522
absolute error = 5.7e-63
relative error = 2.1705497306540103310689016431889e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6754631805511509265657715253413
y2[1] (numeric) = 1.6754631805511509265657715253413
absolute error = 1e-63
relative error = 5.9684988104068370815749986399566e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -14.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=784184140, alloc=4783252, time=41.31
x[1] = 2.41
y1[1] (analytic) = 0.25588863460840756996265560443205
y1[1] (numeric) = 0.25588863460840756996265560443205
absolute error = 5.7e-63
relative error = 2.2275315231263963017578039106272e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6680555934164910646857498006547
y2[1] (numeric) = 1.6680555934164910646857498006547
absolute error = 2e-63
relative error = 1.1990008054249705561159210582795e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.96
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = -14.27
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.42
y1[1] (analytic) = 0.24924539527450906125646743108926
y1[1] (numeric) = 0.24924539527450906125646743108926
absolute error = 5.7e-63
relative error = 2.2869028307312335730463988485844e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6605812012792006925063341065602
y2[1] (numeric) = 1.6605812012792006925063341065602
absolute error = 2e-63
relative error = 1.2043975919150076890966614461712e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4779
Order of pole (three term test) = -14.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.72
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=788184880, alloc=4783252, time=41.52
x[1] = 2.43
y1[1] (analytic) = 0.2426772307754563497986447558221
y1[1] (numeric) = 0.2426772307754563497986447558221
absolute error = 5.7e-63
relative error = 2.3487988476653084394370121227541e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6530407515722648997124970471899
y2[1] (numeric) = 1.6530407515722648997124970471899
absolute error = 2e-63
relative error = 1.2098915275365897778349891334245e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4765
Order of pole (three term test) = -14.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.38
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=792186084, alloc=4783252, time=41.74
x[1] = 2.44
y1[1] (analytic) = 0.2361847979222258886893249074626
y1[1] (numeric) = 0.2361847979222258886893249074626
absolute error = 5.8e-63
relative error = 2.4557041990102606507295877326566e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6454349983343706927400610729825
y2[1] (numeric) = 1.6454349983343706927400610729825
absolute error = 2e-63
relative error = 1.2154840525602930899436952389789e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.475
Order of pole (three term test) = -14.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=796186976, alloc=4783252, time=41.95
x[1] = 2.45
y1[1] (analytic) = 0.22976874595269265829809693266351
y1[1] (numeric) = 0.22976874595269265829809693266351
absolute error = 5.8e-63
relative error = 2.5242771709230499202670927943196e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6377647021345037544385328556338
y2[1] (numeric) = 1.6377647021345037544385328556338
absolute error = 1e-63
relative error = 6.1058832120187773981101872107211e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4733
Order of pole (three term test) = -15.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.73
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.46
y1[1] (analytic) = 0.2234297164667069197957236853138
y1[1] (numeric) = 0.2234297164667069197957236853138
absolute error = 5.8e-63
relative error = 2.5958946248156087507090214414568e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6300306299958921793081937186159
y2[1] (numeric) = 1.6300306299958921793081937186159
absolute error = 1e-63
relative error = 6.1348540426048318370418742023058e-62 %
Correct digits = 64
h = 0.01
bytes used=800188612, alloc=4783252, time=42.17
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4714
Order of pole (three term test) = -15.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.41
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.47
y1[1] (analytic) = 0.21716834336193476479278441593845
y1[1] (numeric) = 0.21716834336193476479278441593845
absolute error = 5.9e-63
relative error = 2.7167863919130264591590190796650e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6222335553193047898745424048558
y2[1] (numeric) = 1.6222335553193047898745424048558
absolute error = 1e-63
relative error = 6.1643404966011176812438993960884e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4693
Order of pole (three term test) = -15.7
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=804189924, alloc=4783252, time=42.38
x[1] = 2.48
y1[1] (analytic) = 0.21098525277046887697680796640967
y1[1] (numeric) = 0.21098525277046887697680796640967
absolute error = 5.8e-63
relative error = 2.7490072997233732383393569141035e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6143742578057117043045348806656
y2[1] (numeric) = 1.6143742578057117043045348806656
absolute error = 1e-63
relative error = 6.1943505055588478063216065453407e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = -15.93
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=808190836, alloc=4783252, time=42.59
x[1] = 2.49
y1[1] (analytic) = 0.20488106299621584461890866742843
y1[1] (numeric) = 0.20488106299621584461890866742843
absolute error = 5.9e-63
relative error = 2.8797195376270441655427433200156e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6064535233783148891434102397918
y2[1] (numeric) = 1.6064535233783148891434102397918
absolute error = 2e-63
relative error = 1.2449784390861621708001213306392e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4646
Order of pole (three term test) = -16.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=812191648, alloc=4783252, time=42.81
x[1] = 2.5
y1[1] (analytic) = 0.19885638445306628516649720953265
y1[1] (numeric) = 0.19885638445306628516649720953265
absolute error = 5.9e-63
relative error = 2.9669653384412744621497926822297e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5984721441039564940518547021862
y2[1] (numeric) = 1.5984721441039564940518547021862
absolute error = 1e-63
relative error = 6.2559738916223809323680023061472e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.94
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4619
Order of pole (three term test) = -16.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.51
y1[1] (analytic) = 0.19291181960385396485808249212159
y1[1] (numeric) = 0.19291181960385396485808249212159
absolute error = 6.0e-63
relative error = 3.1102293329258156323477369492172e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5904309181139128276445371550241
y2[1] (numeric) = 1.5904309181139128276445371550241
absolute error = 1e-63
relative error = 6.2876041242074000193085289702263e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4591
Order of pole (three term test) = -16.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=816192536, alloc=4783252, time=43.01
x[1] = 2.52
y1[1] (analytic) = 0.18704796290011001739733573954815
y1[1] (numeric) = 0.18704796290011001739733573954815
absolute error = 5.9e-63
relative error = 3.1542711871985480751444917363250e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5823306495240818949664275822971
y2[1] (numeric) = 1.5823306495240818949664275822971
absolute error = 1e-63
relative error = 6.3197916333148847608647696410310e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4561
Order of pole (three term test) = -16.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=820193432, alloc=4783252, time=43.22
x[1] = 2.53
y1[1] (analytic) = 0.18126540072261828621434482744501
y1[1] (numeric) = 0.18126540072261828621434482744501
absolute error = 5.9e-63
relative error = 3.2548958469070917080800246489712e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5741721483545724777866405874022
y2[1] (numeric) = 1.5741721483545724777866405874022
absolute error = 1e-63
relative error = 6.3525453746927570759199622077066e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4529
Order of pole (three term test) = -17.08
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=824194320, alloc=4783252, time=43.44
x[1] = 2.54
y1[1] (analytic) = 0.17556471132277773473029564419343
y1[1] (numeric) = 0.17556471132277773473029564419343
absolute error = 5.9e-63
relative error = 3.3605842287706567367462005995320e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.565956230448702798734765747982
y2[1] (numeric) = 1.565956230448702798734765747982
absolute error = 1e-63
relative error = 6.3858745254550570855095175873893e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4495
Order of pole (three term test) = -17.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=828195900, alloc=4783252, time=43.65
x[1] = 2.55
y1[1] (analytic) = 0.16994646476477778833568952416771
y1[1] (numeric) = 0.16994646476477778833568952416771
absolute error = 5.9e-63
relative error = 3.4716815134496419433480149952548e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5576837173914168693457702817662
y2[1] (numeric) = 1.5576837173914168693457702817662
absolute error = 1e-63
relative error = 6.4197884900193679609315766945900e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.446
Order of pole (three term test) = -17.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.56
y1[1] (analytic) = 0.16441122286859239049971187661756
y1[1] (numeric) = 0.16441122286859239049971187661756
absolute error = 6.0e-63
relative error = 3.6493859088899124509964849982391e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5493554364271266803106833831373
y2[1] (numeric) = 1.5493554364271266803106833831373
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4422
Order of pole (three term test) = -17.76
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=832196900, alloc=4783252, time=43.86
x[1] = 2.57
y1[1] (analytic) = 0.15895953915379847355763627843287
y1[1] (numeric) = 0.15895953915379847355763627843287
absolute error = 6.0e-63
relative error = 3.7745454169911796013247425418155e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5409722203769884496455725487458
y2[1] (numeric) = 1.5409722203769884496455725487458
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4383
Order of pole (three term test) = -17.98
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=836197964, alloc=4783252, time=44.07
x[1] = 2.58
y1[1] (analytic) = 0.15359195878422446228236750543077
y1[1] (numeric) = 0.15359195878422446228236750543077
absolute error = 6.0e-63
relative error = 3.9064545093986158633145409615120e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5325349075556212010850587644716
y2[1] (numeric) = 1.5325349075556212010850587644716
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4342
Order of pole (three term test) = -18.2
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=840198624, alloc=4783252, time=44.28
x[1] = 2.59
y1[1] (analytic) = 0.14830901851343434534364025459169
y1[1] (numeric) = 0.14830901851343434534364025459169
absolute error = 6.0e-63
relative error = 4.0456069766630538300735108341022e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5240443416872760007731302488759
y2[1] (numeric) = 1.5240443416872760007731302488759
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.43
Order of pole (three term test) = -18.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.6
y1[1] (analytic) = 0.1431112466310527662022978483548
y1[1] (numeric) = 0.1431112466310527662022978483548
absolute error = 6.1e-63
relative error = 4.2624183239253547270180490655914e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5155013718214642352577269352094
y2[1] (numeric) = 1.5155013718214642352577269352094
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4255
Order of pole (three term test) = -18.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=844199372, alloc=4783252, time=44.49
x[1] = 2.61
y1[1] (analytic) = 0.13799916290993650088583255127735
y1[1] (numeric) = 0.13799916290993650088583255127735
absolute error = 6.0e-63
relative error = 4.3478524604644363402520747513489e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5069068522480533678909866995555
y2[1] (numeric) = 1.5069068522480533678909866995555
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4209
Order of pole (three term test) = -18.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=848200196, alloc=4783252, time=44.71
x[1] = 2.62
y1[1] (analytic) = 0.13297327855419760545338632325165
y1[1] (numeric) = 0.13297327855419760545338632325165
absolute error = 6.0e-63
relative error = 4.5121847526339691703093458321892e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4982616424118386639887600099976
y2[1] (numeric) = 1.4982616424118386639887600099976
absolute error = 1e-63
relative error = 6.6744016645199699610008033416117e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4161
Order of pole (three term test) = -19.05
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=852201736, alloc=4783252, time=44.92
x[1] = 2.63
y1[1] (analytic) = 0.12803409614808343079215160980507
y1[1] (numeric) = 0.12803409614808343079215160980507
absolute error = 6.1e-63
relative error = 4.7643558891881255944059640129370e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4895666068265994275056870536116
y2[1] (numeric) = 1.4895666068265994275056870536116
absolute error = 1e-63
relative error = 6.7133620975192154204027839981551e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4112
Order of pole (three term test) = -19.26
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=856202620, alloc=4783252, time=45.13
x[1] = 2.64
y1[1] (analytic) = 0.12318210960571861670109268373401
y1[1] (numeric) = 0.12318210960571861670109268373401
absolute error = 6.0e-63
relative error = 4.8708371850464359081352360341224e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4808226149886483435305502695329
y2[1] (numeric) = 1.4808226149886483435305502695329
absolute error = 1e-63
relative error = 6.7530032961285223035000128588588e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4061
Order of pole (three term test) = -19.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.65
y1[1] (analytic) = 0.11841780412171409102069763394619
y1[1] (numeric) = 0.11841780412171409102069763394619
absolute error = 6.0e-63
relative error = 5.0668056585756171841182049860794e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4720305412898825715956107783974
y2[1] (numeric) = 1.4720305412898825715956107783974
absolute error = 1e-63
relative error = 6.7933373116276463929622807634632e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4008
Order of pole (three term test) = -19.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=860204084, alloc=4783252, time=45.34
x[1] = 2.66
y1[1] (analytic) = 0.11374165612264801286768899611741
y1[1] (numeric) = 0.11374165612264801286768899611741
absolute error = 6.0e-63
relative error = 5.2751122188076632953996578079533e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4631912649303452846181405937963
y2[1] (numeric) = 1.4631912649303452846181405937963
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3954
Order of pole (three term test) = -19.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=864205240, alloc=4783252, time=45.56
x[1] = 2.67
y1[1] (analytic) = 0.10915413321942351183993714157026
y1[1] (numeric) = 0.10915413321942351183993714157026
absolute error = 6.1e-63
relative error = 5.5884278680841845129290272610297e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4543056698303063972473913211913
y2[1] (numeric) = 1.4543056698303063972473913211913
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3898
Order of pole (three term test) = -20.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=868206040, alloc=4783252, time=45.78
x[1] = 2.68
y1[1] (analytic) = 0.10465569416050798737795418137934
y1[1] (numeric) = 0.10465569416050798737795418137934
absolute error = 6.0e-63
relative error = 5.7330850921479155294960357277233e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4453746445418712754708988319295
y2[1] (numeric) = 1.4453746445418712754708988319295
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3841
Order of pole (three term test) = -20.25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.69
y1[1] (analytic) = 0.10024678878605864431406511567113
y1[1] (numeric) = 0.10024678878605864431406511567113
absolute error = 6.0e-63
relative error = 5.9852291256978618361805417014665e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.436399082160126266535504118761
y2[1] (numeric) = 1.436399082160126266535504118761
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3782
Order of pole (three term test) = -20.44
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=872206744, alloc=4783252, time=45.99
TOP MAIN SOLVE Loop
x[1] = 2.7
y1[1] (analytic) = 0.09592785798293885201747271805667
y1[1] (numeric) = 0.09592785798293885201747271805667
absolute error = 5.99e-63
relative error = 6.2442757776008561880466341927583e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4273798802338299345560530858579
y2[1] (numeric) = 1.4273798802338299345560530858579
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3722
Order of pole (three term test) = -20.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=876207596, alloc=4783252, time=46.20
x[1] = 2.71
y1[1] (analytic) = 0.091699333640629825461815406283923
y1[1] (numeric) = 0.091699333640629825461815406283923
absolute error = 6.05e-63
relative error = 6.5976488157591003492020430809984e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4183179406756589326137906811086
y2[1] (numeric) = 1.4183179406756589326137906811086
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.366
Order of pole (three term test) = -20.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=880208908, alloc=4783252, time=46.42
x[1] = 2.72
y1[1] (analytic) = 0.087561638608042037010371200012937
y1[1] (numeric) = 0.087561638608042037010371200012937
absolute error = 6.01e-63
relative error = 6.8637363296762422443669787552228e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4092141696720174866824446740074
y2[1] (numeric) = 1.4092141696720174866824446740074
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3596
Order of pole (three term test) = -21
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=884209676, alloc=4783252, time=46.63
x[1] = 2.73
y1[1] (analytic) = 0.083515186651230677741738875107214
y1[1] (numeric) = 0.083515186651230677741738875107214
absolute error = 5.99e-63
relative error = 7.1723482161573203009105010459109e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4000694775924195103584479578945
y2[1] (numeric) = 1.4000694775924195103584479578945
absolute error = 1e-63
relative error = 7.1425026829355283900967676110504e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3532
Order of pole (three term test) = -21.18
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.74
y1[1] (analytic) = 0.079560382412019396734626748220724
y1[1] (numeric) = 0.079560382412019396734626748220724
absolute error = 5.94e-63
relative error = 7.4660274623097192893693398392843e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3908847788984524121083117016403
y2[1] (numeric) = 1.3908847788984524121083117016403
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3465
Order of pole (three term test) = -21.35
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=888210408, alloc=4783252, time=46.84
x[1] = 2.75
y1[1] (analytic) = 0.075697621367536455903340510473287
y1[1] (numeric) = 0.075697621367536455903340510473287
absolute error = 5.99e-63
relative error = 7.9130623813350897384483607412393e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3816609920523316985765613723778
y2[1] (numeric) = 1.3816609920523316985765613723778
absolute error = 1e-63
relative error = 7.2376654313341435597607314864692e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3398
Order of pole (three term test) = -21.52
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=892211268, alloc=4783252, time=47.05
x[1] = 2.76
y1[1] (analytic) = 0.071927289790667346734766802859897
y1[1] (numeric) = 0.071927289790667346734766802859897
absolute error = 5.94e-63
relative error = 8.2583398002168604148059969205415e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3723990394250555184177005924498
y2[1] (numeric) = 1.3723990394250555184177005924498
absolute error = 1e-63
relative error = 7.2865104920135611559264296092513e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3329
Order of pole (three term test) = -21.69
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=896212116, alloc=4783252, time=47.27
x[1] = 2.77
y1[1] (analytic) = 0.068249764711427823632222792170926
y1[1] (numeric) = 0.068249764711427823632222792170926
absolute error = 5.99e-63
relative error = 8.7765870334158487038603700214690e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3630998472041683311212820091725
y2[1] (numeric) = 1.3630998472041683311212820091725
absolute error = 1e-63
relative error = 7.3362197351212645686264814474797e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3258
Order of pole (three term test) = -21.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.78
bytes used=900213512, alloc=4783252, time=47.48
y1[1] (analytic) = 0.064665413879261216530648330882405
y1[1] (numeric) = 0.064665413879261216530648330882405
absolute error = 5.91e-63
relative error = 9.1393523144145381971917006958334e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3537643453011429243863393172273
y2[1] (numeric) = 1.3537643453011429243863393172273
absolute error = 1e-63
relative error = 7.3868099974043225636108880988956e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3187
Order of pole (three term test) = -22.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.79
y1[1] (analytic) = 0.061174595726263793020460380375909
y1[1] (numeric) = 0.061174595726263793020460380375909
absolute error = 5.97e-63
relative error = 9.7589529266589477474521883241979e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3443934672583900417662615955623
y2[1] (numeric) = 1.3443934672583900417662615955623
absolute error = 1e-63
relative error = 7.4382985662619392383536878462157e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3114
Order of pole (three term test) = -22.18
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=904214368, alloc=4783252, time=47.70
x[1] = 2.8
y1[1] (analytic) = 0.057777659331341847413211882633846
y1[1] (numeric) = 0.057777659331341847413211882633846
absolute error = 5.89e-63
relative error = 1.0194251667798063943652911693634e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3349881501559049195438537527124
y2[1] (numeric) = 1.3349881501559049195438537527124
absolute error = 1e-63
relative error = 7.4907031937565607014942380243117e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.304
Order of pole (three term test) = -22.33
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=908215212, alloc=4783252, time=47.91
x[1] = 2.81
y1[1] (analytic) = 0.054474944385304101010279521641165
y1[1] (numeric) = 0.054474944385304101010279521641165
absolute error = 5.97e-63
relative error = 1.0959166764400677530221291250954e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3255493345175600681051012812063
y2[1] (numeric) = 1.3255493345175600681051012812063
absolute error = 1e-63
relative error = 7.5440421111444691436647174241085e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2965
Order of pole (three term test) = -22.48
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=912216264, alloc=4783252, time=48.12
x[1] = 2.82
y1[1] (analytic) = 0.051266781156892904305463936239962
y1[1] (numeric) = 0.051266781156892904305463936239962
absolute error = 5.88e-63
relative error = 1.1469415218414632580454803654865e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3160779642170536684554128560246
y2[1] (numeric) = 1.3160779642170536684554128560246
absolute error = 1e-63
relative error = 7.5983340439478353894932854601517e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2888
Order of pole (three term test) = -22.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.83
y1[1] (analytic) = 0.04815349045975763797297488727547
y1[1] (numeric) = 0.04815349045975763797297488727547
absolute error = 5.86e-63
relative error = 1.2169418964337095430733072271372e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3065749863835229889603130778681
y2[1] (numeric) = 1.3065749863835229889603130778681
absolute error = 1e-63
relative error = 7.6535982275912552419343862107572e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.281
Order of pole (three term test) = -22.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=916217660, alloc=4783252, time=48.33
x[1] = 2.84
y1[1] (analytic) = 0.045135383620373615273180506413763
y1[1] (numeric) = 0.045135383620373615273180506413763
absolute error = 5.94e-63
relative error = 1.3160406589119471653601946099322e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2970413513068322608902560680973
y2[1] (numeric) = 1.2970413513068322608902560680973
absolute error = 1e-63
relative error = 7.7098544236269055820285983146568e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2732
Order of pole (three term test) = -22.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=920218380, alloc=4783252, time=48.55
x[1] = 2.85
y1[1] (analytic) = 0.042212762446909693959145892825075
y1[1] (numeric) = 0.042212762446909693959145892825075
absolute error = 5.87e-63
relative error = 1.3905747124184548939427610003610e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2874780123425444839030789266917
y2[1] (numeric) = 1.2874780123425444839030789266917
absolute error = 1e-63
relative error = 7.7671229365736266121798592981736e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2652
Order of pole (three term test) = -23.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=924219148, alloc=4783252, time=48.76
x[1] = 2.86
y1[1] (analytic) = 0.039385919199047710896826833607233
y1[1] (numeric) = 0.039385919199047710896826833607233
absolute error = 5.87e-63
relative error = 1.4903803489603277550495340804264e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2778859258165866642043569097532
y2[1] (numeric) = 1.2778859258165866642043569097532
absolute error = 1e-63
relative error = 7.8254246313964703885954037633078e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2571
Order of pole (three term test) = -23.17
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=928220196, alloc=4783252, time=48.97
x[1] = 2.87
y1[1] (analytic) = 0.036655136558756757430306241262063
y1[1] (numeric) = 0.036655136558756757430306241262063
absolute error = 5.86e-63
relative error = 1.5986845365059950187591222794077e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2682660509296180187823989209871
y2[1] (numeric) = 1.2682660509296180187823989209871
absolute error = 1e-63
relative error = 7.8847809516545566706525756944805e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2489
Order of pole (three term test) = -23.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.88
y1[1] (analytic) = 0.034020687602025218040182095234475
y1[1] (numeric) = 0.034020687602025218040182095234475
absolute error = 5.86e-63
relative error = 1.7224813526846999909156947051421e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2586193496611107088177669201177
y2[1] (numeric) = 1.2586193496611107088177669201177
absolute error = 1e-63
relative error = 7.9452139383464491626141189354785e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2406
Order of pole (three term test) = -23.42
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=932221040, alloc=4783252, time=49.19
x[1] = 2.89
y1[1] (analytic) = 0.031482835771553399067684492790717
y1[1] (numeric) = 0.031482835771553399067684492790717
absolute error = 5.82e-63
relative error = 1.8486263569874203088840354785917e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2489467866731526941140458405805
y2[1] (numeric) = 1.2489467866731526941140458405805
absolute error = 1e-63
relative error = 8.0067462494837127440852444379963e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2322
Order of pole (three term test) = -23.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=936221776, alloc=4783252, time=49.40
x[1] = 2.9
y1[1] (analytic) = 0.029041834850409478218893330654468
y1[1] (numeric) = 0.029041834850409478218893330654468
absolute error = 5.76e-63
relative error = 1.9833457595461763019746457815059e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2392493292139823281842569187396
y2[1] (numeric) = 1.2392493292139823281842569187396
absolute error = 1e-63
relative error = 8.0694011804248398736554020254220e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2237
Order of pole (three term test) = -23.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=940222484, alloc=4783252, time=49.61
x[1] = 2.91
y1[1] (analytic) = 0.026697928936651409232152893397248
y1[1] (numeric) = 0.026697928936651409232152893397248
absolute error = 5.80e-63
relative error = 2.1724531568580411610247974079318e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.229527947021264340453018223827
y2[1] (numeric) = 1.229527947021264340453018223827
absolute error = 1e-63
relative error = 8.1332026850033469057313643118625e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2151
Order of pole (three term test) = -23.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.92
y1[1] (analytic) = 0.024451352418917319497068264841735
y1[1] (numeric) = 0.024451352418917319497068264841735
absolute error = 5.74e-63
relative error = 2.3475184119301002007671356901307e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2197836122251168778956290930646
y2[1] (numeric) = 1.2197836122251168778956290930646
absolute error = 1e-63
relative error = 8.1981753974855438130589479735715e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2065
Order of pole (three term test) = -23.87
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=944223420, alloc=4783252, time=49.82
x[1] = 2.93
y1[1] (analytic) = 0.022302329952986841564980395323675
y1[1] (numeric) = 0.022302329952986841564980395323675
absolute error = 5.79e-63
relative error = 2.5961413055072184168878092100371e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2100172992508993033291040342591
y2[1] (numeric) = 1.2100172992508993033291040342591
absolute error = 2e-63
relative error = 1.6528689310790558678599057049813e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1977
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=948224324, alloc=4783252, time=50.03
x[1] = 2.94
y1[1] (analytic) = 0.020251076439315722398236618671679
y1[1] (numeric) = 0.020251076439315722398236618671679
absolute error = 5.74e-63
relative error = 2.8344172307089236499383983854573e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2002299847217704714943170944231
y2[1] (numeric) = 1.2002299847217704714943170944231
absolute error = 2e-63
relative error = 1.6663473046489727757461410596202e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1889
Order of pole (three term test) = -24.07
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=952225008, alloc=4783252, time=50.25
x[1] = 2.95
y1[1] (analytic) = 0.018297797001545956878610595298032
y1[1] (numeric) = 0.018297797001545956878610595298032
absolute error = 5.72e-63
relative error = 3.1260593827315521641387192864676e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1904226473610272270204473140574
y2[1] (numeric) = 1.1904226473610272270204473140574
absolute error = 3e-63
relative error = 2.5201133451640142286525338036620e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.18
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=956225792, alloc=4783252, time=50.46
x[1] = 2.96
y1[1] (analytic) = 0.016442686965993594543612677023842
y1[1] (numeric) = 0.016442686965993594543612677023842
absolute error = 5.73e-63
relative error = 3.4848318963017788037313726397153e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1805962678942328903405445088013
y2[1] (numeric) = 1.1805962678942328903405445088013
absolute error = 2e-63
relative error = 1.6940592261631439850894137849017e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1711
Order of pole (three term test) = -24.25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.97
y1[1] (analytic) = 0.014685931842116270752923625193857
y1[1] (numeric) = 0.014685931842116270752923625193857
absolute error = 5.66e-63
relative error = 3.8540285089491353778186333129219e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.170751828951145518628064498668
y2[1] (numeric) = 1.170751828951145518628064498668
absolute error = 2e-63
relative error = 1.7083039723215826849614839948675e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.162
Order of pole (three term test) = -24.33
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=960226884, alloc=4783252, time=50.68
x[1] = 2.98
y1[1] (analytic) = 0.013027707303962415515558035604598
y1[1] (numeric) = 0.013027707303962415515558035604598
absolute error = 5.61e-63
relative error = 4.3062066633118952483752492923215e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1608903149674557488465539545413
y2[1] (numeric) = 1.1608903149674557488465539545413
absolute error = 2e-63
relative error = 1.7228156477953455448828846248518e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1529
Order of pole (three term test) = -24.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=964228216, alloc=4783252, time=50.89
x[1] = 2.99
y1[1] (analytic) = 0.01146817917260399504141581278916
y1[1] (numeric) = 0.01146817917260399504141581278916
absolute error = 5.61e-63
relative error = 4.8917966100508513317736123913211e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1510127120863440490462950356105
y2[1] (numeric) = 1.1510127120863440490462950356105
absolute error = 3e-63
relative error = 2.6064004059191944315529243141445e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1438
Order of pole (three term test) = -24.49
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=968228912, alloc=4783252, time=51.10
x[1] = 3
y1[1] (analytic) = 0.010007503399554542728427205268739
y1[1] (numeric) = 0.010007503399554542728427205268739
absolute error = 5.64e-63
relative error = 5.6357712556470872931953173182588e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1411200080598672221007448028081
y2[1] (numeric) = 1.1411200080598672221007448028081
absolute error = 3e-63
relative error = 2.6289960554636154528328783203420e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1345
Order of pole (three term test) = -24.56
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.01
y1[1] (analytic) = 0.0086458260511741377683744258175829
y1[1] (numeric) = 0.0086458260511741377683744258175829
absolute error = 5.606e-63
relative error = 6.4840536541198197843145032628996e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1312131921501840231502181246849
y2[1] (numeric) = 1.1312131921501840231502181246849
absolute error = 3e-63
bytes used=972230092, alloc=4783252, time=51.31
relative error = 2.6520199912959545544553436322262e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1253
Order of pole (three term test) = -24.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.02
y1[1] (analytic) = 0.007383283294062890860533466736964
y1[1] (numeric) = 0.007383283294062890860533466736964
absolute error = 5.581e-63
relative error = 7.5589677081574827644815126682608e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1212932550306297681087579963391
y2[1] (numeric) = 1.1212932550306297681087579963391
absolute error = 3e-63
relative error = 2.6754820708504579425038196999236e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1159
Order of pole (three term test) = -24.68
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=976230988, alloc=4783252, time=51.52
x[1] = 3.03
y1[1] (analytic) = 0.0062200013814443976723926912915734
y1[1] (numeric) = 0.0062200013814443976723926912915734
absolute error = 5.488e-63
relative error = 8.8231491658054686608023011756636e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1113611886866498256909050329173
y2[1] (numeric) = 1.1113611886866498256909050329173
absolute error = 3e-63
relative error = 2.6993924482330065371596013246168e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1066
Order of pole (three term test) = -24.74
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=980231796, alloc=4783252, time=51.73
x[1] = 3.04
y1[1] (analytic) = 0.0051560966405405216907550451568149
y1[1] (numeric) = 0.0051560966405405216907550451568149
absolute error = 5.469e-63
relative error = 1.0606860928476849029217587640831e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1014179863166018995266083126088
y2[1] (numeric) = 1.1014179863166018995266083126088
absolute error = 3e-63
relative error = 2.7237615848572604555021187058227e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09716
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=984232860, alloc=4783252, time=51.95
x[1] = 3.05
y1[1] (analytic) = 0.004191675460938768974417798435083
y1[1] (numeric) = 0.004191675460938768974417798435083
absolute error = 5.422e-63
relative error = 1.2935161728350236229965258735486e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0914646422324370200534015886964
y2[1] (numeric) = 1.0914646422324370200534015886964
absolute error = 3e-63
relative error = 2.7486002605305867032605781720218e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08771
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.06
y1[1] (analytic) = 0.0033268342839534180612607282068477
y1[1] (numeric) = 0.0033268342839534180612607282068477
absolute error = 5.423e-63
relative error = 1.6300781875902816090717410954860e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0815021517602691780038900888357
y2[1] (numeric) = 1.0815021517602691780038900888357
absolute error = 3e-63
relative error = 2.7739195850116015509009725259660e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07822
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=988233780, alloc=4783252, time=52.15
x[1] = 3.07
y1[1] (analytic) = 0.0025616595929814689078863372732293
y1[1] (numeric) = 0.0025616595929814689078863372732293
absolute error = 5.435e-63
relative error = 2.1216714410029408184946738275986e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0715315111408435424423407903189
y2[1] (numeric) = 1.0715315111408435424423407903189
absolute error = 3e-63
relative error = 2.7997310100623592082651729507190e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06871
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=992234820, alloc=4783252, time=52.37
x[1] = 3.08
y1[1] (analytic) = 0.0018962279048543752588814626402055
y1[1] (numeric) = 0.0018962279048543752588814626402055
absolute error = 5.372e-63
relative error = 2.8329927991501389929007080494806e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0615537174299132164456296371357
y2[1] (numeric) = 1.0615537174299132164456296371357
absolute error = 3e-63
relative error = 2.8260463420194922903538701742815e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05916
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=996235624, alloc=4783252, time=52.58
x[1] = 3.09
y1[1] (analytic) = 0.0013306057621864252652564819142417
y1[1] (numeric) = 0.0013306057621864252652564819142417
absolute error = 5.364e-63
relative error = 4.0312466340037341405572193804969e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0515697683985344926699585105746
y2[1] (numeric) = 1.0515697683985344926699585105746
absolute error = 3e-63
relative error = 2.8528777549099621997668042292424e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04959
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1000236832, alloc=4783252, time=52.79
x[1] = 3.1
y1[1] (analytic) = 0.00086484972672053550762394545853374
y1[1] (numeric) = 0.00086484972672053550762394545853374
absolute error = 5.3688e-63
relative error = 6.2077836578132551213849760633907e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0415806624332905791946982715967
y2[1] (numeric) = 1.0415806624332905791946982715967
absolute error = 3e-63
relative error = 2.8802378041385143281647803944122e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04001
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.11
y1[1] (analytic) = 0.00049900637367212383916916328316572
y1[1] (numeric) = 0.00049900637367212383916916328316572
absolute error = 5.3302e-63
relative error = 1.0681627091805947316993569013734e-57 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0315873984364537731876268727034
y2[1] (numeric) = 1.0315873984364537731876268727034
absolute error = 3e-63
relative error = 2.9081394407754596941264645635299e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0304
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1004237772, alloc=4783252, time=53.00
x[1] = 3.12
y1[1] (analytic) = 0.00023311228707162665641502602440867
y1[1] (numeric) = 0.00023311228707162665641502602440867
absolute error = 5.2232e-63
relative error = 2.2406369332197005481459452108483e-57 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0215909757260960660909981042019
y2[1] (numeric) = 1.0215909757260960660909981042019
absolute error = 3e-63
relative error = 2.9365960264750275201658139150552e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02079
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1008238556, alloc=4783252, time=53.22
x[1] = 3.13
y1[1] (analytic) = 6.7194056106126342172760860792849e-05
y1[1] (numeric) = 6.7194056106126342172760860792849e-05
absolute error = 5.23650e-63
relative error = 7.7931000202301644161278787028134e-57 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0115923939361581691846814831183
y2[1] (numeric) = 1.0115923939361581691846814831183
absolute error = 3e-63
relative error = 2.9656213490562590137750149477089e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01116
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1012239416, alloc=4783252, time=53.43
x[1] = 3.14
y1[1] (analytic) = 1.2682724604547148856936549500161e-06
y1[1] (numeric) = 1.2682724604547148856936549500161e-06
absolute error = 5.158590e-63
relative error = 4.0674146611608092533063174299263e-55 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0015926529164869525405414363244
y2[1] (numeric) = 1.0015926529164869525405414363244
absolute error = 3e-63
relative error = 2.9952296387802484758995449833356e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001534
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.15
y1[1] (analytic) = 3.5341528658038371805343205274808e-05
y1[1] (numeric) = 3.5341528658038371805343205274808e-05
absolute error = 5.15005e-63
relative error = 1.4572233277828602665114729308335e-56 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.99159275263285129354085848342893
y2[1] (numeric) = 0.99159275263285129354085848342893
absolute error = 3.4e-63
relative error = 3.4288269967407571367411476307534e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.008107
Order of pole (three term test) = -0.8946
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1016240152, alloc=4783252, time=53.65
x[1] = 3.16
y1[1] (analytic) = 0.00016941041740165184008290572604826
y1[1] (numeric) = 0.00016941041740165184008290572604826
absolute error = 5.1058e-63
relative error = 3.0138642465502925927689247350406e-57 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.98159369306694633329262072881263
y2[1] (numeric) = 0.98159369306694633329262072881263
absolute error = 3.4e-63
relative error = 3.4637549365021381688695991947324e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01775
Order of pole (three term test) = -0.901
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1020241036, alloc=4783252, time=53.86
x[1] = 3.17
y1[1] (analytic) = 0.00040346153191414445991164986472299
y1[1] (numeric) = 0.00040346153191414445991164986472299
absolute error = 5.0551e-63
relative error = 1.2529323368245455987418150910258e-57 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.97159647411639614042871472510327
y2[1] (numeric) = 0.97159647411639614042871472510327
absolute error = 3.5e-63
relative error = 3.6023185481225861513406024557822e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02738
Order of pole (three term test) = -0.9124
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1024241824, alloc=4783252, time=54.07
x[1] = 3.18
y1[1] (analytic) = 0.00073747146727910692731584613969177
y1[1] (numeric) = 0.00073747146727910692731584613969177
absolute error = 5.0449e-63
relative error = 6.8408070330003470746599651757221e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.96160209549476478194630475327388
y2[1] (numeric) = 0.96160209549476478194630475327388
absolute error = 3.6e-63
relative error = 3.7437522410428226436002701328752e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.037
Order of pole (three term test) = -0.9285
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1028242540, alloc=4783252, time=54.29
x[1] = 3.19
y1[1] (analytic) = 0.0011714068227813434310491703005194
y1[1] (numeric) = 0.0011714068227813434310491703005194
absolute error = 5.027e-63
relative error = 4.2914211375891460228145769763867e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.95161155663158579989199285154883
y2[1] (numeric) = 0.95161155663158579989199285154883
absolute error = 3.6e-63
relative error = 3.7830562007284781474706478439596e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04661
Order of pole (three term test) = -0.9495
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.2
y1[1] (analytic) = 0.0017052242052469153383392777164173
y1[1] (numeric) = 0.0017052242052469153383392777164173
absolute error = 4.944e-63
relative error = 2.8993254873977771540742858403410e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.9416258565724200908627825853809
y2[1] (numeric) = 0.9416258565724200908627825853809
absolute error = 3.7e-63
relative error = 3.9293738316280340907138817627055e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05619
Order of pole (three term test) = -0.9752
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1032243420, alloc=4783252, time=54.50
x[1] = 3.21
y1[1] (analytic) = 0.00233887023338242242789333479576
y1[1] (numeric) = 0.00233887023338242242789333479576
absolute error = 4.924e-63
relative error = 2.1052899514134309414510535139261e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.93164599387895218245161163932314
y2[1] (numeric) = 0.93164599387895218245161163932314
absolute error = 3.7e-63
relative error = 3.9714655827530314494764980522226e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06576
Order of pole (three term test) = -1.006
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1036244160, alloc=4783252, time=54.71
x[1] = 3.22
y1[1] (analytic) = 0.0030722815431130877456572625241352
y1[1] (numeric) = 0.0030722815431130877456572625241352
absolute error = 4.966e-63
relative error = 1.6163883193361378367853394379746e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.92167296652913489692655585208396
y2[1] (numeric) = 0.92167296652913489692655585208396
absolute error = 3.7e-63
relative error = 4.0144391062413131224476728151400e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0753
Order of pole (three term test) = -1.041
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1040244896, alloc=4783252, time=54.93
x[1] = 3.23
y1[1] (analytic) = 0.0039053847939191122792915054150527
y1[1] (numeric) = 0.0039053847939191122792915054150527
absolute error = 4.917e-63
relative error = 1.2590308662173380032548879859620e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.91170777181739238759412427147028
y2[1] (numeric) = 0.91170777181739238759412427147028
absolute error = 3.8e-63
relative error = 4.1680022014346817814627790012013e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08481
Order of pole (three term test) = -1.081
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.24
y1[1] (analytic) = 0.0048380966761696658211761562575268
y1[1] (numeric) = 0.0048380966761696658211761562575268
absolute error = 4.870e-63
relative error = 1.0065941889891278746191827014864e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.90175140625489152745984504056236
y2[1] (numeric) = 0.90175140625489152745984504056236
absolute error = 3.8e-63
relative error = 4.2140217066940526294358889203876e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09428
Order of pole (three term test) = -1.126
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1044245732, alloc=4783252, time=55.14
TOP MAIN SOLVE Loop
x[1] = 3.25
y1[1] (analytic) = 0.0058703239194537806269707748284005
y1[1] (numeric) = 0.0058703239194537806269707748284005
absolute error = 4.826e-63
relative error = 8.2210114232487660928382022073868e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.89180486546989162296416915743917
y2[1] (numeric) = 0.89180486546989162296416915743917
absolute error = 3.9e-63
relative error = 4.3731539835736280460707807075185e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1037
Order of pole (three term test) = -1.176
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1048246576, alloc=4783252, time=55.35
x[1] = 3.26
y1[1] (analytic) = 0.0070019633019073147873054328283443
y1[1] (numeric) = 0.0070019633019073147873054328283443
absolute error = 4.788e-63
relative error = 6.8380821114783085012697317345295e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.88186914410818241773927688966392
y2[1] (numeric) = 0.88186914410818241773927688966392
absolute error = 4.0e-63
relative error = 4.5358203387931486457795502189857e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1131
Order of pole (three term test) = -1.23
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1052247236, alloc=4783252, time=55.56
x[1] = 3.27
y1[1] (analytic) = 0.0082329016605350526240382595052596
y1[1] (numeric) = 0.0082329016605350526240382595052596
absolute error = 4.697e-63
relative error = 5.7051574203969588714442702979986e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.87194523573362034250344310924638
y2[1] (numeric) = 0.87194523573362034250344310924638
absolute error = 4.1e-63
relative error = 4.7021301705380862065196971229628e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1225
Order of pole (three term test) = -1.289
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1056248312, alloc=4783252, time=55.77
x[1] = 3.28
y1[1] (analytic) = 0.0095630159025269099096415838682884
y1[1] (numeric) = 0.0095630159025269099096415838682884
absolute error = 4.640e-63
relative error = 4.8520258120389999449568935731995e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.86203413272877295738508592941475
y2[1] (numeric) = 0.86203413272877295738508592941475
absolute error = 4.1e-63
relative error = 4.7561921788658546526277401656278e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1318
Order of pole (three term test) = -1.353
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.29
y1[1] (analytic) = 0.010992173017567112298624874460517
y1[1] (numeric) = 0.010992173017567112298624874460517
absolute error = 4.67e-63
relative error = 4.2484775235402971046565494496560e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.85213682619568152214947021625736
y2[1] (numeric) = 0.85213682619568152214947021625736
absolute error = 4.1e-63
relative error = 4.8114338847485641862294803692272e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.141
Order of pole (three term test) = -1.421
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1060249132, alloc=4783252, time=55.98
x[1] = 3.3
y1[1] (analytic) = 0.012520230091135116063408948897147
y1[1] (numeric) = 0.012520230091135116063408948897147
absolute error = 4.65e-63
relative error = 3.7139892527154180390876930606919e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.84225430585675161798834572239752
y2[1] (numeric) = 0.84225430585675161798834572239752
absolute error = 4.2e-63
relative error = 4.9866174275330150442771640522455e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1502
Order of pole (three term test) = -1.494
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1064250024, alloc=4783252, time=56.20
x[1] = 3.31
y1[1] (analytic) = 0.014147034318796941053661929414471
y1[1] (numeric) = 0.014147034318796941053661929414471
absolute error = 4.53e-63
relative error = 3.2020845485481437966188341235648e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.83238755995578173172775000568302
y2[1] (numeric) = 0.83238755995578173172775000568302
absolute error = 4.3e-63
relative error = 5.1658628827038519302295407078664e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1593
Order of pole (three term test) = -1.572
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1068250828, alloc=4783252, time=56.41
x[1] = 3.32
y1[1] (analytic) = 0.015872423021485486757710415268806
y1[1] (numeric) = 0.015872423021485486757710415268806
absolute error = 4.53e-63
relative error = 2.8540065961372299032274637398697e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.82253757515913969951307944769159
y2[1] (numeric) = 0.82253757515913969951307944769159
absolute error = 4.3e-63
relative error = 5.2277247020211343679749267165639e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1684
Order of pole (three term test) = -1.654
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1072251600, alloc=4783252, time=56.63
x[1] = 3.33
y1[1] (analytic) = 0.017696223661768303447153285140733
y1[1] (numeric) = 0.017696223661768303447153285140733
absolute error = 4.46e-63
relative error = 2.5203117259619515956705892620325e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.81270533645709689224470717586405
y2[1] (numeric) = 0.81270533645709689224470717586405
absolute error = 4.4e-63
relative error = 5.4140163754569835139075044768475e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1774
Order of pole (three term test) = -1.741
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.34
y1[1] (analytic) = 0.019618253861101191641120098930087
y1[1] (numeric) = 0.019618253861101191641120098930087
absolute error = 4.42e-63
relative error = 2.2530037745937808491588811062266e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.80289182706533000926338308940728
y2[1] (numeric) = 0.80289182706533000926338308940728
absolute error = 4.4e-63
relative error = 5.4801902967209792224602085855056e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1863
Order of pole (three term test) = -1.832
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1076252596, alloc=4783252, time=56.84
x[1] = 3.35
y1[1] (analytic) = 0.021638321418065904544605624728466
y1[1] (numeric) = 0.021638321418065904544605624728466
absolute error = 4.43e-63
relative error = 2.0472937407711203838787775135399e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.79309802832660033002396588397449
y2[1] (numeric) = 0.79309802832660033002396588397449
absolute error = 4.5e-63
relative error = 5.6739518184086134981130800210702e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1952
Order of pole (three term test) = -1.928
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1080253412, alloc=4783252, time=57.05
x[1] = 3.36
y1[1] (analytic) = 0.023756224327590129705834692221679
y1[1] (numeric) = 0.023756224327590129705834692221679
absolute error = 4.30e-63
relative error = 1.8100519428948324974871314858949e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.78332491961262025575038601809447
y2[1] (numeric) = 0.78332491961262025575038601809447
absolute error = 4.5e-63
relative error = 5.7447425548843727602729431021063e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.204
