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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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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_2,
> #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_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_2,
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_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_2,
> #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_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_2,
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_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_2,
> #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_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_2,
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_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_2,
> #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_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_2,
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_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_2,
> #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_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_2,
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_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_2,
> #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_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_2,
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_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_2,
> #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_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 - 2 - 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 - 2 - 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 - 2 - 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_2,
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_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 - 12;
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 - 3;
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 - 3;
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_2,
> #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_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_2,
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_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_2,
> #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_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 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_tmp2[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 diff $eq_no = 2 i = 1 order_d = 1
> array_tmp4[1] := array_y1_higher[2,1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * expt(glob_h , (2)) * factorial_3(0,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y2_higher[3,1] := 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 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_tmp2[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 diff $eq_no = 2 i = 2 order_d = 1
> array_tmp4[2] := array_y1_higher[2,2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (2)) * factorial_3(1,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[2,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[3,2] := 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 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_tmp2[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 diff $eq_no = 2 i = 3 order_d = 1
> array_tmp4[3] := array_y1_higher[2,3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (2)) * factorial_3(2,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[2,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,3] := 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 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_tmp2[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 diff $eq_no = 2 i = 4 order_d = 1
> array_tmp4[4] := array_y1_higher[2,4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (2)) * factorial_3(3,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[2,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[3,4] := 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 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_tmp2[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 diff $eq_no = 2 i = 5 order_d = 1
> array_tmp4[5] := array_y1_higher[2,5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,7]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (2)) * factorial_3(4,6);
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (6.0);
> array_y2_higher[2,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[3,5] := 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 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_tmp2[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 diff $eq_no = 2
> array_tmp4[kkk] := array_y1_higher[2,kkk];
> #emit assign $eq_no = 2
> order_d := 2;
> 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_tmp4[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_2,
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_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];
if not array_y1_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[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_tmp4[1] := array_y1_higher[2, 1];
if not array_y2_set_initial[2, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 2)*factorial_3(0, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y2_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_m1, array_y2, 1);
array_tmp2[2] := array_tmp1[2];
if not array_y1_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[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_tmp4[2] := array_y1_higher[2, 2];
if not array_y2_set_initial[2, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 2)*factorial_3(1, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[2, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_m1, array_y2, 1);
array_tmp2[3] := array_tmp1[3];
if not array_y1_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[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_tmp4[3] := array_y1_higher[2, 3];
if not array_y2_set_initial[2, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 2)*factorial_3(2, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_m1, array_y2, 1);
array_tmp2[4] := array_tmp1[4];
if not array_y1_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[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_tmp4[4] := array_y1_higher[2, 4];
if not array_y2_set_initial[2, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 2)*factorial_3(3, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[2, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_m1, array_y2, 1);
array_tmp2[5] := array_tmp1[5];
if not array_y1_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[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_tmp4[5] := array_y1_higher[2, 5];
if not array_y2_set_initial[2, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 2)*factorial_3(4, 6);
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary;
temporary := temporary*6.0/glob_h;
array_y2_higher[2, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[3, 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];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := array_tmp2[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_tmp4[kkk] := array_y1_higher[2, kkk];
order_d := 2;
if kkk + order_d < glob_max_terms then
if not array_y2_set_initial[2, kkk + order_d] then
temporary := array_tmp4[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( - cos(x));
> end;
exact_soln_y1 := proc(x) return -cos(x) end proc
> exact_soln_y2 := proc(x)
> return( - sin(x));
> end;
exact_soln_y2 := proc(x) return -sin(x) end proc
> exact_soln_y2p := proc(x)
> return( - cos(x));
> end;
exact_soln_y2p := proc(x) return -cos(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_2,
> #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_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/mtest5postode.ode#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 ;");
> omniout_str(ALWAYS,"diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> 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 := 0.5;");
> omniout_str(ALWAYS,"x_end := 5.0;");
> 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,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"glob_max_iter := 20;");
> 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( - cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return( - sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return( - cos(x));");
> omniout_str(ALWAYS,"end;");
> 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:=32;
> 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_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..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(0..(3+ 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_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 <=3) 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 <=3) 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 <=3) 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_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_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2[1] := 2;
> 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 := 0.5;
> x_end := 5.0;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> glob_max_iter := 20;
> #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] := true;
> 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 := 2;
> #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 <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + 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 := 2;
> #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 <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + 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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,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 := 3;
> 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 := 2;
> calc_term := 2;
> #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 := 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 := 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 := 3;
> #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 := 3;
> #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 ;");
> omniout_str(INFO,"diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;");
> 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,"2013-05-26T03:19:56-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest5")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 ;")
> ;
> 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,"mtest5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest5 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 , 2 ) = diff ( y1, x , 1) ;")
> ;
> 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_2,
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_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/mtest5postode.ode#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 ;");
omniout_str(ALWAYS, "diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
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 := 0.5;");
omniout_str(ALWAYS, "x_end := 5.0;");
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, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "glob_max_iter := 20;");
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( - cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return( - sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return( - cos(x));");
omniout_str(ALWAYS, "end;");
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 := 32;
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_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 .. 4, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 4, 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_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 <= 3 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 <= 3 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 <= 3 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_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_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