Order of pole (three term test) = -2.028
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1084254204, alloc=4783252, time=57.26
x[1] = 3.37
y1[1] (analytic) = 0.025971750801147827910508234029151
y1[1] (numeric) = 0.025971750801147827910508234029151
absolute error = 4.28e-63
relative error = 1.6479443502941836127492790336513e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.77357347822611695433589651569143
y2[1] (numeric) = 0.77357347822611695433589651569143
absolute error = 4.5e-63
relative error = 5.8171591020919692142646408306585e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2127
Order of pole (three term test) = -2.132
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.38
y1[1] (analytic) = 0.028284679287937909295874650009428
y1[1] (numeric) = 0.028284679287937909295874650009428
absolute error = 4.20e-63
relative error = 1.4849028186757992509987160536610e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.76384467930310290204250822241037
y2[1] (numeric) = 0.76384467930310290204250822241037
absolute error = 4.5e-63
relative error = 5.8912500432752834758245523190851e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2213
Order of pole (three term test) = -2.241
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1088255184, alloc=4783252, time=57.47
x[1] = 3.39
y1[1] (analytic) = 0.030694778497039128834663925327525
y1[1] (numeric) = 0.030694778497039128834663925327525
absolute error = 4.17e-63
relative error = 1.3585372510188484915627146594934e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.75413949571536309486399862844206
y2[1] (numeric) = 0.75413949571536309486399862844206
absolute error = 4.5e-63
relative error = 5.9670658088678691144681818294129e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2298
Order of pole (three term test) = -2.354
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1092256136, alloc=4783252, time=57.68
x[1] = 3.4
y1[1] (analytic) = 0.033201807420538985717798460234306
y1[1] (numeric) = 0.033201807420538985717798460234306
absolute error = 4.16e-63
relative error = 1.2529438374570477273856513394572e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.74445889797316868075009757063626
y2[1] (numeric) = 0.74445889797316868075009757063626
absolute error = 4.5e-63
relative error = 6.0446587612177162384846023855965e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2382
Order of pole (three term test) = -2.472
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1096256996, alloc=4783252, time=57.90
x[1] = 3.41
y1[1] (analytic) = 0.035805515357634313765216359047038
y1[1] (numeric) = 0.035805515357634313765216359047038
absolute error = 4.13e-63
relative error = 1.1534535835467083545158700465553e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.73480385412822674124755569242589
y2[1] (numeric) = 0.73480385412822674124755569242589
absolute error = 4.6e-63
relative error = 6.2601740235255737857367261824398e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2465
Order of pole (three term test) = -2.593
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1100257988, alloc=4783252, time=58.11
x[1] = 3.42
y1[1] (analytic) = 0.038505641939701152825849854398592
y1[1] (numeric) = 0.038505641939701152825849854398592
absolute error = 4.11e-63
relative error = 1.0673760500957637668285725312611e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.7251753296768759274990566423338
y2[1] (numeric) = 0.7251753296768759274990566423338
absolute error = 4.6e-63
relative error = 6.3432935619164965923419833910518e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2548
Order of pole (three term test) = -2.719
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.43
y1[1] (analytic) = 0.041301917156331394200510358774443
y1[1] (numeric) = 0.041301917156331394200510358774443
absolute error = 4.06e-63
relative error = 9.8300521610959181529548679749134e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.71557428746353763095570308540863
y2[1] (numeric) = 0.71557428746353763095570308540863
absolute error = 4.7e-63
relative error = 6.5681510394397595611465216209394e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2629
Order of pole (three term test) = -2.849
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1104258924, alloc=4783252, time=58.32
x[1] = 3.44
y1[1] (analytic) = 0.044194061382333596444834987027515
y1[1] (numeric) = 0.044194061382333596444834987027515
absolute error = 3.98e-63
relative error = 9.0057348781956244163843410476124e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.70600168758443234360554818943968
y2[1] (numeric) = 0.70600168758443234360554818943968
absolute error = 4.7e-63
relative error = 6.6572078830022857935007229792542e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2709
Order of pole (three term test) = -2.982
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1108260400, alloc=4783252, time=58.54
x[1] = 3.45
y1[1] (analytic) = 0.047181785405695271493214860052253
y1[1] (numeric) = 0.047181785405695271493214860052253
absolute error = 3.94e-63
relative error = 8.3506801748210361121982312495271e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.69645848729157083600191363378011
y2[1] (numeric) = 0.69645848729157083600191363378011
absolute error = 4.8e-63
relative error = 6.8920116382909271732208727705618e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2789
Order of pole (three term test) = -3.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1112261816, alloc=4783252, time=58.75
x[1] = 3.46
y1[1] (analytic) = 0.05026479045650384489839462421797
y1[1] (numeric) = 0.05026479045650384489839462421797
absolute error = 3.92e-63
relative error = 7.7986995755848907065565989540712e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.68694564089702975389368422402507
y2[1] (numeric) = 0.68694564089702975389368422402507
absolute error = 4.9e-63
relative error = 7.1330243738084790835049611581477e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2867
Order of pole (three term test) = -3.262
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.47
y1[1] (analytic) = 0.053442768236823398114819946473319
y1[1] (numeric) = 0.053442768236823398114819946473319
absolute error = 3.83e-63
relative error = 7.1665449346260372561412180584218e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.67746409967752120581814601284274
y2[1] (numeric) = 0.67746409967752120581814601284274
absolute error = 5.0e-63
relative error = 7.3804648871874442015772053823607e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2944
Order of pole (three term test) = -3.408
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1116262624, alloc=4783252, time=58.96
TOP MAIN SOLVE Loop
x[1] = 3.48
y1[1] (analytic) = 0.056715400951524205176401852617717
y1[1] (numeric) = 0.056715400951524205176401852617717
absolute error = 3.83e-63
relative error = 6.7530158224105267182662535914491e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.66801481177926588461808356455725
y2[1] (numeric) = 0.66801481177926588461808356455725
absolute error = 5.0e-63
relative error = 7.4848639758187949108774187845967e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3019
Order of pole (three term test) = -3.557
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1120263504, alloc=4783252, time=59.18
x[1] = 3.49
y1[1] (analytic) = 0.060082361340061980840721327233228
y1[1] (numeric) = 0.060082361340061980840721327233228
absolute error = 3.72e-63
relative error = 6.1915009946847113310047961536147e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.6585987221231792354917125192625
y2[1] (numeric) = 0.6585987221231792354917125192625
absolute error = 5.0e-63
relative error = 7.5918762549084303977326787909048e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3094
Order of pole (three term test) = -3.71
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1124264504, alloc=4783252, time=59.39
x[1] = 3.5
y1[1] (analytic) = 0.06354331270920366230134237332824
y1[1] (numeric) = 0.06354331270920366230134237332824
absolute error = 3.74e-63
relative error = 5.8857491694138500943201307489801e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.64921677231038015187963119995636
y2[1] (numeric) = 0.64921677231038015187963119995636
absolute error = 5.0e-63
relative error = 7.7015878413097744124514873526199e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3167
Order of pole (three term test) = -3.867
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1128265372, alloc=4783252, time=59.61
x[1] = 3.51
y1[1] (analytic) = 0.067097908966696451917333694242418
y1[1] (numeric) = 0.067097908966696451917333694242418
absolute error = 3.62e-63
relative error = 5.3951010631296424999888171373410e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.63986990052803164824046007658263
y2[1] (numeric) = 0.63986990052803164824046007658263
absolute error = 5.0e-63
relative error = 7.8140884512209653800015436432356e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3239
Order of pole (three term test) = -4.028
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.52
y1[1] (analytic) = 0.070745794655876754083783487727762
y1[1] (numeric) = 0.070745794655876754083783487727762
absolute error = 3.55e-63
relative error = 5.0179661098839695791225696586931e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.63055904145552292556942567856704
y2[1] (numeric) = 0.63055904145552292556942567856704
absolute error = 5.1e-63
relative error = 8.0880610136485265063050751704621e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.331
Order of pole (three term test) = -4.192
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1132266088, alloc=4783252, time=59.82
x[1] = 3.53
y1[1] (analytic) = 0.074486604991215545378460985315985
y1[1] (numeric) = 0.074486604991215545378460985315985
absolute error = 3.55e-63
relative error = 4.7659575844793347492349585692401e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.62128512617100221137515574599336
y2[1] (numeric) = 0.62128512617100221137515574599336
absolute error = 5.1e-63
relative error = 8.2087913989369810183809517680610e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3379
Order of pole (three term test) = -4.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1136267724, alloc=4783252, time=60.03
x[1] = 3.54
y1[1] (analytic) = 0.078319965894796623477231113870234
y1[1] (numeric) = 0.078319965894796623477231113870234
absolute error = 3.53e-63
relative error = 4.5071521159006583467425334421966e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.61204908205826972075279889951549
y2[1] (numeric) = 0.61204908205826972075279889951549
absolute error = 5.2e-63
relative error = 8.4960506476258998804628589761641e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3447
Order of pole (three term test) = -4.531
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1140268656, alloc=4783252, time=60.25
x[1] = 3.55
y1[1] (analytic) = 0.082245494033724087043729177289527
y1[1] (numeric) = 0.082245494033724087043729177289527
absolute error = 3.49e-63
relative error = 4.2433935633834897521273939675432e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.60285183271404004917977257656305
y2[1] (numeric) = 0.60285183271404004917977257656305
absolute error = 5.2e-63
relative error = 8.6256683944869015764924520236139e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3514
Order of pole (three term test) = -4.705
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1144269628, alloc=4783252, time=60.46
x[1] = 3.56
y1[1] (analytic) = 0.086262796858455305876479386896339
y1[1] (numeric) = 0.086262796858455305876479386896339
absolute error = 3.36e-63
relative error = 3.8950742641851399197325209670881e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.59369429785558327071757857731409
y2[1] (numeric) = 0.59369429785558327071757857731409
absolute error = 5.2e-63
relative error = 8.7587164282735037810376135497297e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3579
Order of pole (three term test) = -4.883
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.57
y1[1] (analytic) = 0.090371472642055548048386563963263
y1[1] (numeric) = 0.090371472642055548048386563963263
absolute error = 3.36e-63
relative error = 3.7179874375936416983315037858228e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.58457739322875397743290054393371
y2[1] (numeric) = 0.58457739322875397743290054393371
absolute error = 5.2e-63
relative error = 8.8953149065159988741068120332325e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3643
Order of pole (three term test) = -5.064
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1148270364, alloc=4783252, time=60.67
x[1] = 3.58
y1[1] (analytic) = 0.094571110520370338608599145450982
y1[1] (numeric) = 0.094571110520370338608599145450982
absolute error = 3.29e-63
relative error = 3.4788636634348749579574821997224e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.57550203051641745705739905165624
y2[1] (numeric) = 0.57550203051641745705739905165624
absolute error = 5.3e-63
relative error = 9.2093506520630875187558948249018e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3705
Order of pole (three term test) = -5.249
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1152271300, alloc=4783252, time=60.88
x[1] = 3.59
y1[1] (analytic) = 0.098861290533111532644350160652166
y1[1] (numeric) = 0.098861290533111532644350160652166
absolute error = 3.21e-63
relative error = 3.2469735957218536186305682785992e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.56646911724728216619212706795597
y2[1] (numeric) = 0.56646911724728216619212706795597
absolute error = 5.4e-63
relative error = 9.5327350345962896171609795562906e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3766
Order of pole (three term test) = -5.436
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1156272132, alloc=4783252, time=61.10
x[1] = 3.6
y1[1] (analytic) = 0.10324158366585299412970827473406
y1[1] (numeric) = 0.10324158366585299412970827473406
absolute error = 3.2e-63
relative error = 3.0995262629416594419772758537806e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.55747955670514761573327265250731
y2[1] (numeric) = 0.55747955670514761573327265250731
absolute error = 5.4e-63
relative error = 9.6864538529725387107577483208285e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3826
Order of pole (three term test) = -5.626
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.61
y1[1] (analytic) = 0.10771155189293168102835030646159
y1[1] (numeric) = 0.10771155189293168102835030646159
absolute error = 3.1e-63
relative error = 2.8780571308465478141481901564330e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.54853424783857674365505981360747
y2[1] (numeric) = 0.54853424783857674365505981360747
absolute error = 5.4e-63
relative error = 9.8444172287837128555890989011514e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3883
Order of pole (three term test) = -5.819
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1160272868, alloc=4783252, time=61.31
x[1] = 3.62
y1[1] (analytic) = 0.112270748221249846577595727932
y1[1] (numeric) = 0.112270748221249846577595727932
absolute error = 3.1e-63
relative error = 2.7611822750934984886961538515729e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.53963408517100180783725645920515
y2[1] (numeric) = 0.53963408517100180783725645920515
absolute error = 5.4e-63
relative error = 1.0006780795339905916739371739795e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.394
Order of pole (three term test) = -6.015
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1164273596, alloc=4783252, time=61.52
x[1] = 3.63
y1[1] (analytic) = 0.11691871673497397657007645560199
y1[1] (numeric) = 0.11691871673497397657007645560199
absolute error = 3.1e-63
relative error = 2.6514146635965384802912185551979e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.53077995871127278827309518546809
y2[1] (numeric) = 0.53077995871127278827309518546809
absolute error = 5.5e-63
relative error = 1.0362109400953895011221714304471e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3994
Order of pole (three term test) = -6.214
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1168274432, alloc=4783252, time=61.73
x[1] = 3.64
y1[1] (analytic) = 0.12165499264112599277656275586591
y1[1] (numeric) = 0.12165499264112599277656275586591
absolute error = 3.1e-63
relative error = 2.5481897065620566116792258247819e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.52197275386465724374284336112709
y2[1] (numeric) = 0.52197275386465724374284336112709
absolute error = 5.5e-63
relative error = 1.0536948450428314206263232798160e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4048
Order of pole (three term test) = -6.416
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1172275508, alloc=4783252, time=61.95
x[1] = 3.65
y1[1] (analytic) = 0.12647910231606216342759552547173
y1[1] (numeric) = 0.12647910231606216342759552547173
absolute error = 3.0e-63
relative error = 2.3719333431883602086757183946347e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.51321335134430052289318861170468
y2[1] (numeric) = 0.51321335134430052289318861170468
absolute error = 5.5e-63
relative error = 1.0716790562040938420077298870891e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4099
Order of pole (three term test) = -6.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.66
y1[1] (analytic) = 0.13139056335283507290160907984007
y1[1] (numeric) = 0.13139056335283507290160907984007
absolute error = 3.0e-63
relative error = 2.2832689985077742338125571840425e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.50450262708315518362754885358965
y2[1] (numeric) = 0.50450262708315518362754885358965
absolute error = 5.6e-63
relative error = 1.1100041306775938803707496793502e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4149
Order of pole (three term test) = -6.827
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1176276456, alloc=4783252, time=62.16
x[1] = 3.67
y1[1] (analytic) = 0.13638888460943391446204381352019
y1[1] (numeric) = 0.13638888460943391446204381352019
absolute error = 2.9e-63
relative error = 2.1262729791393933182135862525947e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.49584145214638842779197594108609
y2[1] (numeric) = 0.49584145214638842779197594108609
absolute error = 5.6e-63
relative error = 1.1293932719337670351989456019436e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4197
Order of pole (three term test) = -7.036
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1180277540, alloc=4783252, time=62.37
x[1] = 3.68
y1[1] (analytic) = 0.14147356625789828205437513146384
y1[1] (numeric) = 0.14147356625789828205437513146384
absolute error = 2.9e-63
relative error = 2.0498528995257422064849305436989e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.48723069264427631034019077495596
y2[1] (numeric) = 0.48723069264427631034019077495596
absolute error = 5.7e-63
relative error = 1.1698770389577098681390520111541e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4244
Order of pole (three term test) = -7.248
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1184278272, alloc=4783252, time=62.58
x[1] = 3.69
y1[1] (analytic) = 0.14664409983430054982480697162784
y1[1] (numeric) = 0.14664409983430054982480697162784
absolute error = 2.8e-63
relative error = 1.9093846961206348862321581402887e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.47867120964559343348424545187534
y2[1] (numeric) = 0.47867120964559343348424545187534
absolute error = 5.7e-63
relative error = 1.1907964977087844873142796446173e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4288
Order of pole (three term test) = -7.461
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.7
y1[1] (analytic) = 0.1518999682895918411643298936456
y1[1] (numeric) = 0.1518999682895918411643298936456
absolute error = 2.8e-63
relative error = 1.8433183571585087042181577414427e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.47016385909150678678922237429879
y2[1] (numeric) = 0.47016385909150678678922237429879
absolute error = 5.7e-63
relative error = 1.2123432904889917559611478896054e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4331
Order of pole (three term test) = -7.677
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1188279124, alloc=4783252, time=62.79
x[1] = 3.71
y1[1] (analytic) = 0.15724064604130650272361082739025
y1[1] (numeric) = 0.15724064604130650272361082739025
absolute error = 2.7e-63
relative error = 1.7171132706302418524149514062617e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.46170949170998234375620595674963
y2[1] (numeric) = 0.46170949170998234375620595674963
absolute error = 5.7e-63
relative error = 1.2345425212918064256698320259111e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4373
Order of pole (three term test) = -7.896
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1192280064, alloc=4783252, time=63.01
x[1] = 3.72
y1[1] (analytic) = 0.16266559902611991299439991051033
y1[1] (numeric) = 0.16266559902611991299439991051033
absolute error = 2.6e-63
relative error = 1.5983711464293730890359032565180e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.45330895293071297416254103294378
y2[1] (numeric) = 0.45330895293071297416254103294378
absolute error = 5.8e-63
relative error = 1.2794805755549491732562419375244e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4412
Order of pole (three term test) = -8.116
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1196280996, alloc=4783252, time=63.22
x[1] = 3.73
y1[1] (analytic) = 0.16817428475325436972039430207837
y1[1] (numeric) = 0.16817428475325436972039430207837
absolute error = 2.5e-63
relative error = 1.4865530741920530551719222822849e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.44496308280057617929725076783427
y2[1] (numeric) = 0.44496308280057617929725076783427
absolute error = 5.8e-63
relative error = 1.3034789231266287928327246643968e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.445
Order of pole (three term test) = -8.338
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1200282336, alloc=4783252, time=63.43
x[1] = 3.74
y1[1] (analytic) = 0.17376615235872771559332264379747
y1[1] (numeric) = 0.17376615235872771559332264379747
absolute error = 2.4e-63
relative error = 1.3811665663433536400217658304970e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.43667271589963010424763888032052
y2[1] (numeric) = 0.43667271589963010424763888032052
absolute error = 5.9e-63
relative error = 1.3511263207376858598161483571860e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4486
Order of pole (three term test) = -8.562
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.75
y1[1] (analytic) = 0.17944064266043927741688759770929
y1[1] (numeric) = 0.17944064266043927741688759770929
absolute error = 2.4e-63
relative error = 1.3374896369166429455942148381823e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.42843868125765622756584442664971
y2[1] (numeric) = 0.42843868125765622756584442664971
absolute error = 5.9e-63
relative error = 1.3770932126578537333795223913967e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.452
Order of pole (three term test) = -8.788
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1204283136, alloc=4783252, time=63.64
x[1] = 3.76
y1[1] (analytic) = 0.18519718821408761019055486243691
y1[1] (numeric) = 0.18519718821408761019055486243691
absolute error = 2.4e-63
relative error = 1.2959160034468797647962271081071e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.42026180227125707397683496224605
y2[1] (numeric) = 0.42026180227125707397683496224605
absolute error = 6.0e-63
relative error = 1.4276814993829282012799402273599e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4553
Order of pole (three term test) = -9.015
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1208284552, alloc=4783252, time=63.86
x[1] = 3.77
y1[1] (analytic) = 0.19103521336991445438537825380378
y1[1] (numeric) = 0.19103521336991445438537825380378
absolute error = 2.3e-63
relative error = 1.2039665145641781950782365028585e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.41214289662151724028748227352559
y2[1] (numeric) = 0.41214289662151724028748227352559
absolute error = 6.0e-63
relative error = 1.4558057530978081590905559978410e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.53
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.81
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4584
Order of pole (three term test) = -9.244
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1212285776, alloc=4783252, time=64.07
x[1] = 3.78
y1[1] (analytic) = 0.19695413433026923206341974076229
y1[1] (numeric) = 0.19695413433026923206341974076229
absolute error = 2.2e-63
relative error = 1.1170113323495181119619826231527e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.40408277619223596832551418909979
y2[1] (numeric) = 0.40408277619223596832551418909979
absolute error = 6.0e-63
relative error = 1.4848442827826928250133220934105e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4612
Order of pole (three term test) = -9.474
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.79
y1[1] (analytic) = 0.20295335920798832543912274815984
y1[1] (numeric) = 0.20295335920798832543912274815984
absolute error = 2.2e-63
relative error = 1.0839928979669764044848685257565e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.39608224698873944158290927976732
y2[1] (numeric) = 0.39608224698873944158290927976732
absolute error = 6.1e-63
relative error = 1.5400841735210167291420417796466e-60 %
Correct digits = 64
h = 0.01
bytes used=1216288144, alloc=4783252, time=64.28
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4639
Order of pole (three term test) = -9.706
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.8
y1[1] (analytic) = 0.20903228808558330000343182564927
y1[1] (numeric) = 0.20903228808558330000343182564927
absolute error = 2.1e-63
relative error = 1.0046294853454433477922205257451e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.38814210905728092426641391388112
y2[1] (numeric) = 0.38814210905728092426641391388112
absolute error = 6.1e-63
relative error = 1.5715893374248087835918516791368e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4664
Order of pole (three term test) = -9.939
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1220288920, alloc=4783252, time=64.49
x[1] = 3.81
y1[1] (analytic) = 0.21519031307523215343766962563504
y1[1] (numeric) = 0.21519031307523215343766962563504
absolute error = 2.0e-63
relative error = 9.2940986581528181693058265395836e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.38026315640503680267411028948219
y2[1] (numeric) = 0.38026315640503680267411028948219
absolute error = 6.1e-63
relative error = 1.6041522554192952089802409313263e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4688
Order of pole (three term test) = -10.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1224289796, alloc=4783252, time=64.71
x[1] = 3.82
y1[1] (analytic) = 0.2214268183795675912422723433438
y1[1] (numeric) = 0.2214268183795675912422723433438
absolute error = 1.9e-63
relative error = 8.5807130947572908692656681994085e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.37244617692070652922722804311009
y2[1] (numeric) = 0.37244617692070652922722804311009
absolute error = 6.2e-63
relative error = 1.6646700608555245468844107654675e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.12
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.31
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4709
Order of pole (three term test) = -10.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1228290688, alloc=4783252, time=64.92
x[1] = 3.83
y1[1] (analytic) = 0.22774118035325625030347747297652
y1[1] (numeric) = 0.22774118035325625030347747297652
absolute error = 1.8e-63
relative error = 7.9037089261062291030264653647063e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.36469195229572440909662976137772
y2[1] (numeric) = 0.36469195229572440909662976137772
absolute error = 6.2e-63
relative error = 1.7000649345210922060952127629309e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4728
Order of pole (three term test) = -10.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.84
y1[1] (analytic) = 0.23413276756536271252692305975232
y1[1] (numeric) = 0.23413276756536271252692305975232
absolute error = 1.8e-63
relative error = 7.6879456844821817446060488830067e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.35700125794609110817965112113726
y2[1] (numeric) = 0.35700125794609110817965112113726
absolute error = 6.2e-63
relative error = 1.7366885583737157464554544825618e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4746
Order of pole (three term test) = -10.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1232291860, alloc=4783252, time=65.13
x[1] = 3.85
y1[1] (analytic) = 0.24060094086249207218876492604721
y1[1] (numeric) = 0.24060094086249207218876492604721
absolute error = 1.7e-63
relative error = 7.0656415303528747441425327341401e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.349374862934832699211357781338
y2[1] (numeric) = 0.349374862934832699211357781338
absolute error = 6.2e-63
relative error = 1.7745981917297976132285060678790e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.14
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4762
Order of pole (three term test) = -11.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1236292556, alloc=4783252, time=65.34
x[1] = 3.86
y1[1] (analytic) = 0.24714505343270474280019539063516
y1[1] (numeric) = 0.24714505343270474280019539063516
absolute error = 1.7e-63
relative error = 6.8785515889877759513526216123046e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.3418135298950950000409906547043
y2[1] (numeric) = 0.3418135298950950000409906547043
absolute error = 6.2e-63
relative error = 1.8138544726134228898872436263505e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4775
Order of pole (three term test) = -11.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1240293240, alloc=4783252, time=65.55
x[1] = 3.87
y1[1] (analytic) = 0.25376445087019711205793919067272
y1[1] (numeric) = 0.25376445087019711205793919067272
absolute error = 1.6e-63
relative error = 6.3050596508429581073448997136456e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.33431801495388089457568407689649
y2[1] (numeric) = 0.33431801495388089457568407689649
absolute error = 6.2e-63
relative error = 1.8545216598200036571194528651561e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4787
Order of pole (three term test) = -11.6
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1244294464, alloc=4783252, time=65.77
x[1] = 3.88
y1[1] (analytic) = 0.26045847124074157686913192295872
y1[1] (numeric) = 0.26045847124074157686913192295872
absolute error = 1.5e-63
relative error = 5.7590754981186658477870392882790e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.32688906765643826259581048063146
y2[1] (numeric) = 0.32688906765643826259581048063146
absolute error = 6.2e-63
relative error = 1.8966678954574966619627831907867e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.29
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4797
Order of pole (three term test) = -11.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.89
y1[1] (analytic) = 0.26722644514787941450161169736831
y1[1] (numeric) = 0.26722644514787941450161169736831
absolute error = 1.4e-63
relative error = 5.2390024468770648263621836287303e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.31952743089130607958596019184132
y2[1] (numeric) = 0.31952743089130607958596019184132
absolute error = 6.3e-63
relative error = 1.9716617075493203609294366295355e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.57
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4805
Order of pole (three term test) = -12.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1248295228, alloc=4783252, time=65.97
x[1] = 3.9
y1[1] (analytic) = 0.27406769579985987062766951538565
y1[1] (numeric) = 0.27406769579985987062766951538565
absolute error = 1.3e-63
relative error = 4.7433536309559642861311179178766e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.31223384081602618190911187462131
y2[1] (numeric) = 0.31223384081602618190911187462131
absolute error = 6.2e-63
relative error = 1.9856912318652711237532159234692e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4811
Order of pole (three term test) = -12.32
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1252296800, alloc=4783252, time=66.19
x[1] = 3.91
y1[1] (analytic) = 0.28098153907731877040823638612561
y1[1] (numeric) = 0.28098153907731877040823638612561
absolute error = 1.3e-63
relative error = 4.6266384769224073537476207867193e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.30500902678352812608556955192351
y2[1] (numeric) = 0.30500902678352812608556955192351
absolute error = 6.3e-63
relative error = 2.0655126395558299055804405298047e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4815
Order of pole (three term test) = -12.56
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1256297808, alloc=4783252, time=66.40
x[1] = 3.92
y1[1] (analytic) = 0.28796728360168988481279741570741
y1[1] (numeric) = 0.28796728360168988481279741570741
absolute error = 1.2e-63
relative error = 4.1671400479639695199046763986486e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.29785371126919450362939256217935
y2[1] (numeric) = 0.29785371126919450362939256217935
absolute error = 6.3e-63
relative error = 2.1151322819362758090788394764300e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.27
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -12.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.93
y1[1] (analytic) = 0.29502423080434221109541016047305
y1[1] (numeric) = 0.29502423080434221109541016047305
absolute error = 1.2e-63
relative error = 4.0674625156325912845476529544472e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.29076860979861400485005610714845
y2[1] (numeric) = 0.29076860979861400485005610714845
absolute error = 6.3e-63
relative error = 2.1666712938385517428187768975970e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -13.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1260298572, alloc=4783252, time=66.61
x[1] = 3.94
y1[1] (analytic) = 0.30215167499643625375639385056441
y1[1] (numeric) = 0.30215167499643625375639385056441
absolute error = 1.1e-63
relative error = 3.6405556911540338694762793465040e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.28375443087602945625275664545921
y2[1] (numeric) = 0.28375443087602945625275664545921
absolute error = 6.3e-63
relative error = 2.2202296473574471745488023440413e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4816
Order of pole (three term test) = -13.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1264299236, alloc=4783252, time=66.82
x[1] = 3.95
y1[1] (analytic) = 0.30934890343949232041980668835977
y1[1] (numeric) = 0.30934890343949232041980668835977
absolute error = 1.1e-63
relative error = 3.5558555009235924616210980524441e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.27681187591348798667399566455718
y2[1] (numeric) = 0.27681187591348798667399566455718
absolute error = 6.2e-63
relative error = 2.2397882964882929912776710228231e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4813
Order of pole (three term test) = -13.53
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1268300464, alloc=4783252, time=67.04
x[1] = 3.96
y1[1] (analytic) = 0.31661519641666377585593019124849
y1[1] (numeric) = 0.31661519641666377585593019124849
absolute error = 1.0e-63
relative error = 3.1584080970137824863096410435952e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.26994163916070040707678694126831
y2[1] (numeric) = 0.26994163916070040707678694126831
absolute error = 6.2e-63
relative error = 2.2967927509357104776029681191328e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4807
Order of pole (three term test) = -13.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1272301948, alloc=4783252, time=67.25
x[1] = 3.97
y1[1] (analytic) = 0.32394982730470812688275251068066
y1[1] (numeric) = 0.32394982730470812688275251068066
absolute error = 1.0e-63
relative error = 3.0868977715471882692294612148878e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.26314440763561681800905744824866
y2[1] (numeric) = 0.26314440763561681800905744824866
absolute error = 6.2e-63
relative error = 2.3561207535085859674371487207997e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.48
Order of pole (three term test) = -14.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.98
y1[1] (analytic) = 0.33135206264664874109793628332516
y1[1] (numeric) = 0.33135206264664874109793628332516
absolute error = 9e-64
relative error = 2.7161442509556760792969350636038e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.2564208610557253871066425986234
y2[1] (numeric) = 0.2564208610557253871066425986234
absolute error = 6.2e-63
relative error = 2.4179000002081015807183188564578e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4791
Order of pole (three term test) = -14.25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1276302688, alloc=4783252, time=67.46
x[1] = 3.99
y1[1] (analytic) = 0.33882116222511993332994904798987
y1[1] (numeric) = 0.33882116222511993332994904798987
absolute error = 9e-64
relative error = 2.6562685579893649007643574426834e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.24977167177008116670587470137992
y2[1] (numeric) = 0.24977167177008116670587470137992
absolute error = 6.3e-63
relative error = 2.5223036525131845736266770448164e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.478
Order of pole (three term test) = -14.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1280303404, alloc=4783252, time=67.67
x[1] = 4
y1[1] (analytic) = 0.34635637913638808536083181690225
y1[1] (numeric) = 0.34635637913638808536083181690225
absolute error = 8e-64
relative error = 2.3097596816167670449651070417293e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.24319750469207174862736090548817
y2[1] (numeric) = 0.24319750469207174862736090548817
absolute error = 6.3e-63
relative error = 2.5904871055222551095120701455973e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.41
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4766
Order of pole (three term test) = -14.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1284304068, alloc=4783252, time=67.88
x[1] = 4.01
y1[1] (analytic) = 0.35395695986504139687031758531497
y1[1] (numeric) = 0.35395695986504139687031758531497
absolute error = 8e-64
relative error = 2.2601618013247381250925351112688e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.2366990172329264795094438207023
y2[1] (numeric) = 0.2366990172329264795094438207023
absolute error = 6.3e-63
relative error = 2.6616080090439962267322895112772e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4751
Order of pole (three term test) = -14.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.02
y1[1] (analytic) = 0.36162214435934079868844661923465
y1[1] (numeric) = 0.36162214435934079868844661923465
absolute error = 7e-64
relative error = 1.9357221644712555306899856487553e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.23027685923597588571440266645551
y2[1] (numeric) = 0.23027685923597588571440266645551
absolute error = 6.3e-63
relative error = 2.7358372095669777713183614170062e-60 %
Correct digits = 64
h = 0.01
bytes used=1288305132, alloc=4783252, time=68.10
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4734
Order of pole (three term test) = -15.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.03
y1[1] (analytic) = 0.36935116610722449332814547814755
y1[1] (numeric) = 0.36935116610722449332814547814755
absolute error = 6e-64
relative error = 1.6244703010517015534292677729658e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.2239316729116678818101206987675
y2[1] (numeric) = 0.2239316729116678818101206987675
absolute error = 6.4e-63
relative error = 2.8580146420486685112643648753713e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4716
Order of pole (three term test) = -15.44
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1292306164, alloc=4783252, time=68.31
x[1] = 4.04
y1[1] (analytic) = 0.37714325221295852240705342082732
y1[1] (numeric) = 0.37714325221295852240705342082732
absolute error = 5e-64
relative error = 1.3257561869824172841045958422601e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.21766409277334726095221776933351
y2[1] (numeric) = 0.21766409277334726095221776933351
absolute error = 6.4e-63
relative error = 2.9403104198101678180824661177740e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4695
Order of pole (three term test) = -15.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1296307420, alloc=4783252, time=68.51
x[1] = 4.05
y1[1] (analytic) = 0.38499762347442569596572927151763
y1[1] (numeric) = 0.38499762347442569596572927151763
absolute error = 4e-64
relative error = 1.0389674522927824501406234962001e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.21147474557380488916409289058062
y2[1] (numeric) = 0.21147474557380488916409289058062
absolute error = 6.3e-63
relative error = 2.9790791249829374797359501611379e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.82
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4672
Order of pole (three term test) = -15.91
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1300308544, alloc=4783252, time=68.73
x[1] = 4.06
y1[1] (analytic) = 0.39291349446104515485371415221066
y1[1] (numeric) = 0.39291349446104515485371415221066
absolute error = 4e-64
relative error = 1.0180357906736578796202913743453e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.20536425024260294854257330725366
y2[1] (numeric) = 0.20536425024260294854257330725366
absolute error = 6.4e-63
relative error = 3.1164138804292801874174990785338e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4648
Order of pole (three term test) = -16.15
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.07
y1[1] (analytic) = 0.40089007359231477429214422696039
y1[1] (numeric) = 0.40089007359231477429214422696039
absolute error = 3e-64
relative error = 7.4833481735216284980222168406078e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.19933321782418249681262071972431
y2[1] (numeric) = 0.19933321782418249681262071972431
absolute error = 6.3e-63
relative error = 3.1605369485164169427075376873284e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.22
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4621
Order of pole (three term test) = -16.38
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1304309296, alloc=4783252, time=68.94
x[1] = 4.08
y1[1] (analytic) = 0.40892656321696855443800898175208
y1[1] (numeric) = 0.40892656321696855443800898175208
absolute error = 3e-64
relative error = 7.3362805693017741425786040038751e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.19338225141675953242356232661989
y2[1] (numeric) = 0.19338225141675953242356232661989
absolute error = 6.3e-63
relative error = 3.2577963871269773406960201406051e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4593
Order of pole (three term test) = -16.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1308310072, alloc=4783252, time=69.15
x[1] = 4.09
y1[1] (analytic) = 0.41702215969274108227696288635572
y1[1] (numeric) = 0.41702215969274108227696288635572
absolute error = 2e-64
relative error = 4.7959082113851829037795929101827e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.18751194611201567552941728764728
y2[1] (numeric) = 0.18751194611201567552941728764728
absolute error = 6.3e-63
relative error = 3.3597859393110415929118237722911e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4563
Order of pole (three term test) = -16.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1312310976, alloc=4783252, time=69.36
x[1] = 4.1
y1[1] (analytic) = 0.42517605346673108846497132034021
y1[1] (numeric) = 0.42517605346673108846497132034021
absolute error = 1e-64
relative error = 2.3519668895892966332899622621527e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.18172288893558949573496297564155
y2[1] (numeric) = 0.18172288893558949573496297564155
absolute error = 6.3e-63
relative error = 3.4668169964175477693063492237949e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4531
Order of pole (three term test) = -17.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1316311648, alloc=4783252, time=69.58
x[1] = 4.11
y1[1] (analytic) = 0.43338742915635606283007600612553
y1[1] (numeric) = 0.43338742915635606283007600612553
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.17601565878837443742517601630396
y2[1] (numeric) = 0.17601565878837443742517601630396
absolute error = 6.3e-63
relative error = 3.5792270093279367231300107190303e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4498
Order of pole (three term test) = -17.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.12
y1[1] (analytic) = 0.4416554656308898331401917272407
y1[1] (numeric) = 0.4416554656308898331401917272407
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.17039082638862921283659693902778
y2[1] (numeric) = 0.17039082638862921283659693902778
absolute error = 6.3e-63
relative error = 3.6973821499233138615057719394618e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4462
Order of pole (three term test) = -17.52
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1320312560, alloc=4783252, time=69.79
x[1] = 4.13
y1[1] (analytic) = 0.44997933609357495344700530792948
y1[1] (numeric) = 0.44997933609357495344700530792948
absolute error = 1e-64
relative error = 2.2223242708906217635897397192983e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.16484895421490645178307012404365
y2[1] (numeric) = 0.16484895421490645178307012404365
absolute error = 6.2e-63
relative error = 3.7610187031683125839690441984854e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4425
Order of pole (three term test) = -17.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1324314164, alloc=4783252, time=70.00
x[1] = 4.14
y1[1] (analytic) = 0.45835820816430169083556922640269
y1[1] (numeric) = 0.45835820816430169083556922640269
absolute error = 2e-64
relative error = 4.3633995516517205597253265131229e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.15939059644980531512332717185912
y2[1] (numeric) = 0.15939059644980531512332717185912
absolute error = 6.2e-63
relative error = 3.8898154207939617019701373828031e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4386
Order of pole (three term test) = -17.96
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1328314964, alloc=4783252, time=70.21
x[1] = 4.15
y1[1] (analytic) = 0.46679124396284534274981382833728
y1[1] (numeric) = 0.46679124396284534274981382833728
absolute error = 3e-64
relative error = 6.4268557707538910549032104267013e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.15401629892455369666219427078778
y2[1] (numeric) = 0.15401629892455369666219427078778
absolute error = 6.2e-63
relative error = 4.0255479733590580143659768591490e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4345
Order of pole (three term test) = -18.18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.16
y1[1] (analytic) = 0.47527760019265356123160978929078
y1[1] (numeric) = 0.47527760019265356123160978929078
absolute error = 3e-64
relative error = 6.3121005466783020088269131955044e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.14872659906442555521905209735327
y2[1] (numeric) = 0.14872659906442555521905209735327
absolute error = 6.2e-63
relative error = 4.1687230387849298138783288265344e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4303
Order of pole (three term test) = -18.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1332315656, alloc=4783252, time=70.42
x[1] = 4.17
y1[1] (analytic) = 0.48381642822517530541077945724221
y1[1] (numeric) = 0.48381642822517530541077945724221
absolute error = 3e-64
relative error = 6.2006989117859299494028660709900e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.14352202583499883508485599858706
y2[1] (numeric) = 0.14352202583499883508485599858706
absolute error = 6.1e-63
relative error = 4.2502187134767108072164611891232e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4259
Order of pole (three term test) = -18.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1336316576, alloc=4783252, time=70.64
x[1] = 4.18
y1[1] (analytic) = 0.49240687418472298942108196695328
y1[1] (numeric) = 0.49240687418472298942108196695328
absolute error = 4e-64
relative error = 8.1233634413061179583939073332217e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.13840309968925934903088583719909
y2[1] (numeric) = 0.13840309968925934903088583719909
absolute error = 6.2e-63
relative error = 4.4796684567904555056127587007683e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4213
Order of pole (three term test) = -18.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1340317260, alloc=4783252, time=70.85
x[1] = 4.19
y1[1] (analytic) = 0.50104807903385933959809874850755
y1[1] (numeric) = 0.50104807903385933959809874850755
absolute error = 5e-64
relative error = 9.9790822661992779832040705030699e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.13337033251555591343684467407746
y2[1] (numeric) = 0.13337033251555591343684467407746
absolute error = 6.2e-63
relative error = 4.6487100114838888136412452511956e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4165
Order of pole (three term test) = -19.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1344318164, alloc=4783252, time=71.07
x[1] = 4.2
y1[1] (analytic) = 0.50973917865930042234445511862287
y1[1] (numeric) = 0.50973917865930042234445511862287
absolute error = 6e-64
relative error = 1.1770725600847489968802358022421e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.12842422758641193998142290209118
y2[1] (numeric) = 0.12842422758641193998142290209118
absolute error = 6.2e-63
relative error = 4.8277494959650413338816788384022e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4116
Order of pole (three term test) = -19.24
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.21
y1[1] (analytic) = 0.51847930395832625243117705051315
y1[1] (numeric) = 0.51847930395832625243117705051315
absolute error = 6e-64
relative error = 1.1572303762547600676824988070562e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.1235652795081986026935019100478
y2[1] (numeric) = 0.1235652795081986026935019100478
absolute error = 6.2e-63
relative error = 5.0175907218245944824100744789223e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4065
Order of pole (three term test) = -19.44
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1348318952, alloc=4783252, time=71.28
x[1] = 4.22
y1[1] (analytic) = 0.52726758092569034074636158684479
y1[1] (numeric) = 0.52726758092569034074636158684479
absolute error = 7e-64
relative error = 1.3275991646803967671830278395018e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.11879397417167461300535326877877
y2[1] (numeric) = 0.11879397417167461300535326877877
absolute error = 6.2e-63
relative error = 5.2191199454612874819257499812404e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4013
Order of pole (three term test) = -19.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1352319620, alloc=4783252, time=71.49
x[1] = 4.23
y1[1] (analytic) = 0.53610313074101949060881041045516
y1[1] (numeric) = 0.53610313074101949060881041045516
absolute error = 8e-64
relative error = 1.4922501924102057053076523640419e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.11411078870339754878911140270074
y2[1] (numeric) = 0.11411078870339754878911140270074
absolute error = 6.2e-63
relative error = 5.4333162275438732729594128098019e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3959
Order of pole (three term test) = -19.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1356320600, alloc=4783252, time=71.70
x[1] = 4.24
y1[1] (analytic) = 0.54498506985669510273982813029406
y1[1] (numeric) = 0.54498506985669510273982813029406
absolute error = 9e-64
relative error = 1.6514213870788364389662696204037e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.10951619141801159620312567541779
y2[1] (numeric) = 0.10951619141801159620312567541779
absolute error = 6.2e-63
relative error = 5.6612633435500534641165332823046e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3903
Order of pole (three term test) = -20.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.25
y1[1] (analytic) = 0.55391251008620720083592227945516
y1[1] (numeric) = 0.55391251008620720083592227945516
absolute error = 1.0e-63
relative error = 1.8053392580795237067344147473851e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.10501064177141647553424717156172
y2[1] (numeric) = 0.10501064177141647553424717156172
absolute error = 6.2e-63
relative error = 5.9041635165852476708329163097911e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3846
Order of pole (three term test) = -20.24
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1360321304, alloc=4783252, time=71.91
TOP MAIN SOLVE Loop
x[1] = 4.26
y1[1] (analytic) = 0.56288455869297234241347586451402
y1[1] (numeric) = 0.56288455869297234241347586451402
absolute error = 1.1e-63
relative error = 1.9542195340270462916396196973982e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.10059459031482223410444018114688
y2[1] (numeric) = 0.10059459031482223410444018114688
absolute error = 6.1e-63
relative error = 6.0639443740556573139246044464301e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3787
Order of pole (three term test) = -20.43
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1364322100, alloc=4783252, time=72.12
x[1] = 4.27
y1[1] (analytic) = 0.57190031847960653320832267790571
y1[1] (numeric) = 0.57190031847960653320832267790571
absolute error = 1.1e-63
relative error = 1.9234121130135811264694240158134e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.096268478649694500724140180338675
y2[1] (numeric) = 0.096268478649694500724140180338675
absolute error = 6.15e-63
relative error = 6.3883839095233447595182694362555e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3727
Order of pole (three term test) = -20.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1368323028, alloc=4783252, time=72.34
x[1] = 4.28
y1[1] (analytic) = 0.58095888787764421791317926316396
y1[1] (numeric) = 0.58095888787764421791317926316396
absolute error = 1.2e-63
relative error = 2.0655506354052579077418983326605e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.092032739383594707129367476700577
y2[1] (numeric) = 0.092032739383594707129367476700577
absolute error = 6.16e-63
relative error = 6.6932702875712190234979424992496e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3665
Order of pole (three term test) = -20.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1372324452, alloc=4783252, time=72.55
x[1] = 4.29
y1[1] (analytic) = 0.59005936103769437542862536622075
y1[1] (numeric) = 0.59005936103769437542862536622075
absolute error = 1.3e-63
relative error = 2.2031681655109831433329860739019e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.087887796086919692343653114751977
y2[1] (numeric) = 0.087887796086919692343653114751977
absolute error = 6.07e-63
relative error = 6.9065334099365313569492086983539e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3601
Order of pole (three term test) = -20.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.3
y1[1] (analytic) = 0.59920082792002470309323760366397
y1[1] (numeric) = 0.59920082792002470309323760366397
absolute error = 1.4e-63