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 := 0.5;
x_end := 5.0;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(x_start);
glob_max_iter := 20;
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] := true;
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 := 2;
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 <= 3 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 3 + 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 := 2;
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 <= 3 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 3 + 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 := 3;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
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 := 2;
calc_term := 2;
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 := 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 := 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 := 3;
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 := 3;
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 ;");
omniout_str(INFO, "diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;");
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, "2013-05-26T03:19:56-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest5");
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 ;");
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,
"mtest5 diffeq.mxt");
logitem_str(html_log_file,
"mtest5 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 , 2 ) = diff ( y1, x , 1) ;");
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/mtest5postode.ode#################
diff ( y1 , x , 1 ) = m1 * y2 ;
diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.5;
x_end := 5.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
glob_max_iter := 20;
#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( - cos(x));
end;
exact_soln_y2 := proc(x)
return( - sin(x));
end;
exact_soln_y2p := proc(x)
return( - cos(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 = 4.5
estimated_steps = 4500000
step_error = 2.2222222222222222222222222222222e-17
est_needed_step_err = 2.2222222222222222222222222222222e-17
opt_iter = 1
bytes used=4000496, alloc=3276200, time=0.41
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.1760504191201347172640125560893e-183
estimated_step_error = 2.1760504191201347172640125560893e-183
best_h = 2.0e-06
opt_iter = 2
bytes used=8002184, alloc=4521156, time=0.89
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.4603227015650941259925623828007e-175
estimated_step_error = 1.4603227015650941259925623828007e-175
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.8000595592556264960821340759545e-168
estimated_step_error = 9.8000595592556264960821340759545e-168
best_h = 8.000e-06
opt_iter = 4
bytes used=12003840, alloc=4521156, time=1.36
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.5767083754010533133506200318762e-160
estimated_step_error = 6.5767083754010533133506200318762e-160
best_h = 1.60000e-05
opt_iter = 5
bytes used=16004576, alloc=4521156, time=1.83
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.4135539221189055046517224808234e-152
estimated_step_error = 4.4135539221189055046517224808234e-152
best_h = 3.200000e-05
opt_iter = 6
bytes used=20005340, alloc=4521156, time=2.31
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.9618854197278297629265913043536e-144
estimated_step_error = 2.9618854197278297629265913043536e-144
best_h = 6.4000000e-05
opt_iter = 7
bytes used=24006472, alloc=4521156, time=2.78
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.9876870146750669269415596204014e-136
estimated_step_error = 1.9876870146750669269415596204014e-136
best_h = 0.000128
opt_iter = 8
bytes used=28008388, alloc=4521156, time=3.25
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3339133117490700886825683454309e-128
estimated_step_error = 1.3339133117490700886825683454309e-128
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 8.9517291104750232104266630304315e-121
estimated_step_error = 8.9517291104750232104266630304315e-121
best_h = 0.000512
opt_iter = 10
bytes used=32009264, alloc=4521156, time=3.71
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.0073881555206778057824142455026e-113
estimated_step_error = 6.0073881555206778057824142455026e-113
best_h = 0.001024
opt_iter = 11
bytes used=36011240, alloc=4521156, time=4.18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.0314690639458288589709402905376e-105
estimated_step_error = 4.0314690639458288589709402905376e-105
best_h = 0.002048
opt_iter = 12
bytes used=40012132, alloc=4521156, time=4.64
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.7054450608346626620567681632845e-97
estimated_step_error = 2.7054450608346626620567681632845e-97
best_h = 0.004096
opt_iter = 13
bytes used=44015044, alloc=4521156, time=5.10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.8155558208048948153888608098124e-89
estimated_step_error = 1.8155558208048948153888608098124e-89
best_h = 0.008192
opt_iter = 14
bytes used=48016136, alloc=4521156, time=5.56
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.2183483761748801207239377571011e-81
estimated_step_error = 1.2183483761748801207239377571011e-81
best_h = 0.016384
opt_iter = 15
bytes used=52017408, alloc=4521156, time=6.02
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 8.1755193361148759155424465667867e-74
estimated_step_error = 8.1755193361148759155424465667867e-74
best_h = 0.032768
opt_iter = 16
bytes used=56018812, alloc=4521156, time=6.48
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.4855871411416643488751115852213e-66
estimated_step_error = 5.4855871411416643488751115852213e-66
best_h = 0.065536
opt_iter = 17
bytes used=60020848, alloc=4521156, time=6.94
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.6800905139569868890031721847892e-58
estimated_step_error = 3.6800905139569868890031721847892e-58
best_h = 0.131072
opt_iter = 18
bytes used=64021752, alloc=4521156, time=7.39
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.4680179083383405292585812506907e-50
estimated_step_error = 2.4680179083383405292585812506907e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.5
y1[1] (analytic) = -0.87758256189037271611628158260383
y1[1] (numeric) = -0.87758256189037271611628158260383
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.47942553860420300027328793521557
y2[1] (numeric) = -0.47942553860420300027328793521557
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=68022532, alloc=4586680, time=7.87
x[1] = 0.51
y1[1] (analytic) = -0.87274450764575126310580847357551
y1[1] (numeric) = -0.87274450764575126310580847357551
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.48817724688290749450013023767457
y2[1] (numeric) = -0.48817724688290749450013023767457
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=72024136, alloc=4586680, time=8.36
x[1] = 0.52
y1[1] (analytic) = -0.86781917967764990038784757198851
y1[1] (numeric) = -0.86781917967764990038784757198851
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.49688013784373671433445894254775
y2[1] (numeric) = -0.49688013784373671433445894254775
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=76026092, alloc=4586680, time=8.85
x[1] = 0.53
y1[1] (analytic) = -0.8628070705147610118066950185642
y1[1] (numeric) = -0.8628070705147610118066950185642
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.50553334120484696181366102246608
y2[1] (numeric) = -0.50553334120484696181366102246608
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=80027116, alloc=4586680, time=9.35
x[1] = 0.54
y1[1] (analytic) = -0.8577086813638241425379687789178
y1[1] (numeric) = -0.85770868136382414253796877891779
absolute error = 1e-32
relative error = 1.1658970250947227087204260706763e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.51413599165311310467728068295824
y2[1] (numeric) = -0.51413599165311310467728068295824
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 0.55
y1[1] (analytic) = -0.85252452205950574280498179761777
y1[1] (numeric) = -0.85252452205950574280498179761777
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.52268722893065916778837810775729
y2[1] (numeric) = -0.52268722893065916778837810775729
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=84029244, alloc=4586680, time=9.83
x[1] = 0.56
y1[1] (analytic) = -0.84725511101341612609452550386632
y1[1] (numeric) = -0.84725511101341612609452550386632
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.53118619792088340385186944111203
y2[1] (numeric) = -0.53118619792088340385186944111203
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=88030916, alloc=4586680, time=10.32
x[1] = 0.57
y1[1] (analytic) = -0.84190097516226874013375636391601
y1[1] (numeric) = -0.84190097516226874013375636391601
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.53963204873396924099446349307883
y2[1] (numeric) = -0.53963204873396924099446349307882
absolute error = 1e-32
relative error = 1.8531145478592311512083539534776e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=92031576, alloc=4586680, time=10.80
x[1] = 0.58
y1[1] (analytic) = -0.83646264991518693465788732805002
y1[1] (numeric) = -0.83646264991518693465788732805002
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.54802393679187355618269605957646
y2[1] (numeric) = -0.54802393679187355618269605957646
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=96032816, alloc=4652204, time=11.29
x[1] = 0.59
y1[1] (analytic) = -0.83094067910016349524799652249068
y1[1] (numeric) = -0.83094067910016349524799652249068
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.55636102291278377572254337887577
y2[1] (numeric) = -0.55636102291278377572254337887577
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=100034540, alloc=4652204, time=11.78
x[1] = 0.6
y1[1] (analytic) = -0.82533561490967829724095249895538
y1[1] (numeric) = -0.82533561490967829724095249895538
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.56464247339503535720094544565866
y2[1] (numeric) = -0.56464247339503535720094544565866
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 0.61
y1[1] (analytic) = -0.81964801784547951790074657865482
y1[1] (numeric) = -0.81964801784547951790074657865483
absolute error = 1e-32
relative error = 1.2200358912946465931687778838392e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.57286746010048126119097603216272
y2[1] (numeric) = -0.57286746010048126119097603216272
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=104036056, alloc=4652204, time=12.26
x[1] = 0.62
y1[1] (analytic) = -0.8138784566625339286839996543607
y1[1] (numeric) = -0.8138784566625339286839996543607
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.58103516053730507584296322758221
y2[1] (numeric) = -0.58103516053730507584296322758221
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=108036964, alloc=4652204, time=12.74
x[1] = 0.63
y1[1] (analytic) = -0.80802750831215187252370896577706
y1[1] (numeric) = -0.80802750831215187252370896577706
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.58914475794226951311811209079462
y2[1] (numeric) = -0.58914475794226951311811209079461
absolute error = 1e-32
relative error = 1.6973757069361725967914220639108e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=112039072, alloc=4652204, time=13.23
x[1] = 0.64
y1[1] (analytic) = -0.80209575788429261358611077926032
y1[1] (numeric) = -0.80209575788429261358611077926033
absolute error = 1e-32
relative error = 1.2467339344091835043765333244264e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.59719544136239205188354623920793
y2[1] (numeric) = -0.59719544136239205188354623920792
absolute error = 1e-32
relative error = 1.6744936929168164811188136616446e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=116041708, alloc=4652204, time=13.72
x[1] = 0.65
y1[1] (analytic) = -0.79608379854905582891760457067991
y1[1] (numeric) = -0.79608379854905582891760457067991
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.60518640573603956037252167860594
y2[1] (numeric) = -0.60518640573603956037252167860593
absolute error = 1e-32
relative error = 1.6523834483423011016172799055209e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=120043556, alloc=4652204, time=14.20
x[1] = 0.66
y1[1] (analytic) = -0.78999223149736509278381709123024
y1[1] (numeric) = -0.78999223149736509278381709123025
absolute error = 1e-32
relative error = 1.2658352324611882697842840177057e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.6131168519734337886151454793963
y2[1] (numeric) = -0.61311685197343378861514547939629
absolute error = 1e-32
relative error = 1.6310104620046062095590933145473e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.67
y1[1] (analytic) = -0.78382166588084928530294214483812
y1[1] (numeric) = -0.78382166588084928530294214483812
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.62098598703655968035744391412659
y2[1] (numeric) = -0.62098598703655968035744391412658
absolute error = 1e-32
relative error = 1.6103422957612188443809399991484e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=124045452, alloc=4652204, time=14.68
x[1] = 0.68
y1[1] (analytic) = -0.77757271875092793718239408404432
y1[1] (numeric) = -0.77757271875092793718239408404432
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.62879302401846851370417818742025
y2[1] (numeric) = -0.62879302401846851370417818742023
absolute error = 2e-32
relative error = 3.1806968646351541844819338546206e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=128046160, alloc=4652204, time=15.18
x[1] = 0.69
y1[1] (analytic) = -0.77124601499710660197353931549777
y1[1] (numeric) = -0.77124601499710660197353931549777
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.63653718222196794023742920700872
y2[1] (numeric) = -0.63653718222196794023742920700871
absolute error = 1e-32
relative error = 1.5710001362517238398235222357594e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=132048412, alloc=4652204, time=15.68
x[1] = 0.7
y1[1] (analytic) = -0.76484218728448842625585999019186
y1[1] (numeric) = -0.76484218728448842625585999019187
absolute error = 1e-32
relative error = 1.3074592597335938698746728353053e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.64421768723769105367261435139872
y2[1] (numeric) = -0.64421768723769105367261435139871
absolute error = 1e-32
relative error = 1.5522703269571039119899736409549e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=136049744, alloc=4652204, time=16.16
x[1] = 0.71
y1[1] (analytic) = -0.75836187599050816654145794413955
y1[1] (numeric) = -0.75836187599050816654145794413956
absolute error = 1e-32
relative error = 1.3186316871399746265297346929438e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.65183377102153668121012797285284
y2[1] (numeric) = -0.65183377102153668121012797285283
absolute error = 1e-32
relative error = 1.5341334623286338698889510906510e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.72
y1[1] (analytic) = -0.75180572914089497944548696225195
y1[1] (numeric) = -0.75180572914089497944548696225195
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.65938467197147315361800383264817
y2[1] (numeric) = -0.65938467197147315361800383264816
absolute error = 1e-32
relative error = 1.5165654321477203357119039156049e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=140050808, alloc=4652204, time=16.65
TOP MAIN SOLVE Loop
x[1] = 0.73
y1[1] (analytic) = -0.74517440234487038879013215855033
y1[1] (numeric) = -0.74517440234487038879013215855034
absolute error = 1e-32
relative error = 1.3419677284314378095774142725353e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.66686963500369787373259413076153
y2[1] (numeric) = -0.66686963500369787373259413076152
absolute error = 1e-32
relative error = 1.4995434602363547076596292654967e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=144052716, alloc=4652204, time=17.13
x[1] = 0.74
y1[1] (analytic) = -0.73846855872958790979142456069883
y1[1] (numeric) = -0.73846855872958790979142456069884
absolute error = 1e-32
relative error = 1.3541537932506339212970812949552e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.67428791162814506748388115760817
y2[1] (numeric) = -0.67428791162814506748388115760816
absolute error = 1e-32
relative error = 1.4830460145509444868398300234299e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=148055340, alloc=4652204, time=17.62
x[1] = 0.75
y1[1] (analytic) = -0.73168886887382088631183875300008
y1[1] (numeric) = -0.73168886887382088631183875300009
absolute error = 1e-32
relative error = 1.3667011246722261352150686601568e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.68163876002333416673324195277989
y2[1] (numeric) = -0.68163876002333416673324195277988
absolute error = 1e-32
relative error = 1.4670527244750101169725783295448e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=152057636, alloc=4652204, time=18.11
x[1] = 0.76
y1[1] (analytic) = -0.72483601074090517233968836666701
y1[1] (numeric) = -0.72483601074090517233968836666701
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.68892144511055133914775563876973
y2[1] (numeric) = -0.68892144511055133914775563876971
absolute error = 2e-32
relative error = 2.9030886092957371454415397095206e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=156058688, alloc=4652204, time=18.60
x[1] = 0.77
y1[1] (analytic) = -0.71791066961094336337129056532434
y1[1] (numeric) = -0.71791066961094336337129056532435
absolute error = 1e-32
relative error = 1.3929309624858048638846923337441e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.69613523862735674701988373445221
y2[1] (numeric) = -0.69613523862735674701988373445219
absolute error = 2e-32
relative error = 2.8730049694706029924906087380248e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.78
y1[1] (analytic) = -0.71091353801227735721626502376456
y1[1] (numeric) = -0.71091353801227735721626502376457
absolute error = 1e-32
relative error = 1.4066408171041612210983571067735e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.70327941920041018436789732511792
y2[1] (numeric) = -0.70327941920041018436789732511791
absolute error = 1e-32
relative error = 1.4219099446091351719853706495587e-30 %
Correct digits = 32
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 = 18.2
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=160059812, alloc=4652204, time=19.08
x[1] = 0.79
y1[1] (analytic) = -0.70384531565223609691278086108495
y1[1] (numeric) = -0.70384531565223609691278086108496
absolute error = 1e-32
relative error = 1.4207667192802507471305291751001e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.7103532724176078098140288749692
y2[1] (numeric) = -0.71035327241760780981402887496918
absolute error = 2e-32
relative error = 2.8155005089132960296161411393593e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 17.84
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
bytes used=164060508, alloc=4652204, time=19.57
x[1] = 0.8
y1[1] (analytic) = -0.69670670934716542092074998164232
y1[1] (numeric) = -0.69670670934716542092074998164233
absolute error = 1e-32
relative error = 1.4353241996722398004969524081629e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.71735609089952276162717461058139
y2[1] (numeric) = -0.71735609089952276162717461058137
absolute error = 2e-32
relative error = 2.7880156387772723490049644522139e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 17.48
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=168062136, alloc=4652204, time=20.05
x[1] = 0.81
y1[1] (analytic) = -0.6894984329517470175496392406801
y1[1] (numeric) = -0.68949843295174701754963924068011
absolute error = 1e-32
relative error = 1.4503296196323374815898349922412e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.72428717437014251092817685251454
y2[1] (numeric) = -0.72428717437014251092817685251453
absolute error = 1e-32
relative error = 1.3806678281575591497744905002579e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 17.14
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=172063224, alloc=4652204, time=20.54
x[1] = 0.82
y1[1] (analytic) = -0.68222120728761355166655797843693
y1[1] (numeric) = -0.68222120728761355166655797843694
absolute error = 1e-32
relative error = 1.4658002262577216994844494554605e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.73114582972689587938131336468772
y2[1] (numeric) = -0.73114582972689587938131336468771
absolute error = 1e-32
relative error = 1.3677162056351041919994290452163e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.8
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=176064460, alloc=4652204, time=21.04
x[1] = 0.83
y1[1] (analytic) = -0.67487576007126710211246291786445
y1[1] (numeric) = -0.67487576007126710211246291786446
absolute error = 1e-32
relative error = 1.4817542119076845659331474984770e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.73793137110996271872858022613808
y2[1] (numeric) = -0.73793137110996271872858022613807
absolute error = 1e-32
relative error = 1.3551395687323139549321573017265e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.46
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
x[1] = 0.84
y1[1] (analytic) = -0.66746282584130811792267103687086
y1[1] (numeric) = -0.66746282584130811792267103687086
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.74464311997085932125657267062965
y2[1] (numeric) = -0.74464311997085932125657267062963
absolute error = 2e-32
relative error = 2.6858503709512115049324626494095e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.13
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=180067156, alloc=4652204, time=21.52
x[1] = 0.85
y1[1] (analytic) = -0.65998314588498217039541602946147
y1[1] (numeric) = -0.65998314588498217039541602946147
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.75128040514029270271207152423547
y2[1] (numeric) = -0.75128040514029270271207152423545
absolute error = 2e-32
relative error = 2.6621218739579980491485171088475e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.81
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
bytes used=184068444, alloc=4652204, time=22.01
x[1] = 0.86
y1[1] (analytic) = -0.65243746816405184627203066422386
y1[1] (numeric) = -0.65243746816405184627203066422386
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.75784256289527697229458872952865
y2[1] (numeric) = -0.75784256289527697229458872952863
absolute error = 2e-32
relative error = 2.6390705641540635661109487598376e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.5
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=188070640, alloc=4652204, time=22.50
x[1] = 0.87
y1[1] (analytic) = -0.64482654724000119477766380548283
y1[1] (numeric) = -0.64482654724000119477766380548283
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.76432893702550507814480282372285
y2[1] (numeric) = -0.76432893702550507814480282372284
absolute error = 1e-32
relative error = 1.3083372244045115314688242731840e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.19
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
bytes used=192072808, alloc=4652204, time=22.99
x[1] = 0.88
y1[1] (analytic) = -0.63715114419858020801549860572209
y1[1] (numeric) = -0.63715114419858020801549860572209
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.77073887889896929120964513075599
y2[1] (numeric) = -0.77073887889896929120964513075598
absolute error = 1e-32
relative error = 1.2974562817286954688159028980636e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.88
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=196075104, alloc=4652204, time=23.48
x[1] = 0.89
y1[1] (analytic) = -0.62941202657369688020355305738025
y1[1] (numeric) = -0.62941202657369688020355305738025
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.77707174752682386549033371297318
y2[1] (numeric) = -0.77707174752682386549033371297317
absolute error = 1e-32
relative error = 1.2868824573569776297419516230397e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.58
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] = 0.9
y1[1] (analytic) = -0.62160996827066445648471615140713
y1[1] (numeric) = -0.62160996827066445648471615140713
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.78332690962748338846138231571355
y2[1] (numeric) = -0.78332690962748338846138231571354
absolute error = 1e-32
relative error = 1.2766062134588954960156456522320e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.28