relative error = 2.3364453698432771727739441107214e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.083834063250545015968290639715365
y2[1] (numeric) = 0.083834063250545015968290639715365
absolute error = 6.06e-63
relative error = 7.2285652931901796670624794302972e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3537
Order of pole (three term test) = -21.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1376325160, alloc=4783252, time=72.76
x[1] = 4.31
y1[1] (analytic) = 0.60838237438556483154993990315575
y1[1] (numeric) = 0.60838237438556483154993990315575
absolute error = 1.5e-63
relative error = 2.4655546629123230182816593484867e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.079871946244376216034287573009006
y2[1] (numeric) = 0.079871946244376216034287573009006
absolute error = 6.11e-63
relative error = 7.6497447317808474181807262550036e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3471
Order of pole (three term test) = -21.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1380326128, alloc=4783252, time=72.97
x[1] = 4.32
y1[1] (analytic) = 0.61760308228731947000291984056992
y1[1] (numeric) = 0.61760308228731947000291984056992
absolute error = 1.6e-63
relative error = 2.5906606457894145617206673208597e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.076001841276812156255690901016019
y2[1] (numeric) = 0.076001841276812156255690901016019
absolute error = 6.10e-63
relative error = 8.0261213380116942963943722366155e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3403
Order of pole (three term test) = -21.51
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1384326860, alloc=4783252, time=73.19
x[1] = 4.33
y1[1] (analytic) = 0.62686202956218234062676254933714
y1[1] (numeric) = 0.62686202956218234062676254933714
absolute error = 1.6e-63
relative error = 2.5523957817599575252057764581654e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.072224135355124516315780813227023
y2[1] (numeric) = 0.072224135355124516315780813227023
absolute error = 6.08e-63
relative error = 8.4182385432581104515076608353245e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3334
Order of pole (three term test) = -21.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1388327700, alloc=4783252, time=73.40
x[1] = 4.34
y1[1] (analytic) = 0.63615829032314172081087264557633
y1[1] (numeric) = 0.63615829032314172081087264557633
absolute error = 1.6e-63
relative error = 2.5150973025711370194364342207439e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.068539206246757387204087089011161
y2[1] (numeric) = 0.068539206246757387204087089011161
absolute error = 6.00e-63
relative error = 8.7541136359218662660353750698755e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3264
Order of pole (three term test) = -21.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.35
y1[1] (analytic) = 0.64549093495186837276179742256413
y1[1] (numeric) = 0.64549093495186837276179742256413
absolute error = 1.7e-63
relative error = 2.6336543364884931634216364227649e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.064947422441550841612444201658582
y2[1] (numeric) = 0.064947422441550841612444201658582
absolute error = 6.03e-63
relative error = 9.2844331203854518166918507698084e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3193
Order of pole (three term test) = -22.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1392328504, alloc=4783252, time=73.61
x[1] = 4.36
y1[1] (analytic) = 0.65485903019167660174764743303657
y1[1] (numeric) = 0.65485903019167660174764743303657
absolute error = 1.8e-63
relative error = 2.7486831776193751947392295544138e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.06144914311489225700156528111504
y2[1] (numeric) = 0.06144914311489225700156528111504
absolute error = 6.02e-63
relative error = 9.7967191971161065701562022688198e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.312
Order of pole (three term test) = -22.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1396329292, alloc=4783252, time=73.82
x[1] = 4.37
y1[1] (analytic) = 0.66426163924084914695625730757717
y1[1] (numeric) = 0.66426163924084914695625730757717
absolute error = 1.9e-63
relative error = 2.8603187174430445725028940524414e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.058044718091799076175121149591737
y2[1] (numeric) = 0.058044718091799076175121149591737
absolute error = 5.96e-63
relative error = 1.0267945466759130295628082993075e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3046
Order of pole (three term test) = -22.32
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1400330384, alloc=4783252, time=74.04
x[1] = 4.38
y1[1] (analytic) = 0.67369782184631657255577147615592
y1[1] (numeric) = 0.67369782184631657255577147615592
absolute error = 2.0e-63
relative error = 2.9686900196869546317829203850419e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.054734487811936597055336089061836
y2[1] (numeric) = 0.054734487811936597055336089061836
absolute error = 5.96e-63
relative error = 1.0888929883619432200394632040880e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2971
Order of pole (three term test) = -22.47
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.39
y1[1] (analytic) = 0.68316663439768179109661463324426
y1[1] (numeric) = 0.68316663439768179109661463324426
absolute error = 2.0e-63
relative error = 2.9275434415255257923808111430098e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.051518783295574289851971036385868
y2[1] (numeric) = 0.051518783295574289851971036385868
absolute error = 5.91e-63
relative error = 1.1471544205718261393894567507376e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2894
Order of pole (three term test) = -22.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1404331380, alloc=4783252, time=74.25
x[1] = 4.4
y1[1] (analytic) = 0.69266713002158031688086025778229
y1[1] (numeric) = 0.69266713002158031688086025778229
absolute error = 2.1e-63
relative error = 3.0317592808750339777379471558933e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.048397926110484045964607666619612
y2[1] (numeric) = 0.048397926110484045964607666619612
absolute error = 5.87e-63
relative error = 1.2128618872221531043174626214454e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2817
Order of pole (three term test) = -22.76
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1408332116, alloc=4783252, time=74.47
x[1] = 4.41
y1[1] (analytic) = 0.70219835867636681335229353350936
y1[1] (numeric) = 0.70219835867636681335229353350936
absolute error = 2.1e-63
relative error = 2.9906079586378811000154584443216e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.045372228339783668765758435463846
y2[1] (numeric) = 0.045372228339783668765758435463846
absolute error = 5.86e-63
relative error = 1.2915389467133101405531174895237e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2738
Order of pole (three term test) = -22.9
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1412332964, alloc=4783252, time=74.68
x[1] = 4.42
y1[1] (analytic) = 0.71175936724711846593133485650678
y1[1] (numeric) = 0.71175936724711846593133485650678
absolute error = 2.1e-63
relative error = 2.9504353530634925128022563790430e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.042441992550728821888927268161108
y2[1] (numeric) = 0.042441992550728821888927268161108
absolute error = 5.87e-63
relative error = 1.3830641888417180956642130859917e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2658
Order of pole (three term test) = -23.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1416333988, alloc=4783252, time=74.89
x[1] = 4.43
y1[1] (analytic) = 0.72134919964094568003670965106636
y1[1] (numeric) = 0.72134919964094568003670965106636
absolute error = 2.2e-63
relative error = 3.0498404948602679602036828031338e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.039607511764456555800785465699523
y2[1] (numeric) = 0.039607511764456555800785465699523
absolute error = 5.89e-63
relative error = 1.4870916494394974607056906762811e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2577
Order of pole (three term test) = -23.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.44
y1[1] (analytic) = 0.73096689688260057330348764383661
y1[1] (numeric) = 0.73096689688260057330348764383661
absolute error = 2.3e-63
relative error = 3.1465173181014780334652570755474e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.036869069426683438279591966922158
y2[1] (numeric) = 0.036869069426683438279591966922158
absolute error = 5.83e-63
relative error = 1.5812712635976172979972361074679e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2495
Order of pole (three term test) = -23.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1420335024, alloc=4783252, time=75.10
x[1] = 4.45
y1[1] (analytic) = 0.74061149721037370122794327025554
y1[1] (numeric) = 0.74061149721037370122794327025554
absolute error = 2.3e-63
relative error = 3.1055418511099290515925192315933e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.034226939379361218962391981308307
y2[1] (numeric) = 0.034226939379361218962391981308307
absolute error = 5.83e-63
relative error = 1.7033366423395365579950201140481e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2413
Order of pole (three term test) = -23.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1424335840, alloc=4783252, time=75.31
x[1] = 4.46
y1[1] (analytic) = 0.75028203617226942664658639888734
y1[1] (numeric) = 0.75028203617226942664658639888734
absolute error = 2.4e-63
relative error = 3.1987970980141460536932522573070e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.031681385833292862370919071753561
y2[1] (numeric) = 0.031681385833292862370919071753561
absolute error = 5.74e-63
relative error = 1.8117894306151324933975762186805e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2329
Order of pole (three term test) = -23.53
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1428336484, alloc=4783252, time=75.52
x[1] = 4.47
y1[1] (analytic) = 0.75997754672245031559256134466984
y1[1] (numeric) = 0.75997754672245031559256134466984
absolute error = 2.5e-63
relative error = 3.2895708705891798629255162677856e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.029232663341711687790078200728413
y2[1] (numeric) = 0.029232663341711687790078200728413
absolute error = 5.71e-63
relative error = 1.9532944820161080021765100072491e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2244
Order of pole (three term test) = -23.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.48
y1[1] (analytic) = 0.76969705931794091517019859315115
y1[1] (numeric) = 0.76969705931794091517019859315115
absolute error = 2.5e-63
relative error = 3.2480311178729838616704138016814e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.026881016774826258063004581467315
y2[1] (numeric) = 0.026881016774826258063004581467315
absolute error = 5.73e-63
relative error = 2.1316157971249341277018164116019e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2158
Order of pole (three term test) = -23.76
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1432337292, alloc=4783252, time=75.74
TOP MAIN SOLVE Loop
x[1] = 4.49
y1[1] (analytic) = 0.7794396020155812431505179934839
y1[1] (numeric) = 0.7794396020155812431505179934839
absolute error = 2.6e-63
relative error = 3.3357299183625842776430226060619e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.024626681295333562792606306340817
y2[1] (numeric) = 0.024626681295333562792606306340817
absolute error = 5.72e-63
relative error = 2.3226840561273133989244664305975e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2072
Order of pole (three term test) = -23.86
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1436338216, alloc=4783252, time=75.95
x[1] = 4.5
y1[1] (analytic) = 0.78920420056922029401951817520617
y1[1] (numeric) = 0.78920420056922029401951817520617
absolute error = 2.7e-63
relative error = 3.4211678017585332896009664055515e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.02246988233490294461086498550137
y2[1] (numeric) = 0.02246988233490294461086498550137
absolute error = 5.68e-63
relative error = 2.5278281013412943330413796840642e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1984
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1440339440, alloc=4783252, time=76.16
x[1] = 4.51
y1[1] (analytic) = 0.79898987852713984220964167825923
y1[1] (numeric) = 0.79898987852713984220964167825923
absolute error = 2.7e-63
relative error = 3.3792668374938459639650393562122e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.020410835571633120103670802952336
y2[1] (numeric) = 0.020410835571633120103670802952336
absolute error = 5.61e-63
relative error = 2.7485400978864141577324156757266e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1896
Order of pole (three term test) = -24.06
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1444340432, alloc=4783252, time=76.37
x[1] = 4.52
y1[1] (analytic) = 0.80879565732969880021527888180112
y1[1] (numeric) = 0.80879565732969880021527888180112
absolute error = 2.7e-63
relative error = 3.3382968559874049024703343260710e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.018449746908484549670313753257891
y2[1] (numeric) = 0.018449746908484549670313753257891
absolute error = 5.66e-63
relative error = 3.0677927605592876694046017951584e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1807
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.53
y1[1] (analytic) = 0.8186205564071883672378692086186
y1[1] (numeric) = 0.8186205564071883672378692086186
absolute error = 2.8e-63
relative error = 3.4203880883333911285165305659228e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.016586812452689313062672144563041
y2[1] (numeric) = 0.016586812452689313062672144563041
absolute error = 5.58e-63
relative error = 3.3641183415534931547191419310095e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1718
Order of pole (three term test) = -24.24
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1448341472, alloc=4783252, time=76.58
x[1] = 4.54
y1[1] (analytic) = 0.8284635932778881829272807804022
y1[1] (numeric) = 0.8284635932778881829272807804022
absolute error = 2.9e-63
relative error = 3.5004555704444392671236147693030e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.014822218496140549599386069217458
y2[1] (numeric) = 0.014822218496140549599386069217458
absolute error = 5.61e-63
relative error = 3.7848585226703731119324156319535e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1627
Order of pole (three term test) = -24.33
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1452342152, alloc=4783252, time=76.79
x[1] = 4.55
y1[1] (analytic) = 0.83832378364631368068580757499206
y1[1] (numeric) = 0.83832378364631368068580757499206
absolute error = 3.0e-63
relative error = 3.5785695915144059747115839226684e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.013156141496763424094652345974906
y2[1] (numeric) = 0.013156141496763424094652345974906
absolute error = 5.55e-63
relative error = 4.2185621075642654400270109483863e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1536
Order of pole (three term test) = -24.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1456342872, alloc=4783252, time=77.01
x[1] = 4.56
y1[1] (analytic) = 0.8482001415016448158813262073901
y1[1] (numeric) = 0.8482001415016448158813262073901
absolute error = 3.1e-63
relative error = 3.6547977868900043452269188818632e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.011588748060869481389523910961909
y2[1] (numeric) = 0.011588748060869481389523910961909
absolute error = 5.46e-63
relative error = 4.7114666496514954377880790995815e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1445
Order of pole (three term test) = -24.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.57
bytes used=1460347288, alloc=4783252, time=77.22
y1[1] (analytic) = 0.85809167921632632617881468562541
y1[1] (numeric) = 0.85809167921632632617881468562541
absolute error = 3.2e-63
relative error = 3.7292052556930513335850620174197e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.010120194926496154035555871934926
y2[1] (numeric) = 0.010120194926496154035555871934926
absolute error = 5.46e-63
relative error = 5.3951529981946489108073888389419e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1353
Order of pole (three term test) = -24.55
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.58
y1[1] (analytic) = 0.8679974076448296640463665993177
y1[1] (numeric) = 0.8679974076448296640463665993177
absolute error = 3.2e-63
relative error = 3.6866469551823680533554788225694e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0087506289477330891661461639026889
y2[1] (numeric) = 0.0087506289477330891661461639026889
absolute error = 5.442e-63
relative error = 6.2189815526457531555180166310044e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.126
Order of pole (three term test) = -24.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1464348044, alloc=4783252, time=77.43
x[1] = 4.59
y1[1] (analytic) = 0.8779163362225667253247514756035
y1[1] (numeric) = 0.8779163362225667253247514756035
absolute error = 3.2e-63
relative error = 3.6449942528336157596220910374978e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0074801870800368619098223213121856
y2[1] (numeric) = 0.0074801870800368619098223213121856
absolute error = 5.453e-63
relative error = 7.2899246257529804262374109224907e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1167
Order of pole (three term test) = -24.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1468349668, alloc=4783252, time=77.64
x[1] = 4.6
y1[1] (analytic) = 0.88784747306494548257009217877081
y1[1] (numeric) = 0.88784747306494548257009217877081
absolute error = 3.3e-63
relative error = 3.7168546401422342976619321695229e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0063089963665355438618953400911705
y2[1] (numeric) = 0.0063089963665355438618953400911705
absolute error = 5.354e-63
relative error = 8.4862943152082356373405004021685e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1073
Order of pole (three term test) = -24.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1472350536, alloc=4783252, time=77.86
x[1] = 4.61
y1[1] (analytic) = 0.89778982506655761768887117182731
y1[1] (numeric) = 0.89778982506655761768887117182731
absolute error = 3.3e-63
relative error = 3.6756932500937562017019912696893e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0052371739253244961462206425968638
y2[1] (numeric) = 0.0052371739253244961462206425968638
absolute error = 5.307e-63
relative error = 1.0133327775000669695845872405532e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09791
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.62
y1[1] (analytic) = 0.90774239800048823518465822438418
y1[1] (numeric) = 0.90774239800048823518465822438418
absolute error = 3.4e-63
relative error = 3.7455560162104175371643021829072e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0042648269377546574771731655485343
y2[1] (numeric) = 0.0042648269377546574771731655485343
absolute error = 5.332e-63
relative error = 1.2502265807782547220989495976129e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08846
Order of pole (three term test) = -24.83
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1476351328, alloc=4783252, time=78.06
x[1] = 4.63
y1[1] (analytic) = 0.91770419661773772512799271259738
y1[1] (numeric) = 0.91770419661773772512799271259738
absolute error = 3.5e-63
relative error = 3.8138650917141841795604218596364e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0033920526377144983832706460192959
y2[1] (numeric) = 0.0033920526377144983832706460192959
absolute error = 5.294e-63
relative error = 1.5607069127226156998165620864847e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07898
Order of pole (three term test) = -24.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1480352024, alloc=4783252, time=78.28
x[1] = 4.64
y1[1] (analytic) = 0.92767422474674583374597479923988
y1[1] (numeric) = 0.92767422474674583374597479923988
absolute error = 3.5e-63
relative error = 3.7728761957954546116076860897300e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.002618938301906713388091068117169
y2[1] (numeric) = 0.002618938301906713388091068117169
absolute error = 5.209e-63
relative error = 1.9889739274146308769605037923778e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06947
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1484352828, alloc=4783252, time=78.49
x[1] = 4.65
y1[1] (analytic) = 0.93765148539300798930744298382293
y1[1] (numeric) = 0.93765148539300798930744298382293
absolute error = 3.6e-63
relative error = 3.8393796160746155453468224874407e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0019455612411206234711634491039746
y2[1] (numeric) = 0.0019455612411206234711634491039746
absolute error = 5.216e-63
relative error = 2.6809744611254884442871598837684e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05992
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1488354164, alloc=4783252, time=78.70
x[1] = 4.66
y1[1] (analytic) = 0.94763498083877392175416283320404
y1[1] (numeric) = 0.94763498083877392175416283320404
absolute error = 3.6e-63
relative error = 3.7989310998350395032035529348120e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0013719887925011615613129021674769
y2[1] (numeric) = 0.0013719887925011615613129021674769
absolute error = 5.163e-63
relative error = 3.7631502736897385189299531369586e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05036
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.67
y1[1] (analytic) = 0.95762371274281860629914567989472
y1[1] (numeric) = 0.95762371274281860629914567989472
absolute error = 3.6e-63
relative error = 3.7593054057620473769544583167194e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.00089827831281521415746815072661771
y2[1] (numeric) = 0.00089827831281521415746815072661771
absolute error = 5.1419e-63
relative error = 5.7241724826743602291649771159318e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04077
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1492355404, alloc=4783252, time=78.91
x[1] = 4.68
y1[1] (analytic) = 0.96761668224027555398087963205543
y1[1] (numeric) = 0.96761668224027555398087963205543
absolute error = 3.7e-63
relative error = 3.8238282451203415177126670788071e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.00052447717271599243715805024032733
y2[1] (numeric) = 0.00052447717271599243715805024032733
absolute error = 5.1108e-63
relative error = 9.7445613763013650308993454870347e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03117
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1496356288, alloc=4783252, time=79.12
x[1] = 4.69
y1[1] (analytic) = 0.97761289004252246592761160355799
y1[1] (numeric) = 0.97761289004252246592761160355799
absolute error = 3.7e-63
relative error = 3.7847291475862843663779062026540e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.00025062275200600641080659305708347
y2[1] (numeric) = 0.00025062275200600641080659305708347
absolute error = 5.0776e-63
relative error = 2.0259932345959996973524501268529e-57 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02155
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1500357132, alloc=4783252, time=79.34
x[1] = 4.7
y1[1] (analytic) = 0.98761133653710926284949170367289
y1[1] (numeric) = 0.98761133653710926284949170367289
absolute error = 3.8e-63
relative error = 3.8476674572449238962048535958092e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 7.6742435899115820463458425028554e-05
y2[1] (numeric) = 7.6742435899115820463458425028554e-05
absolute error = 5.05740e-63
relative error = 6.5900957413553617444967783550810e-57 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01193
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.71
y1[1] (analytic) = 0.9976110218877184970389038522753
y1[1] (numeric) = 0.9976110218877184970389038522753
absolute error = 3.8e-63
relative error = 3.8090998561839180008390339330634e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 2.8536122820315747652874064262784e-06
y2[1] (numeric) = 2.8536122820315747652874064262784e-06
absolute error = 5.028030e-63
relative error = 1.7619877905839366754845766999887e-55 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0023
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1504357768, alloc=4783252, time=79.55
x[1] = 4.72
y1[1] (analytic) = 1.0076109461341481509210826531746
y1[1] (numeric) = 1.0076109461341481509210826531746
absolute error = 3e-63
relative error = 2.9773396284646905713322794085100e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 2.8963669975541567702112038360479e-05
y2[1] (numeric) = 2.8963669975541567702112038360479e-05
absolute error = 4.93429e-63
relative error = 1.7036135283155662298345586918143e-56 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.007339
Order of pole (three term test) = -0.8943
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1508358908, alloc=4783252, time=79.76
x[1] = 4.73
y1[1] (analytic) = 1.0176101092923068239584801849428
y1[1] (numeric) = 1.0176101092923068239584801849428
absolute error = 4e-63
relative error = 3.9307785599553302034417673470662e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.00015506999799563475715808844231872
y2[1] (numeric) = 0.00015506999799563475715808844231872
absolute error = 4.8842e-63
relative error = 3.1496743813316428465257358670914e-57 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01698
Order of pole (three term test) = -0.9004
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1512360236, alloc=4783252, time=79.97
x[1] = 4.74
y1[1] (analytic) = 1.027607511454211308473521317219
y1[1] (numeric) = 1.027607511454211308473521317219
absolute error = 4e-63
relative error = 3.8925367471666580595752066480661e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.00038115998581459739020295192722966
y2[1] (numeric) = 0.00038115998581459739020295192722966
absolute error = 4.8550e-63
relative error = 1.2737433573002475203551922020477e-57 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02661
Order of pole (three term test) = -0.9113
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1516361268, alloc=4783252, time=80.19
x[1] = 4.75
y1[1] (analytic) = 1.0376021528879765547154963123733
y1[1] (numeric) = 1.0376021528879765547154963123733
absolute error = 4e-63
relative error = 3.8550421169296235063376193148237e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.00070721102462205526572924440292074
y2[1] (numeric) = 0.00070721102462205526572924440292074
absolute error = 4.8490e-63
relative error = 6.8565107601247903866599652829648e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03623
Order of pole (three term test) = -0.927
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.76
y1[1] (analytic) = 1.0475930341377880262584087164105
y1[1] (numeric) = 1.0475930341377880262584087164105
absolute error = 4e-63
relative error = 3.8182766300008512651522407536324e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0011331905095858359312599154305637
y2[1] (numeric) = 0.0011331905095858359312599154305637
absolute error = 4.788e-63
relative error = 4.2252383509194247548132345393355e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04584
Order of pole (three term test) = -0.9476
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1520362144, alloc=4783252, time=80.40
x[1] = 4.77
y1[1] (analytic) = 1.0575791561238464485775487727873
y1[1] (numeric) = 1.0575791561238464485775487727873
absolute error = 4e-63
relative error = 3.7822228027455423281346723107062e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0016590558431124247295906617005143
y2[1] (numeric) = 0.0016590558431124247295906617005143
absolute error = 4.726e-63
relative error = 2.8486081524139184739636945326938e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05543
Order of pole (three term test) = -0.973
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1524362968, alloc=4783252, time=80.61
x[1] = 4.78
y1[1] (analytic) = 1.0675595202422749564132217146596
y1[1] (numeric) = 1.0675595202422749564132217146596
absolute error = 4e-63
relative error = 3.7468636868998449506310026169620e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0022847544391066886523793783523275
y2[1] (numeric) = 0.0022847544391066886523793783523275
absolute error = 4.685e-63
relative error = 2.0505485927983483103743358410152e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.065
Order of pole (three term test) = -1.003
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1528364328, alloc=4783252, time=80.83
x[1] = 4.79
y1[1] (analytic) = 1.0775331284649786492901502413476
y1[1] (numeric) = 1.0775331284649786492901502413476
absolute error = 4e-63
relative error = 3.7121828501906757454238376321981e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.003010223728230442031847121237262
y2[1] (numeric) = 0.003010223728230442031847121237262
absolute error = 4.730e-63
relative error = 1.5713117784705415494299547803502e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07454
Order of pole (three term test) = -1.038
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.8
y1[1] (analytic) = 1.0874989834394465693202152576495
y1[1] (numeric) = 1.0874989834394465693202152576495
absolute error = 4e-63
relative error = 3.6781643577717656510041120214024e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0038353911641593282184035334963654
y2[1] (numeric) = 0.0038353911641593282184035334963654
absolute error = 4.612e-63
relative error = 1.2024849103001193183081414648758e-58 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08405
Order of pole (three term test) = -1.078
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1532365160, alloc=4783252, time=81.04
TOP MAIN SOLVE Loop
x[1] = 4.81
y1[1] (analytic) = 1.0974560885884861211739226395384
y1[1] (numeric) = 1.0974560885884861211739226395384
absolute error = 4e-63
relative error = 3.6447927544369229007899929081408e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0047601742308373915612430245959728
y2[1] (numeric) = 0.0047601742308373915612430245959728
absolute error = 4.563e-63
relative error = 9.5857835842224929902765702844710e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09353
Order of pole (three term test) = -1.122
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1536366228, alloc=4783252, time=81.25
x[1] = 4.82
y1[1] (analytic) = 1.1074034482098799608617106191698
y1[1] (numeric) = 1.1074034482098799608617106191698
absolute error = 4e-63
relative error = 3.6120530475735907657611268381449e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0057844804507286142407590987016601
y2[1] (numeric) = 0.0057844804507286142407590987016601
absolute error = 4.563e-63
relative error = 7.8883488999003249557972407441402e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.103
Order of pole (three term test) = -1.172
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1540367108, alloc=4783252, time=81.47
x[1] = 4.83
y1[1] (analytic) = 1.1173400675759553877192667889538
y1[1] (numeric) = 1.1173400675759553877192667889538
absolute error = 4e-63
relative error = 3.5799306908217403349947728534110e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0069082073940645928059698487305991
y2[1] (numeric) = 0.0069082073940645928059698487305991
absolute error = 4.481e-63
relative error = 6.4864873684162904244136842793645e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1124
Order of pole (three term test) = -1.226
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1544367892, alloc=4783252, time=81.68
x[1] = 4.84
y1[1] (analytic) = 1.1272649530330562827406304097327
y1[1] (numeric) = 1.1272649530330562827406304097327
absolute error = 5e-63
relative error = 4.4355144605062323621209495972153e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.008131242689087429657007244959484
y2[1] (numeric) = 0.008131242689087429657007244959484
absolute error = 4.525e-63
relative error = 5.5649550419553905765142636881865e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1217
Order of pole (three term test) = -1.284
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.85
y1[1] (analytic) = 1.1371771121009076461481397184653
y1[1] (numeric) = 1.1371771121009076461481397184653
absolute error = 5e-63
relative error = 4.3968524751281873902806729849141e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.0094534640332868151920576837088197
y2[1] (numeric) = 0.0094534640332868151920576837088197
absolute error = 4.457e-63
relative error = 4.7146738849445580689818953683145e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.131
Order of pole (three term test) = -1.348
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1548368552, alloc=4783252, time=81.89
x[1] = 4.86
y1[1] (analytic) = 1.1470755535718627978282707459854
y1[1] (numeric) = 1.1470755535718627978282707459854
absolute error = 4e-63
relative error = 3.4871286268323433330747658802123e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.010874739205630176919903305957091
y2[1] (numeric) = 0.010874739205630176919903305957091
absolute error = 4.34e-63
relative error = 3.9909003038464154818212854810115e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1403
Order of pole (three term test) = -1.416
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1552369292, alloc=4783252, time=82.10
x[1] = 4.87
y1[1] (analytic) = 1.156959287610023315996029785628
y1[1] (numeric) = 1.156959287610023315996029785628
absolute error = 4e-63
relative error = 3.4573385968169706603069524330727e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.012394926079784672533344588707492
y2[1] (numeric) = 0.012394926079784672533344588707492
absolute error = 4.39e-63
relative error = 3.5417718280384162448512978281708e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1495
Order of pole (three term test) = -1.488
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1556370312, alloc=4783252, time=82.32
x[1] = 4.88
y1[1] (analytic) = 1.1668273258502218021766327470316
y1[1] (numeric) = 1.1668273258502218021766327470316
absolute error = 4e-63
relative error = 3.4280993523059251210472885374115e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.014013872638329704755215157681578
y2[1] (numeric) = 0.014013872638329704755215157681578
absolute error = 4.28e-63
relative error = 3.0541165247168448869429253179896e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1586
Order of pole (three term test) = -1.566
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1560371020, alloc=4783252, time=82.53
x[1] = 4.89
y1[1] (analytic) = 1.1766786814968575743104585897138
y1[1] (numeric) = 1.1766786814968575743104585897138
absolute error = 5e-63
relative error = 4.2492483960357642863617610448280e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.015731416987958536717347942751101
y2[1] (numeric) = 0.015731416987958536717347942751101
absolute error = 4.29e-63
relative error = 2.7270270715497145840622019473206e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1677
Order of pole (three term test) = -1.648
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.9
y1[1] (analytic) = 1.1865123694225754044943291441219
y1[1] (numeric) = 1.1865123694225754044943291441219
absolute error = 5e-63
relative error = 4.2140310786926605670891027960233e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.017547387375667487723622750081671
y2[1] (numeric) = 0.017547387375667487723622750081671
absolute error = 4.21e-63
relative error = 2.3992175643411731388589232311431e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1767
Order of pole (three term test) = -1.734
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1564372184, alloc=4783252, time=82.74
x[1] = 4.91
y1[1] (analytic) = 1.1963274062667774335675731995194
y1[1] (numeric) = 1.1963274062667774335675731995194
absolute error = 5e-63
relative error = 4.1794578756687071617795244809446e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.01946160220593109049100989773031
y2[1] (numeric) = 0.01946160220593109049100989773031
absolute error = 4.18e-63
relative error = 2.1478190519823229581980537588426e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1856
Order of pole (three term test) = -1.825
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1568372868, alloc=4783252, time=82.95
x[1] = 4.92
y1[1] (analytic) = 1.2061228105339584114335092408118
y1[1] (numeric) = 1.2061228105339584114335092408118
absolute error = 5e-63
relative error = 4.1455148317661511482865452331361e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.021473870058861492367198393658874
y2[1] (numeric) = 0.021473870058861492367198393658874
absolute error = 4.10e-63
relative error = 1.9092972010921141541419067077560e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1945
Order of pole (three term test) = -1.92
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1572374296, alloc=4783252, time=83.17
x[1] = 4.93
y1[1] (analytic) = 1.2158976026918544296742604464858
y1[1] (numeric) = 1.2158976026918544296742604464858
absolute error = 6e-63
relative error = 4.9346260628499513231470339245466e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.023583989709350284599819677250865
y2[1] (numeric) = 0.023583989709350284599819677250865
absolute error = 4.07e-63
relative error = 1.7257470216696954459786408332783e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2033
Order of pole (three term test) = -2.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.94
y1[1] (analytic) = 1.2256508052693953316674308040397
y1[1] (numeric) = 1.2256508052693953316674308040397
absolute error = 5e-63
relative error = 4.0794653571014552363451182351083e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.025791750147190845490291473176844
y2[1] (numeric) = 0.025791750147190845490291473176844
absolute error = 3.98e-63
relative error = 1.5431290925534531067644108467782e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.212
Order of pole (three term test) = -2.124
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1576375332, alloc=4783252, time=83.37
x[1] = 4.95
y1[1] (analytic) = 1.2353814429544510050452574116347
y1[1] (numeric) = 1.2353814429544510050452574116347
absolute error = 5e-63
relative error = 4.0473329339012517022132666369228e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.028096930598179185214734936622646
y2[1] (numeric) = 0.028096930598179185214734936622646
absolute error = 3.93e-63
relative error = 1.3987292975890692838040321072638e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2206
Order of pole (three term test) = -2.232
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1580376304, alloc=4783252, time=83.59
x[1] = 4.96
y1[1] (analytic) = 1.2450885426913617819484480229353
y1[1] (numeric) = 1.2450885426913617819484480229353
absolute error = 6e-63
relative error = 4.8189343924332514910852705673233e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.030499300546191182245066976903265
y2[1] (numeric) = 0.030499300546191182245066976903265
absolute error = 3.89e-63
relative error = 1.2754390855975847955817996880021e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2291
Order of pole (three term test) = -2.345
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1584377060, alloc=4783252, time=83.80
x[1] = 4.97
y1[1] (analytic) = 1.2547711337782431941159535140125
y1[1] (numeric) = 1.2547711337782431941159535140125
absolute error = 6e-63
relative error = 4.7817485105298774559121332554294e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.032998619756234003665023285922095
y2[1] (numeric) = 0.032998619756234003665023285922095
absolute error = 3.85e-63
relative error = 1.1667154652044709086317460394923e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2375
Order of pole (three term test) = -2.462
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1588377852, alloc=4783252, time=84.01
x[1] = 4.98
y1[1] (analytic) = 1.2644282479640553524162533206808
y1[1] (numeric) = 1.2644282479640553524162533206808
absolute error = 6e-63
relative error = 4.7452277419940759967034484307054e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.035594638298469404258289922071078
y2[1] (numeric) = 0.035594638298469404258289922071078
absolute error = 3.78e-63
relative error = 1.0619576938256295730934780517507e-59 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2459
Order of pole (three term test) = -2.583
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.99
y1[1] (analytic) = 1.2740589195454272439630915976969
y1[1] (numeric) = 1.2740589195454272439630915976969
absolute error = 6e-63
relative error = 4.7093583412459025053139247812776e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.038287096573206502058853985588893
y2[1] (numeric) = 0.038287096573206502058853985588893
absolute error = 3.76e-63
relative error = 9.8205409564309100392081362301257e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2541
Order of pole (three term test) = -2.709
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1592378788, alloc=4783252, time=84.22
x[1] = 5
y1[1] (analytic) = 1.2836621854632262644666391715136
y1[1] (numeric) = 1.2836621854632262644666391715136
absolute error = 6e-63
relative error = 4.6741269377151759276910596514521e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.041075725336861531106845593844006
y2[1] (numeric) = 0.041075725336861531106845593844006
absolute error = 3.68e-63
relative error = 8.9590627306526278299428380701732e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2623
Order of pole (three term test) = -2.838
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1596379472, alloc=4783252, time=84.43
x[1] = 5.01
y1[1] (analytic) = 1.2932370853988633289473205124347
y1[1] (numeric) = 1.2932370853988633289473205124347
absolute error = 7e-63
relative error = 5.4127739445710706367727333201472e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.043960245728881975456228627531302
y2[1] (numeric) = 0.043960245728881975456228627531302
absolute error = 3.58e-63
relative error = 8.1437215389538469842895933707646e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2703
Order of pole (three term test) = -2.972
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1600380344, alloc=4783252, time=84.64
x[1] = 5.02
y1[1] (analytic) = 1.3027826618703239303814883348922
y1[1] (numeric) = 1.3027826618703239303814883348922
absolute error = 7e-63
relative error = 5.3731141846411556934549832434758e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.046940369299632392043376182258299
y2[1] (numeric) = 0.046940369299632392043376182258299
absolute error = 3.51e-63
relative error = 7.4775721886523124357433967858729e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2782
Order of pole (three term test) = -3.109
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.03
y1[1] (analytic) = 1.3122979603279155432531068738344
y1[1] (numeric) = 1.3122979603279155432531068738344
absolute error = 7e-63
relative error = 5.3341544463353793881794638706536e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.050015798039239133857481976239102
y2[1] (numeric) = 0.050015798039239133857481976239102
absolute error = 3.47e-63
relative error = 6.9378079247634202729847259116013e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.286
Order of pole (three term test) = -3.251
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1604381156, alloc=4783252, time=84.85
TOP MAIN SOLVE Loop
x[1] = 5.04
y1[1] (analytic) = 1.3217820292497217973508779058945
y1[1] (numeric) = 1.3217820292497217973508779058945
absolute error = 7e-63
relative error = 5.2958807466715097405710614882499e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.053186224407391088964527862139932
y2[1] (numeric) = 0.053186224407391088964527862139932
absolute error = 3.39e-63
relative error = 6.3738308890542425653764657031193e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2937
Order of pole (three term test) = -3.396
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1608381932, alloc=4783252, time=85.07
x[1] = 5.05
y1[1] (analytic) = 1.3312339202367538764729746824182
y1[1] (numeric) = 1.3312339202367538764729746824182
absolute error = 7e-63
relative error = 5.2582794755974081178565771126887e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.056451331364093455335738912731992
y2[1] (numeric) = 0.056451331364093455335738912731992
absolute error = 3.29e-63
relative error = 5.8280290659232243716431474720186e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3013
Order of pole (three term test) = -3.545
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1612382740, alloc=4783252, time=85.28
x[1] = 5.06
y1[1] (analytic) = 1.3406526881077896269788058689017
y1[1] (numeric) = 1.3406526881077896269788058689017
absolute error = 7e-63
relative error = 5.2213373844644795811561300209267e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.059810792401371476128671295106488
y2[1] (numeric) = 0.059810792401371476128671295106488
absolute error = 3.23e-63
relative error = 5.4003631624280826420981184120770e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3088
Order of pole (three term test) = -3.698
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1616383932, alloc=4783252, time=85.49
x[1] = 5.07
y1[1] (analytic) = 1.3500373909938908923559866414642
y1[1] (numeric) = 1.3500373909938908923559866414642
absolute error = 7e-63
relative error = 5.1850415749201097328124828993135e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.063264271575920965073824515999517
y2[1] (numeric) = 0.063264271575920965073824515999517
absolute error = 3.16e-63
relative error = 4.9949203891612159572240923341416e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3161
Order of pole (three term test) = -3.855
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.08
y1[1] (analytic) = 1.359387090432589622147824426171
y1[1] (numeric) = 1.359387090432589622147824426171
absolute error = 8e-63
relative error = 5.8850051293735678001372513419147e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.06681142354270235694144805746205
y2[1] (numeric) = 0.06681142354270235694144805746205
absolute error = 3.05e-63
relative error = 4.5650875827403976892192282862871e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3233
Order of pole (three term test) = -4.015
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1620385344, alloc=4783252, time=85.70
x[1] = 5.09
y1[1] (analytic) = 1.3687008514617333367089146951106
y1[1] (numeric) = 1.3687008514617333367089146951106
absolute error = 8e-63
relative error = 5.8449587369338076779420585227312e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.070451893589474923711490670950491
y2[1] (numeric) = 0.070451893589474923711490670950491
absolute error = 3.04e-63
relative error = 4.3150011236236766815752794967820e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3304
Order of pole (three term test) = -4.179
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1624386020, alloc=4783252, time=85.91
x[1] = 5.1
y1[1] (analytic) = 1.377977742712980563320575552929
y1[1] (numeric) = 1.377977742712980563320575552929
absolute error = 8e-63
relative error = 5.8056090109623219276535122883397e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.074185317672267703053853752455137
y2[1] (numeric) = 0.074185317672267703053853752455137
absolute error = 2.96e-63
relative error = 3.9900078517915692981299841050271e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3374
Order of pole (three term test) = -4.346
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1628387188, alloc=4783252, time=86.12
x[1] = 5.11
y1[1] (analytic) = 1.3872168365049368942004221740824
y1[1] (numeric) = 1.3872168365049368942004221740824
absolute error = 8e-63
relative error = 5.7669426938010849423977607512655e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.078011322451783592055659781865728
y2[1] (numeric) = 0.078011322451783592055659781865728
absolute error = 2.89e-63
relative error = 3.7045904481188874129547850155333e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3442
Order of pole (three term test) = -4.517
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.12
bytes used=1632388204, alloc=4783252, time=86.34
y1[1] (analytic) = 1.3964172089359223528778932563282
y1[1] (numeric) = 1.3964172089359223528778932563282
absolute error = 8e-63
relative error = 5.7289468711833222874532638654495e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.081929525330732965816499743380584
y2[1] (numeric) = 0.081929525330732965816499743380584
absolute error = 2.74e-63
relative error = 3.3443376962568411695912389053311e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3509
Order of pole (three term test) = -4.691
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.13
y1[1] (analytic) = 1.4055779399763607922763978187695
y1[1] (numeric) = 1.4055779399763607922763978187695
absolute error = 9e-63
relative error = 6.4030600822828531780683678351675e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.085939534492093087580911247342328
y2[1] (numeric) = 0.085939534492093087580911247342328
absolute error = 2.68e-63
relative error = 3.1184716275680720849214502619976e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3574
Order of pole (three term test) = -4.869
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1636389240, alloc=4783252, time=86.55
x[1] = 5.14
y1[1] (analytic) = 1.4146981135607820856392650382033
y1[1] (numeric) = 1.4146981135607820856392650382033
absolute error = 8e-63
relative error = 5.6549167086001647999899973050705e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.090040948938289484498956841189151
y2[1] (numeric) = 0.090040948938289484498956841189151
absolute error = 2.60e-63
relative error = 2.8875750762932734805585171592380e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3638
Order of pole (three term test) = -5.05
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1640389952, alloc=4783252, time=86.76
x[1] = 5.15
y1[1] (analytic) = 1.4237768176794279101570727656681
y1[1] (numeric) = 1.4237768176794279101570727656681
absolute error = 8e-63
relative error = 5.6188581669976657149965207055302e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.094233358531295370909977489320687
y2[1] (numeric) = 0.094233358531295370909977489320687
absolute error = 2.50e-63
relative error = 2.6529883249037945129833813704004e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.37
Order of pole (three term test) = -5.234
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1644390888, alloc=4783252, time=86.97
x[1] = 5.16
y1[1] (analytic) = 1.4328131444694519627943298888998
y1[1] (numeric) = 1.4328131444694519627943298888998
absolute error = 8e-63
relative error = 5.5834216979927786904562622053152e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.098516344033645109240608921213243
y2[1] (numeric) = 0.098516344033645109240608921213243
absolute error = 2.45e-63
relative error = 2.4868969956531078631085726898717e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3761
Order of pole (three term test) = -5.421
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.17
y1[1] (analytic) = 1.4418061903057054883699297989835
y1[1] (numeric) = 1.4418061903057054883699297989835
absolute error = 8e-63
relative error = 5.5485959581736597779755008274587e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.10288947715035760720514881630516
y2[1] (numeric) = 0.10288947715035760720514881630516
absolute error = 2.3e-63
relative error = 2.2354083854842545660161394642357e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3821
Order of pole (three term test) = -5.611
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1648391620, alloc=4783252, time=87.18
x[1] = 5.18
y1[1] (analytic) = 1.4507550558910990414142212704052
y1[1] (numeric) = 1.4507550558910990414142212704052
absolute error = 8e-63
relative error = 5.5143698913984830304598651360916e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.10735232057176545900349083681378
y2[1] (numeric) = 0.10735232057176545900349083681378
absolute error = 2.3e-63
relative error = 2.1424781390379360541814991237059e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3879
Order of pole (three term test) = -5.804
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1652392460, alloc=4783252, time=87.40
x[1] = 5.19
y1[1] (analytic) = 1.4596588463465314457018122646263
y1[1] (numeric) = 1.4596588463465314457018122646263
absolute error = 8e-63
relative error = 5.4807327205419846212786624276761e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.1119044280172455476381965471094
y2[1] (numeric) = 0.1119044280172455476381965471094
absolute error = 2.2e-63
relative error = 1.9659633126054304664111804278891e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3935
Order of pole (three term test) = -6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1656393132, alloc=4783252, time=87.61
x[1] = 5.2
y1[1] (analytic) = 1.4685166713003769586390939266086
y1[1] (numeric) = 1.4685166713003769586390939266086
absolute error = 8e-63
relative error = 5.4476739395242754247140901894985e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.1165453442798467353269155595782
y2[1] (numeric) = 0.1165453442798467353269155595782
absolute error = 2.1e-63
relative error = 1.8018737796659770920518827868036e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.399
Order of pole (three term test) = -6.198
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1660394088, alloc=4783252, time=87.83
x[1] = 5.21
y1[1] (analytic) = 1.4773276449775216918646184103044
y1[1] (numeric) = 1.4773276449775216918646184103044
absolute error = 8e-63
relative error = 5.4151833056110746231605921027741e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.12127460527181017927830228300415
y2[1] (numeric) = 0.12127460527181017927830228300415
absolute error = 2.1e-63
relative error = 1.7316073676705151169434704763777e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4043
Order of pole (three term test) = -6.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.22
y1[1] (analytic) = 1.4860908862879403844944672651737
y1[1] (numeric) = 1.4860908862879403844944672651737
absolute error = 8e-63
relative error = 5.3832508319749864111682343079404e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.12609173807097772083778515183022
y2[1] (numeric) = 0.12609173807097772083778515183022
absolute error = 2.0e-63
relative error = 1.5861467456925601190180443830834e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4095
Order of pole (three term test) = -6.604
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1664395156, alloc=4783252, time=88.04
x[1] = 5.23
y1[1] (analytic) = 1.4948055189148046714090995785478
y1[1] (numeric) = 1.4948055189148046714090995785478
absolute error = 7e-63
relative error = 4.6828834329444028449714214630752e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.13099626096808370720294728808506
y2[1] (numeric) = 0.13099626096808370720294728808506
absolute error = 2.0e-63
relative error = 1.5267611344168712983129283111116e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4145
Order of pole (three term test) = -6.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1668396036, alloc=4783252, time=88.25
x[1] = 5.24
y1[1] (analytic) = 1.5034706714021140358282745011865
y1[1] (numeric) = 1.5034706714021140358282745011865
absolute error = 8e-63
relative error = 5.3210216548749307179724809089120e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.13598768351492551656575677797294
y2[1] (numeric) = 0.13598768351492551656575677797294
absolute error = 1.9e-63
relative error = 1.3971853559748761131294968029082e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4193
Order of pole (three term test) = -7.019
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1672396800, alloc=4783252, time=88.46