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=200078332, alloc=4652204, time=23.97
x[1] = 0.91
y1[1] (analytic) = -0.61374574948881154652117822617468
y1[1] (numeric) = -0.61374574948881154652117822617468
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.78950373968995041187895751787155
y2[1] (numeric) = -0.78950373968995041187895751787154
absolute error = 1e-32
relative error = 1.2666184461554476328851986985698e-30 %
Correct digits = 32
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
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=204079996, alloc=4652204, time=24.46
x[1] = 0.92
y1[1] (analytic) = -0.60582015664346284179740470667438
y1[1] (numeric) = -0.60582015664346284179740470667438
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.79560162003636603026827610248162
y2[1] (numeric) = -0.79560162003636603026827610248161
absolute error = 1e-32
relative error = 1.2569104622415061901025446361799e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.71
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=208080752, alloc=4652204, time=24.95
x[1] = 0.93
y1[1] (analytic) = -0.59783398228729823849490708443298
y1[1] (numeric) = -0.59783398228729823849490708443299
absolute error = 1e-32
relative error = 1.6727051817530083924888988545676e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.80161994088377715208431921591065
y2[1] (numeric) = -0.80161994088377715208431921591064
absolute error = 1e-32
relative error = 1.2474739574186627875214517543531e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.42
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=212083464, alloc=4652204, time=25.44
x[1] = 0.94
y1[1] (analytic) = -0.58978802503109822996098981522402
y1[1] (numeric) = -0.58978802503109822996098981522402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.80755810040511428687021979863415
y2[1] (numeric) = -0.80755810040511428687021979863414
absolute error = 1e-32
relative error = 1.2383009959262950555565426520017e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.15
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
x[1] = 0.95
y1[1] (analytic) = -0.58168308946388349416618097376046
y1[1] (numeric) = -0.58168308946388349416618097376046
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.81341550478937375068542210210256
y2[1] (numeric) = -0.81341550478937375068542210210255
absolute error = 1e-32
relative error = 1.2293839914681003518494659282533e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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
bytes used=216086712, alloc=4652204, time=25.93
TOP MAIN SOLVE Loop
x[1] = 0.96
y1[1] (analytic) = -0.57351998607245666212505080035186
y1[1] (numeric) = -0.57351998607245666212505080035186
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.81919156830099827163322214643043
y2[1] (numeric) = -0.81919156830099827163322214643042
absolute error = 1e-32
relative error = 1.2207156893399160174865568665939e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=220088108, alloc=4652204, time=26.42
x[1] = 0.97
y1[1] (analytic) = -0.56529953116035431303652775484986
y1[1] (numeric) = -0.56529953116035431303652775484986
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.82488571333845005747662003785634
y2[1] (numeric) = -0.82488571333845005747662003785634
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=224089864, alloc=4652204, time=26.92
x[1] = 0.98
y1[1] (analytic) = -0.55702254676621730087665826735994
y1[1] (numeric) = -0.55702254676621730087665826735994
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.83049737049197046808453328771915
y2[1] (numeric) = -0.83049737049197046808453328771914
absolute error = 1e-32
relative error = 1.2040977317093965936477359077356e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=228091204, alloc=4652204, time=27.42
x[1] = 0.99
y1[1] (analytic) = -0.54868986058158757534312640865361
y1[1] (numeric) = -0.54868986058158757534312640865361
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.83602597860052051678925941154711
y2[1] (numeric) = -0.8360259786005205167892594115471
absolute error = 1e-32
relative error = 1.1961350790485799284337371675417e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=232092592, alloc=4717728, time=27.91
x[1] = 1
y1[1] (analytic) = -0.54030230586813971740093660744298
y1[1] (numeric) = -0.54030230586813971740093660744297
absolute error = 1e-32
relative error = 1.8508157176809256179117532413986e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.8414709848078965066525023216303
y2[1] (numeric) = -0.84147098480789650665250232163029
absolute error = 1e-32
relative error = 1.1883951057781212162615994523745e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.01
y1[1] (analytic) = -0.53186072137435546620673135577918
y1[1] (numeric) = -0.53186072137435546620673135577917
absolute error = 1e-32
relative error = 1.8801914858761304160058742988838e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.84683184461801519012309878478201
y2[1] (numeric) = -0.846831844618015190123098784782
absolute error = 1e-32
relative error = 1.1808719834468142374663420640003e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=236093748, alloc=4717728, time=28.39
x[1] = 1.02
y1[1] (analytic) = -0.52336595125164956988961380803381
y1[1] (numeric) = -0.5233659512516495698896138080338
absolute error = 1e-32
relative error = 1.9107089362776886454378422779994e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.85210802194936292361654998545538
y2[1] (numeric) = -0.85210802194936292361654998545537
absolute error = 1e-32
relative error = 1.1735601288112572819824797672248e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=240095740, alloc=4717728, time=28.88
x[1] = 1.03
y1[1] (analytic) = -0.51481884496995534753350229983735
y1[1] (numeric) = -0.51481884496995534753350229983734
absolute error = 1e-32
relative error = 1.9424308371197244332449996487096e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.85729898918860337214627438529442
y2[1] (numeric) = -0.85729898918860337214627438529441
absolute error = 1e-32
relative error = 1.1664541923074667312790368212473e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=244097356, alloc=4717728, time=29.37
x[1] = 1.04
y1[1] (analytic) = -0.50622025723277840373447342099217
y1[1] (numeric) = -0.50622025723277840373447342099216
absolute error = 1e-32
relative error = 1.9754247004385756762283379285025e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.86240422724333840328079169211617
y2[1] (numeric) = -0.86240422724333840328079169211616
absolute error = 1e-32
relative error = 1.1595490471985327900404013996952e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=248098536, alloc=4717728, time=29.86
x[1] = 1.05
y1[1] (analytic) = -0.4975710478917269902908495728121
y1[1] (numeric) = -0.49757104789172699029084957281209
absolute error = 1e-32
relative error = 2.0097632373047619814603684257021e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.86742322559401689438140948500027
y2[1] (numeric) = -0.86742322559401689438140948500026
absolute error = 1e-32
relative error = 1.1528397793536064180769674011258e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=252100960, alloc=4717728, time=30.36
x[1] = 1.06
y1[1] (analytic) = -0.48887208186052756191863753995641
y1[1] (numeric) = -0.4888720818605275619186375399564
absolute error = 1e-32
relative error = 2.0455248665340933506028342705602e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.87235548234498626228294592199742
y2[1] (numeric) = -0.87235548234498626228294592199741
absolute error = 1e-32
relative error = 1.1463216776168946790260800959306e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.07
y1[1] (analytic) = -0.48012422902853412436509306817592
y1[1] (numeric) = -0.48012422902853412436509306817591
absolute error = 1e-32
relative error = 2.0827942843529550116983739353760e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.87720050427468161030706325777682
y2[1] (numeric) = -0.87720050427468161030706325777681
absolute error = 1e-32
relative error = 1.1399902247284454927049148925566e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=256103164, alloc=4717728, time=30.84
x[1] = 1.08
y1[1] (analytic) = -0.47132836417374002391352478852603
y1[1] (numeric) = -0.47132836417374002391352478852602
absolute error = 1e-32
relative error = 2.1216631037112423847777714573716e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.88195780688494747373533498762476
y2[1] (numeric) = -0.88195780688494747373533498762474
absolute error = 2e-32
relative error = 2.2676821775226970277154571941427e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=260104324, alloc=4717728, time=31.34
x[1] = 1.09
y1[1] (analytic) = -0.46248536687530087702789707387514
y1[1] (numeric) = -0.46248536687530087702789707387513
absolute error = 1e-32
relative error = 2.1622305733829374458118142722034e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.88662691444948723160860062863605
y2[1] (numeric) = -0.88662691444948723160860062863603
absolute error = 2e-32
relative error = 2.2557402300851805280872224776897e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=264105276, alloc=4717728, time=31.83
x[1] = 1.1
y1[1] (analytic) = -0.45359612142557738777137005178472
y1[1] (numeric) = -0.4535961214255773877713700517847
absolute error = 2e-32
relative error = 4.4092087774347180679720506661284e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.8912073600614353399518025778717
y2[1] (numeric) = -0.89120736006143533995180257787168
absolute error = 2e-32
relative error = 2.2441466370544000988174833006507e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=268107228, alloc=4717728, time=32.32
x[1] = 1.11
y1[1] (analytic) = -0.44466151674170684864373751193357
y1[1] (numeric) = -0.44466151674170684864373751193356
absolute error = 1e-32
relative error = 2.2489016079636949635358455092129e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.89569868568004762924062595933937
y2[1] (numeric) = -0.89569868568004762924062595933935
absolute error = 2e-32
relative error = 2.2328937531950556528878894438313e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=272108180, alloc=4717728, time=32.82
x[1] = 1.12
y1[1] (analytic) = -0.43568244627671216761398879396113
y1[1] (numeric) = -0.43568244627671216761398879396111
absolute error = 2e-32
relative error = 4.5904993811243727864546572322733e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.90010044217650499711910324733915
y2[1] (numeric) = -0.90010044217650499711910324733913
absolute error = 2e-32
relative error = 2.2219742445230467316799051434832e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.13
y1[1] (analytic) = -0.42665980793015731037121583565354
y1[1] (numeric) = -0.42665980793015731037121583565352
absolute error = 2e-32
relative error = 4.6875753535411352140507026782080e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9044121893788259160370815224114
y2[1] (numeric) = -0.90441218937882591603708152241138
absolute error = 2e-32
relative error = 2.2113810754515069216797302583732e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=276109036, alloc=4717728, time=33.31
x[1] = 1.14
y1[1] (analytic) = -0.41759450395835809217518674082258
y1[1] (numeric) = -0.41759450395835809217518674082256
absolute error = 2e-32
relative error = 4.7893350631823378816383682599086e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9086334961158832645942155781022
y2[1] (numeric) = -0.90863349611588326459421557810219
absolute error = 1e-32
relative error = 1.1005537483206146725447225549655e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=280109868, alloc=4717728, time=33.80
x[1] = 1.15
y1[1] (analytic) = -0.40848744088415729815257671880992
y1[1] (numeric) = -0.4084874408841572981525767188099
absolute error = 2e-32
relative error = 4.8961113606603605924931240884617e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.91276394026052108094403304975368
y2[1] (numeric) = -0.91276394026052108094403304975366
absolute error = 2e-32
relative error = 2.1911470335135719826111150008028e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=284110524, alloc=4717728, time=34.30
x[1] = 1.16
y1[1] (analytic) = -0.39933952940627315445163962339401
y1[1] (numeric) = -0.39933952940627315445163962339399
absolute error = 2e-32
relative error = 5.0082695368864286332773691729060e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.91680310877176692661866166687433
y2[1] (numeric) = -0.91680310877176692661866166687432
absolute error = 1e-32
relative error = 1.0907467376934304006864358212757e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=288111496, alloc=4717728, time=34.79
x[1] = 1.17
y1[1] (analytic) = -0.3901516843082302153326619350505
y1[1] (numeric) = -0.39015168430823021533266193505049
absolute error = 1e-32
relative error = 2.5631056848391647153358290323670e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.92075059773613563957301300896203
y2[1] (numeric) = -0.92075059773613563957301300896201
absolute error = 2e-32
relative error = 2.1721408652000143041485420121306e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=292112236, alloc=4717728, time=35.28
x[1] = 1.18
y1[1] (analytic) = -0.38092482436688177302959946671276
y1[1] (numeric) = -0.38092482436688177302959946671275
absolute error = 1e-32
relative error = 2.6251898958332672918090036648854e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.92460601240802034610753802587476
y2[1] (numeric) = -0.92460601240802034610753802587474
absolute error = 2e-32
relative error = 2.1630834897896142230973730778543e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.19
y1[1] (analytic) = -0.37165987226053293806567955835047
y1[1] (numeric) = -0.37165987226053293806567955835045
absolute error = 2e-32
relative error = 5.3812642937088548613935325903777e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.92836896724916669260202111160267
y2[1] (numeric) = -0.92836896724916669260202111160265
absolute error = 2e-32
relative error = 2.1543158706889609330084255263453e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=296113660, alloc=4717728, time=35.77
x[1] = 1.2
y1[1] (analytic) = -0.36235775447667357763837335562308
y1[1] (numeric) = -0.36235775447667357763837335562306
absolute error = 2e-32
relative error = 5.5194072026648129137668658784755e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.93203908596722634967013443549483
y2[1] (numeric) = -0.9320390859672263496701344354948
absolute error = 3e-32
relative error = 3.2187491331296916861153507673057e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=300114940, alloc=4717728, time=36.26
x[1] = 1.21
y1[1] (analytic) = -0.35301940121933033870301071366479
y1[1] (numeric) = -0.35301940121933033870301071366477
absolute error = 2e-32
relative error = 5.6654110031686430904777888040839e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.93561600155338593341646488854361
y2[1] (numeric) = -0.93561600155338593341646488854358
absolute error = 3e-32
relative error = 3.2064436638740204488227490204825e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=304115636, alloc=4717728, time=36.75
x[1] = 1.22
y1[1] (analytic) = -0.3436457463160470204755229744352
y1[1] (numeric) = -0.34364574631604702047552297443518
absolute error = 2e-32
relative error = 5.8199469117264239878678497503029e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.93909935631906758093524527188837
y2[1] (numeric) = -0.93909935631906758093524527188835
absolute error = 2e-32
relative error = 2.1297001073872334107089126326436e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=308118104, alloc=4717728, time=37.24
x[1] = 1.23
y1[1] (analytic) = -0.33423772712450259823954724549766
y1[1] (numeric) = -0.33423772712450259823954724549765
absolute error = 1e-32
relative error = 2.9918824801830430638065894219944e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.94248880193169751002382356538924
y2[1] (numeric) = -0.94248880193169751002382356538922
absolute error = 2e-32
relative error = 2.1220411275983952675618352134190e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.24
y1[1] (analytic) = -0.32479628443877623657769341569738
y1[1] (numeric) = -0.32479628443877623657769341569737
absolute error = 1e-32
relative error = 3.0788529546387066657065462901600e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.94578399944953898628470596308179
y2[1] (numeric) = -0.94578399944953898628470596308176
absolute error = 3e-32
relative error = 3.1719716148148485389551099569729e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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
bytes used=312119612, alloc=4717728, time=37.73
TOP MAIN SOLVE Loop
x[1] = 1.25
y1[1] (analytic) = -0.31532236239526866544753855243804
y1[1] (numeric) = -0.31532236239526866544753855243803
absolute error = 1e-32
relative error = 3.1713576937701033608479299546555e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.94898461935558621434849084703605
y2[1] (numeric) = -0.94898461935558621434849084703602
absolute error = 3e-32
relative error = 3.1612735747362989631759231890560e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=316120972, alloc=4717728, time=38.23
x[1] = 1.26
y1[1] (analytic) = -0.30581690837828932688634248917648
y1[1] (numeric) = -0.30581690837828932688634248917648
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.95209034159051576385681622142542
y2[1] (numeric) = -0.9520903415905157638568162214254
absolute error = 2e-32
relative error = 2.1006409923861819534960845647385e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=320122464, alloc=4717728, time=38.73
x[1] = 1.27
y1[1] (analytic) = -0.29628087292531873355113701608796
y1[1] (numeric) = -0.29628087292531873355113701608795
absolute error = 1e-32
relative error = 3.3751756909804379950299232532105e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.95510085558469223509018174218289
y2[1] (numeric) = -0.95510085558469223509018174218286
absolute error = 3e-32
relative error = 3.1410295388788699371739444480923e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=324123148, alloc=4717728, time=39.22
x[1] = 1.28
y1[1] (analytic) = -0.28671520963195551277938689359259
y1[1] (numeric) = -0.28671520963195551277938689359258
absolute error = 1e-32
relative error = 3.4877814863175858325385099206348e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.95801586028922496370075385916029
y2[1] (numeric) = -0.95801586028922496370075385916026
absolute error = 3e-32
relative error = 3.1314721648703186153781013544840e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=328124880, alloc=4717728, time=39.71
x[1] = 1.29
y1[1] (analytic) = -0.27712087505655764138660609006118
y1[1] (numeric) = -0.27712087505655764138660609006117
absolute error = 1e-32
relative error = 3.6085336400439333502208771241743e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.96083506420607265890556129128537
y2[1] (numeric) = -0.96083506420607265890556129128535
absolute error = 2e-32
relative error = 2.0815227030172736098408450886038e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.3
y1[1] (analytic) = -0.26749882862458740699798410929287
y1[1] (numeric) = -0.26749882862458740699798410929286
absolute error = 1e-32
relative error = 3.7383341270754411719436683964147e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.96355818541719296470134863003955
y2[1] (numeric) = -0.96355818541719296470134863003953
absolute error = 2e-32
relative error = 2.0756400913496028853066938324360e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=332125876, alloc=4717728, time=40.20
x[1] = 1.31
y1[1] (analytic) = -0.2578500325326696613381769786162
y1[1] (numeric) = -0.25785003253266966133817697861618
absolute error = 2e-32
relative error = 7.7564465684005663928806699624399e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9661849516127340291692578059375
y2[1] (numeric) = -0.96618495161273402916925780593747
absolute error = 3e-32
relative error = 3.1049955756322513352726932282974e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=336127400, alloc=4717728, time=40.69
x[1] = 1.32
y1[1] (analytic) = -0.24817545165237295957398272942735
y1[1] (numeric) = -0.24817545165237295957398272942734
absolute error = 1e-32
relative error = 4.0294073944135738581860237987434e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.96871510011826526273589984597277
y2[1] (numeric) = -0.96871510011826526273589984597275
absolute error = 2e-32
relative error = 2.0645905073182307793178455494037e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=340129332, alloc=4717728, time=41.18
x[1] = 1.33
y1[1] (analytic) = -0.23847605343372320751578498601058
y1[1] (numeric) = -0.23847605343372320751578498601056
absolute error = 2e-32
relative error = 8.3865862890750833359123504948680e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9711483779210445623376830377638
y2[1] (numeric) = -0.97114837792104456233768303776377
absolute error = 3e-32
relative error = 3.0891263046972862465940813612778e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=344131524, alloc=4717728, time=41.68
x[1] = 1.34
y1[1] (analytic) = -0.22875280780845946523263949230014
y1[1] (numeric) = -0.22875280780845946523263949230013
absolute error = 1e-32
relative error = 4.3715310407788541476741032102713e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.97348454169531937478787034808955
y2[1] (numeric) = -0.97348454169531937478787034808953
absolute error = 2e-32
relative error = 2.0544753556302066436267292789820e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=348134556, alloc=4717728, time=42.18
x[1] = 1.35
y1[1] (analytic) = -0.21900668709304158142002217301063
y1[1] (numeric) = -0.21900668709304158142002217301061
absolute error = 2e-32
relative error = 9.1321412443919172973506823621498e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.97572335782665906926111353926522
y2[1] (numeric) = -0.97572335782665906926111353926519
absolute error = 3e-32
relative error = 3.0746419832382052117105986469068e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.36
y1[1] (analytic) = -0.20923866589141935767597525239186
y1[1] (numeric) = -0.20923866589141935767597525239184
absolute error = 2e-32
relative error = 9.5584627797133060877550893995346e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.97786460243531618567849243942663
y2[1] (numeric) = -0.9778646024353161856784924394266
absolute error = 3e-32
relative error = 3.0679093941315296578650955118218e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=352136432, alloc=4717728, time=42.66
x[1] = 1.37
y1[1] (analytic) = -0.19944972099757296568819838964531
y1[1] (numeric) = -0.19944972099757296568819838964529
absolute error = 2e-32
relative error = 1.0027589860726540222418547501368e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.97990806139861422288768850489193
y2[1] (numeric) = -0.9799080613986142228876885048919
absolute error = 3e-32
relative error = 3.0615117052084725025716087432751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=356138124, alloc=4717728, time=43.16
x[1] = 1.38
y1[1] (analytic) = -0.1896408312978343632091500735982
y1[1] (numeric) = -0.18964083129783436320915007359819
absolute error = 1e-32
relative error = 5.2731260096064537536605461963399e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98185353037235972787813108520605
y2[1] (numeric) = -0.98185353037235972787813108520602
absolute error = 3e-32
relative error = 3.0554455498696176470477246956131e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=360139796, alloc=4717728, time=43.65
x[1] = 1.39
y1[1] (analytic) = -0.17981297767299947659616321780405
y1[1] (numeric) = -0.17981297767299947659616321780404
absolute error = 1e-32
relative error = 5.5613338533248644647924530616214e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98370081481127654484003822444291
y2[1] (numeric) = -0.98370081481127654484003822444288
absolute error = 3e-32
relative error = 3.0497077514117454340774764863295e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=364141632, alloc=4717728, time=44.14
x[1] = 1.4
y1[1] (analytic) = -0.16996714290024093861674803520365
y1[1] (numeric) = -0.16996714290024093861674803520364
absolute error = 1e-32
relative error = 5.8834900848273448269942703098450e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9854497299884601806594745788061
y2[1] (numeric) = -0.98544972998846018065947457880607
absolute error = 3e-32
relative error = 3.0442953188846382027007465438561e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=368144392, alloc=4717728, time=44.64
x[1] = 1.41