x[1] = 5.25
y1[1] (analytic) = 1.5120854772418406831518162141691
y1[1] (numeric) = 1.5120854772418406831518162141691
absolute error = 8e-63
relative error = 5.2907061938010347015161580161482e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.14106550657340796966927431057729
y2[1] (numeric) = 0.14106550657340796966927431057729
absolute error = 1.8e-63
relative error = 1.2760029320585980064909585016655e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.424
Order of pole (three term test) = -7.231
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.26
y1[1] (analytic) = 1.5206490749605796216514577467554
y1[1] (numeric) = 1.5206490749605796216514577467554
absolute error = 8e-63
relative error = 5.2609113645811984046680438443276e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.14622922236545672337855271464404
y2[1] (numeric) = 0.14622922236545672337855271464404
absolute error = 1.8e-63
relative error = 1.2309441101324002041731760755223e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4285
Order of pole (three term test) = -7.444
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1676397564, alloc=4783252, time=88.68
x[1] = 5.27
y1[1] (analytic) = 1.5291606082056952850779026207164
y1[1] (numeric) = 1.5291606082056952850779026207164
absolute error = 8e-63
relative error = 5.2316283568062451120406445640596e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.1514783145237956549679656594851
y2[1] (numeric) = 0.1514783145237956549679656594851
absolute error = 1.7e-63
relative error = 1.1222728516252059461805780832102e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4328
Order of pole (three term test) = -7.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1680398252, alloc=4783252, time=88.89
x[1] = 5.28
y1[1] (analytic) = 1.5376192258309560825926322278478
y1[1] (numeric) = 1.5376192258309560825926322278478
absolute error = 7e-63
relative error = 4.5524925042590298405176317144076e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.15681225814358315942885113299026
y2[1] (numeric) = 0.15681225814358315942885113299026
absolute error = 1.6e-63
relative error = 1.0203283971173862255520241458817e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.437
Order of pole (three term test) = -7.878
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1684399216, alloc=4783252, time=89.11
x[1] = 5.29
y1[1] (analytic) = 1.5460240819816483126408276469977
y1[1] (numeric) = 1.5460240819816483126408276469977
absolute error = 8e-63
relative error = 5.1745636392324721718838888355674e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.16223051983490219621076903672188
y2[1] (numeric) = 0.16223051983490219621076903672188
absolute error = 1.5e-63
relative error = 9.2461024074046683760418939074607e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4409
Order of pole (three term test) = -8.098
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1688400140, alloc=4783252, time=89.32
x[1] = 5.3
y1[1] (analytic) = 1.5543743361791609294449466335608
y1[1] (numeric) = 1.5543743361791609294449466335608
absolute error = 8e-63
relative error = 5.1467653664849885512427091842180e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.16773255777609883643544033214541
y2[1] (numeric) = 0.16773255777609883643544033214541
absolute error = 1.5e-63
relative error = 8.9428076450268232197087544497593e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4447
Order of pole (three term test) = -8.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.31
y1[1] (analytic) = 1.562669153405032703712793494195
y1[1] (numeric) = 1.562669153405032703712793494195
absolute error = 9e-63
relative error = 5.7593765003866203304702211155888e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.17331782176796397677309498526352
y2[1] (numeric) = 0.17331782176796397677309498526352
absolute error = 1.4e-63
relative error = 8.0776459438447411475357302681939e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4483
Order of pole (three term test) = -8.544
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1692401000, alloc=4783252, time=89.53
x[1] = 5.32
y1[1] (analytic) = 1.5709077041844533729140501068966
y1[1] (numeric) = 1.5709077041844533729140501068966
absolute error = 9e-63
relative error = 5.7291717241099194147717551956479e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.17898575328875280185499235258526
y2[1] (numeric) = 0.17898575328875280185499235258526
absolute error = 1.4e-63
relative error = 7.8218515958720939984423761520675e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4518
Order of pole (three term test) = -8.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1696402408, alloc=4783252, time=89.74
x[1] = 5.33
y1[1] (analytic) = 1.5790891646692104310798244932856
y1[1] (numeric) = 1.5790891646692104310798244932856
absolute error = 9e-63
relative error = 5.6994881615094428388477684422672e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.18473578555003649332172215557053
y2[1] (numeric) = 0.18473578555003649332172215557053
absolute error = 1.3e-63
relative error = 7.0370772838048171748751818277299e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.455
Order of pole (three term test) = -8.997
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1700403308, alloc=4783252, time=89.95
x[1] = 5.34
y1[1] (analytic) = 1.5872127167200732635153590826657
y1[1] (numeric) = 1.5872127167200732635153590826657
absolute error = 8e-63
relative error = 5.0402821976702381389472344773816e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.19056734355338060038292414918256
y2[1] (numeric) = 0.19056734355338060038292414918256
absolute error = 1.2e-63
relative error = 6.2969865540675025316741955618823e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4581
Order of pole (three term test) = -9.226
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.35
y1[1] (analytic) = 1.5952775479886063880810806137854
y1[1] (numeric) = 1.5952775479886063880810806137854
absolute error = 8e-63
relative error = 5.0148013491989148840094161317716e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.19647984414784440409860233060843
y2[1] (numeric) = 0.19647984414784440409860233060843
absolute error = 1.1e-63
relative error = 5.5985386428354828626950162273526e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.461
Order of pole (three term test) = -9.456
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1704404444, alloc=4783252, time=90.16
TOP MAIN SOLVE Loop
x[1] = 5.36
y1[1] (analytic) = 1.6032828519984036217860410431167
y1[1] (numeric) = 1.6032828519984036217860410431167
absolute error = 8e-63
relative error = 4.9897620934624488502287316235724e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.20247269608829552549352153390762
y2[1] (numeric) = 0.20247269608829552549352153390762
absolute error = 1.0e-63
relative error = 4.9389375422941664901002495347434e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4637
Order of pole (three term test) = -9.688
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1708405172, alloc=4783252, time=90.37
x[1] = 5.37
y1[1] (analytic) = 1.611227828225735049344785028739
y1[1] (numeric) = 1.611227828225735049344785028739
absolute error = 8e-63
relative error = 4.9651575400168609288069362046054e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.20854530009453394609247031570643
y2[1] (numeric) = 0.20854530009453394609247031570643
absolute error = 1.0e-63
relative error = 4.7951212496598977118055038187866e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4662
Order of pole (three term test) = -9.921
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1712406004, alloc=4783252, time=90.58
x[1] = 5.38
y1[1] (analytic) = 1.6191116821795987290679938861927
y1[1] (numeric) = 1.6191116821795987290679938861927
absolute error = 7e-63
relative error = 4.3233583433706152064099121223011e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.21469704891121952852360645852928
y2[1] (numeric) = 0.21469704891121952852360645852928
absolute error = 9e-64
relative error = 4.1919532875003027604319552805117e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4686
Order of pole (three term test) = -10.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1716407292, alloc=4783252, time=90.79
x[1] = 5.39
y1[1] (analytic) = 1.6269336254811691309830264844484
y1[1] (numeric) = 1.6269336254811691309830264844484
absolute error = 7e-63
relative error = 4.3025725760199558802560714011735e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.2209273273685970444877641912544
y2[1] (numeric) = 0.2209273273685970444877641912544
absolute error = 8e-64
relative error = 3.6211002483421761159820892099865e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.29
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4707
Order of pole (three term test) = -10.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.4
y1[1] (analytic) = 1.6346928759426343624067518389807
y1[1] (numeric) = 1.6346928759426343624067518389807
absolute error = 8e-63
relative error = 4.8938856452695159787001668441201e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.22723551244401263764153021726577
y2[1] (numeric) = 0.22723551244401263764153021726577
absolute error = 7e-64
relative error = 3.0805044179547830011600914928889e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4727
Order of pole (three term test) = -10.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1720408572, alloc=4783252, time=91.00
x[1] = 5.41
y1[1] (analytic) = 1.6423886576454142973138135876736
y1[1] (numeric) = 1.6423886576454142973138135876736
absolute error = 8e-63
relative error = 4.8709542426267599887882753699364e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.23362097332421556979906379088919
y2[1] (numeric) = 0.23362097332421556979906379088919
absolute error = 7e-64
relative error = 2.9963063248972549976533901079166e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.93
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4745
Order of pole (three term test) = -10.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1724409424, alloc=4783252, time=91.22
x[1] = 5.42
y1[1] (analytic) = 1.6500202010177517877525710803082
y1[1] (numeric) = 1.6500202010177517877525710803082
absolute error = 8e-63
relative error = 4.8484254890125019625653022030870e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.24008307146843902032995860887945
y2[1] (numeric) = 0.24008307146843902032995860887945
absolute error = 6e-64
relative error = 2.4991349716170019427292009938223e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.476
Order of pole (three term test) = -11.1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1728410224, alloc=4783252, time=91.43
x[1] = 5.43
y1[1] (analytic) = 1.6575867429116691982522346148438
y1[1] (numeric) = 1.6575867429116691982522346148438
absolute error = 8e-63
relative error = 4.8262934257952800047040834153507e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.24662116067225363072577388837689
y2[1] (numeric) = 0.24662116067225363072577388837689
absolute error = 5e-64
relative error = 2.0274010495979837393941000336111e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4774
Order of pole (three term test) = -11.34
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1732411176, alloc=4783252, time=91.64
x[1] = 5.44
y1[1] (analytic) = 1.6650875266792825676318843385363
y1[1] (numeric) = 1.6650875266792825676318843385363
absolute error = 9e-63
relative error = 5.4051212658765635051389286314872e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.25323458713218740903398908799371
y2[1] (numeric) = 0.25323458713218740903398908799371
absolute error = 4e-64
relative error = 1.5795630625732876344914303789767e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.92
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4786
Order of pole (three term test) = -11.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.45
y1[1] (analytic) = 1.6725218022484657668587868348645
y1[1] (numeric) = 1.6725218022484657668587868348645
absolute error = 8e-63
relative error = 4.7831962424915161001729517317491e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.25992268951110553222278861742014
y2[1] (numeric) = 0.25992268951110553222278861742014
absolute error = 3e-64
relative error = 1.1541893497804165841582450275957e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.27
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4796
Order of pole (three term test) = -11.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1736412044, alloc=4783252, time=91.85
x[1] = 5.46
y1[1] (analytic) = 1.6798888261978570866032768193071
y1[1] (numeric) = 1.6798888261978570866032768193071
absolute error = 9e-63
relative error = 5.3574973889016041202879373660478e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.2666847990043435085509230441066
y2[1] (numeric) = 0.2666847990043435085509230441066
absolute error = 3e-64
relative error = 1.1249235094015009273842421791853e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = -12.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1740412740, alloc=4783252, time=92.07
x[1] = 5.47
y1[1] (analytic) = 1.6871878618312007538939537370804
y1[1] (numeric) = 1.6871878618312007538939537370804
absolute error = 9e-63
relative error = 5.3343200265984542739545880696046e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.27352023940658708668152059583978
y2[1] (numeric) = 0.27352023940658708668152059583978
absolute error = 1e-64
relative error = 3.6560365776570659514864515040821e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.97
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -12.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1744413432, alloc=4783252, time=92.28
x[1] = 5.48
y1[1] (analytic) = 1.6944181792510159437834788005517
y1[1] (numeric) = 1.6944181792510159437834788005517
absolute error = 9e-63
relative error = 5.3115577430704102001745204237476e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.2804283271794922236046706498801
y2[1] (numeric) = 0.2804283271794922236046706498801
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -12.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.49
y1[1] (analytic) = 1.7015790554315859191851965250435
y1[1] (numeric) = 1.7015790554315859191851965250435
absolute error = 9e-63
relative error = 5.2892047367833013858510872596733e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.28740837152003834942833673574752
y2[1] (numeric) = 0.28740837152003834942833673574752
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1748414828, alloc=4783252, time=92.49
x[1] = 5.5
y1[1] (analytic) = 1.7086697742912600000274211813258
y1[1] (numeric) = 1.7086697742912600000274211813258
absolute error = 9e-63
relative error = 5.2672553441364142772753195631350e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.29445967442960809376808082447793
y2[1] (numeric) = 0.29445967442960809376808082447793
absolute error = 2e-64
relative error = 6.7921015122840155580297391494076e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1752415484, alloc=4783252, time=92.70
x[1] = 5.51
y1[1] (analytic) = 1.7156896267640611315887241762732
y1[1] (numeric) = 1.7156896267640611315887241762732
absolute error = 9e-63
relative error = 5.2457040362100793154261276957590e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.30158153078378656582052617869171
y2[1] (numeric) = 0.30158153078378656582052617869171
absolute error = 2e-64
relative error = 6.6317058435314591426290658952509e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -13.27
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1756416652, alloc=4783252, time=92.92
x[1] = 5.52
y1[1] (analytic) = 1.7226379108705918913170616076532
y1[1] (numeric) = 1.7226379108705918913170616076532
absolute error = 9e-63
relative error = 5.2245454156129381393618862668913e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.30877322840287320825071729003055
y2[1] (numeric) = 0.30877322840287320825071729003055
absolute error = 3e-64
relative error = 9.7158682296307664192552222317314e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.13
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -13.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1760417552, alloc=4783252, time=93.13
x[1] = 5.53
y1[1] (analytic) = 1.7295139317882318435911482223455
y1[1] (numeric) = 1.7295139317882318435911482223455
absolute error = 9e-63
relative error = 5.2037742134256445362621522520511e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.31603404812309917376674785034254
y2[1] (numeric) = 0.31603404812309917376674785034254
absolute error = 4e-64
relative error = 1.2656864106116662740272311512809e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4808
Order of pole (three term test) = -13.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.54
y1[1] (analytic) = 1.7363170019206192227470992412368
y1[1] (numeric) = 1.7363170019206192227470992412368
absolute error = 8e-63
relative error = 4.6074535877670011129417085277252e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.32336326386854310270334690980483
y2[1] (numeric) = 0.32336326386854310270334690980483
absolute error = 5e-64
relative error = 1.5462486184060321886931890583214e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4801
Order of pole (three term test) = -13.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1764418488, alloc=4783252, time=93.34
x[1] = 5.55
y1[1] (analytic) = 1.7430464409664099962599385961293
y1[1] (numeric) = 1.7430464409664099962599385961293
absolute error = 8e-63
relative error = 4.5896654340228028835948017608374e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.33076014272373811009659447825526
y2[1] (numeric) = 0.33076014272373811009659447825526
absolute error = 6e-64
relative error = 1.8140033289958397072027501648868e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.01
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4792
Order of pole (three term test) = -14.23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.11
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1768419188, alloc=4783252, time=93.55
x[1] = 5.56
y1[1] (analytic) = 1.7497015759873074322309544561574
y1[1] (numeric) = 1.7497015759873074322309544561574
absolute error = 8e-63
relative error = 4.5722082609920636336026433588662e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.33822394500696272161156471904958
y2[1] (numeric) = 0.33822394500696272161156471904958
absolute error = 7e-64
relative error = 2.0696346616901701327296812663913e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.478
Order of pole (three term test) = -14.47
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.77
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1772419944, alloc=4783252, time=93.76
x[1] = 5.57
y1[1] (analytic) = 1.7562817414753553682808444254304
y1[1] (numeric) = 1.7562817414753553682808444254304
absolute error = 8e-63
relative error = 4.5550778164325966804102749853966e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.3457539243442084292903795474788
y2[1] (numeric) = 0.3457539243442084292903795474788
absolute error = 7e-64
relative error = 2.0245612579168557734439019112515e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4767
Order of pole (three term test) = -14.71
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.58
y1[1] (analytic) = 1.7627862794194884525778386345335
y1[1] (numeric) = 1.7627862794194884525778386345335
absolute error = 8e-63
relative error = 4.5382699499082317064781797228823e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.35334932774381647042673725271193
y2[1] (numeric) = 0.35334932774381647042673725271193
absolute error = 9e-64
relative error = 2.5470545132960134431943269842401e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4753
Order of pole (three term test) = -14.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.11
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1776420732, alloc=4783252, time=93.98
TOP MAIN SOLVE Loop
x[1] = 5.59
y1[1] (analytic) = 1.7692145393713327020321562629051
y1[1] (numeric) = 1.7692145393713327020321562629051
absolute error = 8e-63
relative error = 4.5217806105316631630363649724701e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.36100939567177636595122579880666
y2[1] (numeric) = 0.36100939567177636595122579880666
absolute error = 1.0e-63
relative error = 2.7700110079937727698334594651288e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4736
Order of pole (three term test) = -15.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.78
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1780422096, alloc=4783252, time=94.19
x[1] = 5.6
y1[1] (analytic) = 1.7755658785102497976558096621573
y1[1] (numeric) = 1.7755658785102497976558096621573
absolute error = 8e-63
relative error = 4.5056058447756538433469429789379e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.36873336212767868853633084628333
y2[1] (numeric) = 0.36873336212767868853633084628333
absolute error = 1.1e-63
relative error = 2.9831854477521098141652387122011e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4717
Order of pole (three term test) = -15.42
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1784422940, alloc=4783252, time=94.40
x[1] = 5.61
y1[1] (analytic) = 1.7818396617076186127124234987124
y1[1] (numeric) = 1.7818396617076186127124234987124
absolute error = 8e-63
relative error = 4.4897417943504711000170809651842e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.37652045472131446520762175590142
y2[1] (numeric) = 0.37652045472131446520762175590142
absolute error = 1.2e-63
relative error = 3.1870778465095408802675875448385e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4697
Order of pole (three term test) = -15.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1788423852, alloc=4783252, time=94.61
x[1] = 5.62
y1[1] (analytic) = 1.788035261590347545557821695409
y1[1] (numeric) = 1.788035261590347545557821695409
absolute error = 8e-63
relative error = 4.4741846941455121826251410366109e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.38436989474991355458468707877178
y2[1] (numeric) = 0.38436989474991355458468707877178
absolute error = 1.2e-63
relative error = 3.1219926856674559628848674953839e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4674
Order of pole (three term test) = -15.89
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.63
y1[1] (analytic) = 1.7941520586036113059910248809931
y1[1] (numeric) = 1.7941520586036113059910248809931
absolute error = 8e-63
relative error = 4.4589308702331510599838303111051e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.39228089727601427497846053907225
y2[1] (numeric) = 0.39228089727601427497846053907225
absolute error = 1.3e-63
relative error = 3.3139518366230869164677701667194e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.465
Order of pole (three term test) = -16.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1792424676, alloc=4783252, time=94.83
x[1] = 5.64
y1[1] (analytic) = 1.8001894410728058814893037287734
y1[1] (numeric) = 1.8001894410728058814893037287734
absolute error = 8e-63
relative error = 4.4439767379329120041632517464525e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.4002526712059564964470189172122
y2[1] (numeric) = 0.4002526712059564964470189172122
absolute error = 1.4e-63
relative error = 3.4977905226261621091201372695354e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.99
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4624
Order of pole (three term test) = -16.36
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.24
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1796425432, alloc=4783252, time=95.05
x[1] = 5.65
y1[1] (analytic) = 1.8061468052647154878822936455404
y1[1] (numeric) = 1.8061468052647154878822936455404
absolute error = 9e-63
relative error = 4.9829836499259134431214573938373e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.40828441936899034756605694566804
y2[1] (numeric) = 0.40828441936899034756605694566804
absolute error = 1.5e-63
relative error = 3.6739094828018966430719846914341e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4596
Order of pole (three term test) = -16.59
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1800426336, alloc=4783252, time=95.26
x[1] = 5.66
y1[1] (analytic) = 1.8120235554478853878210756882658
y1[1] (numeric) = 1.8120235554478853878210756882658
absolute error = 9e-63
relative error = 4.9668228500348786147945786157444e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.4163753385969926261092858725629
y2[1] (numeric) = 0.4163753385969926261092858725629
absolute error = 1.6e-63
relative error = 3.8426867580373944746071341311487e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4566
Order of pole (three term test) = -16.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1804427140, alloc=4783252, time=95.47
x[1] = 5.67
y1[1] (analytic) = 1.8178191039521945398106873148475
y1[1] (numeric) = 1.8178191039521945398106873148475
absolute error = 9e-63
relative error = 4.9509876865265270337625526462421e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.42452461980478294206411777393379
y2[1] (numeric) = 0.42452461980478294206411777393379
absolute error = 1.7e-63
relative error = 4.0044791766888399627769509066227e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4534
Order of pole (three term test) = -17.05
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.68
y1[1] (analytic) = 1.8235328712276221205908034265397
y1[1] (numeric) = 1.8235328712276221205908034265397
absolute error = 9e-63
relative error = 4.9354745077565299487396007343170e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.43273144807103156143526394233455
y2[1] (numeric) = 0.43273144807103156143526394233455
absolute error = 1.8e-63
relative error = 4.1596237297376534360256574944563e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4501
Order of pole (three term test) = -17.27
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1808428292, alloc=4783252, time=95.68
x[1] = 5.69
y1[1] (analytic) = 1.8291642859022020442613215727059
y1[1] (numeric) = 1.8291642859022020442613215727059
absolute error = 9e-63
relative error = 4.9202797525433389647217008418441e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.44099500271975086011928997036201
y2[1] (numeric) = 0.44099500271975086011928997036201
absolute error = 1.9e-63
relative error = 4.3084388446175574475448434083369e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4465
Order of pole (three term test) = -17.5
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1812429452, alloc=4783252, time=95.90
x[1] = 5.7
y1[1] (analytic) = 1.8347127848391596827492340309974
y1[1] (numeric) = 1.8347127848391596827492340309974
absolute error = 9e-63
relative error = 4.9053999483570318522283780802707e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.44931445740236223877264939212753
y2[1] (numeric) = 0.44931445740236223877264939212753
absolute error = 2.0e-63
relative error = 4.4512255660827644278289609624904e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4428
Order of pole (three term test) = -17.72
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1816430408, alloc=4783252, time=96.11
x[1] = 5.71
y1[1] (analytic) = 1.840177813193225073992353850756
y1[1] (numeric) = 1.840177813193225073992353850756
absolute error = 9e-63
relative error = 4.8908317095631500699087658488398e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.45768898018033029205009794707004
y2[1] (numeric) = 0.45768898018033029205009794707004
absolute error = 2.1e-63
relative error = 4.5882686517219535721193701658978e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4389
Order of pole (three term test) = -17.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.72
y1[1] (analytic) = 1.8455588244661169865660040040995
y1[1] (numeric) = 1.8455588244661169865660040040995
absolute error = 9e-63
relative error = 4.8765717357199485708580535081230e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.46611773360835596886542620284383
y2[1] (numeric) = 0.46611773360835596886542620284383
absolute error = 2.2e-63
relative error = 4.7198375890338817695996894169664e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4349
Order of pole (three term test) = -18.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1820431212, alloc=4783252, time=96.32
x[1] = 5.73
y1[1] (analytic) = 1.8508552805611922923924435421742
y1[1] (numeric) = 1.8508552805611922923924435421742
absolute error = 9e-63
relative error = 4.8626168099275362714532359335984e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.47459987481812040442781186647779
y2[1] (numeric) = 0.47459987481812040442781186647779
absolute error = 2.3e-63
relative error = 4.8461875403600193318796332883392e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4306
Order of pole (three term test) = -18.38
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1824431936, alloc=4783252, time=96.54
x[1] = 5.74
y1[1] (analytic) = 1.8560666518372551826413008060802
y1[1] (numeric) = 1.8560666518372551826413008060802
absolute error = 9e-63
relative error = 4.8489637972274412306820134796954e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.48313455560257104974037444265051
y2[1] (numeric) = 0.48313455560257104974037444265051
absolute error = 2.4e-63
relative error = 4.9675602214101453015223923616058e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4262
Order of pole (three term test) = -18.59
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1828432868, alloc=4783252, time=96.75
x[1] = 5.75
y1[1] (analytic) = 1.8611924171615208459442645129289
y1[1] (numeric) = 1.8611924171615208459442645129289
absolute error = 9e-63
relative error = 4.8356096430511882102720436334727e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.49172092250074167001822059073657
y2[1] (numeric) = 0.49172092250074167001822059073657
absolute error = 2.4e-63
relative error = 4.8808173298673904690765438753185e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4217
Order of pole (three term test) = -18.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1832434012, alloc=4783252, time=96.96
x[1] = 5.76
y1[1] (analytic) = 1.8662320639617283126003474993147
y1[1] (numeric) = 1.8662320639617283126003474993147
absolute error = 9e-63
relative error = 4.8225513717165279497454290474614e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.50035811688309773009682147249262
y2[1] (numeric) = 0.50035811688309773009682147249262
absolute error = 2.5e-63
relative error = 4.9964213942872700561885479017481e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4169
Order of pole (three term test) = -19.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.77
y1[1] (analytic) = 1.8711850882773972535307298212406
y1[1] (numeric) = 1.8711850882773972535307298212406
absolute error = 9e-63
relative error = 4.8097860849700072801985681942338e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.50904527503739863236330217008544
y2[1] (numeric) = 0.50904527503739863236330217008544
absolute error = 2.6e-63
relative error = 5.1076006938852005244343743674315e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.412
Order of pole (three term test) = -19.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1836434888, alloc=4783252, time=97.17
x[1] = 5.78
y1[1] (analytic) = 1.8760509948102236083459995829373
y1[1] (numeric) = 1.8760509948102236083459995829373
absolute error = 9e-63
relative error = 4.7973109605746171967676377084859e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.51778152825506822105840167195699
y2[1] (numeric) = 0.51778152825506822105840167195699
absolute error = 2.7e-63
relative error = 5.2145545035162646033522258861685e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4069
Order of pole (three term test) = -19.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1840435628, alloc=4783252, time=97.39
x[1] = 5.79
y1[1] (analytic) = 1.8808292969736090030049809872269
y1[1] (numeric) = 1.8808292969736090030049809872269
absolute error = 1.0e-62
relative error = 5.3168036121570025438366731729951e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.52656600291806491597064841086205
y2[1] (numeric) = 0.52656600291806491597064841086205
absolute error = 2.8e-63
relative error = 5.3174720443083514428373241408589e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4017
Order of pole (three term test) = -19.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1844436296, alloc=4783252, time=97.60
x[1] = 5.8
y1[1] (analytic) = 1.8855195169413190041646581017615
y1[1] (numeric) = 1.8855195169413190041646581017615
absolute error = 9e-63
relative error = 4.7732202818031595689272627606328e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.53539782058624278858177347329741
y2[1] (numeric) = 0.53539782058624278858177347329741
absolute error = 2.9e-63
relative error = 5.4165330684846579119170936370433e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3963
Order of pole (three term test) = -19.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.81
y1[1] (analytic) = 1.8901211856952653444363077588889
y1[1] (numeric) = 1.8901211856952653444363077588889
absolute error = 9e-63
relative error = 4.7615994509311977886119438759723e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.54427609808519484462854759312049
y2[1] (numeric) = 0.54427609808519484462854759312049
absolute error = 3.0e-63
relative error = 5.5119084055945697982471115917976e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3907
Order of pole (three term test) = -20.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1848437060, alloc=4783252, time=97.81
x[1] = 5.82
y1[1] (analytic) = 1.8946338430724073403651343641758
y1[1] (numeric) = 1.8946338430724073403651343641758
absolute error = 9e-63
relative error = 4.7502582268905699240923222774744e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.55319994759456972882598823711744
y2[1] (numeric) = 0.55319994759456972882598823711744
absolute error = 3.1e-63
relative error = 5.6037604730070114326284084696085e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.385
Order of pole (three term test) = -20.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1852437848, alloc=4783252, time=98.03
x[1] = 5.83
y1[1] (analytic) = 1.8990570378107678130306930348074
y1[1] (numeric) = 1.8990570378107678130306930348074
absolute error = 1.0e-62
relative error = 5.2657712753735906559532738483371e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.56216847673685302015506147042438
y2[1] (numeric) = 0.56216847673685302015506147042438
absolute error = 3.2e-63
relative error = 5.6922437532866090465947427334198e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3792
Order of pole (three term test) = -20.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1856438748, alloc=4783252, time=98.25
x[1] = 5.84
y1[1] (analytic) = 1.903390327594558909714387498229
y1[1] (numeric) = 1.903390327594558909714387498229
absolute error = 1.0e-62
relative error = 5.2537831337189076868416007999943e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.57118078866660423965933399774091
y2[1] (numeric) = 0.57118078866660423965933399774091
absolute error = 3.3e-63
relative error = 5.7775052408602554604629525389552e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3731
Order of pole (three term test) = -20.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1860439876, alloc=4783252, time=98.46
x[1] = 5.85
y1[1] (analytic) = 1.90763327909841331408948072728
y1[1] (numeric) = 1.90763327909841331408948072728
absolute error = 1.0e-62
relative error = 5.2420976869968453689582750386638e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.58023598216014064712415964041523
y2[1] (numeric) = 0.58023598216014064712415964041523
absolute error = 3.4e-63
relative error = 5.8596848601878438392775816871964e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.367
Order of pole (three term test) = -20.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.86
y1[1] (analytic) = 1.9117854680307164218494585297175
y1[1] (numeric) = 1.9117854680307164218494585297175
absolute error = 1.0e-62
relative error = 5.2307124241825920347489552300374e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.5893331517056588583334685788649
y2[1] (numeric) = 0.5893331517056588583334685788649
absolute error = 3.5e-63
relative error = 5.9389158574742241443604220303983e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3607
Order of pole (three term test) = -20.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1864440896, alloc=4783252, time=98.67
x[1] = 5.87
y1[1] (analytic) = 1.9158464791760351485932932817607
y1[1] (numeric) = 1.9158464791760351485932932817607
absolute error = 1.0e-62
relative error = 5.2196249066369803600317103433371e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.59847138759378527081753477878537
y2[1] (numeric) = 0.59847138759378527081753477878537
absolute error = 3.5e-63
relative error = 5.8482328020260148240721031005191e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3542
Order of pole (three term test) = -21.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1868442068, alloc=4783252, time=98.89
x[1] = 5.88
y1[1] (analytic) = 1.9198159064366391271221765013287
y1[1] (numeric) = 1.9198159064366391271221765013287
absolute error = 1.0e-62
relative error = 5.2088327669713659551814502842531e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.60764977600854624312460526099845
y2[1] (numeric) = 0.60764977600854624312460526099845
absolute error = 3.6e-63
relative error = 5.9244652794035886871435866267666e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3476
Order of pole (three term test) = -21.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1872442724, alloc=4783252, time=99.10
x[1] = 5.89
y1[1] (analytic) = 1.9236933528731101420625914701266
y1[1] (numeric) = 1.9236933528731101420625914701266
absolute error = 1.0e-62
relative error = 5.1983337079501858764872704781611e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.6168673991187489306742722820455
y2[1] (numeric) = 0.6168673991187489306742722820455
absolute error = 3.7e-63
relative error = 5.9980475630350798709596898225998e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3409
Order of pole (three term test) = -21.5
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.9
y1[1] (analytic) = 1.9274784307440357409061046800325
y1[1] (numeric) = 1.9274784307440357409061046800325
absolute error = 9e-63
relative error = 4.6693129512872755098828793096911e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.62612333516976364018515353101662
y2[1] (numeric) = 0.62612333516976364018515353101662
absolute error = 3.8e-63
relative error = 6.0690918011699546116030294086530e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.334
Order of pole (three term test) = -21.67
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1876443576, alloc=4783252, time=99.31
TOP MAIN SOLVE Loop
x[1] = 5.91
y1[1] (analytic) = 1.9311707615447830521378500235795
y1[1] (numeric) = 1.9311707615447830521378500235795
absolute error = 9e-63
relative error = 4.6603853886026710736111836779499e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.63541665857569852451792261500197
y2[1] (numeric) = 0.63541665857569852451792261500197
absolute error = 3.9e-63
relative error = 6.1377049961861910925371552615308e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.327
Order of pole (three term test) = -21.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1880444532, alloc=4783252, time=99.53
x[1] = 5.92
y1[1] (analytic) = 1.9347699760453489331042042875189
y1[1] (numeric) = 1.9347699760453489331042042875189
absolute error = 1.0e-62
relative error = 5.1685730726708417380791825934553e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.64474644001195740054101751977893
y2[1] (numeric) = 0.64474644001195740054101751977893
absolute error = 4.0e-63
relative error = 6.2039892766617159069025310275776e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3198
Order of pole (three term test) = -21.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1884445844, alloc=4783252, time=99.74
x[1] = 5.93
y1[1] (analytic) = 1.938275714327282662636408866662
y1[1] (numeric) = 1.938275714327282662636408866662
absolute error = 9e-63
relative error = 4.6433022575034583927818949785062e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.65411174650817143431437173267238
y2[1] (numeric) = 0.65411174650817143431437173267238
absolute error = 4.2e-63
relative error = 6.4209212300814901570195760979300e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3126
Order of pole (three term test) = -22.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1888446528, alloc=4783252, time=99.96
x[1] = 5.94
y1[1] (analytic) = 1.9416876258196774861916441437897
y1[1] (numeric) = 1.9416876258196774861916441437897
absolute error = 9e-63
relative error = 4.6351430993956494707272123093800e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.66351164154149540050009246731935
y2[1] (numeric) = 0.66351164154149540050009246731935
absolute error = 4.2e-63
relative error = 6.3299567589234768673462725738835e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3052
Order of pole (three term test) = -22.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.95
y1[1] (analytic) = 1.9450053693342274143870352824965
y1[1] (numeric) = 1.9450053693342274143870352824965
absolute error = 9e-63
relative error = 4.6272365834551332186860877611477e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.67294518513025918645189154620177
y2[1] (numeric) = 0.67294518513025918645189154620177
absolute error = 4.3e-63
relative error = 6.3898220761735102908646296009876e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2977
Order of pole (three term test) = -22.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1892447548, alloc=4783252, time=100.17
x[1] = 5.96
y1[1] (analytic) = 1.9482286130993457692759499337911
y1[1] (numeric) = 1.9482286130993457692759499337911
absolute error = 9e-63
relative error = 4.6195810591665220379064899205795e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.68241143392796517591090265779117
y2[1] (numeric) = 0.68241143392796517591090265779117
absolute error = 4.5e-63
relative error = 6.5942623119574173571646469520339e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.29
Order of pole (three term test) = -22.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1896448412, alloc=4783252, time=100.38
x[1] = 5.97
y1[1] (analytic) = 1.9513570347933420665403922538039
y1[1] (numeric) = 1.9513570347933420665403922538039
absolute error = 9e-63
relative error = 4.6121749323814247761584805712246e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.69190944131762211264784629855594
y2[1] (numeric) = 0.69190944131762211264784629855594
absolute error = 4.5e-63
relative error = 6.5037412864760548230103622917305e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2823
Order of pole (three term test) = -22.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1900449500, alloc=4783252, time=100.59
x[1] = 5.98
y1[1] (analytic) = 1.9543903215766539159389213028699
y1[1] (numeric) = 1.9543903215766539159389213028699
absolute error = 9e-63
relative error = 4.6050166646033543815286248172595e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.70143825750640601074378947433419
y2[1] (numeric) = 0.70143825750640601074378947433419
absolute error = 4.6e-63
relative error = 6.5579542472531727778404164965030e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2744
Order of pole (three term test) = -22.89
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.99
y1[1] (analytic) = 1.9573281701231307168469088616542
y1[1] (numeric) = 1.9573281701231307168469088616542
absolute error = 1.0e-62
relative error = 5.1090053025553321059706116952282e-61 %
Correct digits = 64
bytes used=1904451032, alloc=4783252, time=100.81
h = 0.01
y2[1] (analytic) = 0.71099692962063864549735591405603
y2[1] (numeric) = 0.71099692962063864549735591405603
absolute error = 4.7e-63
relative error = 6.6104364227110574375803280524384e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2665
Order of pole (three term test) = -23.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6
y1[1] (analytic) = 1.9601702866503660205456522979229
y1[1] (numeric) = 1.9601702866503660205456522979229
absolute error = 1.0e-62
relative error = 5.1015975847121346886927851693976e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.72058450180107412718844455338811
y2[1] (numeric) = 0.72058450180107412718844455338811
absolute error = 4.8e-63
relative error = 6.6612590029380020737432868762754e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2584
Order of pole (three term test) = -23.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1908452440, alloc=4783252, time=101.02
x[1] = 6.01
y1[1] (analytic) = 1.9629163869490755260493904569901
y1[1] (numeric) = 1.9629163869490755260493904569901
absolute error = 1.0e-62
relative error = 5.0944605009604174857161493669980e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.73020001529848402912048512990378
y2[1] (numeric) = 0.73020001529848402912048512990378
absolute error = 4.9e-63
relative error = 6.7104901360444725091113199258718e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2502
Order of pole (three term test) = -23.28
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1912453492, alloc=4783252, time=101.23
x[1] = 6.02
y1[1] (analytic) = 1.9655661964115177716951214558362
y1[1] (numeric) = 1.9655661964115177716951214558362
absolute error = 1.0e-62
relative error = 5.0875925818508354309447609093762e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.73984250856953151150808067207442
y2[1] (numeric) = 0.73984250856953151150808067207442
absolute error = 5.0e-63
relative error = 6.7581950781219439503883411932527e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2419
Order of pole (three term test) = -23.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1916454416, alloc=4783252, time=101.45
x[1] = 6.03
y1[1] (analytic) = 1.9681194500589546804497472298303
y1[1] (numeric) = 1.9681194500589546804497472298303
absolute error = 9e-63
relative error = 4.5728931746141762605718830112174e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.74951101737292485387754295475596
y2[1] (numeric) = 0.74951101737292485387754295475596
absolute error = 5.1e-63
relative error = 6.8044363348730557406848920907736e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2335
Order of pole (three term test) = -23.52
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.04
y1[1] (analytic) = 1.9705758925681492129028978290782
y1[1] (numeric) = 1.9705758925681492129028978290782
absolute error = 9e-63
relative error = 4.5671927855926256372214647697052e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.75920457486584078070720854419957
y2[1] (numeric) = 0.75920457486584078070720854419957
absolute error = 5.1e-63
relative error = 6.7175569916727941234517124111960e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2251
Order of pole (three term test) = -23.64
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1920455088, alloc=4783252, time=101.65
x[1] = 6.05
y1[1] (analytic) = 1.9729352782968974782022174858561
y1[1] (numeric) = 1.9729352782968974782022174858561
absolute error = 9e-63
relative error = 4.5617309898625237988536344401480e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.76892221170060793805532390450696
y2[1] (numeric) = 0.76892221170060793805532390450696
absolute error = 5.2e-63
relative error = 6.7627126917029449750222267169733e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2165
Order of pole (three term test) = -23.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1924456132, alloc=4783252, time=101.86
x[1] = 6.06
y1[1] (analytic) = 1.9751973713085927497412956127139
y1[1] (numeric) = 1.9751973713085927497412956127139
absolute error = 9e-63
relative error = 4.5565066715522147568771463022637e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.77866295612164085290840607231132
y2[1] (numeric) = 0.77866295612164085290840607231132
absolute error = 5.3e-63
relative error = 6.8065392842086695544744595149413e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2079
Order of pole (three term test) = -23.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1928456852, alloc=4848776, time=102.06
x[1] = 6.07
y1[1] (analytic) = 1.9773619453958189292191438829885
y1[1] (numeric) = 1.9773619453958189292191438829885
absolute error = 8e-63
relative error = 4.0457944579279328498567918747431e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.78842583406261468193492209381295
y2[1] (numeric) = 0.78842583406261468193492209381295
absolute error = 5.5e-63
relative error = 6.9759256513190366034365564404297e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1991
Order of pole (three term test) = -23.96
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1932458216, alloc=4848776, time=102.28
x[1] = 6.08
y1[1] (analytic) = 1.9794287841029710997444746005297
y1[1] (numeric) = 1.9794287841029710997444746005297
absolute error = 9e-63
relative error = 4.5467662551338419247862174734445e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.79820986924387103225039054359125
y2[1] (numeric) = 0.79820986924387103225039054359125
absolute error = 5.6e-63
relative error = 7.0156987726859016050918948664997e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1903
Order of pole (three term test) = -24.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.09
y1[1] (analytic) = 1.9813976807479009059483203288902
y1[1] (numeric) = 1.9813976807479009059483203288902
absolute error = 8e-63
relative error = 4.0375539336355283080874425794074e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.80801408327004511369299986177423
y2[1] (numeric) = 0.80801408327004511369299986177423
absolute error = 5.6e-63
relative error = 6.9305722708900270778448182090005e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1814
Order of pole (three term test) = -24.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1936458948, alloc=4848776, time=102.48
x[1] = 6.1
y1[1] (analytic) = 1.983268438442584596585021274648
y1[1] (numeric) = 1.983268438442584596585021274648
absolute error = 8e-63
relative error = 4.0337454299843632191880307759244e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.81783749572790445997587163677534
y2[1] (numeric) = 0.81783749572790445997587163677534
absolute error = 5.8e-63
relative error = 7.0918734226507843175717253836919e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1725
Order of pole (three term test) = -24.24
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1940460308, alloc=4848776, time=102.69
x[1] = 6.11
y1[1] (analytic) = 1.9850408701128116628345436375483
y1[1] (numeric) = 1.9850408701128116628345436375483
absolute error = 8e-63
relative error = 4.0301437216984619491955348220709e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.82767912428438943492538560312259
y2[1] (numeric) = 0.82767912428438943492538560312259
absolute error = 5.8e-63
relative error = 7.0075465598032019394562349133227e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1635
Order of pole (three term test) = -24.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1944461176, alloc=4848776, time=102.90
x[1] = 6.12
y1[1] (analytic) = 1.9867147985168921034587058395238
y1[1] (numeric) = 1.9867147985168921034587058395238
absolute error = 8e-63
relative error = 4.0267480797808028985868540111585e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.83753798478484571983664267141119
y2[1] (numeric) = 0.83753798478484571983664267141119
absolute error = 5.9e-63
relative error = 7.0444566183056700322117985732006e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1544
Order of pole (three term test) = -24.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.13
y1[1] (analytic) = 1.9882900562633804461003863456359
y1[1] (numeric) = 1.9882900562633804461003863456359
absolute error = 7e-63
relative error = 3.5206130906046936210446328872211e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.84741309135143895877919057733864
y2[1] (numeric) = 0.84741309135143895877919057733864
absolute error = 6.0e-63
relative error = 7.0803720891676446914999105747519e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1452
Order of pole (three term test) = -24.48
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1948462064, alloc=4848776, time=103.11
x[1] = 6.14
y1[1] (analytic) = 1.9897664858278147523383531246708
y1[1] (numeric) = 1.9897664858278147523383531246708
absolute error = 7e-63
relative error = 3.5180007552935273588300234206111e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.85730345648174172047049350830549
y2[1] (numeric) = 0.85730345648174172047049350830549
absolute error = 6.1e-63
relative error = 7.1153334958353964689895348432235e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.136
Order of pole (three term test) = -24.55
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1952463144, alloc=4848776, time=103.31
x[1] = 6.15
y1[1] (analytic) = 1.9911439395684689326111583908272
y1[1] (numeric) = 1.9911439395684689326111583908272
absolute error = 7e-63
relative error = 3.5155670370656761238376259782825e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.86720809114748291810311388832781
y2[1] (numeric) = 0.86720809114748291810311388832781
absolute error = 6.1e-63
relative error = 7.0340672120903853991227061332791e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1267
Order of pole (three term test) = -24.61
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1956464004, alloc=4848776, time=103.52
x[1] = 6.16
y1[1] (analytic) = 1.9924222797411167957917331223665
y1[1] (numeric) = 1.9924222797411167957917331223665
absolute error = 6e-63
relative error = 3.0114098105646577195187701665902e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.87712600489344981226591451196916
y2[1] (numeric) = 0.87712600489344981226591451196916
absolute error = 6.1e-63
relative error = 6.9545310091917826386094931125835e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1174
Order of pole (three term test) = -24.67
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1960464716, alloc=4848776, time=103.73
x[1] = 6.17
y1[1] (analytic) = 1.9936013785128063570200272314103
y1[1] (numeric) = 1.9936013785128063570200272314103
absolute error = 6e-63
relative error = 3.0096287375542951952714783185829e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.88705620593653270684140696811863
y2[1] (numeric) = 0.88705620593653270684140696811863
absolute error = 6.1e-63
relative error = 6.8766781170983027269583856796076e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1081
Order of pole (three term test) = -24.73
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.18
y1[1] (analytic) = 1.9946811179746430263743906724648
y1[1] (numeric) = 1.9946811179746430263743906724648
absolute error = 6e-63
relative error = 3.0079995974957004463204338355044e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.89699770126490243349219359023036
y2[1] (numeric) = 0.89699770126490243349219359023036
absolute error = 6.2e-63
relative error = 6.9119463642516165021277204677058e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09866
Order of pole (three term test) = -24.78
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1964465536, alloc=4848776, time=103.94
x[1] = 6.19
y1[1] (analytic) = 1.9956613901535804000734809732792
y1[1] (numeric) = 1.9956613901535804000734809732792
absolute error = 6e-63
relative error = 3.0065220631132504591459373685639e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.90694949673731070707070191707552
y2[1] (numeric) = 0.90694949673731070707070191707552
absolute error = 6.3e-63
relative error = 6.9463625291858285921982225113784e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08922