y1[1] (analytic) = -0.16010431155483119016356254936092
y1[1] (numeric) = -0.16010431155483119016356254936091
absolute error = 1e-32
relative error = 6.2459279846284984956630466211963e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98710010101385034142908886194224
y2[1] (numeric) = -0.98710010101385034142908886194221
absolute error = 3e-32
relative error = 3.0392054432156379314749133768739e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.42
y1[1] (analytic) = -0.15022546991168577348698210297591
y1[1] (numeric) = -0.1502254699116857734869821029759
absolute error = 1e-32
relative error = 6.6566608218158868242394588307625e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9886517628517197927362734733357
y2[1] (numeric) = -0.98865176285171979273627347333567
absolute error = 3e-32
relative error = 3.0344354935924457800398381194336e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=372146812, alloc=4717728, time=45.12
x[1] = 1.43
y1[1] (analytic) = -0.14033160584673666253389762457492
y1[1] (numeric) = -0.14033160584673666253389762457491
absolute error = 1e-32
relative error = 7.1259784562869696005765449324739e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99010456033717779485729149548183
y2[1] (numeric) = -0.9901045603371777948572914954818
absolute error = 3e-32
relative error = 3.0299830140953567660089132712971e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=376148004, alloc=4717728, time=45.62
x[1] = 1.44
y1[1] (analytic) = -0.13042370873814549297752015612917
y1[1] (numeric) = -0.13042370873814549297752015612916
absolute error = 1e-32
relative error = 7.6673176194346817373660360175223e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99145834819168646252760446395798
y2[1] (numeric) = -0.99145834819168646252760446395795
absolute error = 3e-32
relative error = 3.0258457205707912781319328706012e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=380148672, alloc=4717728, time=46.11
x[1] = 1.45
y1[1] (analytic) = -0.12050276936736657053286662724802
y1[1] (numeric) = -0.12050276936736657053286662724801
absolute error = 1e-32
relative error = 8.2985644666089360283162255101862e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99271299103758849766535413432301
y2[1] (numeric) = -0.99271299103758849766535413432298
absolute error = 3e-32
relative error = 3.0220214977386215669938803278051e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=384150400, alloc=4717728, time=46.61
x[1] = 1.46
y1[1] (analytic) = -0.11056977982006955117464810912337
y1[1] (numeric) = -0.11056977982006955117464810912337
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99386836341164484228683230125003
y2[1] (numeric) = -0.99386836341164484228683230125
absolute error = 3e-32
relative error = 3.0185083965263985238359092642818e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=388151160, alloc=4717728, time=47.09
x[1] = 1.47
y1[1] (analytic) = -0.10062573338693170090697460146241
y1[1] (numeric) = -0.1006257333869317009069746014624
absolute error = 1e-32
relative error = 9.9378157688028373545061746907286e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99492434977758089785992846273557
y2[1] (numeric) = -0.99492434977758089785992846273554
absolute error = 3e-32
relative error = 3.0153046316241645395900158976590e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.48
y1[1] (analytic) = -0.090671624464309655776226540647838
y1[1] (numeric) = -0.090671624464309655776226540647832
absolute error = 6e-33
relative error = 6.6172852151355597158742307192576e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99588084453764005648407513256269
y2[1] (numeric) = -0.99588084453764005648407513256266
absolute error = 3e-32
relative error = 3.0124085792540944600162588667607e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=392152340, alloc=4717728, time=47.58
x[1] = 1.49
y1[1] (analytic) = -0.080708448454800614868318484563714
y1[1] (numeric) = -0.080708448454800614868318484563708
absolute error = 6e-33
relative error = 7.4341659576818618964543522687971e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9967377520431433885532007170437
y2[1] (numeric) = -0.99673775204314338855320071704367
absolute error = 3e-32
relative error = 3.0098187751497409110967395816956e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=396154824, alloc=4717728, time=48.07
x[1] = 1.5
y1[1] (analytic) = -0.070737201667702910088189851434269
y1[1] (numeric) = -0.070737201667702910088189851434263
absolute error = 6e-33
relative error = 8.4820997417819418491539370605113e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99749498660405443094172337114149
y2[1] (numeric) = -0.99749498660405443094172337114146
absolute error = 3e-32
relative error = 3.0075339127401747298625509485262e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=400156208, alloc=4717728, time=48.56
x[1] = 1.51
y1[1] (analytic) = -0.060758881219385906581595514916193
y1[1] (numeric) = -0.060758881219385906581595514916188
absolute error = 5e-33
relative error = 8.2292496169344957538401347130756e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99815247249754811924273786483671
y2[1] (numeric) = -0.99815247249754811924273786483668
absolute error = 3e-32
relative error = 3.0055528415348079570850271345298e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=404157364, alloc=4717728, time=49.06
x[1] = 1.52
y1[1] (analytic) = -0.050774484933579196726129270152727
y1[1] (numeric) = -0.050774484933579196726129270152722
absolute error = 5e-33
relative error = 9.8474657232678299652149632858788e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99871014397558300717231239411685
y2[1] (numeric) = -0.99871014397558300717231239411682
absolute error = 3e-32
relative error = 3.0038745657051677886292664950797e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.53
y1[1] (analytic) = -0.040785011241591058688989007076121
y1[1] (numeric) = -0.040785011241591058688989007076115
absolute error = 6e-33
relative error = 1.4711286860898103781269382278386e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.99916794527147601592426506870898
y2[1] (numeric) = -0.99916794527147601592426506870895
absolute error = 3e-32
relative error = 3.0024982428603569134803097180172e-30 %
Correct digits = 32
h = 0.01
bytes used=408158316, alloc=4717728, time=49.55
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 1.54
y1[1] (analytic) = -0.030791459082466157622476807076397
y1[1] (numeric) = -0.030791459082466157622476807076391
absolute error = 6e-33
relative error = 1.9485922976013277072731329223155e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.99952583060547905600596353844003
y2[1] (numeric) = -0.99952583060547905600596353844001
absolute error = 2e-32
relative error = 2.0009487886755937225918666730081e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=412159772, alloc=4717728, time=50.03
x[1] = 1.55
y1[1] (analytic) = -0.020794827803092473643912774695556
y1[1] (numeric) = -0.020794827803092473643912774695551
absolute error = 5e-33
relative error = 2.4044440508694339918709693984240e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.99978376418935696389761134763447
y2[1] (numeric) = -0.99978376418935696389761134763445
absolute error = 2e-32
relative error = 2.0004325651573635306403025905592e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=416161656, alloc=4717728, time=50.54
x[1] = 1.56
y1[1] (analytic) = -0.010796117058267445823920663760906
y1[1] (numeric) = -0.010796117058267445823920663760901
absolute error = 5e-33
relative error = 4.6312947266268312414233422888360e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.99994172022996629574517002341348
y2[1] (numeric) = -0.99994172022996629574517002341346
absolute error = 2e-32
relative error = 2.0001165663335265201073221180553e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=420164244, alloc=4717728, time=51.04
x[1] = 1.57
y1[1] (analytic) = -0.00079632671073332548540853364535419
y1[1] (numeric) = -0.0007963267107333254854085336453493
absolute error = 4.89e-33
relative error = 6.1406956894574983586604671771261e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = -0.99999968293183462021052992382333
y2[1] (numeric) = -0.9999996829318346202105299238233
absolute error = 3e-32
relative error = 3.0000009512047977361285288765229e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=424165828, alloc=4717728, time=51.53
x[1] = 1.58
y1[1] (analytic) = 0.0092035432688082648053890569827275
y1[1] (numeric) = 0.0092035432688082648053890569827321
absolute error = 4.6e-33
relative error = 4.9980750518008247430707146528410e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.99995764649874005255179423225172
y2[1] (numeric) = -0.99995764649874005255179423225169
absolute error = 3e-32
relative error = 3.0001270658854649824820910040972e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.008862
Order of pole (three term test) = -0.8909
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.59
y1[1] (analytic) = 0.019202492901692568095027346243403
y1[1] (numeric) = 0.019202492901692568095027346243408
absolute error = 5e-33
relative error = 2.6038285891303645687127360533955e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.99981561513429087198158434374551
y2[1] (numeric) = -0.99981561513429087198158434374548
absolute error = 3e-32
relative error = 3.0005532566092729875425661606254e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.01849
Order of pole (three term test) = -0.8974
NO COMPLEX POLE (six term test) for Equation 2
bytes used=428166576, alloc=4717728, time=52.02
TOP MAIN SOLVE Loop
x[1] = 1.6
y1[1] (analytic) = 0.029199522301288726205770462946499
y1[1] (numeric) = 0.029199522301288726205770462946503
absolute error = 4e-33
relative error = 1.3698854244007475682118184593316e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.99957360304150516434211382554623
y2[1] (numeric) = -0.9995736030415051643421138255462
absolute error = 3e-32
relative error = 3.0012797365512576379008119576430e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.02811
Order of pole (three term test) = -0.9087
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=432167632, alloc=4717728, time=52.51
x[1] = 1.61
y1[1] (analytic) = 0.039193631772987609585327609601018
y1[1] (numeric) = 0.039193631772987609585327609601022
absolute error = 4e-33
relative error = 1.0205739603740458230429188084879e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.9992316344213905321324131478443
y2[1] (numeric) = -0.99923163442139053213241314784427
absolute error = 3e-32
relative error = 3.0023068692547581122115856994688e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.03771
Order of pole (three term test) = -0.9245
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=436170244, alloc=4717728, time=53.01
x[1] = 1.62
y1[1] (analytic) = 0.049183821914170445143744274712327
y1[1] (numeric) = 0.04918382191417044514374427471233
absolute error = 3e-33
relative error = 6.0995666526998062618493970535457e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9987897434705240139155188912468
y2[1] (numeric) = -0.99878974347052401391551889124676
absolute error = 4e-32
relative error = 4.0048468921007165020633175294879e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.0473
Order of pole (three term test) = -0.945
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=440171504, alloc=4717728, time=53.51
x[1] = 1.63
y1[1] (analytic) = 0.059169093714148245297971697419802
y1[1] (numeric) = 0.059169093714148245297971697419804
absolute error = 2e-33
relative error = 3.3801430349131223417711167977356e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9982479743776324551116699849331
y2[1] (numeric) = -0.99824797437763245511166998493307
absolute error = 3e-32
relative error = 3.0052653018107846275631705160304e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.05688
Order of pole (three term test) = -0.9701
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=444173828, alloc=4717728, time=54.00
x[1] = 1.64
y1[1] (analytic) = 0.069148448654062044364492707456605
y1[1] (numeric) = 0.069148448654062044364492707456607
absolute error = 2e-33
relative error = 2.8923280838962283068738858110495e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99760638131917367213758197436794
y2[1] (numeric) = -0.99760638131917367213758197436791
absolute error = 3e-32
relative error = 3.0071980855144325146425184256964e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.06643
Order of pole (three term test) = -0.9997
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.65
y1[1] (analytic) = 0.079120888806733952359614597341276
y1[1] (numeric) = 0.079120888806733952359614597341278
absolute error = 2e-33
relative error = 2.5277774683311958314673347138389e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99686502845391885177170304020219
y2[1] (numeric) = -0.99686502845391885177170304020216
absolute error = 3e-32
relative error = 3.0094344915006497260087110451188e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.07595
Order of pole (three term test) = -1.034
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=448175512, alloc=4717728, time=54.49
x[1] = 1.66
y1[1] (analytic) = 0.089085416936459041185257931650621
y1[1] (numeric) = 0.089085416936459041185257931650622
absolute error = 1e-33
relative error = 1.1225181790564653402725400811556e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99602398991653672750100059061296
y2[1] (numeric) = -0.99602398991653672750100059061293
absolute error = 3e-32
relative error = 3.0119756455378041085776170901350e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.08544
Order of pole (three term test) = -1.073
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=452176280, alloc=4717728, time=54.98
x[1] = 1.67
y1[1] (analytic) = 0.099041036598728084094782342448611
y1[1] (numeric) = 0.099041036598728084094782342448612
absolute error = 1e-33
relative error = 1.0096824855050460085000116506600e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99508334981018017442629724653424
y2[1] (numeric) = -0.9950833498101801744262972465342
absolute error = 4e-32
relative error = 4.0197637723141793680983275593241e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.0949
Order of pole (three term test) = -1.116
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=456177008, alloc=4717728, time=55.47
x[1] = 1.68
y1[1] (analytic) = 0.10898675223987117624800473417282
y1[1] (numeric) = 0.10898675223987117624800473417282
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99404320219807596406048786919357
y2[1] (numeric) = -0.99404320219807596406048786919354
absolute error = 3e-32
relative error = 3.0179774816288228092661184002861e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1043
Order of pole (three term test) = -1.164
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=460178944, alloc=4717728, time=55.97
x[1] = 1.69
y1[1] (analytic) = 0.11892156929661227207639046983309
y1[1] (numeric) = 0.11892156929661227207639046983308
absolute error = 1e-32
relative error = 8.4089034976137594341836857769806e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99290365109411852003714929394559
y2[1] (numeric) = -0.99290365109411852003714929394556
absolute error = 3e-32
relative error = 3.0214412009606221357185031229109e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1137
Order of pole (three term test) = -1.217
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=464179624, alloc=4717728, time=56.47
x[1] = 1.7
y1[1] (analytic) = 0.12884449429552468408764285733487
y1[1] (numeric) = 0.12884449429552468408764285733487
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99166481045246861534613339864788
y2[1] (numeric) = -0.99166481045246861534613339864784
absolute error = 4e-32
relative error = 4.0336209955609023711423887391225e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.123
Order of pole (three term test) = -1.274
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.71
y1[1] (analytic) = 0.13875453495237759764268978305111
y1[1] (numeric) = 0.1387545349523775976426897830511
absolute error = 1e-32
relative error = 7.2069716520848367499722646064324e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.99032680415615805121775222386113
y2[1] (numeric) = -0.9903268041561580512177522238611
absolute error = 3e-32
relative error = 3.0293030415916622413029594344818e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1323
Order of pole (three term test) = -1.335
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=468181036, alloc=4717728, time=56.95
x[1] = 1.72
y1[1] (analytic) = 0.14865070027136366713637828033119
y1[1] (numeric) = 0.14865070027136366713637828033118
absolute error = 1e-32
relative error = 6.7271798799096660715465999324522e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98888976600470145717817065708548
y2[1] (numeric) = -0.98888976600470145717817065708544
absolute error = 4e-32
relative error = 4.0449402324798484027477905260024e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1416
Order of pole (three term test) = -1.401
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=472182988, alloc=4717728, time=57.44
x[1] = 1.73
y1[1] (analytic) = 0.15853200064419777090494835134257
y1[1] (numeric) = 0.15853200064419777090494835134256
absolute error = 1e-32
relative error = 6.3078747252067794695968576927849e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98735383970071645108567767622206
y2[1] (numeric) = -0.98735383970071645108567767622203
absolute error = 3e-32
relative error = 3.0384244020455224422402222833601e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1507
Order of pole (three term test) = -1.472
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=476184324, alloc=4717728, time=57.94
x[1] = 1.74
y1[1] (analytic) = 0.16839744794907701506737731534509
y1[1] (numeric) = 0.16839744794907701506737731534508
absolute error = 1e-32
relative error = 5.9383322739095048810312180156736e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98571917883555349712068269566555
y2[1] (numeric) = -0.98571917883555349712068269566552
absolute error = 3e-32
relative error = 3.0434631530086997243606855505693e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1598
Order of pole (three term test) = -1.546
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=480185464, alloc=4717728, time=58.43
x[1] = 1.75
y1[1] (analytic) = 0.17824605564949209038267694394263
y1[1] (numeric) = 0.17824605564949209038267694394262
absolute error = 1e-32
relative error = 5.6102223208037057389553331056725e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98398594687393689873166293696799
y2[1] (numeric) = -0.98398594687393689873166293696796
absolute error = 3e-32
relative error = 3.0488240299882496314164822396665e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1689
Order of pole (three term test) = -1.625
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=484186420, alloc=4717728, time=58.92
x[1] = 1.76
y1[1] (analytic) = 0.1880768388928801010698001765041
y1[1] (numeric) = 0.18807683889288010106980017650408
absolute error = 2e-32
relative error = 1.0633951590068502903522191460181e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.98215431713761846242496809945596
y2[1] (numeric) = -0.98215431713761846242496809945593
absolute error = 3e-32
relative error = 3.0545098134305131359654926896528e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1779
Order of pole (three term test) = -1.709
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.77
y1[1] (analytic) = 0.19788881460910900038948584173039
y1[1] (numeric) = 0.19788881460910900038948584173038
absolute error = 1e-32
relative error = 5.0533427165921741754996416250772e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.98022447278804546701848144889842
y2[1] (numeric) = -0.9802244727880454670184814488984
absolute error = 2e-32
relative error = 2.0403489767108285761786555002274e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1868
Order of pole (three term test) = -1.797
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=488188568, alloc=4717728, time=59.41
x[1] = 1.78
y1[1] (analytic) = 0.20768100160878378462655329031263
y1[1] (numeric) = 0.20768100160878378462655329031261
absolute error = 2e-32
relative error = 9.6301538634115042834193614266641e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9781966068080446715477686473056
y2[1] (numeric) = -0.97819660680804467154776864730557
absolute error = 3e-32
relative error = 3.0668681317442983929187334974028e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1956
Order of pole (three term test) = -1.889
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=492189324, alloc=4717728, time=59.90
x[1] = 1.79
y1[1] (analytic) = 0.21745242068136461493517026446461
y1[1] (numeric) = 0.21745242068136461493517026446459
absolute error = 2e-32
relative error = 9.1974142837003486012585058173159e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.97607092198252419340866043310862
y2[1] (numeric) = -0.97607092198252419340866043310859
absolute error = 3e-32
relative error = 3.0735471495315303691984956558714e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2044
Order of pole (three term test) = -1.985
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=496191712, alloc=4717728, time=60.39
x[1] = 1.8
y1[1] (analytic) = 0.22720209469308705531667430653058
y1[1] (numeric) = 0.22720209469308705531667430653056
absolute error = 2e-32
relative error = 8.8027357437072644438879910467243e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.97384763087819518653237317884336
y2[1] (numeric) = -0.97384763087819518653237317884333
absolute error = 3e-32
relative error = 3.0805640480889843939586028778288e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.213
Order of pole (three term test) = -2.086
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=500192536, alloc=4717728, time=60.89
x[1] = 1.81
y1[1] (analytic) = 0.23692904868467463478774985084198
y1[1] (numeric) = 0.23692904868467463478774985084195
absolute error = 3e-32
relative error = 1.2662018509991384007063247977962e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.97152695582231534740845126909038
y2[1] (numeric) = -0.97152695582231534740845126909035
absolute error = 3e-32
relative error = 3.0879225553353317830888532133930e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2216
Order of pole (three term test) = -2.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=504194220, alloc=4717728, time=61.38
x[1] = 1.82
y1[1] (analytic) = 0.24663230996883396256417104483087
y1[1] (numeric) = 0.24663230996883396256417104483084
absolute error = 3e-32
relative error = 1.2163856391642681381308001051063e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.96910912888045637458721531849805
y2[1] (numeric) = -0.96910912888045637458721531849803
absolute error = 2e-32
relative error = 2.0637510682728366751881481993565e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2301
Order of pole (three term test) = -2.299
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.83
y1[1] (analytic) = 0.25631090822752264682983758361853
y1[1] (numeric) = 0.2563109082275226468298375836185
absolute error = 3e-32
relative error = 1.1704535014705473297850042147286e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.96659439183329760489723892974281
y2[1] (numeric) = -0.96659439183329760489723892974279
absolute error = 2e-32
relative error = 2.0691202192955898054828824640410e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2385
Order of pole (three term test) = -2.412
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=508196744, alloc=4717728, time=61.87
x[1] = 1.84
y1[1] (analytic) = 0.2659638756089802903802829832816
y1[1] (numeric) = 0.26596387560898029038028298328157
absolute error = 3e-32
relative error = 1.1279727343162180830575871388935e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = -0.96398299615244814699489367172712
y2[1] (numeric) = -0.9639829961524481469948936717271
absolute error = 2e-32
relative error = 2.0747253924422044041935905298016e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2469
Order of pole (three term test) = -2.529
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=512197584, alloc=4717728, time=62.37
x[1] = 1.85
y1[1] (analytic) = 0.2755902468245128601219498354748
y1[1] (numeric) = 0.27559024682451286012194983547478
absolute error = 2e-32
relative error = 7.2571508717924137937811312151998e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.96127520297529993001245916863613