Order of pole (three term test) = -24.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1968466196, alloc=4848776, time=104.15
x[1] = 6.2
y1[1] (analytic) = 1.9965420970232174751394026238693
y1[1] (numeric) = 1.9965420970232174751394026238693
absolute error = 6e-63
relative error = 3.0051958378167004110740042755987e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.91691059718250342199942071090163
y2[1] (numeric) = 0.91691059718250342199942071090163
absolute error = 6.3e-63
relative error = 6.8708988851898255912957367061879e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07974
Order of pole (three term test) = -24.87
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1972467064, alloc=4848776, time=104.35
x[1] = 6.21
y1[1] (analytic) = 1.9973231505136012078096096586582
y1[1] (numeric) = 1.9973231505136012078096096586582
absolute error = 6e-63
relative error = 3.0040206555745029856645479979420e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.92688000649873694837484364690016
y2[1] (numeric) = 0.92688000649873694837484364690016
absolute error = 6.3e-63
relative error = 6.7969963272787295334300116469397e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07022
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.22
y1[1] (analytic) = 1.9980044725200334354498990129263
y1[1] (numeric) = 1.9980044725200334354498990129263
absolute error = 6e-63
relative error = 3.0029962808002871814654061722655e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.93685672775338747624844024993293
y2[1] (numeric) = 0.93685672775338747624844024993293
absolute error = 6.4e-63
relative error = 6.8313540484972612189431217801980e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06068
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1976467784, alloc=4848776, time=104.56
TOP MAIN SOLVE Loop
x[1] = 6.23
y1[1] (analytic) = 1.9985859949108812812836424313629
y1[1] (numeric) = 1.9985859949108812812836424313629
absolute error = 6e-63
relative error = 3.0021225082524133825750103296523e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.9468397632826434472332334916325
y2[1] (numeric) = 0.9468397632826434472332334916325
absolute error = 6.4e-63
relative error = 6.7593274471400926889063407119755e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05112
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1980468768, alloc=4848776, time=104.77
x[1] = 6.24
y1[1] (analytic) = 1.9990676595343902609032926544429
y1[1] (numeric) = 1.9990676595343902609032926544429
absolute error = 6e-63
relative error = 3.0013991629465311250068495300833e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.95682811479127110427590013953252
y2[1] (numeric) = 0.95682811479127110427590013953252
absolute error = 6.5e-63
relative error = 6.7932786458913297610438690659816e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04153
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1984469472, alloc=4848776, time=104.98
x[1] = 6.25
y1[1] (analytic) = 1.999449418224499409259190301842
y1[1] (numeric) = 1.999449418224499409259190301842
absolute error = 6e-63
relative error = 3.0008261000810755759975112600967e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.96682078345244318312255432921071
y2[1] (numeric) = 0.96682078345244318312255432921071
absolute error = 6.5e-63
relative error = 6.7230660648284746163610135630738e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03193
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1988470184, alloc=4848776, time=105.19
x[1] = 6.26
y1[1] (analytic) = 1.999731232805657846617818495209
y1[1] (numeric) = 1.999731232805657846617818495209
absolute error = 6e-63
relative error = 3.0004032049756482549621539097585e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.97681677000762076269225808000719
y2[1] (numeric) = 0.97681677000762076269225808000719
absolute error = 6.6e-63
relative error = 6.7566407566369988142165396629654e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02232
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.27
y1[1] (analytic) = 1.999913075096642301836923186416
y1[1] (numeric) = 1.999913075096642301836923186416
absolute error = 6e-63
relative error = 3.0001303930222369754782557168545e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.9868150748664782862564560011288
y2[1] (numeric) = 0.9868150748664782862564560011288
absolute error = 6.6e-63
relative error = 6.6881831947014162526725730242359e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0127
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1992471436, alloc=4848776, time=105.39
x[1] = 6.28
y1[1] (analytic) = 1.9999949269133752112083529380473
y1[1] (numeric) = 1.9999949269133752112083529380473
absolute error = 6e-63
relative error = 3.0000076096492393880753075162014e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.99681469820686176100548681808265
y2[1] (numeric) = 0.99681469820686176100548681808265
absolute error = 6.7e-63
relative error = 6.7214097184285271736698264092353e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.003067
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1996472252, alloc=4848776, time=105.61
x[1] = 6.29
y1[1] (analytic) = 1.9999767800707431110610822800232
y1[1] (numeric) = 1.9999767800707431110610822800232
absolute error = 5e-63
relative error = 2.5000290252485532202083427808432e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0068146400747701402655132902638
y2[1] (numeric) = 1.0068146400747701402655132902638
absolute error = 6e-63
relative error = 5.9593889095160710568717386524102e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.006571
Order of pole (three term test) = -0.894
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2000473104, alloc=4848776, time=105.82
x[1] = 6.3
y1[1] (analytic) = 1.9998586363834151422866736621397
y1[1] (numeric) = 1.9998586363834151422866736621397
absolute error = 5e-63
relative error = 2.5001767170114089945631747089485e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0168139004843498903109663674941
y2[1] (numeric) = 1.0168139004843498903109663674941
absolute error = 7e-63
relative error = 6.8842489236876234568965976011603e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01621
Order of pole (three term test) = -0.8997
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.31
bytes used=2004475136, alloc=4848776, time=106.03
y1[1] (analytic) = 1.9996405076656615849374075411613
y1[1] (numeric) = 1.9996405076656615849374075411613
absolute error = 5e-63
relative error = 2.5004494462041555645401210370467e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0268114795178927423991508690108
y2[1] (numeric) = 1.0268114795178927423991508690108
absolute error = 7e-63
relative error = 6.8172202391880458465228237872211e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02584
Order of pole (three term test) = -0.9102
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.32
y1[1] (analytic) = 1.9993224157301724410434695687937
y1[1] (numeric) = 1.9993224157301724410434695687937
absolute error = 5e-63
relative error = 2.5008472673848105914906888150686e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0368063774258266303351404065955
y2[1] (numeric) = 1.0368063774258266303351404065955
absolute error = 7e-63
relative error = 6.7515016809402116452291008865434e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03547
Order of pole (three term test) = -0.9256
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2008475980, alloc=4848776, time=106.23
x[1] = 6.33
y1[1] (analytic) = 1.9989043923858761837899286507793
y1[1] (numeric) = 1.9989043923858761837899286507793
absolute error = 5e-63
relative error = 2.5013702601513823627474242584929e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0467975947266898145565305659031
y2[1] (numeric) = 1.0467975947266898145565305659031
absolute error = 7e-63
relative error = 6.6870616012712964308208614930798e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04508
Order of pole (three term test) = -0.9458
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2012476788, alloc=4848776, time=106.44
x[1] = 6.34
y1[1] (analytic) = 1.9983864794347588911767704763508
y1[1] (numeric) = 1.9983864794347588911767704763508
absolute error = 5e-63
relative error = 2.5020185291757196674626970221840e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0567841323070781954089533630368
y2[1] (numeric) = 1.0567841323070781954089533630368
absolute error = 7e-63
relative error = 6.6238693277104904147273338156042e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05467
Order of pole (three term test) = -0.9708
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2016478112, alloc=4848776, time=106.65
x[1] = 6.35
y1[1] (analytic) = 1.9977687286676840822459698015753
y1[1] (numeric) = 1.9977687286676840822459698015753
absolute error = 5e-63
relative error = 2.5027922042480412097301979604919e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0667649915215558209643145750232
y2[1] (numeric) = 1.0667649915215558209643145750232
absolute error = 7e-63
relative error = 6.5618951274504333632756547844822e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06424
Order of pole (three term test) = -1.001
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.36
y1[1] (analytic) = 1.9970512018592136738884953211603
y1[1] (numeric) = 1.9970512018592136738884953211603
absolute error = 5e-63
relative error = 2.5036914403321770813571703009514e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0767391742925185984142305994414
y2[1] (numeric) = 1.0767391742925185984142305994414
absolute error = 7e-63
relative error = 6.5011101733151062672912180478946e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07378
Order of pole (three term test) = -1.035
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2020478948, alloc=4848776, time=106.86
x[1] = 6.37
y1[1] (analytic) = 1.9962339707614305761312505732947
y1[1] (numeric) = 1.9962339707614305761312505732947
absolute error = 5e-63
relative error = 2.5047164176315626645094097957003e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0867056832100012227507449816142
y2[1] (numeric) = 1.0867056832100012227507449816142
absolute error = 7e-63
relative error = 6.4414865111617162273767268779834e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08329
Order of pole (three term test) = -1.075
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2024480156, alloc=4848776, time=107.07
x[1] = 6.38
y1[1] (analytic) = 1.9953171170967635436392743633319
y1[1] (numeric) = 1.9953171170967635436392743633319
absolute error = 5e-63
relative error = 2.5058673416660332274042564396660e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0966635216314173421246287010364
y2[1] (numeric) = 1.0966635216314173421246287010364
absolute error = 7e-63
relative error = 6.3829970286480104241396306789362e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09277
Order of pole (three term test) = -1.119
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2028481308, alloc=4848776, time=107.28
x[1] = 6.39
y1[1] (analytic) = 1.9943007325498150009420712157889
y1[1] (numeric) = 1.9943007325498150009420712157889
absolute error = 4e-63
relative error = 2.0057155546875803385153253431429e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1066116937812229859478449144211
y2[1] (numeric) = 1.1066116937812229859478449144211
absolute error = 7e-63
relative error = 6.3256154253001227138572185692237e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1022
Order of pole (three term test) = -1.168
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2032482008, alloc=4848776, time=107.49
x[1] = 6.4
y1[1] (analytic) = 1.9931849187581926585947390986722
y1[1] (numeric) = 1.9931849187581926585947390986722
absolute error = 5e-63
relative error = 2.5085479791383999116155245045140e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1165492048504932894804204887989
y2[1] (numeric) = 1.1165492048504932894804204887989
absolute error = 7e-63
relative error = 6.2693161838195073900482675298314e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1116
Order of pole (three term test) = -1.221
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.41
y1[1] (analytic) = 1.9919697873023458371046380129593
y1[1] (numeric) = 1.9919697873023458371046380129593
absolute error = 5e-63
relative error = 2.5100782310415074061751451971544e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1264750610964025573122459647381
y2[1] (numeric) = 1.1264750610964025573122459647381
absolute error = 7e-63
relative error = 6.2140745425707629782735628578234e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.121
Order of pole (three term test) = -1.28
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2036482664, alloc=4848776, time=107.70
x[1] = 6.42
y1[1] (analytic) = 1.9906554596944075149827370785494
y1[1] (numeric) = 1.9906554596944075149827370785494
absolute error = 5e-63
relative error = 2.5117355068403286097743053993064e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1363882699415977178163555462574
y2[1] (numeric) = 1.1363882699415977178163555462574
absolute error = 8e-63
relative error = 7.0398473933659515457662653983223e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1303
Order of pole (three term test) = -1.343
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2040483476, alloc=4848776, time=107.91
x[1] = 6.43
y1[1] (analytic) = 1.989242067366043216705536719677
y1[1] (numeric) = 1.989242067366043216705536719677
absolute error = 4e-63
relative error = 2.0108161121368214068188196306627e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1462878400734552313110527254404
y2[1] (numeric) = 1.1462878400734552313110527254404
absolute error = 8e-63
relative error = 6.9790498689119412429147823417842e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1395
Order of pole (three term test) = -1.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2044484188, alloc=4848776, time=108.11
x[1] = 6.44
y1[1] (analytic) = 1.9877297516553079556886438646254
y1[1] (numeric) = 1.9877297516553079556886438646254
absolute error = 4e-63
relative error = 2.0123459925419678751334884350700e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1561727815432115263227791436111
y2[1] (numeric) = 1.1561727815432115263227791436111
absolute error = 9e-63
relative error = 7.7843036470614477599605198470208e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1487
Order of pole (three term test) = -1.483
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.45
y1[1] (analytic) = 1.9861186637925125465667502912062
y1[1] (numeric) = 1.9861186637925125465667502912062
absolute error = 4e-63
relative error = 2.0139783553324864380900969747703e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1660421058649570509887088237076
y2[1] (numeric) = 1.1660421058649570509887088237076
absolute error = 9e-63
relative error = 7.7184176752553032459424329681034e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1579
Order of pole (three term test) = -1.559
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2048484924, alloc=4848776, time=108.32
x[1] = 6.46
y1[1] (analytic) = 1.9844089648851007001370080863308
y1[1] (numeric) = 1.9844089648851007001370080863308
absolute error = 4e-63
relative error = 2.0157135302155844036645593584617e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1758948261144840402764222822845
y2[1] (numeric) = 1.1758948261144840402764222822845
absolute error = 9e-63
relative error = 7.6537457263408081923137095252245e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.167
Order of pole (three term test) = -1.641
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2052485668, alloc=4848776, time=108.52
x[1] = 6.47
y1[1] (analytic) = 1.9826008259015384132437055032545
y1[1] (numeric) = 1.9826008259015384132437055032545
absolute error = 4e-63
relative error = 2.0175518681028993772327509655872e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1857299570279781143263114185045
y2[1] (numeric) = 1.1857299570279781143263114185045
absolute error = 1.0e-62
relative error = 8.4336234744923823479358954877477e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.176
Order of pole (three term test) = -1.727
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2056487120, alloc=4848776, time=108.73
x[1] = 6.48
y1[1] (analytic) = 1.9806944276542172646518292852309
y1[1] (numeric) = 1.9806944276542172646518292852309
absolute error = 4e-63
relative error = 2.0194937412618934624841830736464e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1955465151005438388391236641071
y2[1] (numeric) = 1.1955465151005438388391236641071
absolute error = 1.0e-62
relative error = 8.3643755167142230146165190715056e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1849
Order of pole (three term test) = -1.817
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2060487816, alloc=4848776, time=108.95
x[1] = 6.49
y1[1] (analytic) = 1.9786899607813733265656788933949
y1[1] (numeric) = 1.9786899607813733265656788933949
absolute error = 4e-63
relative error = 2.0215395434767470706373373855130e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.205343518684554395034710999914
y2[1] (numeric) = 1.205343518684554395034710999914
absolute error = 9e-63
relative error = 7.4667510634828027032727984579699e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1938
Order of pole (three term test) = -1.912
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.5
y1[1] (analytic) = 1.9765876257280234998863132539441
y1[1] (numeric) = 1.9765876257280234998863132539441
absolute error = 3e-63
relative error = 1.5177672676641541564757371626233e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2151199880878155242969457490747
y2[1] (numeric) = 1.2151199880878155242969457490747
absolute error = 9e-63
relative error = 7.4066759564731798877994636165576e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2026
Order of pole (three term test) = -2.012
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2064488616, alloc=4848776, time=109.15
x[1] = 6.51
y1[1] (analytic) = 1.9743876327259211795584179456101
y1[1] (numeric) = 1.9743876327259211795584179456101
absolute error = 3e-63
relative error = 1.5194584641203794369370887992056e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2248749456715339311921416700011
y2[1] (numeric) = 1.2248749456715339311921416700011
absolute error = 9e-63
relative error = 7.3476888655484561413259355771695e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2113
Order of pole (three term test) = -2.115
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2068489480, alloc=4848776, time=109.36
x[1] = 6.52
y1[1] (analytic) = 1.9720902017725332544233545841722
y1[1] (numeric) = 1.9720902017725332544233545841722
absolute error = 3e-63
relative error = 1.5212285915236390982241826836864e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2346074159480803481023185705953
y2[1] (numeric) = 1.2346074159480803481023185705953
absolute error = 1.0e-62
relative error = 8.0997407522623659020033995603057e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2199
Order of pole (three term test) = -2.223
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2072490208, alloc=4848776, time=109.57
x[1] = 6.53
y1[1] (analytic) = 1.9696955626090405438608879906796
y1[1] (numeric) = 1.9696955626090405438608879906796
absolute error = 3e-63
relative error = 1.5230780111146860266765184590499e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2443164256785374852483160662742
y2[1] (numeric) = 1.2443164256785374852483160662742
absolute error = 1.0e-62
relative error = 8.0365410225513222365951612934665e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2284
Order of pole (three term test) = -2.336
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.54
y1[1] (analytic) = 1.9672039546973638711575940623119
y1[1] (numeric) = 1.9672039546973638711575940623119
absolute error = 3e-63
relative error = 1.5250071009853791420927654474248e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2540010039700231113890438578016
y2[1] (numeric) = 1.2540010039700231113890438578016
absolute error = 1.0e-62
relative error = 7.9744752742152110406332444362640e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2369
Order of pole (three term test) = -2.453
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2076490904, alloc=4848776, time=109.78
TOP MAIN SOLVE Loop
x[1] = 6.55
y1[1] (analytic) = 1.9646156271962180709754666300476
y1[1] (numeric) = 1.9646156271962180709754666300476
absolute error = 3e-63
relative error = 1.5270162562441899052712697406268e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2636601823727785329699009008071
y2[1] (numeric) = 1.2636601823727785329699009008071
absolute error = 1.0e-62
relative error = 7.9135198999646960950638259948951e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2452
Order of pole (three term test) = -2.573
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2080491840, alloc=4848776, time=109.99
x[1] = 6.56
y1[1] (analytic) = 1.9619308389361963255000215151936
y1[1] (numeric) = 1.9619308389361963255000215151936
absolute error = 3e-63
relative error = 1.5291058891895845133967295878129e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2732929949770127629533554213434
y2[1] (numeric) = 1.2732929949770127629533554213434
absolute error = 1.0e-62
relative error = 7.8536519398510739147066435140732e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2535
Order of pole (three term test) = -2.698
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2084492672, alloc=4848776, time=110.20
x[1] = 6.57
y1[1] (analytic) = 1.9591498583938873208135199903714
y1[1] (numeric) = 1.9591498583938873208135199903714
absolute error = 3e-63
relative error = 1.5312764294914134280394257699717e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2828984785094926949955059244941
y2[1] (numeric) = 1.2828984785094926949955059244941
absolute error = 1.0e-62
relative error = 7.7948490605572153037144041365452e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2616
Order of pole (three term test) = -2.828
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2088493976, alloc=4848776, time=110.41
x[1] = 6.58
y1[1] (analytic) = 1.9562729636650278117561053581557
y1[1] (numeric) = 1.9562729636650278117561053581557
absolute error = 3e-63
relative error = 1.5335283243804463979453693537674e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2924756724298696240316970834387
y2[1] (numeric) = 1.2924756724298696240316970834387
absolute error = 1.0e-62
relative error = 7.7370895354648193566077120447095e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2697
Order of pole (three term test) = -2.961
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.59
y1[1] (analytic) = 1.9533004424366932799959937456649
y1[1] (numeric) = 1.9533004424366932799959937456649
absolute error = 3e-63
relative error = 1.5358620388461978183666020555377e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.302023619026732480699403780303
y2[1] (numeric) = 1.302023619026732480699403780303
absolute error = 1.0e-62
relative error = 7.6803522254650321611163746150942e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2776
Order of pole (three term test) = -3.098
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2092494916, alloc=4848776, time=110.62
x[1] = 6.6
y1[1] (analytic) = 1.9502325919585294662197377216682
y1[1] (numeric) = 1.9502325919585294662197377216682
absolute error = 3e-63
relative error = 1.5382780558431941189086031668030e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3115413635133781743549851055926
y2[1] (numeric) = 1.3115413635133781743549851055926
absolute error = 1.0e-62
relative error = 7.6246165604810500132304654335020e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2854
Order of pole (three term test) = -3.239
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2096495816, alloc=4848776, time=110.82
x[1] = 6.61
y1[1] (analytic) = 1.9470697190130276532653700665807
y1[1] (numeric) = 1.9470697190130276532653700665807
absolute error = 2e-63
relative error = 1.0271845843372279343612560788600e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.321027954123289467729814993965
y2[1] (numeric) = 1.321027954123289467729814993965
absolute error = 1.1e-62
relative error = 8.3268487738400933541536489389905e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2931
Order of pole (three term test) = -3.384
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2100497032, alloc=4848776, time=111.03
x[1] = 6.62
y1[1] (analytic) = 1.9438121398848466726453438661522
y1[1] (numeric) = 1.9438121398848466726453438661522
absolute error = 3e-63
relative error = 1.5433590203720627686267385638226e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3304824422053108355178885136054
y2[1] (numeric) = 1.3304824422053108355178885136054
absolute error = 1.0e-62
relative error = 7.5160706242952954807309474847693e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3007
Order of pole (three term test) = -3.533
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2104497836, alloc=4848776, time=111.24
x[1] = 6.63
y1[1] (analytic) = 1.9404601803291847022330517254913
y1[1] (numeric) = 1.9404601803291847022330517254913
absolute error = 2e-63
relative error = 1.0306833504105787979625170703049e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3399038823185127893883579996919
y2[1] (numeric) = 1.3399038823185127893883579996919
absolute error = 1.0e-62
relative error = 7.4632219011832584379584893433556e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3082
Order of pole (three term test) = -3.686
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.64
y1[1] (analytic) = 1.9370141755392040179067987040978
y1[1] (numeric) = 1.9370141755392040179067987040978
absolute error = 2e-63
relative error = 1.0325169661927036250377238268722e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3492913323267351830695511189999
y2[1] (numeric) = 1.3492913323267351830695511189999
absolute error = 1.1e-62
relative error = 8.1524276755202004447306656381132e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3155
Order of pole (three term test) = -3.842
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2108498580, alloc=4848776, time=111.45
x[1] = 6.65
y1[1] (analytic) = 1.9334744701125119566489186248007
y1[1] (numeric) = 1.9334744701125119566489186248007
absolute error = 2e-63
relative error = 1.0344072450481421753077588258766e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3586438534928000432527482887922
y2[1] (numeric) = 1.3586438534928000432527482887922
absolute error = 1.0e-62
relative error = 7.3602806020812677249436516226206e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3228
Order of pole (three term test) = -4.002
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2112500112, alloc=4848776, time=111.66
x[1] = 6.66
y1[1] (analytic) = 1.9298414180167014429757914073278
y1[1] (numeric) = 1.9298414180167014429757914073278
absolute error = 2e-63
relative error = 1.0363545840234896352567719961663e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3679605105723845051111395029691
y2[1] (numeric) = 1.3679605105723845051111395029691
absolute error = 1.0e-62
relative error = 7.3101525392833028173564651674616e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3299
Order of pole (three term test) = -4.166
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2116501292, alloc=4848776, time=111.87
x[1] = 6.67
y1[1] (analytic) = 1.9261153825539545246174022925197
y1[1] (numeric) = 1.9261153825539545246174022925197
absolute error = 2e-63
relative error = 1.0383593932716934794294502789363e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3772403719075444652186358553043
y2[1] (numeric) = 1.3772403719075444652186358553043
absolute error = 1.0e-62
relative error = 7.2608966480916594003181956896358e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3368
Order of pole (three term test) = -4.333
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.68
y1[1] (analytic) = 1.9222967363247124570633780459879
y1[1] (numeric) = 1.9222967363247124570633780459879
absolute error = 2e-63
relative error = 1.0404220962388202196621023177089e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3864825095198795995811799962591
y2[1] (numeric) = 1.3864825095198795995811799962591
absolute error = 1.0e-62
relative error = 7.2124963216902509805112433140572e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3437
Order of pole (three term test) = -4.503
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2120502204, alloc=4848776, time=112.08
x[1] = 6.69
y1[1] (analytic) = 1.9183858611904159699367707089691
y1[1] (numeric) = 1.9183858611904159699367707089691
absolute error = 2e-63
relative error = 1.0425431298575876747077686807610e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3956859992033304303563896485654
y2[1] (numeric) = 1.3956859992033304303563896485654
absolute error = 1.0e-62
relative error = 7.1649353835376194849895976534820e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3503
Order of pole (three term test) = -4.677
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2124503496, alloc=4848776, time=112.29
x[1] = 6.7
y1[1] (analytic) = 1.9143831482353194411379018434767
y1[1] (numeric) = 1.9143831482353194411379018434767
absolute error = 2e-63
relative error = 1.0447229447478172120317894418131e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4048499206165981616321928483868
y2[1] (numeric) = 1.4048499206165981616321928483868
absolute error = 1.1e-62
relative error = 7.8300178820325699761519871836835e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3569
Order of pole (three term test) = -4.855
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2128504276, alloc=4848776, time=112.50
x[1] = 6.71
y1[1] (analytic) = 1.9102889977273827973090314718501
y1[1] (numeric) = 1.9102889977273827973090314718501
absolute error = 1e-63
relative error = 5.2348100271198333448246358296598e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4139733573751780423578933216319
y2[1] (numeric) = 1.4139733573751780423578933216319
absolute error = 1.1e-62
relative error = 7.7794959449729602937871165062305e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3633
Order of pole (three term test) = -5.035
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2132505264, alloc=4848776, time=112.71
x[1] = 6.72
y1[1] (analytic) = 1.9061038190782450513972152694962
y1[1] (numeric) = 1.9061038190782450513972152694962
absolute error = 1e-63
relative error = 5.2463039525495555798932830348906e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4230553971429970531680671023396
y2[1] (numeric) = 1.4230553971429970531680671023396
absolute error = 1.1e-62
relative error = 7.7298466539561247361920025399857e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3696
Order of pole (three term test) = -5.219
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.73
y1[1] (analytic) = 1.9018280308022834799282384509219
y1[1] (numeric) = 1.9018280308022834799282384509219
absolute error = 2e-63
relative error = 1.0516197929611452897461600234911e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.432095131723646753406972487949
y2[1] (numeric) = 1.432095131723646753406972487949
absolute error = 1.1e-62
relative error = 7.6810539721342228558427655914439e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3757
Order of pole (three term test) = -5.406
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2136505968, alloc=4848776, time=112.92
x[1] = 6.74
y1[1] (analytic) = 1.8974620604747625340397817171234
y1[1] (numeric) = 1.8974620604747625340397817171234
absolute error = 1e-63
relative error = 5.2701976014729420370251442054659e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4410916571512021651447980095527
y2[1] (numeric) = 1.4410916571512021651447980095527
absolute error = 1.1e-62
relative error = 7.6331022703615988042248813827387e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3816
Order of pole (three term test) = -5.596
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2140507216, alloc=4848776, time=113.13
x[1] = 6.75
y1[1] (analytic) = 1.8930063446890766693478401565171
y1[1] (numeric) = 1.8930063446890766693478401565171
absolute error = 1e-63
relative error = 5.2826024741308959298644708035083e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4500440737806176123730289434098
y2[1] (numeric) = 1.4500440737806176123730289434098
absolute error = 1.1e-62
relative error = 7.5859763154097270539628014023094e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3874
Order of pole (three term test) = -5.788
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2144508364, alloc=4848776, time=113.34
x[1] = 6.76
y1[1] (analytic) = 1.8884613290130913703277776011807
y1[1] (numeric) = 1.8884613290130913703277776011807
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4589514863776904758703424419645
y2[1] (numeric) = 1.4589514863776904758703424419645
absolute error = 1.1e-62
relative error = 7.5396612585871424591996591888787e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3931
Order of pole (three term test) = -5.984
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.77
y1[1] (analytic) = 1.883827467944586735071195974561
y1[1] (numeric) = 1.883827467944586735071195974561
absolute error = 1e-63
relative error = 5.3083417511216332618988728679588e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4678130042085838674385142406797
y2[1] (numeric) = 1.4678130042085838674385142406797
absolute error = 1.1e-62
relative error = 7.4941426247487058972766102827517e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3986
Order of pole (three term test) = -6.182
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2148509216, alloc=4848776, time=113.55
x[1] = 6.78
y1[1] (analytic) = 1.8791052248658080760230137214455
y1[1] (numeric) = 1.8791052248658080760230137214455
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4766277411288992713155153298713
y2[1] (numeric) = 1.4766277411288992713155153298713
absolute error = 1.1e-62
relative error = 7.4494063016792374862882508487033e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4039
Order of pole (three term test) = -6.384
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2152510080, alloc=4848776, time=113.76
x[1] = 6.79
y1[1] (analytic) = 1.8742950719971280816008052392169
y1[1] (numeric) = 1.8742950719971280816008052392169
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4853948156722902455758842356298
y2[1] (numeric) = 1.4853948156722902455758842356298
absolute error = 1.2e-62
relative error = 8.0786602143678517825972829604160e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4091
Order of pole (three term test) = -6.587
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2156510816, alloc=4848776, time=113.97
x[1] = 6.8
y1[1] (analytic) = 1.8693974903498251724416246398463
y1[1] (numeric) = 1.8693974903498251724416246398463
absolute error = 1e-63
relative error = 5.3493171204208015791782507038975e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4941133511386083222220793776203
y2[1] (numeric) = 1.4941133511386083222220793776203
absolute error = 1.2e-62
relative error = 8.0315191553942312673814756509545e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4141
Order of pole (three term test) = -6.794
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2160511936, alloc=4848776, time=114.18
x[1] = 6.81
y1[1] (analytic) = 1.864412969677982774401337921625
y1[1] (numeric) = 1.864412969677982774401337921625
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.502782475681572291450257040417
y2[1] (numeric) = 1.502782475681572291450257040417
absolute error = 1.2e-62
relative error = 7.9851876064481769960838295596651e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4189
Order of pole (three term test) = -7.003
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.82
y1[1] (analytic) = 1.8593420084295143183390798118649
y1[1] (numeric) = 1.8593420084295143183390798118649
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5114013223959521032351058739392
y2[1] (numeric) = 1.5114013223959521032351058739392
absolute error = 1.2e-62
relative error = 7.9396516479004894181637661295472e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4236
Order of pole (three term test) = -7.214
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2164512624, alloc=4848776, time=114.38
x[1] = 6.83
y1[1] (analytic) = 1.8541851136963188641460444707435
y1[1] (numeric) = 1.8541851136963188641460444707435
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.519969029404258667916232448682
y2[1] (numeric) = 1.519969029404258667916232448682
absolute error = 1.2e-62
relative error = 7.8948977037402642833395774351649e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4281
Order of pole (three term test) = -7.427
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2168513580, alloc=4848776, time=114.59
x[1] = 6.84
y1[1] (analytic) = 1.8489428011635723334146703357036
y1[1] (numeric) = 1.8489428011635723334146703357036
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.52848473994293088687828048687
y2[1] (numeric) = 1.52848473994293088687828048687
absolute error = 1.3e-62
relative error = 8.5051552431497495138152958505930e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4325
Order of pole (three term test) = -7.643
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2172514396, alloc=4848776, time=114.80
x[1] = 6.85
y1[1] (analytic) = 1.8436155950581594215826950226731
y1[1] (numeric) = 1.8436155950581594215826950226731
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5369476024480112946935380437703
y2[1] (numeric) = 1.5369476024480112946935380437703
absolute error = 1.3e-62
relative error = 8.4583234843490621125547120716719e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4366
Order of pole (three term test) = -7.861
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.86
y1[1] (analytic) = 1.8382040280962513463178926153105
y1[1] (numeric) = 1.8382040280962513463178926153105
absolute error = 1e-63
relative error = 5.4400925289868768419384095953337e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5453567706403017452342145089099
y2[1] (numeric) = 1.5453567706403017452342145089099
absolute error = 1.3e-62
relative error = 8.4122969187326183593883626526185e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4406
Order of pole (three term test) = -8.081
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2176515160, alloc=4848776, time=115.00
TOP MAIN SOLVE Loop
x[1] = 6.87
y1[1] (analytic) = 1.8327086414300346743249698044871
y1[1] (numeric) = 1.8327086414300346743249698044871
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.553711403609990626256739034717
y2[1] (numeric) = 1.553711403609990626256739034717
absolute error = 1.3e-62
relative error = 8.3670622290568144018239704670302e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4444
Order of pole (three term test) = -8.302
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2180516092, alloc=4848776, time=115.21
x[1] = 6.88
y1[1] (analytic) = 1.8271299845935965536475476920373
y1[1] (numeric) = 1.8271299845935965536475476920373
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5620106659007431398071444064856
y2[1] (numeric) = 1.5620106659007431398071444064856
absolute error = 1.4e-62
relative error = 8.9628069165115547764433424990882e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4481
Order of pole (three term test) = -8.526
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2184516760, alloc=4848776, time=115.42
x[1] = 6.89
y1[1] (analytic) = 1.8214686154479717628969035711689
y1[1] (numeric) = 1.8214686154479717628969035711689
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5702537275932462394895708153654
y2[1] (numeric) = 1.5702537275932462394895708153654
absolute error = 1.4e-62
relative error = 8.9157565774150593296086534259459e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4515
Order of pole (three term test) = -8.752
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2188517684, alloc=4848776, time=115.63
x[1] = 6.9
y1[1] (analytic) = 1.8157251001253570726567558363581
y1[1] (numeric) = 1.8157251001253570726567558363581
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5784397643881998701737832329889
y2[1] (numeric) = 1.5784397643881998701737832329889
absolute error = 1.4e-62
relative error = 8.8695180619872259121777506331035e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4548
Order of pole (three term test) = -8.979
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.91
y1[1] (analytic) = 1.8099000129724984975814636670357
y1[1] (numeric) = 1.8099000129724984975814636670357
absolute error = 1e-63
relative error = 5.5251670967041152213488743667067e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5865679576887462110868907718869
y2[1] (numeric) = 1.5865679576887462110868907718869
absolute error = 1.3e-62
relative error = 8.1937870590415309948380280778790e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4579
Order of pole (three term test) = -9.207
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2192518380, alloc=4848776, time=115.84
x[1] = 6.92
y1[1] (analytic) = 1.8039939364932571004152545324359
y1[1] (numeric) = 1.8039939364932571004152545324359
absolute error = 1e-63
relative error = 5.5432558822446893616743182364585e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5946374946823286794336496667012
y2[1] (numeric) = 1.5946374946823286794336496667012
absolute error = 1.3e-62
relative error = 8.1523230473078517623353504494812e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.05
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4608
Order of pole (three term test) = -9.438
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2196519584, alloc=4848776, time=116.05
x[1] = 6.93
y1[1] (analytic) = 1.7980074612903590913042159244115
y1[1] (numeric) = 1.7980074612903590913042159244115
absolute error = 2e-63
relative error = 1.1123424363126273261738972590534e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6026475684219725087132034548561
y2[1] (numeric) = 1.6026475684219725087132034548561
absolute error = 1.3e-62
relative error = 8.1115775271791616266531319419481e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4635
Order of pole (three term test) = -9.669
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2200520980, alloc=4848776, time=116.26
x[1] = 6.94
y1[1] (analytic) = 1.7919411860063360473425786969406
y1[1] (numeric) = 1.7919411860063360473425786969406
absolute error = 2e-63
relative error = 1.1161080595827815782426298062847e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6105973779069787737421622721598
y2[1] (numeric) = 1.6105973779069787737421622721598
absolute error = 1.3e-62
relative error = 8.0715392799744297619311820667991e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.466
Order of pole (three term test) = -9.902
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.95
y1[1] (analytic) = 1.7857957172636611582821210643353
y1[1] (numeric) = 1.7857957172636611582821210643353
absolute error = 2e-63
relative error = 1.1199489284611790612246748864688e-61 %
Correct digits = 64
bytes used=2204521892, alloc=4848776, time=116.47
h = 0.01
y2[1] (analytic) = 1.6184861281630237930487637521055
y2[1] (numeric) = 1.6184861281630237930487637521055
absolute error = 1.3e-62
relative error = 8.0321973563993133714665554617829e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4684
Order of pole (three term test) = -10.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.96
y1[1] (analytic) = 1.7795716696040874847302360221301
y1[1] (numeric) = 1.7795716696040874847302360221301
absolute error = 2e-63
relative error = 1.1238659471607303087525777448871e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6263130303216558987646253922822
y2[1] (numeric) = 1.6263130303216558987646253922822
absolute error = 1.3e-62
relative error = 7.9935410696603902650441422941521e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.07
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.26
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4706
Order of pole (three term test) = -10.37
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2208523180, alloc=4848776, time=116.67
x[1] = 6.97
y1[1] (analytic) = 1.7732696654271942949602911009115
y1[1] (numeric) = 1.7732696654271942949602911009115
absolute error = 2e-63
relative error = 1.1278600423800655408953628380105e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6340773016991816244033463000763
y2[1] (numeric) = 1.6340773016991816244033463000763
absolute error = 1.2e-62
relative error = 7.3435938358129693724433464307539e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4725
Order of pole (three term test) = -10.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2212524552, alloc=4848776, time=116.88
x[1] = 6.98
y1[1] (analytic) = 1.7668903349281476256493882018266
y1[1] (numeric) = 1.7668903349281476256493882018266
absolute error = 2e-63
relative error = 1.1319321637929113543837152159994e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6417781658749334219729187281771
y2[1] (numeric) = 1.6417781658749334219729187281771
absolute error = 1.2e-62
relative error = 7.3091482451315107569235661529435e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4743
Order of pole (three term test) = -10.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2216525780, alloc=4848776, time=117.09
x[1] = 6.99
y1[1] (analytic) = 1.7604343160346812904355837112889
y1[1] (numeric) = 1.7604343160346812904355837112889
absolute error = 2e-63
relative error = 1.1360832845527189585012697855709e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6494148527689110817154610389165
y2[1] (numeric) = 1.6494148527689110817154610389165
absolute error = 1.2e-62
relative error = 7.2753073490609841776913230842010e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4759
Order of pole (three term test) = -11.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7
y1[1] (analytic) = 1.7539022543433046381411975217192
y1[1] (numeric) = 1.7539022543433046381411975217192
absolute error = 2e-63
relative error = 1.1403144018130241692011552807951e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6569865987187890903969990915936
y2[1] (numeric) = 1.6569865987187890903969990915936
absolute error = 1.2e-62
relative error = 7.2420621924634810498815377179356e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4773
Order of pole (three term test) = -11.32
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2220526972, alloc=4848776, time=117.30
x[1] = 7.01
y1[1] (analytic) = 1.7472948030547434398332286031403
y1[1] (numeric) = 1.7472948030547434398332286031403
absolute error = 2e-63
relative error = 1.1446265372640378682713734056146e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6644926465562822274756396593097
y2[1] (numeric) = 1.6644926465562822274756396593097
absolute error = 1.2e-62
relative error = 7.2094040336117752156236203348513e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.78
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.89
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4785
Order of pole (three term test) = -11.56
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2224527712, alloc=4848776, time=117.50
x[1] = 7.02
y1[1] (analytic) = 1.7406126229086203605783720026158
y1[1] (numeric) = 1.7406126229086203605783720026158
absolute error = 2e-63
relative error = 1.1490207376859848848158780167122e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6719322456828617626521568426536
y2[1] (numeric) = 1.6719322456828617626521568426536
absolute error = 1.2e-62
relative error = 7.1773243389410673461737538043872e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.24
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4796
Order of pole (three term test) = -11.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2228529388, alloc=4848776, time=117.71
x[1] = 7.03
y1[1] (analytic) = 1.7338563821173815477910290110704
y1[1] (numeric) = 1.7338563821173815477910290110704
absolute error = 2e-63
relative error = 1.1534980755197292981567840744097e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6793046521448146832463330425656
y2[1] (numeric) = 1.6793046521448146832463330425656
absolute error = 1.1e-62
relative error = 6.5503302131336059712327716718662e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4804
Order of pole (three term test) = -12.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2232530260, alloc=4848776, time=117.92
x[1] = 7.04
y1[1] (analytic) = 1.7270267562994759434604147036375
y1[1] (numeric) = 1.7270267562994759434604147036375
absolute error = 2e-63
relative error = 1.1580596494552450314764859193670e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6866091287076384455388660059318
y2[1] (numeric) = 1.6866091287076384455388660059318
absolute error = 1.1e-62
relative error = 6.5219616168144023110097309325955e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.94
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.481
Order of pole (three term test) = -12.28
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.05
y1[1] (analytic) = 1.7201244284117940022698564219134
y1[1] (numeric) = 1.7201244284117940022698564219134
absolute error = 2e-63
relative error = 1.1627065850385123429463172761815e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6938449449297638106657031726717
y2[1] (numeric) = 1.6938449449297638106657031726717
absolute error = 1.2e-62
relative error = 7.0844737211159469130807306725239e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.27
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.31
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4815
Order of pole (three term test) = -12.52
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2236530916, alloc=4848776, time=118.12
x[1] = 7.06
y1[1] (analytic) = 1.7131500886813725716801703877066
y1[1] (numeric) = 1.7131500886813725716801703877066
absolute error = 2e-63
relative error = 1.1674400352974434665335592324637e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7010113772355983928426493826761
y2[1] (numeric) = 1.7010113772355983928426493826761
absolute error = 1.2e-62
relative error = 7.0546265360681013987111319669571e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4817
Order of pole (three term test) = -12.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2240531668, alloc=4848776, time=118.33
x[1] = 7.07
y1[1] (analytic) = 1.7061044345363727634321957003992
y1[1] (numeric) = 1.7061044345363727634321957003992
absolute error = 2e-63
relative error = 1.1722611813874642510160168681551e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7081077089878836156262949024486
y2[1] (numeric) = 1.7081077089878836156262949024486
absolute error = 1.2e-62
relative error = 7.0253180972471809471903702836896e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -13.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2244533348, alloc=4848776, time=118.54
x[1] = 7.08
y1[1] (analytic) = 1.6989881705363377186238172158325
y1[1] (numeric) = 1.6989881705363377186238172158325
absolute error = 3e-63
relative error = 1.7657568498861048570383562112350e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7151332305593578405759349412061
y2[1] (numeric) = 1.7151332305593578405759349412061
absolute error = 1.2e-62
relative error = 6.9965410186160464772325447935919e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.57
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4817
Order of pole (three term test) = -13.25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.09
y1[1] (analytic) = 1.6918020083017372405268512690559
y1[1] (numeric) = 1.6918020083017372405268512690559
absolute error = 2e-63
relative error = 1.1821714303363652555616451058383e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7220872394037185020633335393084
y2[1] (numeric) = 1.7220872394037185020633335393084
absolute error = 1.2e-62
relative error = 6.9682880898386200575199689642326e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4814
Order of pole (three term test) = -13.49
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2248534184, alloc=4848776, time=118.75
TOP MAIN SOLVE Loop
x[1] = 7.1
y1[1] (analytic) = 1.6845466664428063406217999420893
y1[1] (numeric) = 1.6845466664428063406217999420893
absolute error = 2e-63
relative error = 1.1872630422422933321748562384215e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7289690401258761520759857678532
y2[1] (numeric) = 1.7289690401258761520759857678532
absolute error = 1.2e-62
relative error = 6.9405522721947351854801789547746e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4808
Order of pole (three term test) = -13.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2252535700, alloc=4848776, time=118.95
x[1] = 7.11
y1[1] (analytic) = 1.6772228704876848139365693873049
y1[1] (numeric) = 1.6772228704876848139365693873049
absolute error = 2e-63
relative error = 1.1924473695129506113101862710630e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.735777944551493389667942755402
y2[1] (numeric) = 1.735777944551493389667942755402
absolute error = 1.2e-62
relative error = 6.9133266946197272496868943228237e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4801
Order of pole (three term test) = -13.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2256536916, alloc=4848776, time=119.16
x[1] = 7.12
y1[1] (analytic) = 1.6698313528098650296717348469898
y1[1] (numeric) = 1.6698313528098650296717348469898
absolute error = 2e-63
relative error = 1.1977257443600830202313872106256e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7425132717958017212232033740469
y2[1] (numeric) = 1.7425132717958017212232033740469
absolute error = 1.1e-62
relative error = 6.3127209290426837839940289048506e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.14
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4792
Order of pole (three term test) = -14.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2260538476, alloc=4848776, time=119.37
x[1] = 7.13
y1[1] (analytic) = 1.6623728525549551922728298696433
y1[1] (numeric) = 1.6623728525549551922728298696433
absolute error = 2e-63
relative error = 1.2030995314475537815160201286274e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7491743483316894699029934380455
y2[1] (numeric) = 1.7491743483316894699029934380455
absolute error = 1.1e-62
relative error = 6.2886812915427631437111086434975e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4781
Order of pole (three term test) = -14.45
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.14
y1[1] (analytic) = 1.6548481155667653965625220817479
y1[1] (numeric) = 1.6548481155667653965625220817479
absolute error = 2e-63
relative error = 1.2085701286942725083485817634342e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7557605080570539255427274225094
y2[1] (numeric) = 1.7557605080570539255427274225094
absolute error = 1.1e-62
relative error = 6.2650913661184546609468979226744e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4769
Order of pole (three term test) = -14.69
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2264539236, alloc=4848776, time=119.58
x[1] = 7.15
y1[1] (analytic) = 1.6472578943127238682655675486971
y1[1] (numeric) = 1.6472578943127238682655675486971
absolute error = 2e-63
relative error = 1.2141389681027746620001541644640e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7622710923614109998397896104677
y2[1] (numeric) = 1.7622710923614109998397896104677
absolute error = 1.1e-62
relative error = 6.2419454348877739290702722632435e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4754
Order of pole (three term test) = -14.93
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2268540348, alloc=4848776, time=119.78
x[1] = 7.16
y1[1] (analytic) = 1.6396029478086308482403383037247
y1[1] (numeric) = 1.6396029478086308482403383037247
absolute error = 3e-63
relative error = 1.8297112749215124579336990808531e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.768705450191755725922123751153
y2[1] (numeric) = 1.768705450191755725922123751153
absolute error = 1.1e-62
relative error = 6.2192379170920887468999485658574e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4737
Order of pole (three term test) = -15.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2272541192, alloc=4848776, time=120.00
x[1] = 7.17
y1[1] (analytic) = 1.6318840415427576449657950046255
y1[1] (numeric) = 1.6318840415427576449657950046255
absolute error = 3e-63
relative error = 1.8383659154873816460863845216008e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7750629381176670163025579372399
y2[1] (numeric) = 1.7750629381176670163025579372399
absolute error = 1.1e-62
relative error = 6.1969633660791478992488606585285e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4719
Order of pole (three term test) = -15.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.18
y1[1] (analytic) = 1.6241019473992984453154054422433
y1[1] (numeric) = 1.6241019473992984453154054422433
absolute error = 3e-63
relative error = 1.8471746830942171272543289209991e-61 %
Correct digits = 64
h = 0.01
bytes used=2276542220, alloc=4848776, time=120.20
y2[1] (analytic) = 1.7813429203956501687973230526633
y2[1] (numeric) = 1.7813429203956501687973230526633
absolute error = 1.0e-62
relative error = 5.6137422421612801729968010398996e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4698
Order of pole (three term test) = -15.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.19
y1[1] (analytic) = 1.6162574435811825383731415638198
y1[1] (numeric) = 1.6162574435811825383731415638198
absolute error = 3e-63
relative error = 1.8561399434936701950052948390031e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7875447690327106862117915153751
y2[1] (numeric) = 1.7875447690327106862117915153751
absolute error = 1.0e-62
relative error = 5.5942654825989467216601216357490e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.87
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4676
Order of pole (three term test) = -15.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2280543664, alloc=4848776, time=120.41
x[1] = 7.2
y1[1] (analytic) = 1.6083513145322546710048504790937
y1[1] (numeric) = 1.6083513145322546710048504790937
absolute error = 3e-63
relative error = 1.8652641204029907978536052110640e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7936678638491530524644457476436
y2[1] (numeric) = 1.7936678638491530524644457476436
absolute error = 1.0e-62
relative error = 5.5751681799886431493476533290595e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.56
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4652
Order of pole (three term test) = -16.11
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2284544352, alloc=4848776, time=120.62
x[1] = 7.21
y1[1] (analytic) = 1.600384350858831317084592824522
y1[1] (numeric) = 1.600384350858831317084592824522
absolute error = 3e-63
relative error = 1.8745496970087704336632842443938e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7997115925405981853237961160432
y2[1] (numeric) = 1.7997115925405981853237961160432
absolute error = 1.0e-62
relative error = 5.5564458446829826606542366982492e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.26
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4626
Order of pole (three term test) = -16.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2288545416, alloc=4848776, time=120.83
x[1] = 7.22
y1[1] (analytic) = 1.5923573492506407046836562940431
y1[1] (numeric) = 1.5923573492506407046836562940431
absolute error = 3e-63
relative error = 1.8839992175197309360346335056680e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8056753507392133640646556876854
y2[1] (numeric) = 1.8056753507392133640646556876854
absolute error = 1.0e-62
relative error = 5.5380940964311036490975823505852e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.97
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4598
Order of pole (three term test) = -16.57
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.23
y1[1] (analytic) = 1.5842711124011545071536423439622
y1[1] (numeric) = 1.5842711124011545071536423439622
absolute error = 3e-63
relative error = 1.8936152887703273933677187359809e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8115585420741485091020309448447
y2[1] (numeric) = 1.8115585420741485091020309448447
absolute error = 1.0e-62
relative error = 5.5201086620973754722988537532323e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4568
Order of pole (three term test) = -16.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2292546412, alloc=4848776, time=121.04
x[1] = 7.24
y1[1] (analytic) = 1.5761264489273191648681277271593
y1[1] (numeric) = 1.5761264489273191648681277271593
absolute error = 3e-63
relative error = 1.9034005818770069658803831763116e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8173605782311727700250284673932
y2[1] (numeric) = 1.8173605782311727700250284673932
absolute error = 9e-63
relative error = 4.9522368361041766213428970856101e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4537
Order of pole (three term test) = -17.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2296547112, alloc=4848776, time=121.25
x[1] = 7.25
y1[1] (analytic) = 1.5679241732886948644238363482182
y1[1] (numeric) = 1.5679241732886948644238363482182
absolute error = 3e-63
relative error = 1.9133578339490422663021192306244e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8230808790115054584216711834121
y2[1] (numeric) = 1.8230808790115054584216711834121
absolute error = 9e-63
relative error = 4.9366981485099548480931534148810e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4503
Order of pole (three term test) = -17.26
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2300548084, alloc=4848776, time=121.46
x[1] = 7.26
y1[1] (analytic) = 1.5596651057060102613360173629058
y1[1] (numeric) = 1.5596651057060102613360173629058
absolute error = 3e-63
relative error = 1.9234898498559384185401981650425e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.82871887238983544245036732029
y2[1] (numeric) = 1.82871887238983544245036732029
absolute error = 9e-63
relative error = 4.9214781647867378612148648932379e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4468
Order of pole (three term test) = -17.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2304549044, alloc=4848776, time=121.67
x[1] = 7.27
y1[1] (analytic) = 1.5513500720791410906878891460087
y1[1] (numeric) = 1.5513500720791410906878891460087
absolute error = 4e-63
relative error = 2.5783993387379961162649450302467e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8342739945715232012669242437267
y2[1] (numeric) = 1.8342739945715232012669242437267
absolute error = 9e-63
relative error = 4.9065734054101077006758572261733e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4431
Order of pole (three term test) = -17.7
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.28
y1[1] (analytic) = 1.5429799039045208678047332531733
y1[1] (numeric) = 1.5429799039045208678047332531733
absolute error = 3e-63
relative error = 1.9442897424707088714923807273225e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8397456900489798191493327030497
y2[1] (numeric) = 1.8397456900489798191493327030497
absolute error = 9e-63
relative error = 4.8919804778889802323227247664305e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4393
Order of pole (three term test) = -17.93
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2308549844, alloc=4848776, time=121.87
x[1] = 7.29
y1[1] (analytic) = 1.5345554381919919378137467806639
y1[1] (numeric) = 1.5345554381919919378137467806639
absolute error = 3e-63
relative error = 1.9549635844597376827152897819351e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8451334116572172814678913429188
y2[1] (numeric) = 1.8451334116572172814678913429188
absolute error = 1.0e-62
relative error = 5.4196623056207312225760454425609e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4352
Order of pole (three term test) = -18.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2312550924, alloc=4848776, time=122.08
x[1] = 7.3
y1[1] (analytic) = 1.5260775173811051889154065767377
y1[1] (numeric) = 1.5260775173811051889154065767377
absolute error = 3e-63
relative error = 1.9658241248113572893553767512474e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8504366206285645175173662279669
y2[1] (numeric) = 1.8504366206285645175173662279669
absolute error = 9e-63
relative error = 4.8637169734258934452224192076734e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.431
Order of pole (three term test) = -18.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2316551664, alloc=4848776, time=122.29
x[1] = 7.31
y1[1] (analytic) = 1.5175469892568767993252681617755
y1[1] (numeric) = 1.5175469892568767993252681617755
absolute error = 4e-63
relative error = 2.6358327144510684596369859293902e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8556547866465437186524987147974
y2[1] (numeric) = 1.8556547866465437186524987147974
absolute error = 9e-63
relative error = 4.8500400315644900788021961000484e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4266
Order of pole (three term test) = -18.58
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.32
y1[1] (analytic) = 1.5089647068650104421413027004031
y1[1] (numeric) = 1.5089647068650104421413027004031
absolute error = 3e-63
relative error = 1.9881180695290941481089386640300e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8607873878989015441399449026743
y2[1] (numeric) = 1.8607873878989015441399449026743
absolute error = 9e-63
relative error = 4.8366621885600285887041564226182e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.422
Order of pole (three term test) = -18.79
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2320552424, alloc=4848776, time=122.50
x[1] = 7.33
y1[1] (analytic) = 1.5003315284265934258456373647886
y1[1] (numeric) = 1.5003315284265934258456373647886
absolute error = 4e-63
relative error = 2.6660774130333871800129318122596e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8658339111297899116502539931945
y2[1] (numeric) = 1.8658339111297899116502539931945
absolute error = 9e-63
relative error = 4.8235804625023496627476231686647e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4173
Order of pole (three term test) = -19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2324553772, alloc=4848776, time=122.72
x[1] = 7.34
y1[1] (analytic) = 1.4916483172522753007555626024528
y1[1] (numeric) = 1.4916483172522753007555626024528
absolute error = 4e-63
relative error = 2.6815972328975578843263523297670e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8707938516910911543543202082359
y2[1] (numeric) = 1.8707938516910911543543202082359
absolute error = 9e-63
relative error = 4.8107919490244808585220229826781e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4124
Order of pole (three term test) = -19.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2328554584, alloc=4848776, time=122.93
x[1] = 7.35
y1[1] (analytic) = 1.4829159416559375134916436182999
y1[1] (numeric) = 1.4829159416559375134916436182999
absolute error = 3e-63
relative error = 2.0230411689080435921858025802924e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8756667135928824121513694426684
y2[1] (numeric) = 1.8756667135928824121513694426684
absolute error = 9e-63
relative error = 4.7982938198867401800793917772863e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4073
Order of pole (three term test) = -19.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2332556144, alloc=4848776, time=123.13
x[1] = 7.36
y1[1] (analytic) = 1.4741352748678627424255475449175
y1[1] (numeric) = 1.4741352748678627424255475449175
absolute error = 3e-63
relative error = 2.0350913862154959928544593673868e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8804520095530342106314113723386
y2[1] (numeric) = 1.8804520095530342106314113723386
absolute error = 9e-63
relative error = 4.7860833216047962371690221329891e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4021
Order of pole (three term test) = -19.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.37
y1[1] (analytic) = 1.4653071949474125971016828724969
y1[1] (numeric) = 1.4653071949474125971016828724969
absolute error = 4e-63
relative error = 2.7298030159085878582822533051551e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8851492610459382679555927834817
y2[1] (numeric) = 1.8851492610459382679555927834817
absolute error = 9e-63
relative error = 4.7741577741205095276061409054612e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3967
Order of pole (three term test) = -19.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2336556968, alloc=4848776, time=123.34
x[1] = 7.38
y1[1] (analytic) = 1.4564325846952224137899406331777
y1[1] (numeric) = 1.4564325846952224137899406331777
absolute error = 4e-63
relative error = 2.7464367675054814628985238272663e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8897579983503596569143704586037
y2[1] (numeric) = 1.8897579983503596569143704586037
absolute error = 9e-63
relative error = 4.7625145695144225707228551653148e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3912
Order of pole (three term test) = -20.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2340558336, alloc=4848776, time=123.56
x[1] = 7.39
y1[1] (analytic) = 1.447512331564921927616811305895
y1[1] (numeric) = 1.447512331564921927616811305895
absolute error = 4e-63
relative error = 2.7633616051308902012574093504971e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8942777605964085369871744703402
y2[1] (numeric) = 1.8942777605964085369871744703402
absolute error = 9e-63
relative error = 4.7511511707588082970698225343362e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3855
Order of pole (three term test) = -20.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2344559064, alloc=4848776, time=123.76
x[1] = 7.4
y1[1] (analytic) = 1.4385473275743906491340984687003
y1[1] (numeric) = 1.4385473275743906491340984687003
absolute error = 4e-63
relative error = 2.7805828305590805376290833686805e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8987080958116267592694988965346
y2[1] (numeric) = 1.8987080958116267592694988965346
absolute error = 8e-63
relative error = 4.2133912093424234056508902641402e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3796
Order of pole (three term test) = -20.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.41
y1[1] (analytic) = 1.4295384692165568197136187208456
y1[1] (numeric) = 1.4295384692165568197136187208456
absolute error = 4e-63
relative error = 2.7981058825175631484597901172432e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9030485609661847356453326235512
y2[1] (numeric) = 1.9030485609661847356453326235512
absolute error = 8e-63
relative error = 4.2037813243916228035620350404590e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3736
Order of pole (three term test) = -20.59
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2348559972, alloc=4848776, time=123.97
TOP MAIN SOLVE Loop
x[1] = 7.42
y1[1] (analytic) = 1.4204866573697488657980144485792
y1[1] (numeric) = 1.4204866573697488657980144485792
absolute error = 4e-63
relative error = 2.8159363407232699770851559366021e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.907298722017184052555676926842
y2[1] (numeric) = 1.907298722017184052555676926842
absolute error = 8e-63
relative error = 4.1944137578717063564123115066842e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3675
Order of pole (three term test) = -20.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2352560772, alloc=4848776, time=124.18
x[1] = 7.43
y1[1] (analytic) = 1.4113927972076083167875474809437
y1[1] (numeric) = 1.4113927972076083167875474809437
absolute error = 4e-63
relative error = 2.8340799300618943403028291283864e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9114581539520613991386916987506
y2[1] (numeric) = 1.9114581539520613991386916987506
absolute error = 8e-63
relative error = 4.1852864963114629496811357870510e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3612
Order of pole (three term test) = -20.96
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2356561460, alloc=4848776, time=124.39
x[1] = 7.44
y1[1] (analytic) = 1.4022577981085731951960126380232
y1[1] (numeric) = 1.4022577981085731951960126380232
absolute error = 4e-63
relative error = 2.8525425249161569245467311355244e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.915526440831089469384826128484
y2[1] (numeric) = 1.915526440831089469384826128484
absolute error = 8e-63
relative error = 4.1763975842218288293577459503270e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3547
Order of pole (three term test) = -21.13
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2360562224, alloc=4848776, time=124.60
x[1] = 7.45
y1[1] (analytic) = 1.3930825735649409306613253235169
y1[1] (numeric) = 1.3930825735649409306613253235169
absolute error = 4e-63
relative error = 2.8713301536490242712709564501959e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9195031758289705882521356215873
y2[1] (numeric) = 1.9195031758289705882521356215873
absolute error = 8e-63
relative error = 4.1677451231853585621435941998362e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3481
Order of pole (three term test) = -21.31
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.46
y1[1] (analytic) = 1.3838680410915198914436014504911
y1[1] (numeric) = 1.3838680410915198914436014504911
absolute error = 4e-63
relative error = 2.8904490032481835607326235118702e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9233879612755189024138346667882
y2[1] (numeric) = 1.9233879612755189024138346667882
absolute error = 7e-63
relative error = 3.6394113621039106504424520203923e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3414
Order of pole (three term test) = -21.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2364563352, alloc=4848776, time=124.80
x[1] = 7.47
y1[1] (analytic) = 1.3746151221338786681814564223101
y1[1] (numeric) = 1.3746151221338786681814564223101
absolute error = 4e-63
relative error = 2.9099054241383689195893765919359e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9271804086954270674529126075413
y2[1] (numeric) = 1.9271804086954270674529126075413
absolute error = 8e-63
relative error = 4.1511422407077434988975361552448e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3345
Order of pole (three term test) = -21.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2368564368, alloc=4848776, time=125.01
x[1] = 7.48
y1[1] (analytic) = 1.3653247419762022849016888635084
y1[1] (numeric) = 1.3653247419762022849016888635084
absolute error = 5e-63
relative error = 3.6621324189605511330861915869382e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9308801388471134548682316522293
y2[1] (numeric) = 1.9308801388471134548682316522293
absolute error = 8e-63
relative error = 4.1431883000136021105033719322312e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3275
Order of pole (three term test) = -21.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2372565568, alloc=4848776, time=125.22
x[1] = 7.49
y1[1] (analytic) = 1.3559978296487645515844618973593
y1[1] (numeric) = 1.3559978296487645515844618973593
absolute error = 4e-63
relative error = 2.9498572287804431268983044841769e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9344867817606459942037790778139
y2[1] (numeric) = 1.9344867817606459942037790778139
absolute error = 8e-63
relative error = 4.1354637702506875124436206599643e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3204
Order of pole (three term test) = -21.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.5
y1[1] (analytic) = 1.3466353178350258109716193361719
y1[1] (numeric) = 1.3466353178350258109716193361719
absolute error = 5e-63
relative error = 3.7129577204602487552087167596485e-61 %
Correct digits = 64
h = 0.01
bytes used=2376568804, alloc=4848776, time=125.42
y2[1] (analytic) = 1.937999976774738857948463798149
y2[1] (numeric) = 1.937999976774738857948463798149
absolute error = 8e-63
relative error = 4.1279670257343199992040020821354e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3132
Order of pole (three term test) = -22.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.51
y1[1] (analytic) = 1.3372381427783653697660376664312
y1[1] (numeric) = 1.3372381427783653697660376664312
absolute error = 5e-63
relative error = 3.7390497922917106905624265951741e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9414193725728182895687977852796
y2[1] (numeric) = 1.9414193725728182895687977852796
absolute error = 8e-63
relative error = 4.1206964929984172853141300023513e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3058
Order of pole (three term test) = -22.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2380570212, alloc=4848776, time=125.63
x[1] = 7.52
y1[1] (analytic) = 1.3278072441884579409011711786587
y1[1] (numeric) = 1.3278072441884579409011711786587
absolute error = 5e-63
relative error = 3.7656068091840757381029468754693e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9447446272181539681217138320954
y2[1] (numeric) = 1.9447446272181539681217138320954
absolute error = 8e-63
relative error = 4.1136506500822901037988473654778e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2983
Order of pole (three term test) = -22.45
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2384570940, alloc=4848776, time=125.83
x[1] = 7.53
y1[1] (analytic) = 1.3183435651473034591585439161043
y1[1] (numeric) = 1.3183435651473034591585439161043
absolute error = 6e-63
relative error = 4.5511656889906369367441796778007e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9479754081880523963403344141535
y2[1] (numeric) = 1.9479754081880523963403344141535
absolute error = 8e-63
relative error = 4.1068280258431789958112989480699e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2906
Order of pole (three term test) = -22.59
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2388571632, alloc=4848776, time=126.04
x[1] = 7.54
y1[1] (analytic) = 1.3088480520149196670733184671152
y1[1] (numeric) = 1.3088480520149196670733184671152
absolute error = 6e-63
relative error = 4.5841837719536946709835051265027e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.951111392407108892882377468875
y2[1] (numeric) = 1.951111392407108892882377468875
absolute error = 7e-63
relative error = 3.5876987993822425048851646414231e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2829
Order of pole (three term test) = -22.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.55
y1[1] (analytic) = 1.2993216543347069017907617945243
y1[1] (numeric) = 1.2993216543347069017907617945243
absolute error = 6e-63
relative error = 4.6177942005224153757048018379399e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.954152266279514863569684152709
y2[1] (numeric) = 1.954152266279514863569684152709
absolute error = 7e-63
relative error = 3.5821159490950053475504963116981e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2751
Order of pole (three term test) = -22.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2392572424, alloc=4848776, time=126.25
x[1] = 7.56
y1[1] (analytic) = 1.2897653247384945463160600407277
y1[1] (numeric) = 1.2897653247384945463160600407277
absolute error = 6e-63
relative error = 4.6520090786411285670529682212835e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9570977257204171209186672597821
y2[1] (numeric) = 1.9570977257204171209186672597821
absolute error = 7e-63
relative error = 3.5767248145072909973436830888727e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2671
Order of pole (three term test) = -23.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2396573148, alloc=4848776, time=126.45
x[1] = 7.57
y1[1] (analytic) = 1.2801800188512786404332296334417
y1[1] (numeric) = 1.2801800188512786404332296334417
absolute error = 6e-63
relative error = 4.6868408439805787520183605871059e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9599474761863261160558599363545
y2[1] (numeric) = 1.9599474761863261160558599363545
absolute error = 7e-63
relative error = 3.5715242806509431951670885917670e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.259
Order of pole (three term test) = -23.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2400573864, alloc=4848776, time=126.66
x[1] = 7.58
y1[1] (analytic) = 1.270566695195660177452647741408
y1[1] (numeric) = 1.270566695195660177452647741408
absolute error = 6e-63
relative error = 4.7223022787292826829203056943534e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9627012327045700422207132450103
y2[1] (numeric) = 1.9627012327045700422207132450103
absolute error = 6e-63
relative error = 3.0570113780038231332452974980229e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2509
Order of pole (three term test) = -23.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2404575212, alloc=4848776, time=126.88
x[1] = 7.59
y1[1] (analytic) = 1.2609263150959936428778928397435
y1[1] (numeric) = 1.2609263150959936428778928397435
absolute error = 5e-63
relative error = 3.9653387673326118873796439473620e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9653587199017918644698373032588
y2[1] (numeric) = 1.9653587199017918644698373032588
absolute error = 6e-63
relative error = 3.0528777974434191008592812429848e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2426
Order of pole (three term test) = -23.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.6
y1[1] (analytic) = 1.2512598425822553800581527493518
y1[1] (numeric) = 1.2512598425822553800581527493518
absolute error = 5e-63
relative error = 3.9959725628862014391210231882770e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9679196720314864259034630180288
y2[1] (numeric) = 1.9679196720314864259034630180288
absolute error = 6e-63
relative error = 3.0489049351319258933010279374237e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2342
Order of pole (three term test) = -23.51
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2408575916, alloc=4848776, time=127.08
x[1] = 7.61
y1[1] (analytic) = 1.2415682442936413959095254813347
y1[1] (numeric) = 1.2415682442936413959095254813347
absolute error = 5e-63
relative error = 4.0271648562054054034472077690614e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9703838330005748767264492819134
y2[1] (numeric) = 1.9703838330005748767264492819134
absolute error = 6e-63
relative error = 3.0450919762485939192604800639450e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2257
Order of pole (three term test) = -23.63
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2412577612, alloc=4848776, time=127.29
x[1] = 7.62
y1[1] (analytic) = 1.2318524893819042468443058622056
y1[1] (numeric) = 1.2318524893819042468443058622056
absolute error = 5e-63
relative error = 4.0589275445705401607506758432562e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9727509563950137687230748141779
y2[1] (numeric) = 1.9727509563950137687230748141779
absolute error = 6e-63
relative error = 3.0414381402528085039643687908925e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2172
Order of pole (three term test) = -23.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2416578880, alloc=4848776, time=127.50
x[1] = 7.63
y1[1] (analytic) = 1.2221135494144386711391126846887
y1[1] (numeric) = 1.2221135494144386711391126846887
absolute error = 5e-63
relative error = 4.0912728628167907755244893064891e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9750208055044362542575080082731
y2[1] (numeric) = 1.9750208055044362542575080082731
absolute error = 6e-63
relative error = 3.0379426805418141271572448181974e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2086
Order of pole (three term test) = -23.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.64
y1[1] (analytic) = 1.2123523982771256590978578675718
y1[1] (numeric) = 1.2123523982771256590978578675718
absolute error = 5e-63
relative error = 4.1242133946412787519803477380049e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9771931533458229257005890029222
y2[1] (numeric) = 1.9771931533458229257005890029222
absolute error = 6e-63
relative error = 3.0346048841241177718294985007315e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1998
Order of pole (three term test) = -23.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2420579736, alloc=4848776, time=127.70
x[1] = 7.65
y1[1] (analytic) = 1.2025700120769446765215783227058
y1[1] (numeric) = 1.2025700120769446765215783227058
absolute error = 5e-63
relative error = 4.1577620843584467673931620302621e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9792677826861999282187069323438
y2[1] (numeric) = 1.9792677826861999282187069323438
absolute error = 6e-63
relative error = 3.0314240713083243729916720739020e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.191
Order of pole (three term test) = -24.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2424580512, alloc=4848776, time=127.91
x[1] = 7.66
y1[1] (analytic) = 1.1927673690443637801816273360472
y1[1] (numeric) = 1.1927673690443637801816273360472
absolute error = 5e-63
relative error = 4.1919322491241207313440369845348e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9812444860643620761324084988271
y2[1] (numeric) = 1.9812444860643620761324084988271
absolute error = 5e-63
relative error = 2.5236663295059747591229589117296e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1822
Order of pole (three term test) = -24.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2428581576, alloc=4848776, time=128.12
x[1] = 7.67
y1[1] (analytic) = 1.1829454494355173862033368443022
y1[1] (numeric) = 1.1829454494355173862033368443022
absolute error = 5e-63
relative error = 4.2267375916496571194952493704904e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9831230658116188005512045434252
y2[1] (numeric) = 1.9831230658116188005512045434252
absolute error = 5e-63
relative error = 2.5212757020471068137395855471859e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1732
Order of pole (three term test) = -24.23
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2432582376, alloc=4848776, time=128.33
x[1] = 7.68
y1[1] (analytic) = 1.173105235434181473501793986326
y1[1] (numeric) = 1.173105235434181473501793986326
absolute error = 4e-63
relative error = 3.4097537707429530680941223448840e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9849033340715608537070993661777
y2[1] (numeric) = 1.9849033340715608537070993661777
absolute error = 6e-63
relative error = 3.0228172309491846610766719574282e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1642
Order of pole (three term test) = -24.31
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.69
y1[1] (analytic) = 1.1632477110535560246677012934441
y1[1] (numeric) = 1.1632477110535560246677012934441
absolute error = 5e-63
relative error = 4.2983106285001746888892885120697e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9865851128188457933328816416347
y2[1] (numeric) = 1.9865851128188457933328816416347
absolute error = 6e-63
relative error = 3.0202582115831714078938631003974e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1551
Order of pole (three term test) = -24.39
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2436583264, alloc=4848776, time=128.54
x[1] = 7.7
y1[1] (analytic) = 1.1533738620378645259773842395721
y1[1] (numeric) = 1.1533738620378645259773842395721
absolute error = 5e-63
relative error = 4.3351077777726275532102945132067e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9881682338770003685523936187237
y2[1] (numeric) = 1.9881682338770003685523936187237
absolute error = 6e-63
relative error = 3.0178532670244820135311376953155e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.146
Order of pole (three term test) = -24.47
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2440583968, alloc=4848776, time=128.75
x[1] = 7.71
y1[1] (analytic) = 1.1434846757637803664949450070563
y1[1] (numeric) = 1.1434846757637803664949450070563
absolute error = 5e-63
relative error = 4.3725990439358487245902366955261e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9896525389352380270590248501636
y2[1] (numeric) = 1.9896525389352380270590248501636
absolute error = 6e-63
relative error = 3.0156019116839859089613793260304e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1367
Order of pole (three term test) = -24.54
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2444585044, alloc=4848776, time=128.95
x[1] = 7.72
y1[1] (analytic) = 1.1335811411416899935445078592584
y1[1] (numeric) = 1.1335811411416899935445078592584
absolute error = 5e-63
relative error = 4.4108002669877107091396095549034e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9910378795642898618457271446539
y2[1] (numeric) = 1.9910378795642898618457271446539
absolute error = 5e-63
relative error = 2.5112530762569813211169402952083e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1275
Order of pole (three term test) = -24.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.73
y1[1] (analytic) = 1.1236642485168026981547284658423
y1[1] (numeric) = 1.1236642485168026981547284658423
absolute error = 4e-63
relative error = 3.5597822083241140461157576695284e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9923241172312474144050701519763
y2[1] (numeric) = 1.9923241172312474144050701519763
absolute error = 6e-63
relative error = 3.0115581837850055783214154591527e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1182
Order of pole (three term test) = -24.67
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2448585852, alloc=4848776, time=129.16
TOP MAIN SOLVE Loop
x[1] = 7.74
y1[1] (analytic) = 1.1137349895701169194146144923951
y1[1] (numeric) = 1.1137349895701169194146144923951
absolute error = 4e-63
relative error = 3.5915186623919691223573417845484e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9935111233134158501313865368873
y2[1] (numeric) = 1.9935111233134158501313865368873
absolute error = 5e-63
relative error = 2.5081374974670306637586602709478e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1088
Order of pole (three term test) = -24.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2452587280, alloc=4848776, time=129.37
x[1] = 7.75
y1[1] (analytic) = 1.1037943572192529710276940677138
y1[1] (numeric) = 1.1037943572192529710276940677138
absolute error = 4e-63
relative error = 3.6238634251374934121356528794203e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9945987791111761206190108016398
y2[1] (numeric) = 1.9945987791111761206190108016398
absolute error = 5e-63
relative error = 2.5067698087271851565596751159675e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09941
Order of pole (three term test) = -24.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2456588284, alloc=4848776, time=129.58
x[1] = 7.76
y1[1] (analytic) = 1.0938433455191621067092375928365
y1[1] (numeric) = 1.0938433455191621067092375928365
absolute error = 4e-63
relative error = 3.6568307668421313430462771357173e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9955869758598548266511003661026
y2[1] (numeric) = 1.9955869758598548266511003661026
absolute error = 5e-63
relative error = 2.5055284788304499953783513875035e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08997
Order of pole (three term test) = -24.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2460589480, alloc=4848776, time=129.79
x[1] = 7.77
y1[1] (analytic) = 1.083882949562721853437250999942
y1[1] (numeric) = 1.083882949562721853437250999942
absolute error = 4e-63
relative error = 3.6904353939821147192047513149969e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9964756147406005949026315428916
y2[1] (numeric) = 1.9964756147406005949026315428916
absolute error = 5e-63
relative error = 2.5044132585860024688531800758806e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08049
Order of pole (three term test) = -24.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.78
y1[1] (analytic) = 1.073914165381227552941078415626
y1[1] (numeric) = 1.073914165381227552941078415626
absolute error = 4e-63
relative error = 3.7246924651376067900710827633945e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9972646068902658807289637249532
y2[1] (numeric) = 1.9972646068902658807289637249532
absolute error = 5e-63
relative error = 2.5034239242766048872824864737195e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07098
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2464590592, alloc=4848776, time=129.99
x[1] = 7.79
y1[1] (analytic) = 1.0639379898447900621905419292717
y1[1] (numeric) = 1.0639379898447900621905419292717
absolute error = 3e-63
relative error = 2.8197132056894100673062355726186e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9979538734102932088679277373902
y2[1] (numeric) = 1.9979538734102932088679277373902
absolute error = 5e-63
relative error = 2.5025602775631329669507391440519e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06144
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2468591304, alloc=4848776, time=130.20
x[1] = 7.8
y1[1] (analytic) = 1.0539554205626495730325679129525
y1[1] (numeric) = 1.0539554205626495730325679129525
absolute error = 4e-63
relative error = 3.7952269346122981042961844919662e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9985433453746049634387733205961
y2[1] (numeric) = 1.9985433453746049634387733205961
absolute error = 5e-63
relative error = 2.5018221454000063264537888717150e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05188
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2472592164, alloc=4848776, time=130.42
x[1] = 7.81
y1[1] (analytic) = 1.043967455783415519510264690171
y1[1] (numeric) = 1.043967455783415519510264690171
absolute error = 4e-63
relative error = 3.8315370635747590434385199067926e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9990329638364959382655506530315
y2[1] (numeric) = 1.9990329638364959382655506530315
absolute error = 5e-63
relative error = 2.5012093799614591512418912720130e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0423
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.82
bytes used=2476593432, alloc=4848776, time=130.63
y1[1] (analytic) = 1.0339750942952425487905865122099
y1[1] (numeric) = 1.0339750942952425487905865122099
absolute error = 4e-63
relative error = 3.8685651347592662318530425394860e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9994226798345279582756373482821
y2[1] (numeric) = 1.9994226798345279582756373482821
absolute error = 5e-63
relative error = 2.5007218585785970736931639353964e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0327
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.83
y1[1] (analytic) = 1.0239793353259525380203046620934
y1[1] (numeric) = 1.0239793353259525380203046620934
absolute error = 4e-63
relative error = 3.9063288310664220613124090005152e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9997124543974259825161832418216
y2[1] (numeric) = 1.9997124543974259825161832418216
absolute error = 5e-63
relative error = 2.5003594836871942467544187138666e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02308
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2480594492, alloc=4848776, time=130.83
x[1] = 7.84
y1[1] (analytic) = 1.0139811784431126448253687138652
y1[1] (numeric) = 1.0139811784431126448253687138652
absolute error = 5e-63
relative error = 4.9310579982136373034571918845104e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9999022585479751991822513952502
y2[1] (numeric) = 1.9999022585479751991822513952502
absolute error = 5e-63
relative error = 2.5001221827861924684660119282346e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01346
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2484595264, alloc=4848776, time=131.04
x[1] = 7.85
y1[1] (analytic) = 1.0039816234540793835653399973692
y1[1] (numeric) = 1.0039816234540793835653399973692
absolute error = 5e-63
relative error = 4.9801708349980496577216742925009e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9999920733059187229504000722697
y2[1] (numeric) = 1.9999920733059187229504000722697
absolute error = 5e-63
relative error = 2.5000099084068720513657871124991e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.003834
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2488596132, alloc=4848776, time=131.25
x[1] = 7.86
y1[1] (analytic) = 0.99398167030601872285197549971847
y1[1] (numeric) = 0.99398167030601872285197549971847
absolute error = 5.0e-63
relative error = 5.0302738464590016251616813247818e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9999818896898556048503870679297
y2[1] (numeric) = 1.9999818896898556048503870679297
absolute error = 4e-63
relative error = 2.0000181104741375468961237075655e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005803
Order of pole (three term test) = -0.8937
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.87
y1[1] (analytic) = 0.98398231898591220223889403738305
y1[1] (numeric) = 0.98398231898591220223889403738305
absolute error = 5.1e-63
relative error = 5.1830199604155868343342765076584e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9998717087181389648755908903309
y2[1] (numeric) = 1.9998717087181389648755908903309
absolute error = 5e-63
relative error = 2.5001603743896443064801090016890e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01544
Order of pole (three term test) = -0.8991
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2492596888, alloc=4848776, time=131.46
x[1] = 7.88
y1[1] (analytic) = 0.97398456942055906738732777394789
y1[1] (numeric) = 0.97398456942055906738732777394789
absolute error = 5.1e-63
relative error = 5.2362225851628036552101358947237e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9996615414087741575196361940153
y2[1] (numeric) = 1.9996615414087741575196361940153
absolute error = 4e-63
relative error = 2.0003385158780294351912422511682e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02508
Order of pole (three term test) = -0.9092
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2496597664, alloc=4848776, time=131.67
x[1] = 7.89
y1[1] (analytic) = 0.96398942137658442341111123213176
y1[1] (numeric) = 0.96398942137658442341111123213176
absolute error = 5.2e-63
relative error = 5.3942500661203930879182367389730e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9993514087783169804225849407293
y2[1] (numeric) = 1.9993514087783169804225849407293
absolute error = 4e-63
relative error = 2.0006488016252023795473823663153e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0347
Order of pole (three term test) = -0.9242
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2500598628, alloc=4848776, time=131.88
x[1] = 7.9
y1[1] (analytic) = 0.95399787436046340550224704004151
y1[1] (numeric) = 0.95399787436046340550224704004151
absolute error = 5.2e-63
relative error = 5.4507458976110942268407011315033e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9989413418397720363049105120439
y2[1] (numeric) = 1.9989413418397720363049105120439
absolute error = 4e-63
relative error = 2.0010592188355598299828991236667e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04431
Order of pole (three term test) = -0.944
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2504599636, alloc=4848776, time=132.09
x[1] = 7.91
y1[1] (analytic) = 0.94401092751857136433667294165175
y1[1] (numeric) = 0.94401092751857136433667294165175
absolute error = 5.3e-63
relative error = 5.6143417893811764304166848450949e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.998431381599491458351310017202
y2[1] (numeric) = 1.998431381599491458351310017202
absolute error = 4e-63
relative error = 2.0015698496480305079048845588943e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0539
Order of pole (three term test) = -0.9686
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.92
y1[1] (analytic) = 0.93402957953727006115839826028491
y1[1] (numeric) = 0.93402957953727006115839826028491
absolute error = 5.3e-63
relative error = 5.6743384964592730622440734628230e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.997821579053074309169232028065
y2[1] (numeric) = 1.997821579053074309169232028065
absolute error = 4e-63
relative error = 2.0021807962930886118959281917629e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06348
Order of pole (three term test) = -0.9981
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2508601848, alloc=4848776, time=132.29
x[1] = 7.93
y1[1] (analytic) = 0.92405482854303986383924017488675
y1[1] (numeric) = 0.92405482854303986383924017488675
absolute error = 5.3e-63
relative error = 5.7355903960336710369963259903409e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9971119951802670633788067322389
y2[1] (numeric) = 1.9971119951802670633788067322389
absolute error = 4e-63
relative error = 2.0028921811362634714144775536490e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07302
Order of pole (three term test) = -1.032
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2512602524, alloc=4848776, time=132.50
x[1] = 7.94
y1[1] (analytic) = 0.91408767200266793061133094292942
y1[1] (numeric) = 0.91408767200266793061133094292942
absolute error = 5.3e-63
relative error = 5.7981309258752709543317774251957e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9963027009388656837816699276909
y2[1] (numeric) = 1.9963027009388656837816699276909
absolute error = 3e-63
relative error = 1.5027781100476862562666240063815e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08254
Order of pole (three term test) = -1.071
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2516603276, alloc=4848776, time=132.71
x[1] = 7.95
y1[1] (analytic) = 0.90412910662350236257084658291809
y1[1] (numeric) = 0.90412910662350236257084658291809
absolute error = 5.3e-63
relative error = 5.8619946655550235948810867324404e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9953937772576199008959823902
y2[1] (numeric) = 1.9953937772576199008959823902
absolute error = 3e-63
relative error = 1.5034626419067348345204221367742e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09202
Order of pole (three term test) = -1.115
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.96
y1[1] (analytic) = 0.89418012825378229945458538112409
y1[1] (numeric) = 0.89418012825378229945458538112409
absolute error = 5.3e-63
relative error = 5.9272173833142679089993313711318e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9943853150281404054237780310308
y2[1] (numeric) = 1.9943853150281404054237780310308
absolute error = 3e-63
relative error = 1.5042228687677990442008221858471e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1015
Order of pole (three term test) = -1.164
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2520604248, alloc=4848776, time=132.92
x[1] = 7.97
y1[1] (analytic) = 0.8842417317830539255967605880346
y1[1] (numeric) = 0.8842417317830539255967605880346
absolute error = 5.3e-63
relative error = 5.9938360851988596363832023320553e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.993277415095809762924650126215
y2[1] (numeric) = 1.993277415095809762924650126215
absolute error = 3e-63
relative error = 1.5050589432659581202639894998979e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1109
Order of pole (three term test) = -1.217
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2524604952, alloc=4848776, time=133.12
x[1] = 7.98
y1[1] (analytic) = 0.87431491104268234438242524016836
y1[1] (numeric) = 0.87431491104268234438242524016836
absolute error = 5.4e-63
relative error = 6.1762643319900814991191540668600e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9920701882496979595967340362938
y2[1] (numeric) = 1.9920701882496979595967340362938
absolute error = 3e-63
relative error = 1.5059710333981274889440303989367e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1202
Order of pole (three term test) = -1.275
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2528605660, alloc=4848776, time=133.33
x[1] = 7.99
y1[1] (analytic) = 0.86440065870646926992717726984173
y1[1] (numeric) = 0.86440065870646926992717726984173
absolute error = 5.4e-63
relative error = 6.2471030599176309998831075251061e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9907637552114835876020046344143
y2[1] (numeric) = 1.9907637552114835876020046344143
absolute error = 3e-63
relative error = 1.5069593225949117383279571621265e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1295
Order of pole (three term test) = -1.337
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2532606568, alloc=4848776, time=133.54
x[1] = 8
y1[1] (analytic) = 0.85449996619138647413115861816881
y1[1] (numeric) = 0.85449996619138647413115861816881
absolute error = 5.4e-63
relative error = 6.3194853290263746886492647701796e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9893582466233817778081235982453
y2[1] (numeric) = 1.9893582466233817778081235982453
absolute error = 3e-63
relative error = 1.5080240097991507316445759034883e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1388
Order of pole (three term test) = -1.405
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.01
y1[1] (analytic) = 0.84461382355843491567992109966912
y1[1] (numeric) = 0.84461382355843491567992109966912
absolute error = 5.5e-63
relative error = 6.5118517440645233441593587950102e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.987853803035080087143502358473
y2[1] (numeric) = 1.987853803035080087143502358473
absolute error = 3e-63
relative error = 1.5091653095512167045551048533533e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.148
Order of pole (three term test) = -1.477
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2536607544, alloc=4848776, time=133.74
x[1] = 8.02
y1[1] (analytic) = 0.83474321941363946499664181478805
y1[1] (numeric) = 0.83474321941363946499664181478805
absolute error = 5.5e-63
relative error = 6.5888525621848634043663916933931e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9862505748896836469659584733293
y2[1] (numeric) = 1.9862505748896836469659584733293
absolute error = 3e-63
relative error = 1.5103834520811252598965544704122e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1572
Order of pole (three term test) = -1.553
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2540608252, alloc=4848776, time=133.95
x[1] = 8.03
y1[1] (analytic) = 0.82488914080918912559068876792971
y1[1] (numeric) = 0.82488914080918912559068876792971
absolute error = 5.6e-63
relative error = 6.7887910301578029291168704518637e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9845487225086709779184162261999
y2[1] (numeric) = 1.9845487225086709779184162261999
absolute error = 3e-63
relative error = 1.5116786834075283165623729395227e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1662
Order of pole (three term test) = -1.634
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2544608988, alloc=4848776, time=134.16
x[1] = 8.04
y1[1] (analytic) = 0.81505257314473263769801896017425
y1[1] (numeric) = 0.81505257314473263769801896017425
absolute error = 5.6e-63
relative error = 6.8707224349877393971410343424153e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9827484160758619756776290970863
y2[1] (numeric) = 1.9827484160758619756776290970863
absolute error = 3e-63
relative error = 1.5130512654436622894782365392339e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1753
Order of pole (three term test) = -1.72
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.05
y1[1] (analytic) = 0.80523450006883933457079152741579
y1[1] (numeric) = 0.80523450006883933457079152741579
absolute error = 5.7e-63
relative error = 7.0786832897903755399122232109410e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9808498356203996707839892683332
y2[1] (numeric) = 1.9808498356203996707839892683332
absolute error = 3e-63
relative error = 1.5145014761103300810378114452011e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1842
Order of pole (three term test) = -1.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2548609772, alloc=4848776, time=134.37
TOP MAIN SOLVE Loop
x[1] = 8.06
y1[1] (analytic) = 0.79543590338063510524845128323445
y1[1] (numeric) = 0.79543590338063510524845128323445
absolute error = 5.6e-63
relative error = 7.0401649915471140827748154741312e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9788531709987474643622593641338
y2[1] (numeric) = 1.9788531709987474643622593641338
absolute error = 3e-63
relative error = 1.5160296094560008571316652068877e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1931
Order of pole (three term test) = -1.905
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2552610504, alloc=4848776, time=134.57
x[1] = 8.07
y1[1] (analytic) = 0.7856577629316233001320358003571
y1[1] (numeric) = 0.7856577629316233001320358003571
absolute error = 5.6e-63
relative error = 7.1277854865253516866673856733554e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9767586218757036399946520970817
y2[1] (numeric) = 1.9767586218757036399946520970817
absolute error = 2e-63
relative error = 1.0117573171894113796031390447308e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2019
Order of pole (three term test) = -2.004
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2556611188, alloc=4848776, time=134.79
x[1] = 8.08
y1[1] (analytic) = 0.77590105652770039718933296069646
y1[1] (numeric) = 0.77590105652770039718933296069646
absolute error = 5.7e-63
relative error = 7.3462975105467002816058782584357e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9745663977044350502792493264352
y2[1] (numeric) = 1.9745663977044350502792493264352
absolute error = 2e-63
relative error = 1.0128806011918025174276154302466e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2106
Order of pole (three term test) = -2.107
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2560612312, alloc=4848776, time=135.00
x[1] = 8.09
y1[1] (analytic) = 0.76616675983137622714261511889606
y1[1] (numeric) = 0.76616675983137622714261511889606
absolute error = 5.7e-63
relative error = 7.4396336396197860280305117510471e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9722767177055319746884661471167
y2[1] (numeric) = 1.9722767177055319746884661471167
absolute error = 2e-63
relative error = 1.0140564871275873425986522709975e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2192
Order of pole (three term test) = -2.215
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.1
y1[1] (analytic) = 0.75645584626420853553494823189785
y1[1] (numeric) = 0.75645584626420853553494823189785
absolute error = 5.7e-63
relative error = 7.5351390674679932897657929029671e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9698898108450862432243199360999
y2[1] (numeric) = 1.9698898108450862432243199360999
absolute error = 2e-63
relative error = 1.0152852149339238583656078096818e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2278
Order of pole (three term test) = -2.327
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2564613004, alloc=4848776, time=135.20
x[1] = 8.11
y1[1] (analytic) = 0.74676928690946163813756506302267
y1[1] (numeric) = 0.74676928690946163813756506302267
absolute error = 5.8e-63
relative error = 7.7667896921732835213125394599866e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.967405915811794818039870659888
y2[1] (numeric) = 1.967405915811794818039870659888
absolute error = 2e-63
relative error = 1.0165670357734774565669327980965e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2362
Order of pole (three term test) = -2.443
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2568613664, alloc=4848776, time=135.41
x[1] = 8.12
y1[1] (analytic) = 0.73710805041499890375164420647488
y1[1] (numeric) = 0.73710805041499890375164420647488
absolute error = 5.8e-63
relative error = 7.8685885966576329729601973792484e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9648252809930911226495900140035
y2[1] (numeric) = 1.9648252809930911226495900140035
absolute error = 2e-63
relative error = 1.0179022121443441268192926308958e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2446
Order of pole (three term test) = -2.564
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2572614760, alloc=4848776, time=135.62
x[1] = 8.13
y1[1] (analytic) = 0.72747310289641877507529209311262
y1[1] (numeric) = 0.72747310289641877507529209311262
absolute error = 5.9e-63
relative error = 8.1102654881799406317435524578551e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9621481644503065055758478648868
y2[1] (numeric) = 1.9621481644503065055758478648868
absolute error = 2e-63
relative error = 1.0192910179952173191349911870845e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2528
Order of pole (three term test) = -2.688
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2576615420, alloc=4848776, time=135.83
x[1] = 8.14
y1[1] (analytic) = 0.71786540784044401395292156573867
y1[1] (numeric) = 0.71786540784044401395292156573867
absolute error = 5.9e-63
relative error = 8.2188108461013355705309617022213e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.95937483389286432226445263426
y2[1] (numeric) = 1.95937483389286432226445263426
absolute error = 2e-63
relative error = 1.0207337388458858816285037553581e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.261
Order of pole (three term test) = -2.817
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.15
y1[1] (analytic) = 0.70828592600857383200199339212464
y1[1] (numeric) = 0.70828592600857383200199339212464
absolute error = 5.9e-63
relative error = 8.3299692727885436521766267032316e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9565055666515092158395492118634
y2[1] (numeric) = 1.9565055666515092158395492118634
absolute error = 2e-63
relative error = 1.0222306719131548315435382679511e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.269
Order of pole (three term test) = -2.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2580616280, alloc=4848776, time=136.04
x[1] = 8.16
y1[1] (analytic) = 0.69873561534100854132376841810555
y1[1] (numeric) = 0.69873561534100854132376841810555
absolute error = 5.9e-63
relative error = 8.4438232007403603824026292200893e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9535406496505742737474900484332
y2[1] (numeric) = 1.9535406496505742737474900484332
absolute error = 1e-63
relative error = 5.1189106312114258103268783267092e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.277
Order of pole (three term test) = -3.087
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2584617396, alloc=4848776, time=136.25
x[1] = 8.17
y1[1] (analytic) = 0.6892154308608563327529367613304
y1[1] (numeric) = 0.6892154308608563327529367613304
absolute error = 6.0e-63
relative error = 8.7055508790709624647388791054932e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9504803793792888335509044160486
y2[1] (numeric) = 1.9504803793792888335509044160486
absolute error = 1e-63
relative error = 5.1269421142202672246488602528338e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2848
Order of pole (three term test) = -3.228
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2588618160, alloc=4848776, time=136.46
x[1] = 8.18
y1[1] (analytic) = 0.67972632457863176088847166404938
y1[1] (numeric) = 0.67972632457863176088847166404938
absolute error = 6.0e-63
relative error = 8.8270819932116826517976723046844e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9473250618621298070684763467843
y2[1] (numeric) = 1.9473250618621298070684763467843
absolute error = 1e-63
relative error = 5.1352494741876833277041043365337e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2925
Order of pole (three term test) = -3.373
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.19
y1[1] (analytic) = 0.67026924539705548597762058902613
y1[1] (numeric) = 0.67026924539705548597762058902613
absolute error = 5.9e-63
relative error = 8.8024328141520886299825498223851e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9440750126282194877033101243501
y2[1] (numeric) = 1.9440750126282194877033101243501
absolute error = 1e-63
relative error = 5.1438344379936626460445329282536e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3001
Order of pole (three term test) = -3.521
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2592619128, alloc=4848776, time=136.66
x[1] = 8.2
y1[1] (analytic) = 0.66084513901616479259951187548036
y1[1] (numeric) = 0.66084513901616479259951187548036
absolute error = 5.9e-63
relative error = 8.9279615626493718568509572624138e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9407305566797729011536487499456
y2[1] (numeric) = 1.9407305566797729011536487499456
absolute error = 1e-63
relative error = 5.1526987945756520523606370279498e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3076
Order of pole (three term test) = -3.673
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2596620804, alloc=4848776, time=136.87
x[1] = 8.21
y1[1] (analytic) = 0.65145494783874437401743429021275
y1[1] (numeric) = 0.65145494783874437401743429021275
absolute error = 6.0e-63
relative error = 9.2101533957267434113085733236719e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9372920284595978547445805237238
y2[1] (numeric) = 1.9372920284595978547445805237238
absolute error = 1e-63
relative error = 5.1618443957317659437539092630106e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.315
Order of pole (three term test) = -3.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2600621764, alloc=4848776, time=137.08
x[1] = 8.22
y1[1] (analytic) = 0.64209961087608683904254682894266
y1[1] (numeric) = 0.64209961087608683904254682894266
absolute error = 6.0e-63
relative error = 9.3443445508611081690450564001393e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9337597718176509353487173692576
y2[1] (numeric) = 1.9337597718176509353487173692576
absolute error = 1e-63
relative error = 5.1712731569549771476097422710048e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3222
Order of pole (three term test) = -3.989
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2604622740, alloc=4848776, time=137.29
x[1] = 8.23
y1[1] (analytic) = 0.63278006365409236527979974770724
y1[1] (numeric) = 0.63278006365409236527979974770724
absolute error = 6.0e-63
relative error = 9.4819675028192496143399523274392e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9301341399766528002681829243461
y2[1] (numeric) = 1.9301341399766528002681829243461
absolute error = 1e-63
relative error = 5.1809870582989436887832390953910e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3293
Order of pole (three term test) = -4.153
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.24
y1[1] (analytic) = 0.62349723811971688871249220409109
y1[1] (numeric) = 0.62349723811971688871249220409109
absolute error = 6.0e-63
relative error = 9.6231380560629650331784812980004e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9264154954967661995201683705964
y2[1] (numeric) = 1.9264154954967661995201683705964
absolute error = 1e-63
relative error = 5.1909881452761531838264816968861e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3363
Order of pole (three term test) = -4.319
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2608623432, alloc=4848776, time=137.50
x[1] = 8.25
y1[1] (analytic) = 0.61425206254777818472854847037505
y1[1] (numeric) = 0.61425206254777818472854847037505
absolute error = 6.0e-63
relative error = 9.7679769687925204027472419322993e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9226042102393402616943925628889
y2[1] (numeric) = 1.9226042102393402616943925628889
absolute error = 1e-63
relative error = 5.2012785297890950917739083579671e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3431
Order of pole (three term test) = -4.49
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2612624292, alloc=4848776, time=137.71
x[1] = 8.26
y1[1] (analytic) = 0.60504546144812915990274875070963
y1[1] (numeric) = 0.60504546144812915990274875070963
absolute error = 6.0e-63
relative error = 9.9166102091559658818561328434480e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9187006653297246689236677183023
y2[1] (numeric) = 1.9187006653297246689236677183023
absolute error = 1e-63
relative error = 5.2118603910952003855535004470991e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3498
Order of pole (three term test) = -4.663
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2616624968, alloc=4848776, time=137.92
x[1] = 8.27
y1[1] (analytic) = 0.59587835547320763712838104690138
y1[1] (numeric) = 0.59587835547320763712838104690138
absolute error = 6.0e-63
relative error = 1.0069169227056740838016632969197e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9147052511191574395190855236994
y2[1] (numeric) = 1.9147052511191574395190855236994
absolute error = 1e-63
relative error = 5.2227359768063184539308233475707e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3564
Order of pole (three term test) = -4.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.28
y1[1] (analytic) = 0.58675166132597187904275931870762
y1[1] (numeric) = 0.58675166132597187904275931870762
absolute error = 6.1e-63
relative error = 1.0396221096698564393437981144190e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9106183671457301294598000680928
y2[1] (numeric) = 1.9106183671457301294598000680928
absolute error = 1e-63
relative error = 5.2339076039235322431607251828502e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3628
Order of pole (three term test) = -5.021
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2620625720, alloc=4848776, time=138.12
TOP MAIN SOLVE Loop
x[1] = 8.29
y1[1] (analytic) = 0.57766629166823105611754524541246
y1[1] (numeric) = 0.57766629166823105611754524541246
absolute error = 6.1e-63
relative error = 1.0559729878618900667157838617165e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.9064404220944343561847297311685
y2[1] (numeric) = 1.9064404220944343561847297311685
absolute error = 1e-63
relative error = 5.2453776599081448440568210515547e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3691
Order of pole (three term test) = -5.204
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2624626476, alloc=4848776, time=138.34
x[1] = 8.3
y1[1] (analytic) = 0.56862315502937982629067353455349
y1[1] (numeric) = 0.56862315502937982629067353455349
absolute error = 6.1e-63
relative error = 1.0727667253868377905886017378288e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.902171833756293640000504405253
y2[1] (numeric) = 1.902171833756293640000504405253
absolute error = 1e-63
relative error = 5.2571486037897039696183511181892e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3752
Order of pole (three term test) = -5.391
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2628627156, alloc=4848776, time=138.55
x[1] = 8.31
y1[1] (analytic) = 0.55962315571554615260586332180965
y1[1] (numeric) = 0.55962315571554615260586332180965
absolute error = 6.1e-63
relative error = 1.0900192277069753043865016043739e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8978130289865846498874605706974
y2[1] (numeric) = 1.8978130289865846498874605706974
absolute error = 1e-63
relative error = 5.2692229673119650981843501278805e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3812
Order of pole (three term test) = -5.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2632627932, alloc=4848776, time=138.75
x[1] = 8.32
y1[1] (analytic) = 0.55066719371916144400224181130983
y1[1] (numeric) = 0.55066719371916144400224181130983
absolute error = 6.1e-63
relative error = 1.1077471237756322608385101511792e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8933644436621520315442881127292
y2[1] (numeric) = 1.8933644436621520315442881127292
absolute error = 1e-63
relative error = 5.2816033561177295268006230303096e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.387
Order of pole (three term test) = -5.773
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.33
y1[1] (analytic) = 0.54175616462896206216464322918317
y1[1] (numeric) = 0.54175616462896206216464322918317
absolute error = 6.1e-63
relative error = 1.1259678058629508586328512231492e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8888265226378210861529535570277
y2[1] (numeric) = 1.8888265226378210861529535570277
absolute error = 1e-63
relative error = 5.2942924509735302406499564825221e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3926
Order of pole (three term test) = -5.968
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2636628588, alloc=4848776, time=138.96
x[1] = 8.34
y1[1] (analytic) = 0.53289095954043119420889956615966
y1[1] (numeric) = 0.53289095954043119420889956615966
absolute error = 6.1e-63
relative error = 1.1446994719633978578280292203655e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8841997197019126585597005850824
y2[1] (numeric) = 1.8841997197019126585597005850824
absolute error = 1e-63
relative error = 5.3072930090351764107617969067656e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3981
Order of pole (three term test) = -6.167
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2640629312, alloc=4848776, time=139.17
x[1] = 8.35
y1[1] (analytic) = 0.52407246496669004694022305615659
y1[1] (numeric) = 0.52407246496669004694022305615659
absolute error = 6.1e-63
relative error = 1.1639611709780850477780453863856e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8794844975308646833462389263335
y2[1] (numeric) = 1.8794844975308646833462389263335
absolute error = 1e-63
relative error = 5.3206078651552065398360521724259e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4035
Order of pole (three term test) = -6.367
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2644630204, alloc=4848776, time=139.38
x[1] = 8.36
y1[1] (analytic) = 0.51530156274984727349099746200915
y1[1] (numeric) = 0.51530156274984727349099746200915
absolute error = 6.2e-63
relative error = 1.2031789631908772186675334041289e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8746813276429649265986992559849
y2[1] (numeric) = 1.8746813276429649265986992559849
absolute error = 1e-63
relative error = 5.3342399332333408433575199229826e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4087
Order of pole (three term test) = -6.571
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.37
y1[1] (analytic) = 0.5065791299728154973214391576657
y1[1] (numeric) = 0.5065791299728154973214391576657
absolute error = 6.1e-63
relative error = 1.2041554100989797309084550010400e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8697906903511995500616212829926
y2[1] (numeric) = 1.8697906903511995500616212829926
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
bytes used=2648630888, alloc=4848776, time=139.59
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4137
Order of pole (three term test) = -6.777
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.38
y1[1] (analytic) = 0.49790603887160375185724195569388
y1[1] (numeric) = 0.49790603887160375185724195569388
absolute error = 6.1e-63
relative error = 1.2251307523452275140720711036351e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.86481307471522221278126689719
y2[1] (numeric) = 1.86481307471522221278126689719
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4186
Order of pole (three term test) = -6.986
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2652632336, alloc=4848776, time=139.80
x[1] = 8.39
y1[1] (analytic) = 0.48928315674809460644715252561116
y1[1] (numeric) = 0.48928315674809460644715252561116
absolute error = 6.1e-63
relative error = 1.2467218451871948599751462590133e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8597489784924485132880684290261
y2[1] (numeric) = 1.8597489784924485132880684290261
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4233
Order of pole (three term test) = -7.197
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2656633176, alloc=4848776, time=140.01
x[1] = 8.4
y1[1] (analytic) = 0.48071134588331470085519515941454
y1[1] (numeric) = 0.48071134588331470085519515941454
absolute error = 6.2e-63
relative error = 1.2897552872623386790579303051678e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8545989080882806628332392814224
y2[1] (numeric) = 1.8545989080882806628332392814224
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4278
Order of pole (three term test) = -7.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2660633944, alloc=4848776, time=140.22
x[1] = 8.41
y1[1] (analytic) = 0.47219146345120736116182234815788
y1[1] (numeric) = 0.47219146345120736116182234815788
absolute error = 6.2e-63
relative error = 1.3130267020679971222285497181914e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8493633785054673671707439719806
y2[1] (numeric) = 1.8493633785054673671707439719806
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4321
Order of pole (three term test) = -7.626
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.42
y1[1] (analytic) = 0.46372436143291591974054514062359
y1[1] (numeric) = 0.46372436143291591974054514062359
absolute error = 6.1e-63
relative error = 1.3154366057351180477831323457146e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8440429132926039808542494306898
y2[1] (numeric) = 1.8440429132926039808542494306898
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4363
Order of pole (three term test) = -7.843
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2664635156, alloc=4848776, time=140.43
x[1] = 8.43
y1[1] (analytic) = 0.45531088653158631090661529246805
y1[1] (numeric) = 0.45531088653158631090661529246805
absolute error = 6.1e-63
relative error = 1.3397439377010864233937451767535e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8386380444917780839907114629715
y2[1] (numeric) = 1.8386380444917780839907114629715
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4403
Order of pole (three term test) = -8.063
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2668636260, alloc=4848776, time=140.63
x[1] = 8.44
y1[1] (analytic) = 0.44695188008769746190719673732551
y1[1] (numeric) = 0.44695188008769746190719673732551
absolute error = 6.1e-63
relative error = 1.3648001656919095842225743939260e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8331493125853657168492924788063
y2[1] (numeric) = 1.8331493125853657168492924788063
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4441
Order of pole (three term test) = -8.285
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2672636988, alloc=4848776, time=140.85
x[1] = 8.45
y1[1] (analytic) = 0.43864817799492794614336959040814
y1[1] (numeric) = 0.43864817799492794614336959040814
absolute error = 6.2e-63
relative error = 1.4134334327661769302818169837220e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8275772664419835926578132727978
y2[1] (numeric) = 1.8275772664419835926578132727978
absolute error = 1e-63
relative error = 5.4717248805947815829525503016178e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4478
Order of pole (three term test) = -8.508
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2676638016, alloc=4848776, time=141.06
x[1] = 8.46
y1[1] (analytic) = 0.43040061061656731188853359559002
y1[1] (numeric) = 0.43040061061656731188853359559002
absolute error = 6.2e-63
relative error = 1.4405184024061291198041936861568e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.821922463261602693320419537459
y2[1] (numeric) = 1.821922463261602693320419537459
absolute error = 1e-63
relative error = 5.4887077807350900759550916784442e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4512
Order of pole (three term test) = -8.734
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.47
y1[1] (analytic) = 0.42221000270248044530068218175304
y1[1] (numeric) = 0.42221000270248044530068218175304
absolute error = 6.2e-63
relative error = 1.4684635513879490484291567312657e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8161854685198287366511528252971
y2[1] (numeric) = 1.8161854685198287366511528252971
absolute error = 1e-63
relative error = 5.5060455957451804002762446663009e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4545
Order of pole (three term test) = -8.961
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2680638868, alloc=4848776, time=141.26
x[1] = 8.48
y1[1] (analytic) = 0.41407717330663327122304976748636
y1[1] (numeric) = 0.41407717330663327122304976748636
absolute error = 6.2e-63
relative error = 1.4973054299249583072334082074927e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.810366855911355087030269813403
y2[1] (numeric) = 1.810366855911355087030269813403
absolute error = 1e-63
relative error = 5.5237423107627041402291206236722e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4576
Order of pole (three term test) = -9.189
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2684639580, alloc=4848776, time=141.47
x[1] = 8.49
y1[1] (analytic) = 0.40600293570518803913432389583803
y1[1] (numeric) = 0.40600293570518803913432389583803
absolute error = 6.2e-63
relative error = 1.5270825540291221001344932626931e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.8044672072925937641451218212426
y2[1] (numeric) = 1.8044672072925937641451218212426
absolute error = 1e-63
relative error = 5.5418020120209939005867274520417e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4606
Order of pole (three term test) = -9.419
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2688640420, alloc=4848776, time=141.68
x[1] = 8.5
y1[1] (analytic) = 0.397988097315176384651573477043
y1[1] (numeric) = 0.397988097315176384651573477043
absolute error = 6.1e-63
relative error = 1.5327091541557492109388883507652e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7984871126234902866669131603391
y2[1] (numeric) = 1.7984871126234902866669131603391
absolute error = 2e-63
relative error = 1.1120457777885095343512874607727e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4633
Order of pole (three term test) = -9.651
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.51
y1[1] (analytic) = 0.39003345961375829921197062356349
y1[1] (numeric) = 0.39003345961375829921197062356349
absolute error = 6.2e-63
relative error = 1.5896072111709918242081078178941e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7924271699085281693304831713681
y2[1] (numeric) = 1.7924271699085281693304831713681
absolute error = 2e-63
relative error = 1.1158054472595752757596574258110e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4659
Order of pole (three term test) = -9.884
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2692641164, alloc=4848776, time=141.89
x[1] = 8.52
y1[1] (analytic) = 0.38213981805807508196905393760653
y1[1] (numeric) = 0.38213981805807508196905393760653
absolute error = 6.2e-63
relative error = 1.6224428094163600110707195046227e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7862879851369289729182412152366
y2[1] (numeric) = 1.7862879851369289729182412152366
absolute error = 2e-63
relative error = 1.1196402912863397023164106907546e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.93
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4682
Order of pole (three term test) = -10.12
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2696642204, alloc=4848776, time=142.10
x[1] = 8.53
y1[1] (analytic) = 0.37430796200570428854155464066714
y1[1] (numeric) = 0.37430796200570428854155464066714
absolute error = 6.2e-63
relative error = 1.6563900930072961498267938394453e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7800701722220538870934230990784
y2[1] (numeric) = 1.7800701722220538870934230990784
absolute error = 1e-63
relative error = 5.6177560615585414291118667295314e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.24
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4704
Order of pole (three term test) = -10.35
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2700643980, alloc=4848776, time=142.31
x[1] = 8.54
y1[1] (analytic) = 0.36653867463572463105362334073292
y1[1] (numeric) = 0.36653867463572463105362334073292
absolute error = 6.1e-63
relative error = 1.6642172905935052216192150876893e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7737743529400129058738870988791
y2[1] (numeric) = 1.7737743529400129058738870988791
absolute error = 1e-63
relative error = 5.6376956761298876335587558712645e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4724
Order of pole (three term test) = -10.59
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2704644856, alloc=4848776, time=142.52
x[1] = 8.55
y1[1] (analytic) = 0.35883273287039872291067438377066
y1[1] (numeric) = 0.35883273287039872291067438377066
absolute error = 6.1e-63
relative error = 1.6999563978471175876732408994926e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7674011568674877347777433492199
y2[1] (numeric) = 1.7674011568674877347777433492199
absolute error = 1e-63
relative error = 5.6580250392750861567069740918783e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4742
Order of pole (three term test) = -10.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.56
y1[1] (analytic) = 0.35119090729748149997110604325389
y1[1] (numeric) = 0.35119090729748149997110604325389
absolute error = 6.1e-63
relative error = 1.7369470203375464815768804584018e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7609512213187746472982879658692
y2[1] (numeric) = 1.7609512213187746472982879658692
absolute error = 1e-63
relative error = 5.6787490073183343379484757827473e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4758
Order of pole (three term test) = -11.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2708645716, alloc=4848776, time=142.73
x[1] = 8.57
y1[1] (analytic) = 0.34361396209316208720703660916504
y1[1] (numeric) = 0.34361396209316208720703660916504
absolute error = 6.0e-63
relative error = 1.7461455766961106007318052819557e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.754425191282053586370130296421
y2[1] (numeric) = 1.754425191282053586370130296421
absolute error = 1e-63
relative error = 5.6998725563741238503580034901276e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4772
Order of pole (three term test) = -11.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2712646964, alloc=4848776, time=142.94
x[1] = 8.58
y1[1] (analytic) = 0.33610265494564681660317540579733
y1[1] (numeric) = 0.33610265494564681660317540579733
absolute error = 6.0e-63
relative error = 1.7851688797192917488666864870032e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7478237193548898838632577811713
y2[1] (numeric) = 1.7478237193548898838632577811713
absolute error = 1e-63
relative error = 5.7214007850236370089378616349995e-62 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4785
Order of pole (three term test) = -11.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2716647624, alloc=4848776, time=143.15
x[1] = 8.59
y1[1] (analytic) = 0.32865773697939103792835824510594
y1[1] (numeric) = 0.32865773697939103792835824510594
absolute error = 6.0e-63
relative error = 1.8256074100504862718976203753958e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7411474656789750478793406298218
y2[1] (numeric) = 1.7411474656789750478793406298218
absolute error = 2e-63
relative error = 1.1486677834149350679831064105705e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.21
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4795
Order of pole (three term test) = -11.78
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.6
y1[1] (analytic) = 0.32127995267998729913553021483952
y1[1] (numeric) = 0.32127995267998729913553021483952
absolute error = 6.0e-63
relative error = 1.8675301555389401125188149317393e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7343970978741131437171641875635
y2[1] (numeric) = 1.7343970978741131437171641875635
absolute error = 2e-63
relative error = 1.1531384608815604554818088651748e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4803
Order of pole (three term test) = -12.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2720648560, alloc=4848776, time=143.35
TOP MAIN SOLVE Loop
x[1] = 8.61
y1[1] (analytic) = 0.31397003981971740750954282881698
y1[1] (numeric) = 0.31397003981971740750954282881698
absolute error = 5.9e-63
relative error = 1.8791601910130656763960605205864e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7275732909714593698140812814806
y2[1] (numeric) = 1.7275732909714593698140812814806
absolute error = 2e-63
relative error = 1.1576932859822971736045100632146e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.92
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.481
Order of pole (three term test) = -12.26
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2724649608, alloc=4848776, time=143.56
x[1] = 8.62
y1[1] (analytic) = 0.30672872938377581629461101739017
y1[1] (numeric) = 0.30672872938377581629461101739017
absolute error = 5.9e-63
relative error = 1.9235237637678148413607658241301e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7206767273460175047502560674387
y2[1] (numeric) = 1.7206767273460175047502560674387
absolute error = 2e-63
relative error = 1.1623333821018271396874654346258e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -12.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2728650460, alloc=4848776, time=143.77
x[1] = 8.63
y1[1] (analytic) = 0.29955674549717171440128690618464
y1[1] (numeric) = 0.29955674549717171440128690618464
absolute error = 5.9e-63
relative error = 1.9695767458709105435447685328582e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7137080966484029755147470130818
y2[1] (numeric) = 1.7137080966484029755147470130818
absolute error = 2e-63
relative error = 1.1670599000562082238068689866437e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -12.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2732651256, alloc=4848776, time=143.97
x[1] = 8.64
y1[1] (analytic) = 0.29245480535231712892306496354556
y1[1] (numeric) = 0.29245480535231712892306496354556
absolute error = 5.9e-63
relative error = 2.0174057297134625824814608658938e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.7066680957358783706697384884108
y2[1] (numeric) = 1.7066680957358783706697384884108
absolute error = 2e-63
relative error = 1.1718740187368670863104847903672e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.02
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.98
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.65
y1[1] (analytic) = 0.28542361913730828159202380941506
y1[1] (numeric) = 0.28542361913730828159202380941506
absolute error = 5.9e-63
relative error = 2.0671029320673340930625661611184e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6995574286026682948041343266528
y2[1] (numeric) = 1.6995574286026682948041343266528
absolute error = 2e-63
relative error = 1.1767769457748466530341073726831e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -13.23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2736652600, alloc=4848776, time=144.18
x[1] = 8.66
y1[1] (analytic) = 0.27846388996490737097809378439138
y1[1] (numeric) = 0.27846388996490737097809378439138
absolute error = 5.9e-63
relative error = 2.1187666381962598152967436233347e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6923768063095605327329972350144
y2[1] (numeric) = 1.6923768063095605327329972350144
absolute error = 2e-63
relative error = 1.1817699182259832238247621401914e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4814
Order of pole (three term test) = -13.47
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.23
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2740653700, alloc=4848776, time=144.38
x[1] = 8.67
y1[1] (analytic) = 0.27157631380223188219454870131795
y1[1] (numeric) = 0.27157631380223188219454870131795
absolute error = 5.9e-63
relative error = 2.1725016874249628767374823139129e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6851269469128005632677486104297
y2[1] (numeric) = 1.6851269469128005632677486104297
absolute error = 2e-63
relative error = 1.1868542032777148498172593318813e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.81
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = -13.71
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.87
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2744654428, alloc=4848776, time=144.59
x[1] = 8.68
y1[1] (analytic) = 0.26476157940115845512015918362236
y1[1] (numeric) = 0.26476157940115845512015918362236
absolute error = 5.9e-63
relative error = 2.2284200046489769332285122366982e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6778085753922865330464973659755
y2[1] (numeric) = 1.6778085753922865330464973659755
absolute error = 2e-63
relative error = 1.1920310989782503959953929806835e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4802
Order of pole (three term test) = -13.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2748655224, alloc=4848776, time=144.80
x[1] = 8.69
y1[1] (analytic) = 0.2580203682294482706931887919121
y1[1] (numeric) = 0.2580203682294482706931887919121
absolute error = 5.9e-63
relative error = 2.2866411828206296291538456073515e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6704224235790718708672774127254
y2[1] (numeric) = 1.6704224235790718708672774127254
absolute error = 2e-63
relative error = 1.1973019349888576828048187832702e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4793
Order of pole (three term test) = -14.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.7
y1[1] (analytic) = 0.25135335440260084268120821911072
y1[1] (numeric) = 0.25135335440260084268120821911072
absolute error = 5.9e-63
relative error = 2.3472931220761741298758565193167e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6629692300821827922023461866156
y2[1] (numeric) = 1.6629692300821827922023461866156
absolute error = 2e-63
relative error = 1.2026680733600593317283773220652e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4782
Order of pole (three term test) = -14.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2752656604, alloc=4848776, time=145.01
x[1] = 8.71
y1[1] (analytic) = 0.24476120461644302949076225515113
y1[1] (numeric) = 0.24476120461644302949076225515113
absolute error = 5.8e-63
relative error = 2.3696565838891759846655507817143e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6554497402147580120821075808528
y2[1] (numeric) = 1.6554497402147580120821075808528
absolute error = 2e-63
relative error = 1.2081309093325564855727913648178e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.477
Order of pole (three term test) = -14.67
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2756657404, alloc=4848776, time=145.22
x[1] = 8.72
y1[1] (analytic) = 0.23824457808046000705953291829004
y1[1] (numeric) = 0.23824457808046000705953291829004
absolute error = 5.8e-63
relative error = 2.4344730305011276385884289576032e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.647864705919518052315820857473
y2[1] (numeric) = 1.647864705919518052315820857473
absolute error = 3e-63
relative error = 1.8205378082456002481069538476631e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.01
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4755
Order of pole (three term test) = -14.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.16
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2760658908, alloc=4848776, time=145.43
x[1] = 8.73
y1[1] (analytic) = 0.23180412645187486967815219933192
y1[1] (numeric) = 0.23180412645187486967815219933192
absolute error = 5.8e-63
relative error = 2.5021124898758628857075112816317e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6402148856935715960562647635402
y2[1] (numeric) = 1.6402148856935715960562647635402
absolute error = 3e-63
relative error = 1.8290286389709465949861215340725e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4739
Order of pole (three term test) = -15.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.74
y1[1] (analytic) = 0.22544049377048345072664875461818
y1[1] (numeric) = 0.22544049377048345072664875461818
absolute error = 5.8e-63
relative error = 2.5727409938628267692027330909304e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6325010445125664090102392232487
y2[1] (numeric) = 1.6325010445125664090102392232487
absolute error = 3e-63
relative error = 1.8376711059904666868075777949683e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.33
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.472
Order of pole (three term test) = -15.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2764659800, alloc=4848776, time=145.63
x[1] = 8.75
y1[1] (analytic) = 0.21915431639425087978915076807331
y1[1] (numeric) = 0.21915431639425087978915076807331
absolute error = 5.7e-63
relative error = 2.6009070201227071387763326096702e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6247239537541924121395762007922
y2[1] (numeric) = 1.6247239537541924121395762007922
absolute error = 3e-63
relative error = 1.8464675141078616273700156931128e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.47
Order of pole (three term test) = -15.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2768660564, alloc=4848776, time=145.84
x[1] = 8.76
y1[1] (analytic) = 0.2129462229356763164374641551822
y1[1] (numeric) = 0.2129462229356763164374641551822
absolute error = 5.7e-63
relative error = 2.6767321445855241651784882847871e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6168843911210445554816424059899
y2[1] (numeric) = 1.6168843911210445554816424059899
absolute error = 3e-63
relative error = 1.8554202245220459201594703271791e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4678
Order of pole (three term test) = -15.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2772661256, alloc=4848776, time=146.05
x[1] = 8.77
y1[1] (analytic) = 0.20681683419893222415711853932893
y1[1] (numeric) = 0.20681683419893222415711853932893
absolute error = 5.6e-63
relative error = 2.7077099510253079160382707702903e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6089831405628532067376710681854
y2[1] (numeric) = 1.6089831405628532067376710681854
absolute error = 3e-63
relative error = 1.8645316562798429188008702946527e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4654
Order of pole (three term test) = -16.09
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.59
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2776661928, alloc=4848776, time=146.26
x[1] = 8.78
y1[1] (analytic) = 0.20076676311778447043610463211708
y1[1] (numeric) = 0.20076676311778447043610463211708
absolute error = 5.6e-63
relative error = 2.7893063139712176010170425255761e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.6010209921980898315252561517565
y2[1] (numeric) = 1.6010209921980898315252561517565
absolute error = 3e-63
relative error = 1.8738042877758959604716851669953e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.04
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4628
Order of pole (three term test) = -16.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.29
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.79
y1[1] (analytic) = 0.19479661469429946095456106645153
y1[1] (numeric) = 0.19479661469429946095456106645153
absolute error = 5.5e-63
relative error = 2.8234576913111787810369183083636e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5929987422349558046616553817875
y2[1] (numeric) = 1.5929987422349558046616553817875
absolute error = 3e-63
relative error = 1.8832406583014876453412970611916e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.46
Order of pole (three term test) = -16.55
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.99
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2780662860, alloc=4848776, time=146.46
x[1] = 8.8
y1[1] (analytic) = 0.18890698593834443711091449578068
y1[1] (numeric) = 0.18890698593834443711091449578068
absolute error = 5.5e-63
relative error = 2.9114857625197052984144840119642e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5849171928917622535309313118124
y2[1] (numeric) = 1.5849171928917622535309313118124
absolute error = 4e-63
relative error = 2.5237911595253730506194238863723e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4571
Order of pole (three term test) = -16.78
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2784663600, alloc=4848776, time=146.68
x[1] = 8.81
y1[1] (analytic) = 0.18309846580788698680430409481551
y1[1] (numeric) = 0.18309846580788698680430409481551
absolute error = 5.5e-63
relative error = 3.0038482167135050279195086457515e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.576777152316708895484243810161
y2[1] (numeric) = 1.576777152316708895484243810161
absolute error = 4e-63
relative error = 2.5368201169854131059271840875591e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4539
Order of pole (three term test) = -17.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2788664264, alloc=4848776, time=146.88
x[1] = 8.82
y1[1] (analytic) = 0.17737163515009973847246197742839
y1[1] (numeric) = 0.17737163515009973847246197742839
absolute error = 5.5e-63
relative error = 3.1008340174265497690076616471254e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5685794345070698913227031896634
y2[1] (numeric) = 1.5685794345070698913227031896634
absolute error = 4e-63
relative error = 2.5500780591688748328143825225925e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4506
Order of pole (three term test) = -17.24
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.83
y1[1] (analytic) = 0.17172706664327612786656648565256
y1[1] (numeric) = 0.17172706664327612786656648565256
absolute error = 5.4e-63
relative error = 3.1445246841706498216528457491053e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5603248592277947962100907977845
y2[1] (numeric) = 1.5603248592277947962100907977845
absolute error = 5e-63
relative error = 3.2044608982737744632154970027393e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4471
Order of pole (three term test) = -17.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2792665056, alloc=4848776, time=147.10
TOP MAIN SOLVE Loop
x[1] = 8.84
y1[1] (analytic) = 0.1661653247395630459379874981106
y1[1] (numeric) = 0.1661653247395630459379874981106
absolute error = 5.3e-63
relative error = 3.1895944646134099702027003104053e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5520142519295327478525234803321
y2[1] (numeric) = 1.5520142519295327478525234803321
absolute error = 5e-63
relative error = 3.2216199005800229609344468279950e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4434
Order of pole (three term test) = -17.69
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2796666044, alloc=4848776, time=147.30
x[1] = 8.85
y1[1] (analytic) = 0.16068696560851609452441244898895
y1[1] (numeric) = 0.16068696560851609452441244898895
absolute error = 5.2e-63
relative error = 3.2361056668832945977905446128995e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5436484436660880894579310034853
y2[1] (numeric) = 1.5436484436660880894579310034853
absolute error = 5e-63
relative error = 3.2390794811578012499528778657290e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4396
Order of pole (three term test) = -17.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2800667056, alloc=4848776, time=147.51
x[1] = 8.86
y1[1] (analytic) = 0.15529253708148309426274731481916
y1[1] (numeric) = 0.15529253708148309426274731481916
absolute error = 5.2e-63
relative error = 3.3485189293233860712916862131875e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.535228271011315681844263734824
y2[1] (numeric) = 1.535228271011315681844263734824
absolute error = 5e-63
relative error = 3.2568446623942782916509735197626e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4355
Order of pole (three term test) = -18.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2804668244, alloc=4848776, time=147.72
x[1] = 8.87
y1[1] (analytic) = 0.14998257859682140633165435671775
y1[1] (numeric) = 0.14998257859682140633165435671775
absolute error = 5.1e-63
relative error = 3.4003949310070634683538750177793e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5267545759754642150959660868594
y2[1] (numeric) = 1.5267545759754642150959660868594
absolute error = 5e-63
relative error = 3.2749205921360557606911941824039e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4313
Order of pole (three term test) = -18.34
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.88
y1[1] (analytic) = 0.14475762114595454624590028460325
y1[1] (numeric) = 0.14475762114595454624590028460325
absolute error = 5.1e-63
relative error = 3.5231305679290147811482732093398e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5182282059209758853678364011496
y2[1] (numeric) = 1.5182282059209758853678364011496
absolute error = 5e-63
relative error = 3.2933125471522501197989876501942e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.427
Order of pole (three term test) = -18.56
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2808669572, alloc=4848776, time=147.93
x[1] = 8.89
y1[1] (analytic) = 0.13961818722027348399618273657824
y1[1] (numeric) = 0.13961818722027348399618273657824
absolute error = 5.0e-63
relative error = 3.5811953295966923555516347301109e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5096500134777508567984261849018
y2[1] (numeric) = 1.5096500134777508567984261849018
absolute error = 5e-63
relative error = 3.3120259367146951900804205220862e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4224
Order of pole (three term test) = -18.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2812670644, alloc=4848776, time=148.15
x[1] = 8.9
y1[1] (analytic) = 0.13456479075888794036017232177465
y1[1] (numeric) = 0.13456479075888794036017232177465
absolute error = 4.9e-63
relative error = 3.6413685722439674161235953108424e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.5010208564578849820161746471113
y2[1] (numeric) = 1.5010208564578849820161746471113
absolute error = 5e-63
relative error = 3.3310663062997139090019880364425e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4177
Order of pole (three term test) = -18.98
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2816671704, alloc=4848776, time=148.36
x[1] = 8.91
y1[1] (analytic) = 0.12959793709723290421159868118538
y1[1] (numeric) = 0.12959793709723290421159868118538
absolute error = 4.8e-63
relative error = 3.7037626581962674315803825007556e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.492341597769889307395176258041
y2[1] (numeric) = 1.492341597769889307395176258041
absolute error = 5e-63
relative error = 3.3504393414161011126513599647418e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4128
Order of pole (three term test) = -19.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2820673004, alloc=4848776, time=148.57
x[1] = 8.92
y1[1] (analytic) = 0.12471812291653551013282189839333
y1[1] (numeric) = 0.12471812291653551013282189839333
absolute error = 4.8e-63
relative error = 3.8486788349214333158247000928149e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4836131053323999410385722479477
y2[1] (numeric) = 1.4836131053323999410385722479477
absolute error = 5e-63
relative error = 3.3701508715641616343103007303253e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4078
Order of pole (three term test) = -19.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.93
y1[1] (analytic) = 0.11992583619414732960101720810331
y1[1] (numeric) = 0.11992583619414732960101720810331
absolute error = 4.8e-63
relative error = 4.0024736556594062680147170064973e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.474836251987386912430859502249
y2[1] (numeric) = 1.474836251987386912430859502249
absolute error = 4e-63
relative error = 2.7121654994646882201446929094721e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4025
Order of pole (three term test) = -19.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2824673888, alloc=4848776, time=148.77
x[1] = 8.94
y1[1] (analytic) = 0.1152215561547470424774647646268
y1[1] (numeric) = 0.1152215561547470424774647646268
absolute error = 4.7e-63
relative error = 4.0790978327768084853979298289262e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4660119154128707028008259130412
y2[1] (numeric) = 1.4660119154128707028008259130412
absolute error = 5e-63
relative error = 3.4106134796263628018907972098060e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3972
Order of pole (three term test) = -19.8
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2828674772, alloc=4848776, time=148.98
x[1] = 8.95
y1[1] (analytic) = 0.11060575322241836849213123646506
y1[1] (numeric) = 0.11060575322241836849213123646506
absolute error = 4.7e-63
relative error = 4.2493268777336713097076858033154e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4571409780351551744693399111853
y2[1] (numeric) = 1.4571409780351551744693399111853
absolute error = 5e-63
relative error = 3.4313769740674806166947163206650e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3916
Order of pole (three term test) = -20
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2832675688, alloc=4848776, time=149.19
x[1] = 8.96
y1[1] (analytic) = 0.10607888897360805089045984485144
y1[1] (numeric) = 0.10607888897360805089045984485144
absolute error = 4.6e-63
relative error = 4.3363953417201223249757495027312e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4482243269405856758159204182652
y2[1] (numeric) = 1.4482243269405856758159204182652
absolute error = 4e-63
relative error = 2.7620030444110213764404270902682e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3859
Order of pole (three term test) = -20.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.97
y1[1] (analytic) = 0.10164141609096859640480261762689
y1[1] (numeric) = 0.10164141609096859640480261762689
absolute error = 4.6e-63
relative error = 4.5257141989078756202694467295928e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4392628537868411459800558940076
y2[1] (numeric) = 1.4392628537868411459800558940076
absolute error = 4e-63
relative error = 2.7792004702098781376050350230490e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3801
Order of pole (three term test) = -20.38
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2836676888, alloc=4848776, time=149.40
x[1] = 8.98
y1[1] (analytic) = 0.097293778318090387238033460080346
y1[1] (numeric) = 0.097293778318090387238033460080346
absolute error = 4.53e-63
relative error = 4.6560017282808218966499616932728e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4302574547137690900128793475898
y2[1] (numeric) = 1.4302574547137690900128793475898
absolute error = 4e-63
relative error = 2.7966992843260528791391443508449e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3741
Order of pole (three term test) = -20.57
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2840677556, alloc=4848776, time=149.61
x[1] = 8.99
y1[1] (analytic) = 0.093036410415127691810420567177367
y1[1] (numeric) = 0.093036410415127691810420567177367
absolute error = 4.50e-63
relative error = 4.8368160163542824945542641936373e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4212090302537723409073802056387
y2[1] (numeric) = 1.4212090302537723409073802056387
absolute error = 4e-63
relative error = 2.8145050550978813184659793169937e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.368
Order of pole (three term test) = -20.76
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2844678784, alloc=4848776, time=149.81
x[1] = 9
y1[1] (analytic) = 0.088869738115323011631705288818835
y1[1] (numeric) = 0.088869738115323011631705288818835
absolute error = 4.45e-63
relative error = 5.0073288099773599130359529233717e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4121184852417565697562725663524
y2[1] (numeric) = 1.4121184852417565697562725663524
absolute error = 5e-63
relative error = 3.5407793696178358045765648864313e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3617
Order of pole (three term test) = -20.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2848679872, alloc=4848776, time=150.02
x[1] = 9.01
y1[1] (analytic) = 0.084794178082434111827470650068928
y1[1] (numeric) = 0.084794178082434111827470650068928
absolute error = 4.41e-63
relative error = 5.2008287593904654686655600669229e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.4029867287246475492114605615293
y2[1] (numeric) = 1.4029867287246475492114605615293
absolute error = 5e-63
relative error = 3.5638255855385985687117320633540e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3552
Order of pole (three term test) = -21.12
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.02
y1[1] (analytic) = 0.080810137869067992581269533196919
y1[1] (numeric) = 0.080810137869067992581269533196919
absolute error = 4.35e-63
relative error = 5.3829879699599748340701544173951e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3938146738704872184433528508576
y2[1] (numeric) = 1.3938146738704872184433528508576
absolute error = 4e-63
relative error = 2.8698219892407867047602948350208e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3487
Order of pole (three term test) = -21.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2852681288, alloc=4848776, time=150.23
x[1] = 9.03
y1[1] (analytic) = 0.076918015875925968060646733988494
y1[1] (numeric) = 0.076918015875925968060646733988494
absolute error = 4.34e-63
relative error = 5.6423712319890277519832891396691e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3846032378771176399177772903271
y2[1] (numeric) = 1.3846032378771176399177772903271
absolute error = 4e-63
relative error = 2.8889142323058734598603244988234e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3419
Order of pole (three term test) = -21.47
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2856681980, alloc=4848776, time=150.44
x[1] = 9.04
y1[1] (analytic) = 0.07311820131196392828519996910056
y1[1] (numeric) = 0.07311820131196392828519996910056
absolute error = 4.25e-63
relative error = 5.8125062210804082295404512239037e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3753533418804619795187216342643
y2[1] (numeric) = 1.3753533418804619795187216342643
absolute error = 4e-63
relative error = 2.9083435348555379662109802892884e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3351
Order of pole (three term test) = -21.64
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2860682828, alloc=4848776, time=150.65
x[1] = 9.05
y1[1] (analytic) = 0.069411074155471767877293357247927
y1[1] (numeric) = 0.069411074155471767877293357247927
absolute error = 4.25e-63
relative error = 6.1229422706822738482107049425383e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3660659108624116818424557351316
y2[1] (numeric) = 1.3660659108624116818424557351316
absolute error = 4e-63
relative error = 2.9281164021395996983778823463499e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3281
Order of pole (three term test) = -21.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.06
y1[1] (analytic) = 0.065797005116075873720114601611839
y1[1] (numeric) = 0.065797005116075873720114601611839
absolute error = 4.17e-63
relative error = 6.3376744771946519101585286033412e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3567418735583290518687453974845
y2[1] (numeric) = 1.3567418735583290518687453974845
absolute error = 3e-63
relative error = 2.2111796344369436080589975463545e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.321
Order of pole (three term test) = -21.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2864683680, alloc=4848776, time=150.86
x[1] = 9.07
y1[1] (analytic) = 0.0622763555976684712426455796823
y1[1] (numeric) = 0.0622763555976684712426455796823
absolute error = 4.17e-63
relative error = 6.6959602243585978852814153306004e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3473821623641744926739098396967
y2[1] (numeric) = 1.3473821623641744926739098396967
absolute error = 4e-63
relative error = 2.9687197231269772450343624020585e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3137
Order of pole (three term test) = -22.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2868684868, alloc=4848776, time=151.07
x[1] = 9.08
y1[1] (analytic) = 0.058849477662267536366025735019854
y1[1] (numeric) = 0.058849477662267536366025735019854
absolute error = 4.12e-63
relative error = 7.0009117559961224301194877458778e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3379877132432676863845577471149
y2[1] (numeric) = 1.3379877132432676863845577471149
absolute error = 4e-63
relative error = 2.9895640747731856519907639287428e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3064
Order of pole (three term test) = -22.28
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2872685812, alloc=4848776, time=151.28
x[1] = 9.09
y1[1] (analytic) = 0.055516713994810887089996994941924
y1[1] (numeric) = 0.055516713994810887089996994941924
absolute error = 4.07e-63
relative error = 7.3311255424455063784422968653707e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3285594656326920421762077861611
y2[1] (numeric) = 1.3285594656326920421762077861611
absolute error = 4e-63
relative error = 3.0107797983247242763462297682175e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2989
Order of pole (three term test) = -22.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2876686720, alloc=4848776, time=151.48
x[1] = 9.1
y1[1] (analytic) = 0.052278397868887975280933410424631
y1[1] (numeric) = 0.052278397868887975280933410424631
absolute error = 4.02e-63
relative error = 7.6896006072756687169502962830505e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3190983623493517707939976839854
y2[1] (numeric) = 1.3190983623493517707939976839854
absolute error = 4e-63
relative error = 3.0323743203470331210042991301934e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2913
Order of pole (three term test) = -22.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.11
y1[1] (analytic) = 0.04913485311341280545371997026879
y1[1] (numeric) = 0.04913485311341280545371997026879
absolute error = 4.06e-63
relative error = 8.2629737197519033801236068237260e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3096053494956909798097442924788
y2[1] (numeric) = 1.3096053494956909798097442924788
absolute error = 4e-63
relative error = 3.0543552693491508057739797745048e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2835
Order of pole (three term test) = -22.73
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2880688404, alloc=4848776, time=151.69
x[1] = 9.12
y1[1] (analytic) = 0.04608639408024131322782992654193
y1[1] (numeric) = 0.04608639408024131322782992654193
absolute error = 3.99e-63
relative error = 8.6576528271076831848081909215438e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.3000813763650842176272617719129
y2[1] (numeric) = 1.3000813763650842176272617719129
absolute error = 4e-63
relative error = 3.0767304821977037990096578811225e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2757
Order of pole (three term test) = -22.87
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2884689528, alloc=4848776, time=151.90
x[1] = 9.13
y1[1] (analytic) = 0.043133325612736441692769595562116
y1[1] (numeric) = 0.043133325612736441692769595562116
absolute error = 3.89e-63
relative error = 9.0185487549129710422711090629914e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.290527395346907927102696411862
y2[1] (numeric) = 1.290527395346907927102696411862
absolute error = 4e-63
relative error = 3.0995080107731894377526722969930e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2677
Order of pole (three term test) = -23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2888690296, alloc=4848776, time=152.11
x[1] = 9.14
y1[1] (analytic) = 0.040275943015284059149058407567067
y1[1] (numeric) = 0.040275943015284059149058407567067
absolute error = 3.88e-63
relative error = 9.6335422823684195287823787104251e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.280944361831302301555409197633
y2[1] (numeric) = 1.280944361831302301555409197633
absolute error = 4e-63
relative error = 3.1226961288790087589172917376389e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2597
Order of pole (three term test) = -23.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.15
y1[1] (analytic) = 0.037514532023762766607566789858955
y1[1] (numeric) = 0.037514532023762766607566789858955
absolute error = 3.84e-63
relative error = 1.0236033325879249382342174599913e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2713332341136330669044401785046
y2[1] (numeric) = 1.2713332341136330669044401785046
absolute error = 4e-63
relative error = 3.1463033394142167938722199311234e-61 %
Correct digits = 64
h = 0.01
bytes used=2892691104, alloc=4848776, time=152.32
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2515
Order of pole (three term test) = -23.26
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.16
y1[1] (analytic) = 0.034849368776970548041853537914185
y1[1] (numeric) = 0.034849368776970548041853537914185
absolute error = 3.79e-63
relative error = 1.0875376321032648273158536766847e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2616949732986627436727260751701
y2[1] (numeric) = 1.2616949732986627436727260751701
absolute error = 3e-63
relative error = 2.3777537863661231615176457407368e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2432
Order of pole (three term test) = -23.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2896691768, alloc=4848776, time=152.53
x[1] = 9.17
y1[1] (analytic) = 0.032280719789011120704666395301587
y1[1] (numeric) = 0.032280719789011120704666395301587
absolute error = 3.78e-63
relative error = 1.1709776066662470016295615342159e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2520305432044409716530136891507
y2[1] (numeric) = 1.2520305432044409716530136891507
absolute error = 3e-63
relative error = 2.3961076798668300680127872843525e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2349
Order of pole (three term test) = -23.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2900693040, alloc=4848776, time=152.74
x[1] = 9.18
y1[1] (analytic) = 0.029808841922642746850562894319242
y1[1] (numeric) = 0.029808841922642746850562894319242
absolute error = 3.75e-63
relative error = 1.2580159973110214066695469814763e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2423409102659235081229113936966
y2[1] (numeric) = 1.2423409102659235081229113936966
absolute error = 4e-63
relative error = 3.2197281494527927888130350525350e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2264
Order of pole (three term test) = -23.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2904694344, alloc=4848776, time=152.94
x[1] = 9.19
y1[1] (analytic) = 0.027433982363592171961269945732327
y1[1] (numeric) = 0.027433982363592171961269945732327
absolute error = 3.68e-63
relative error = 1.3414020433590981280726913645632e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2326270434383295376289399672643
y2[1] (numeric) = 1.2326270434383295376289399672643
absolute error = 3e-63
relative error = 2.4338262055582550484805911109812e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2179
Order of pole (three term test) = -23.73
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.2
y1[1] (analytic) = 0.025156378595836258058554661524196
y1[1] (numeric) = 0.025156378595836258058554661524196
absolute error = 3.66e-63
relative error = 1.4548993950209441366744319213862e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2228899141002469575280690577583
y2[1] (numeric) = 1.2228899141002469575280690577583
absolute error = 4e-63
relative error = 3.2709403797340487172224357249045e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2092
Order of pole (three term test) = -23.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2908694996, alloc=4848776, time=153.15
x[1] = 9.21
y1[1] (analytic) = 0.022976258377853783920676553334472
y1[1] (numeric) = 0.022976258377853783920676553334472
absolute error = 3.63e-63
relative error = 1.5798917039942684078878389634650e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2131304959564953286774397976603
y2[1] (numeric) = 1.2131304959564953286774397976603
absolute error = 4e-63
relative error = 3.2972545108151711765721229103612e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2005
Order of pole (three term test) = -23.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2912696200, alloc=4848776, time=153.36
x[1] = 9.22
y1[1] (analytic) = 0.020893839719849787002609360845137
y1[1] (numeric) = 0.020893839719849787002609360845137
absolute error = 3.58e-63
relative error = 1.7134236923426240635786269875020e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.2033497649407562048962573265169
y2[1] (numeric) = 1.2033497649407562048962573265169
absolute error = 4e-63
relative error = 3.3240543327790732512461756946221e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1917
Order of pole (three term test) = -24.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2916697272, alloc=4848776, time=153.57
x[1] = 9.23
y1[1] (analytic) = 0.018909330861954724606860836130891
y1[1] (numeric) = 0.018909330861954724606860836130891
absolute error = 3.60e-63
relative error = 1.9038219946974132272326259396975e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1935486991179805780857659098894
y2[1] (numeric) = 1.1935486991179805780857659098894
absolute error = 4e-63
relative error = 3.3513504752306765604075937861716e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1829
Order of pole (three term test) = -24.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2920698152, alloc=4848776, time=153.78
x[1] = 9.24
y1[1] (analytic) = 0.017022930253400634370606096862142
y1[1] (numeric) = 0.017022930253400634370606096862142
absolute error = 3.55e-63
relative error = 2.0854223962357033638276900388078e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1837282785865831981814677992768
y2[1] (numeric) = 1.1837282785865831981814677992768
absolute error = 5e-63
relative error = 4.2239423442432169308873158485030e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1739
Order of pole (three term test) = -24.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.25
y1[1] (analytic) = 0.015234826532676376435732693275154
y1[1] (numeric) = 0.015234826532676376435732693275154
absolute error = 3.49e-63
relative error = 2.2908038975793278316792279772483e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1738894853804335484240861494355
y2[1] (numeric) = 1.1738894853804335484240861494355
absolute error = 4e-63
relative error = 3.4074757886630885824398876419233e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1649
Order of pole (three term test) = -24.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2924699172, alloc=4848776, time=153.99
x[1] = 9.26
y1[1] (analytic) = 0.013545198508663941761043141335247
y1[1] (numeric) = 0.013545198508663941761043141335247
absolute error = 3.46e-63
relative error = 2.5544106996932333227949642256750e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1640333033706532767700709817761
y2[1] (numeric) = 1.1640333033706532767700709817761
absolute error = 4e-63
relative error = 3.4363277995718253441006706460086e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1558
Order of pole (three term test) = -24.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2928700184, alloc=4848776, time=154.20
x[1] = 9.27
y1[1] (analytic) = 0.011954215142757712930064011165613
y1[1] (numeric) = 0.011954215142757712930064011165613
absolute error = 3.35e-63
relative error = 2.8023587997992061319983124875241e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1541607181672299036166719422002
y2[1] (numeric) = 1.1541607181672299036166719422002
absolute error = 4e-63
relative error = 3.4657218332225613589701078983601e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1467
Order of pole (three term test) = -24.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2932700948, alloc=4848776, time=154.40
x[1] = 9.28
y1[1] (analytic) = 0.010462035531968465513480223508068
y1[1] (numeric) = 0.010462035531968465513480223508068
absolute error = 3.35e-63
relative error = 3.2020537396986710138894725792742e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1442727170204566443888170425023
y2[1] (numeric) = 1.1442727170204566443888170425023
absolute error = 4e-63
relative error = 3.4956701671743959953993351737345e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1375
Order of pole (three term test) = -24.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.29
y1[1] (analytic) = 0.0090688088930137995719783588546681
y1[1] (numeric) = 0.0090688088930137995719783588546681
absolute error = 3.308e-63
relative error = 3.6476675592406999185579963902229e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.13437028872220820292340549006
y2[1] (numeric) = 1.13437028872220820292340549006
absolute error = 5e-63
relative error = 4.4077318047814559246464025567564e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1282
Order of pole (three term test) = -24.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2936701864, alloc=4848776, time=154.61
x[1] = 9.3
y1[1] (analytic) = 0.0077746745473965922430907653648447
y1[1] (numeric) = 0.0077746745473965922430907653648447
absolute error = 3.280e-63
relative error = 4.2188261129185561378158785652416e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1244544235070624079894062785863
y2[1] (numeric) = 1.1244544235070624079894062785863
absolute error = 5e-63
relative error = 4.4466008541328809940886600628778e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1189
Order of pole (three term test) = -24.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2940703136, alloc=4848776, time=154.82
x[1] = 9.31
y1[1] (analytic) = 0.0065797619074729635543471997616135
y1[1] (numeric) = 0.0065797619074729635543471997616135
absolute error = 3.241e-63
relative error = 4.9257101481423435069366447407925e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1145261129532775806977121685111
y2[1] (numeric) = 1.1145261129532775806977121685111
absolute error = 5e-63
relative error = 4.4862116211444986219375460310234e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1096
Order of pole (three term test) = -24.72
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2944704404, alloc=4848776, time=155.03
x[1] = 9.32
y1[1] (analytic) = 0.0054841904635111486545426962537714
y1[1] (numeric) = 0.0054841904635111486545426962537714
absolute error = 3.121e-63
relative error = 5.6909037364137041664229545540956e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.1045863498836355349814894861648
y2[1] (numeric) = 1.1045863498836355349814894861648
absolute error = 6e-63
relative error = 5.4318976516703106681265066093862e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1002
Order of pole (three term test) = -24.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2948705296, alloc=4848776, time=155.23
x[1] = 9.33
y1[1] (analytic) = 0.0044880697717425705651142995040825
y1[1] (numeric) = 0.0044880697717425705651142995040825
absolute error = 3.119e-63
relative error = 6.9495354542783643214522243403233e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0946361282661601267643451492879
y2[1] (numeric) = 1.0946361282661601267643451492879
absolute error = 6e-63
relative error = 5.4812734981656877589355199566022e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09072
Order of pole (three term test) = -24.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.34
y1[1] (analytic) = 0.0035914994434063083343941177877119
y1[1] (numeric) = 0.0035914994434063083343941177877119
absolute error = 3.031e-63
relative error = 8.4393720443550721166924624534929e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0846764431147212798786598355838
y2[1] (numeric) = 1.0846764431147212798786598355838
absolute error = 6e-63
relative error = 5.5316034916095318644818129616767e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08125
Order of pole (three term test) = -24.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2952706164, alloc=4848776, time=155.44
x[1] = 9.35
y1[1] (analytic) = 0.0027945691347880561387936915961134
y1[1] (numeric) = 0.0027945691347880561387936915961134
absolute error = 3.023e-63
relative error = 1.0817409962660552906928840749210e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0747082903895344282486657586974
y2[1] (numeric) = 1.0747082903895344282486657586974
absolute error = 5e-63
relative error = 4.6524252624753831436547334210840e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07174
Order of pole (three term test) = -24.9
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2956707252, alloc=4848776, time=155.65
x[1] = 9.36
y1[1] (analytic) = 0.0020973585382545694267087195033409
y1[1] (numeric) = 0.0020973585382545694267087195033409
absolute error = 2.906e-63
relative error = 1.3855523254590440172194145005433e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0647326668975653243111338887167
y2[1] (numeric) = 1.0647326668975653243111338887167
absolute error = 6e-63
relative error = 5.6352173522419423071135790983231e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0622
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2960708704, alloc=4848776, time=155.86
x[1] = 9.37
y1[1] (analytic) = 0.0014999373742844946530584808463874
y1[1] (numeric) = 0.0014999373742844946530584808463874
absolute error = 2.899e-63
relative error = 1.9327473597908653154385650490905e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.054750570192850173109832832146
y2[1] (numeric) = 1.054750570192850173109832832146
absolute error = 6e-63
relative error = 5.6885487143211142286459784775072e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05264
Order of pole (three term test) = -24.96
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.38
y1[1] (analytic) = 0.0010023653844963795148455481926131
y1[1] (numeric) = 0.0010023653844963795148455481926131
absolute error = 2.844e-63
relative error = 2.8372887212470098638907740050576e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0447629984767410599672836474296
y2[1] (numeric) = 1.0447629984767410599672836474296
absolute error = 6e-63
relative error = 5.7429292660134100714041871216787e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04306
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2964709404, alloc=4848776, time=156.07
TOP MAIN SOLVE Loop
x[1] = 9.39
y1[1] (analytic) = 0.00060469232567456088090226151925041
y1[1] (numeric) = 0.00060469232567456088090226151925041
absolute error = 2.7311e-63
relative error = 4.5165117598496687528990615453596e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0347709504980866471079148873655
y2[1] (numeric) = 1.0347709504980866471079148873655
absolute error = 6e-63
relative error = 5.7983846542192762842230294984246e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03346
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2968710132, alloc=4848776, time=156.28
x[1] = 9.4
y1[1] (analytic) = 0.00030695796479352782205257932708477
y1[1] (numeric) = 0.00030695796479352782205257932708477
absolute error = 2.6862e-63
relative error = 8.7510353471585118419151641867003e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0247754254533581210797730773676
y2[1] (numeric) = 1.0247754254533581210797730773676
absolute error = 6e-63
relative error = 5.8549413373623931275099533806254e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02385
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2972711484, alloc=4848776, time=156.49
x[1] = 9.41
y1[1] (analytic) = 0.00010919207504125730123994018285572
y1[1] (numeric) = 0.00010919207504125730123994018285572
absolute error = 2.6649e-63
relative error = 2.4405617339839819817175568600461e-57 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0147774228867303782968183588059
y2[1] (numeric) = 1.0147774228867303782968183588059
absolute error = 6e-63
relative error = 5.9126266161222242525988157685505e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01423
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2976712160, alloc=4848776, time=156.70
x[1] = 9.42
y1[1] (analytic) = 1.1414432841920186738246025601479e-05
y1[1] (numeric) = 1.1414432841920186738246025601479e-05
absolute error = 2.57139e-63
relative error = 2.2527531902911694033377370324582e-56 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 1.0047779425901284404999856666986
y2[1] (numeric) = 1.0047779425901284404999856666986
absolute error = 6e-63
relative error = 5.9714686655373118341325367825612e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004601
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.43
y1[1] (analytic) = 1.3634815878255315363576086538077e-05
y1[1] (numeric) = 1.3634815878255315363576086538077e-05
absolute error = 2.54730e-63
relative error = 1.8682320485621017239875683224181e-56 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.99477798450324909541217095950362
y2[1] (numeric) = 0.99477798450324909541217095950362
absolute error = 5.6e-63
relative error = 5.6293967973129280211694920885696e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.005035
Order of pole (three term test) = -0.8935
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2980713080, alloc=4848776, time=156.90
x[1] = 9.44
y1[1] (analytic) = 0.00011585300211380936663229413048657
y1[1] (numeric) = 0.00011585300211380936663229413048657
absolute error = 2.4749e-63
relative error = 2.1362415775542501616399888171170e-57 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.98477854861356776033976198064944
y2[1] (numeric) = 0.98477854861356776033976198064944
absolute error = 5.6e-63
relative error = 5.6865576609929479819473498898189e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01468
Order of pole (three term test) = -0.8985
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2984714036, alloc=4848776, time=157.11
x[1] = 9.45
y1[1] (analytic) = 0.00031805876981514032306333581925136
y1[1] (numeric) = 0.00031805876981514032306333581925136
absolute error = 2.3992e-63
relative error = 7.5432600125896374716426708303989e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.97478063485634056795102606282269
y2[1] (numeric) = 0.97478063485634056795102606282269
absolute error = 5.6e-63
relative error = 5.7448822840282485978106349738732e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02431
Order of pole (three term test) = -0.9082
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2988714944, alloc=4848776, time=157.32
x[1] = 9.46
y1[1] (analytic) = 0.00062023189857398229629714879012246
y1[1] (numeric) = 0.00062023189857398229629714879012246
absolute error = 2.2900e-63
relative error = 3.6921674058768923136895716041644e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.9647852430146116739394458188179
y2[1] (numeric) = 0.9647852430146116739394458188179
absolute error = 5.7e-63
relative error = 5.9080505649003521206718098368214e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03394
Order of pole (three term test) = -0.9228
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2992715744, alloc=4848776, time=157.53
x[1] = 9.47
y1[1] (analytic) = 0.0010223421713292695034004747379178
y1[1] (numeric) = 0.0010223421713292695034004747379178
absolute error = 2.289e-63
relative error = 2.2389764055451189549147325043922e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.95479337261923578575790941952403
y2[1] (numeric) = 0.95479337261923578575790941952403
absolute error = 5.7e-63
relative error = 5.9698780526340288348778661475885e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04355
Order of pole (three term test) = -0.9423
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.48
y1[1] (analytic) = 0.0015243493773888171926443573858882
y1[1] (numeric) = 0.0015243493773888171926443573858882
absolute error = 2.217e-63
relative error = 1.4543909899433165040634853497785e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.94480602284892591008756775834644
y2[1] (numeric) = 0.94480602284892591008756775834644
absolute error = 5.8e-63
relative error = 6.1388262349460250917293672751890e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05314
Order of pole (three term test) = -0.9665
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2996716944, alloc=4848776, time=157.74
x[1] = 9.49
y1[1] (analytic) = 0.0021262033164503573531808575892935
y1[1] (numeric) = 0.0021262033164503573531808575892935
absolute error = 2.189e-63
relative error = 1.0295346560057483690394575867344e-58 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.93482419243033631418331835021631
y2[1] (numeric) = 0.93482419243033631418331835021631
absolute error = 5.8e-63
relative error = 6.2043751616240073311412490836092e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06271
Order of pole (three term test) = -0.9956
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3000717952, alloc=4848776, time=157.95
x[1] = 9.5
y1[1] (analytic) = 0.002827843803621527108398359822012
y1[1] (numeric) = 0.002827843803621527108398359822012
absolute error = 2.066e-63
relative error = 7.3059197872037392726068115216357e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.92484887953819069271651749546599
y2[1] (numeric) = 0.92484887953819069271651749546599
absolute error = 5.8e-63
relative error = 6.2712948334825710367093366573659e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07226
Order of pole (three term test) = -1.029
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3004718644, alloc=4848776, time=158.16
x[1] = 9.51
y1[1] (analytic) = 0.0036292006754383077982994442322779
y1[1] (numeric) = 0.0036292006754383077982994442322779
absolute error = 2.061e-63
relative error = 5.6789364499693525125698570436074e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.91488108169546552721501018714384
y2[1] (numeric) = 0.91488108169546552721501018714384
absolute error = 5.8e-63
relative error = 6.3396217454309907414842398778769e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08178
Order of pole (three term test) = -1.068
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.52
y1[1] (analytic) = 0.0045301937968813129120084356644659
y1[1] (numeric) = 0.0045301937968813129120084356644659
absolute error = 2.035e-63
relative error = 4.4920815559831892284276729395105e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.90492179567363861968135350224591
y2[1] (numeric) = 0.90492179567363861968135350224591
absolute error = 5.9e-63
relative error = 6.5199004247742129775924214470359e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09127
Order of pole (three term test) = -1.111
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3008719460, alloc=4848776, time=158.37
x[1] = 9.53
y1[1] (analytic) = 0.0055307330693892232474622660127888
y1[1] (numeric) = 0.0055307330693892232474622660127888
absolute error = 1.959e-63
relative error = 3.5420259401821731926666426088319e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.89497201739301277545274570962751
y2[1] (numeric) = 0.89497201739301277545274570962751
absolute error = 5.9e-63
relative error = 6.5923848850450801519034567496266e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1007
Order of pole (three term test) = -1.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3012720468, alloc=4848776, time=158.58
x[1] = 9.54
y1[1] (analytic) = 0.0066307184398685679614465211942478
y1[1] (numeric) = 0.0066307184398685679614465211942478
absolute error = 1.887e-63
relative error = 2.8458454647297669407355510540212e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.88503274182312460285131178094508
y2[1] (numeric) = 0.88503274182312460285131178094508
absolute error = 5.9e-63
relative error = 6.6664200330558230250273836116456e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1101
Order of pole (three term test) = -1.212
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3016721240, alloc=4848776, time=158.79
x[1] = 9.55
y1[1] (analytic) = 0.0078300399106989505393797949840419
y1[1] (numeric) = 0.0078300399106989505393797949840419
absolute error = 1.825e-63
relative error = 2.3307671746427802085257452996678e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.87510496288324838866178788576117
y2[1] (numeric) = 0.87510496288324838866178788576117
absolute error = 5.9e-63
relative error = 6.7420483830431036104642339537173e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1195
Order of pole (three term test) = -1.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3020721972, alloc=4848776, time=158.99
x[1] = 9.56
y1[1] (analytic) = 0.0091285775507327191705870317939627
y1[1] (numeric) = 0.0091285775507327191705870317939627
absolute error = 1.733e-63
relative error = 1.8984337815708189031217713967462e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.86518967334300499896614394163858
y2[1] (numeric) = 0.86518967334300499896614394163858
absolute error = 6.0e-63
relative error = 6.9348955320012195351476478536397e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1288
Order of pole (three term test) = -1.332
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.57
y1[1] (analytic) = 0.010526201507287981571190692484306
y1[1] (numeric) = 0.010526201507287981571190692484306
absolute error = 1.67e-63
relative error = 1.5865172245123268545996915896407e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.85528786472308574436223511708336
y2[1] (numeric) = 0.85528786472308574436223511708336
absolute error = 6.0e-63
relative error = 7.0151819609209630150334288785171e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1381
Order of pole (three term test) = -1.399
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3024722736, alloc=4848776, time=159.20
x[1] = 9.58
y1[1] (analytic) = 0.01202277201913376496313159979792
y1[1] (numeric) = 0.01202277201913376496313159979792
absolute error = 1.62e-63
relative error = 1.3474430001848444213402947390851e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.84540052719610113709723058563525
y2[1] (numeric) = 0.84540052719610113709723058563525
absolute error = 6.0e-63
relative error = 7.0972276536187037258464619264986e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1473
Order of pole (three term test) = -1.471
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3028723736, alloc=4848776, time=159.41
x[1] = 9.59
y1[1] (analytic) = 0.013618139430466022704142491911221
y1[1] (numeric) = 0.013618139430466022704142491911221
absolute error = 1.62e-63
relative error = 1.1895898175163289642145092125317e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.83552864948756445515748042792753
y2[1] (numeric) = 0.83552864948756445515748042792753
absolute error = 6.0e-63
relative error = 7.1810823048136551911489349969909e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1564
Order of pole (three term test) = -1.547
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3032724460, alloc=4848776, time=159.62
x[1] = 9.6
y1[1] (analytic) = 0.015312144205873089979657920116266
y1[1] (numeric) = 0.015312144205873089979657920116266
absolute error = 1.54e-63
relative error = 1.0057376545665767867311737601641e-59 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.82567321877702001487589827347958
y2[1] (numeric) = 0.82567321877702001487589827347958
absolute error = 6.0e-63
relative error = 7.2667974006558524169573472211539e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1655
Order of pole (three term test) = -1.628
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.61
y1[1] (analytic) = 0.017104616946289092023562471150107
y1[1] (numeric) = 0.017104616946289092023562471150107
absolute error = 1.46e-63
relative error = 8.5357070818049055167180535113029e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.81583522059932603914720611244047
y2[1] (numeric) = 0.81583522059932603914720611244047
absolute error = 6.0e-63
relative error = 7.3544262965164715707036122943233e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1745
Order of pole (three term test) = -1.713
NO COMPLEX POLE (six term test) for Equation 2
bytes used=3036726508, alloc=4848776, time=159.83
TOP MAIN SOLVE Loop
x[1] = 9.62
y1[1] (analytic) = 0.018995378405933709540249701884841
y1[1] (numeric) = 0.018995378405933709540249701884841
absolute error = 1.36e-63
relative error = 7.1596362596028515031675741061126e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.80601563874610199288195575052908
y2[1] (numeric) = 0.80601563874610199288195575052908
absolute error = 6.1e-63
relative error = 7.5680913703977440028694724437855e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1835
Order of pole (three term test) = -1.803
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3040727984, alloc=4848776, time=160.03
x[1] = 9.63
y1[1] (analytic) = 0.020984239510236607365566004615135
y1[1] (numeric) = 0.020984239510236607365566004615135
absolute error = 1.36e-63
relative error = 6.4810545044368174373556565003535e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.79621545516735024088365455832705
y2[1] (numeric) = 0.79621545516735024088365455832705
absolute error = 6.0e-63
relative error = 7.5356487506750385376027670427942e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1924
Order of pole (three term test) = -1.897
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3044728852, alloc=4848776, time=160.24
x[1] = 9.64
y1[1] (analytic) = 0.023071001374744733938710282650819
y1[1] (numeric) = 0.023071001374744733938710282650819
absolute error = 1.24e-63
relative error = 5.3747125226969902903156227336772e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.78643564987326186590122612385328
y2[1] (numeric) = 0.78643564987326186590122612385328
absolute error = 6.0e-63
relative error = 7.6293591229834643681480896243285e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2012
Order of pole (three term test) = -1.996
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3048730248, alloc=4848776, time=160.46
x[1] = 9.65
y1[1] (analytic) = 0.025255455325010600870898276620058
y1[1] (numeric) = 0.025255455325010600870898276620058
absolute error = 1.19e-63
relative error = 4.7118532795626819787574641445637e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.77667720083621646619317235015962
y2[1] (numeric) = 0.77667720083621646619317235015962
absolute error = 6.0e-63
relative error = 7.7252171089096554509550846363242e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2099
Order of pole (three term test) = -2.099
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.66
y1[1] (analytic) = 0.027537382917459553799408186112568
y1[1] (numeric) = 0.027537382917459553799408186112568
absolute error = 1.20e-63
relative error = 4.3577125814638065239516548998352e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.76694108389298573254201401859704
y2[1] (numeric) = 0.76694108389298573254201401859704
absolute error = 6.1e-63
relative error = 7.9536748364508748708809643473840e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2185
Order of pole (three term test) = -2.206
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3052731096, alloc=4848776, time=160.66
x[1] = 9.67
y1[1] (analytic) = 0.029916555961233947817311516514547
y1[1] (numeric) = 0.029916555961233947817311516514547
absolute error = 1.06e-63
relative error = 3.5431885988933831192938045506723e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.75722827264715058427981162619756
y2[1] (numeric) = 0.75722827264715058427981162619756
absolute error = 6.0e-63
relative error = 7.9236344134707840909864490346869e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2271
Order of pole (three term test) = -2.318
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3056731768, alloc=4848776, time=160.88
x[1] = 9.68
y1[1] (analytic) = 0.032392736541012043079549596797259
y1[1] (numeric) = 0.032392736541012043079549596797259
absolute error = 1.08e-63
relative error = 3.3340807703375889782024712651179e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.7475397383717416225298451628392
y2[1] (numeric) = 0.7475397383717416225298451628392
absolute error = 6.1e-63
relative error = 8.1601013121881029663727067652381e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2355
Order of pole (three term test) = -2.434
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3060732536, alloc=4848776, time=161.09
x[1] = 9.69
y1[1] (analytic) = 0.034965677040799338714810843560169
y1[1] (numeric) = 0.034965677040799338714810843560169
absolute error = 9.5e-64
relative error = 2.7169501076484299814017592641032e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.73787644991211263653799597502699
y2[1] (numeric) = 0.73787644991211263653799597502699
absolute error = 6.0e-63
relative error = 8.1314426022332750306001765801876e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2439
Order of pole (three term test) = -2.554
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3064733340, alloc=4848776, time=161.30
x[1] = 9.7
y1[1] (analytic) = 0.03763512016868996592964362910856
y1[1] (numeric) = 0.03763512016868996592964362910856
absolute error = 8.9e-64
relative error = 2.3648124305457209027430920885317e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.72823937358905687566225910317516
y2[1] (numeric) = 0.72823937358905687566225910317516
absolute error = 6.0e-63
relative error = 8.2390491610328400120357653083577e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2522
Order of pole (three term test) = -2.678
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.71
y1[1] (analytic) = 0.040400798982595664186128767750693
y1[1] (numeric) = 0.040400798982595664186128767750693
absolute error = 8.2e-64
relative error = 2.0296628300674185548514922606218e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.71862947310217577531245097026894
y2[1] (numeric) = 0.71862947310217577531245097026894
absolute error = 6.1e-63
relative error = 8.4883799347493408456687861475045e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2603
Order of pole (three term test) = -2.807
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3068734232, alloc=4848776, time=161.50
x[1] = 9.72
y1[1] (analytic) = 0.043262436916939767576934595078059
y1[1] (numeric) = 0.043262436916939767576934595078059
absolute error = 8.0e-64
relative error = 1.8491792349467797444370920443490e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.70904770943350979988699265784006
y2[1] (numeric) = 0.70904770943350979988699265784006
absolute error = 6.0e-63
relative error = 8.4620539918162497967746908617108e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2684
Order of pole (three term test) = -2.939
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3072735516, alloc=4848776, time=161.72
x[1] = 9.73
y1[1] (analytic) = 0.046219747810313532021362049216815
y1[1] (numeric) = 0.046219747810313532021362049216815
absolute error = 7.4e-64
relative error = 1.6010472472436889399867874706433e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.69949504075144103954216772773388
y2[1] (numeric) = 0.69949504075144103954216772773388
absolute error = 6.1e-63
relative error = 8.7205764796373694726045771615258e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2763
Order of pole (three term test) = -3.076
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3076736220, alloc=4848776, time=161.92
x[1] = 9.74
y1[1] (analytic) = 0.049272435934092037672707012049341
y1[1] (numeric) = 0.049272435934092037672707012049341
absolute error = 6.4e-64
relative error = 1.2989006690395395990154339722612e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.68997242231487717045409676146381
y2[1] (numeric) = 0.68997242231487717045409676146381
absolute error = 6.1e-63
relative error = 8.8409330615480628780923523207090e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2842
Order of pole (three term test) = -3.216
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.75
y1[1] (analytic) = 0.052420196022006804970545680022781
y1[1] (numeric) = 0.052420196022006804970545680022781
absolute error = 6.1e-64
relative error = 1.1636736340015070009879909889703e-60 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.68048080637772636009755598607246
y2[1] (numeric) = 0.68048080637772636009755598607246
absolute error = 6.1e-63
relative error = 8.9642498992307602494796626087525e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2919
Order of pole (three term test) = -3.361
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3080737376, alloc=4848776, time=162.13
x[1] = 9.76
y1[1] (analytic) = 0.055662713300672167100981500571712
y1[1] (numeric) = 0.055662713300672167100981500571712
absolute error = 5.3e-64
relative error = 9.5216342965013146543525516870006e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.67102114209367266997150812438323
y2[1] (numeric) = 0.67102114209367266997150812438323
absolute error = 6.2e-63
relative error = 9.2396492615049338997944114865671e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2995
Order of pole (three term test) = -3.509
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3084738256, alloc=4848776, time=162.34
x[1] = 9.77
y1[1] (analytic) = 0.058999663521062346253046208382863
y1[1] (numeric) = 0.058999663521062346253046208382863
absolute error = 5.1e-64
relative error = 8.6441170942938447896081197114358e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.66159437542126147815171935000727
y2[1] (numeric) = 0.66159437542126147815171935000727
absolute error = 6.1e-63
relative error = 9.2201509363133651004615518981695e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.307
Order of pole (three term test) = -3.661
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3088739192, alloc=4848776, time=162.55
x[1] = 9.78
y1[1] (analytic) = 0.062430712990936085989860130842391
y1[1] (numeric) = 0.062430712990936085989860130842391
absolute error = 4.1e-64
relative error = 6.5672804355049615587105481636707e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.65220144902930441304911186785548
y2[1] (numeric) = 0.65220144902930441304911186785548
absolute error = 6.1e-63
relative error = 9.3529384350170580943884811747421e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3144
Order of pole (three term test) = -3.817
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3092740460, alloc=4848776, time=162.76
x[1] = 9.79
y1[1] (analytic) = 0.065955518608205597298335083542914
y1[1] (numeric) = 0.065955518608205597298335083542914
absolute error = 3.9e-64
relative error = 5.9130760887001755577388797398672e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.64284330220261325780164732579296
y2[1] (numeric) = 0.64284330220261325780164732579296
absolute error = 6.1e-63
relative error = 9.4890931881831817165900648386496e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3216
Order of pole (three term test) = -3.976
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.8
y1[1] (analytic) = 0.069573727895246481450622247910779
y1[1] (numeric) = 0.069573727895246481450622247910779
absolute error = 2.6e-64
relative error = 3.7370428158092719126060835991791e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.63352087074807225183074705127114
y2[1] (numeric) = 0.63352087074807225183074705127114
absolute error = 6.1e-63
relative error = 9.6287277683480513216030744106933e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3287
Order of pole (three term test) = -4.139
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3096741392, alloc=4848776, time=162.97
x[1] = 9.81
y1[1] (analytic) = 0.073284979034145198713610393245203
y1[1] (numeric) = 0.073284979034145198713610393245203
absolute error = 2.4e-64
relative error = 3.2748866570348385353428864345119e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.62423508690105818225382064978751
y2[1] (numeric) = 0.62423508690105818225382064978751
absolute error = 6.1e-63
relative error = 9.7719595197423682110733254688561e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3357
Order of pole (three term test) = -4.306
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3100742876, alloc=4848776, time=163.18
x[1] = 9.82
y1[1] (analytic) = 0.077088900902880558188976286028855
y1[1] (numeric) = 0.077088900902880558188976286028855
absolute error = 2.1e-64
relative error = 2.7241275662311718343785176211783e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.6149868792322176230657787151004
y2[1] (numeric) = 0.6149868792322176230657787151004
absolute error = 6.0e-63
relative error = 9.7563057076774053884490482215789e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3426
Order of pole (three term test) = -4.476
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3104744188, alloc=4848776, time=163.39
x[1] = 9.83
y1[1] (analytic) = 0.08098511311243561066495442249836
y1[1] (numeric) = 0.08098511311243561066495442249836
absolute error = 8e-65
relative error = 9.8783587409370003916060234130704e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.60577717255461064428792612486422
y2[1] (numeric) = 0.60577717255461064428792612486422
absolute error = 6.0e-63
relative error = 9.9046320525706202013980218942958e-61 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3493
Order of pole (three term test) = -4.649
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.84
y1[1] (analytic) = 0.084973226044836233321467381789552
y1[1] (numeric) = 0.084973226044836233321467381789552
absolute error = 2e-65
relative error = 2.3536825575442991853136860376239e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.59660688783123027663594104791333
y2[1] (numeric) = 0.59660688783123027663594104791333
absolute error = 6.0e-63
relative error = 1.0056873499752982668313823223817e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3559
Order of pole (three term test) = -4.826
NO COMPLEX POLE (six term test) for Equation 2
bytes used=3108745056, alloc=4848776, time=163.60
TOP MAIN SOLVE Loop
x[1] = 9.85
y1[1] (analytic) = 0.089052840892112602461845001547209
y1[1] (numeric) = 0.089052840892112602461845001547209
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.5874769420829069796834060094069
y2[1] (numeric) = 0.5874769420829069796834060094069
absolute error = 6.1e-63
relative error = 1.0383386245547565350225150790357e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3623
Order of pole (three term test) = -5.006
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3112746340, alloc=4848776, time=163.80
x[1] = 9.86
y1[1] (analytic) = 0.093223549696179658156326989798697
y1[1] (numeric) = 0.093223549696179658156326989798697
absolute error = 4e-65
relative error = 4.2907613076697955319856699559845e-62 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.57838824829660732299732864001849
y2[1] (numeric) = 0.57838824829660732299732864001849
absolute error = 6.1e-63
relative error = 1.0546548997087880553053011862629e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3686
Order of pole (three term test) = -5.189
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3116747192, alloc=4848776, time=164.02
x[1] = 9.87
y1[1] (analytic) = 0.097484935389632572784118232587709
y1[1] (numeric) = 0.097484935389632572784118232587709
absolute error = 1.4e-64
relative error = 1.4361193290064883462680709681955e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.56934171533413605030112104610044
y2[1] (numeric) = 0.56934171533413605030112104610044
absolute error = 6.1e-63
relative error = 1.0714127975709673048944998657852e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3747
Order of pole (three term test) = -5.376
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3120748536, alloc=4848776, time=164.22
x[1] = 9.88
y1[1] (analytic) = 0.10183657183745314396113870230185
y1[1] (numeric) = 0.10183657183745314396113870230185
absolute error = 2e-64
relative error = 1.9639309964128683450202932452911e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.56033824784125065638254014329326
y2[1] (numeric) = 0.56033824784125065638254014329326
absolute error = 6.0e-63
relative error = 1.0707818042254825849016731115816e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3807
Order of pole (three term test) = -5.565
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.89
y1[1] (analytic) = 0.10627802387962294124893040329212
y1[1] (numeric) = 0.10627802387962294124893040329212
absolute error = 2e-64
relative error = 1.8818565936691894246848597886752e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.55137874615719756521316055942936
y2[1] (numeric) = 0.55137874615719756521316055942936
absolute error = 6.0e-63
relative error = 1.0881812260295948381686002720938e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3865
Order of pole (three term test) = -5.757
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3124749412, alloc=4848776, time=164.43
x[1] = 9.9
y1[1] (analytic) = 0.11080884737463894536556130131089
y1[1] (numeric) = 0.11080884737463894536556130131089
absolute error = 3e-64
relative error = 2.7073650444690180290436657249342e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.54246410622467895558618189249464
y2[1] (numeric) = 0.54246410622467895558618189249464
absolute error = 6.0e-63
relative error = 1.1060639646293771621740442102086e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3922
Order of pole (three term test) = -5.953
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3128750512, alloc=4848776, time=164.64
x[1] = 9.91
y1[1] (analytic) = 0.11542858924392732837086805817458
y1[1] (numeric) = 0.11542858924392732837086805817458
absolute error = 5e-64
relative error = 4.3316824997608197435602363947167e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.53359521950025923751497914771223
y2[1] (numeric) = 0.53359521950025923751497914771223
absolute error = 6.0e-63
relative error = 1.1244478549900286371144086907184e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3977
Order of pole (three term test) = -6.151
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3132751348, alloc=4848776, time=164.85
x[1] = 9.92
y1[1] (analytic) = 0.12013678751715093348503040749387
y1[1] (numeric) = 0.12013678751715093348503040749387
absolute error = 5e-64
relative error = 4.1619225079463619242886864196834e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.52477297286522013867009547790727
y2[1] (numeric) = 0.52477297286522013867009547790727
absolute error = 6.0e-63
relative error = 1.1433515653903555079515144501666e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4031
Order of pole (three term test) = -6.351
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.93
y1[1] (analytic) = 0.12493297137840592383025142136221
y1[1] (numeric) = 0.12493297137840592383025142136221
absolute error = 5e-64
relative error = 4.0021460666741385693658529426457e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.51599824853687331527174634753366
y2[1] (numeric) = 0.51599824853687331527174634753366
absolute error = 6.1e-63
relative error = 1.1821745553006645620739196333592e-60 %
Correct digits = 64
h = 0.01
bytes used=3136752100, alloc=4848776, time=165.06
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4083
Order of pole (three term test) = -6.555
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.94
y1[1] (analytic) = 0.12981666121330298046916657893683
y1[1] (numeric) = 0.12981666121330298046916657893683
absolute error = 6e-64
relative error = 4.6219028774290716105027684055490e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.50727192398033935610283995871037
y2[1] (numeric) = 0.50727192398033935610283995871037
absolute error = 6.1e-63
relative error = 1.2025108648111227576937954959505e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4133
Order of pole (three term test) = -6.761
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3140752784, alloc=4848776, time=165.27
x[1] = 9.95
y1[1] (analytic) = 0.13478736865692834165941199692317
y1[1] (numeric) = 0.13478736865692834165941199692317
absolute error = 6e-64
relative error = 4.4514556963209830719857479308097e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.4985948718208020016685953856268
y2[1] (numeric) = 0.4985948718208020016685953856268
absolute error = 6.1e-63
relative error = 1.2234381749101456302705916786856e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4182
Order of pole (three term test) = -6.969
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3144753564, alloc=4848776, time=165.48
x[1] = 9.96
y1[1] (analytic) = 0.13984459664267988726039376462704
y1[1] (numeric) = 0.13984459664267988726039376462704
absolute error = 7e-64
relative error = 5.0055562875166777947088234894833e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.48996795975624635300772121520774
y2[1] (numeric) = 0.48996795975624635300772121520774
absolute error = 6.1e-63
relative error = 1.2449793662089012125273568516614e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4229
Order of pole (three term test) = -7.18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3148754328, alloc=4848776, time=165.69
x[1] = 9.97
y1[1] (analytic) = 0.14498783945197338472451430799106
y1[1] (numeric) = 0.14498783945197338472451430799106
absolute error = 7e-64
relative error = 4.8279911104673855879884469191708e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.48139205047068979626155565924353
y2[1] (numeric) = 0.48139205047068979626155565924353
absolute error = 6.1e-63
relative error = 1.2671584406172919801121274489409e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4274
Order of pole (three term test) = -7.393
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.98
y1[1] (analytic) = 0.15021658276481392608967839356558
y1[1] (numeric) = 0.15021658276481392608967839356558
absolute error = 8e-64
relative error = 5.3256437157308872919038788786055e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.47286800154791431983640390213977
y2[1] (numeric) = 0.47286800154791431983640390213977
absolute error = 6.2e-63
relative error = 1.3111481385301078122063685542733e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4318
Order of pole (three term test) = -7.608
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=3152755232, alloc=4848776, time=165.90
x[1] = 9.99
y1[1] (analytic) = 0.15553030371122749887152224549834
y1[1] (numeric) = 0.15553030371122749887152224549834
absolute error = 8e-64
relative error = 5.1436921352983200170751049764559e-61 %
Correct digits = 64
h = 0.01
y2[1] (analytic) = 0.46439666538570885085546695448582
y2[1] (numeric) = 0.46439666538570885085546695448582
absolute error = 6.2e-63
relative error = 1.3350655726286350315730911320105e-60 %
Correct digits = 64
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.436
Order of pole (three term test) = -7.826
NO COMPLEX POLE (six term test) for Equation 2
Finished!
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
diff ( y2 , x , 1 ) = y1 - 1.0;
Iterations = 990
Total Elapsed Time = 2 Minutes 46 Seconds
Elapsed Time(since restart) = 2 Minutes 43 Seconds
Time to Timeout = 13 Seconds
Percent Done = 100.1 %
> quit
bytes used=3155675376, alloc=4848776, time=166.04