y2[1] (numeric) = -0.96127520297529993001245916863611
absolute error = 2e-32
relative error = 2.0805696368840903260509773546865e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2551
Order of pole (three term test) = -2.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=516199280, alloc=4717728, time=62.87
x[1] = 1.86
y1[1] (analytic) = 0.28518905924502075207093548828912
y1[1] (numeric) = 0.2851890592450207520709354882891
absolute error = 2e-32
relative error = 7.0128917473012034093643202129961e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9584712830789141819789777659032
y2[1] (numeric) = -0.95847128307891418197897776590318
absolute error = 2e-32
relative error = 2.0866561526761289901266268234546e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2632
Order of pole (three term test) = -2.774
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=520201000, alloc=4717728, time=63.35
x[1] = 1.87
y1[1] (analytic) = 0.29475935299726089912514806480989
y1[1] (numeric) = 0.29475935299726089912514806480987
absolute error = 2e-32
relative error = 6.7851960579469223372137213129011e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.95557151685294394934425049217263
y2[1] (numeric) = -0.95557151685294394934425049217262
absolute error = 1e-32
relative error = 1.0464941476001458678685505995315e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2712
Order of pole (three term test) = -2.903
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.88
y1[1] (analytic) = 0.30430017105983329547931375952224
y1[1] (numeric) = 0.30430017105983329547931375952222
absolute error = 2e-32
relative error = 6.5724576921343504499090039097593e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.95257619427159536533145742581513
y2[1] (numeric) = -0.95257619427159536533145742581511
absolute error = 2e-32
relative error = 2.0995695798689743792995432793856e-30 %
Correct digits = 32
h = 0.01
bytes used=524202732, alloc=4717728, time=63.85
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
Radius of convergence (three term test) for eq 2 = 0.2791
Order of pole (three term test) = -3.035
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.89
y1[1] (analytic) = 0.31381055935888233911038241555123
y1[1] (numeric) = 0.31381055935888233911038241555121
absolute error = 2e-32
relative error = 6.3732718366329582156693488786626e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.94948561486463047096820167213832
y2[1] (numeric) = -0.94948561486463047096820167213831
absolute error = 1e-32
relative error = 1.0532018435503853710694052094469e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2869
Order of pole (three term test) = -3.172
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=528203884, alloc=4717728, time=64.33
x[1] = 1.9
y1[1] (analytic) = 0.32328956686350342227883369508031
y1[1] (numeric) = 0.32328956686350342227883369508029
absolute error = 2e-32
relative error = 6.1864044033453854991113860277268e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.94630008768741448848970961163496
y2[1] (numeric) = -0.94630008768741448848970961163495
absolute error = 1e-32
relative error = 1.0567472337911521726622641141563e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2946
Order of pole (three term test) = -3.312
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=532204940, alloc=4717728, time=64.83
x[1] = 1.91
y1[1] (analytic) = 0.33273624568084522946633893939753
y1[1] (numeric) = 0.3327362456808452294663389393975
absolute error = 3e-32
relative error = 9.0161502960442349248329201766593e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.94301993129001054236188657694821
y2[1] (numeric) = -0.94301993129001054236188657694821
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3021
Order of pole (three term test) = -3.455
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=536205712, alloc=4717728, time=65.32
x[1] = 1.92
y1[1] (analytic) = 0.34214965115089823259923660315905
y1[1] (numeric) = 0.34214965115089823259923660315902
absolute error = 3e-32
relative error = 8.7680931133754400524760675860459e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.93964547368532491842637133968703
y2[1] (numeric) = -0.93964547368532491842637133968703
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3095
Order of pole (three term test) = -3.602
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=540207120, alloc=4717728, time=65.82
x[1] = 1.93
y1[1] (analytic) = 0.35152884194095990478728906471187
y1[1] (numeric) = 0.35152884194095990478728906471185
absolute error = 2e-32
relative error = 5.6894335866071117449295365202584e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.93617705231630604661512937274878
y2[1] (numeric) = -0.93617705231630604661512937274878
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3168
Order of pole (three term test) = -3.753
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.94
y1[1] (analytic) = 0.36087288013976720613506768584073
y1[1] (numeric) = 0.3608728801397672061350676858407
absolute error = 3e-32
relative error = 8.3131766477937896741660787069603e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.9326150140222004873089793388657
y2[1] (numeric) = -0.9326150140222004873089793388657
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.324
Order of pole (three term test) = -3.908
NO COMPLEX POLE (six term test) for Equation 2
bytes used=544209032, alloc=4717728, time=66.30
TOP MAIN SOLVE Loop
x[1] = 1.95
y1[1] (analytic) = 0.37018083135128692845582845913069
y1[1] (numeric) = 0.37018083135128692845582845913066
absolute error = 3e-32
relative error = 8.1041473407711891297445891378239e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.92895971500386929571329703509148
y2[1] (numeric) = -0.92895971500386929571329703509149
absolute error = 1e-32
relative error = 1.0764729447883913974130191869883e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3311
Order of pole (three term test) = -4.065
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=548210012, alloc=4717728, time=66.80
x[1] = 1.96
y1[1] (analytic) = 0.37945176478815451993156521544745
y1[1] (numeric) = 0.37945176478815451993156521544742
absolute error = 3e-32
relative error = 7.9061432265966155338035230709437e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.92521152078816823258555628949003
y2[1] (numeric) = -0.92521152078816823258555628949003
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.338
Order of pole (three term test) = -4.226
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=552210800, alloc=4717728, time=67.29
x[1] = 1.97
y1[1] (analytic) = 0.38868475336475204591463981387931
y1[1] (numeric) = 0.38868475336475204591463981387928
absolute error = 3e-32
relative error = 7.7183372232373640515944072044727e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.92137080619139538326395099715317
y2[1] (numeric) = -0.92137080619139538326395099715317
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3448
Order of pole (three term test) = -4.391
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=556211676, alloc=4717728, time=67.78
x[1] = 1.98
y1[1] (analytic) = 0.39787887378991597815247385990719
y1[1] (numeric) = 0.39787887378991597815247385990717
absolute error = 2e-32
relative error = 5.0266554264351818499094138133063e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.917437955281809840204735217402
y2[1] (numeric) = -0.917437955281809840204735217402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3514
Order of pole (three term test) = -4.558
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=560213944, alloc=4717728, time=68.29
x[1] = 1.99
y1[1] (analytic) = 0.40703320665926554173363571613029
y1[1] (numeric) = 0.40703320665926554173363571613027
absolute error = 2e-32
relative error = 4.9136040187360787088299364222843e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.91341336134122519712879327105761
y2[1] (numeric) = -0.91341336134122519712879327105762
absolute error = 1e-32
relative error = 1.0947945829603739534239322114247e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3579
Order of pole (three term test) = -4.729
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2
y1[1] (analytic) = 0.41614683654714238699756822950076
y1[1] (numeric) = 0.41614683654714238699756822950074
absolute error = 2e-32
relative error = 4.8059959234447619795092008028402e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.90929742682568169539601986591174
y2[1] (numeric) = -0.90929742682568169539601986591175
absolute error = 1e-32
relative error = 1.0997501702946164667566973970263e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3643
Order of pole (three term test) = -4.903
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=564215684, alloc=4717728, time=68.77
x[1] = 2.01
y1[1] (analytic) = 0.42521885209815239251738234016543
y1[1] (numeric) = 0.42521885209815239251738234016541
absolute error = 2e-32
relative error = 4.7034603243281041454310061394566e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.90509056332520095536009971027372
y2[1] (numeric) = -0.90509056332520095536009971027372
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3705
Order of pole (three term test) = -5.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=568217740, alloc=4717728, time=69.26
x[1] = 2.02
y1[1] (analytic) = 0.4342483461183004450517028740902
y1[1] (numeric) = 0.43424834611830044505170287409018
absolute error = 2e-32
relative error = 4.6056594524257518692344113007603e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.90079319152262731719701352455371
y2[1] (numeric) = -0.90079319152262731719701352455371
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3766
Order of pole (three term test) = -5.259
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=572219152, alloc=4717728, time=69.75
x[1] = 2.03
y1[1] (analytic) = 0.4432344156657090830635167316961
y1[1] (numeric) = 0.44323441566570908306351673169608
absolute error = 2e-32
relative error = 4.5122849880601687891884331490848e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.89640574115155990703888883196757
y2[1] (numeric) = -0.89640574115155990703888883196757
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3825
Order of pole (three term test) = -5.442
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=576220420, alloc=4717728, time=70.25
x[1] = 2.04
y1[1] (analytic) = 0.45217616214091193201727020529136
y1[1] (numeric) = 0.45217616214091193201727020529135
absolute error = 1e-32
relative error = 2.2115274614772138136154039325036e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.8919286509533796351715256485842
y2[1] (numeric) = -0.8919286509533796351715256485842
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3883
Order of pole (three term test) = -5.628
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=580221160, alloc=4717728, time=70.74
x[1] = 2.05
y1[1] (analytic) = 0.4610726913767129021859299941674
y1[1] (numeric) = 0.46107269137671290218592999416739
absolute error = 1e-32
relative error = 2.1688554076237063126612835928559e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.88736236863337542355996660468034
y2[1] (numeric) = -0.88736236863337542355996660468033
absolute error = 1e-32
relative error = 1.1269353258016761656221986601155e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3939
Order of pole (three term test) = -5.816
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.06
y1[1] (analytic) = 0.4699231137276021631231096264879
y1[1] (numeric) = 0.46992311372760216312310962648789
absolute error = 1e-32
relative error = 2.1280076905935397163185023347168e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.8827073508159740500427975851999
y2[1] (numeric) = -0.88270735081597405004279758519989
absolute error = 1e-32
relative error = 1.1328782966128023156341294283346e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3993
Order of pole (three term test) = -6.007
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=584223328, alloc=4717728, time=71.23
x[1] = 2.07
y1[1] (analytic) = 0.47872654415871995327732713901173
y1[1] (numeric) = 0.47872654415871995327732713901172
absolute error = 1e-32
relative error = 2.0888751881459362481795224245323e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.87796406299907808617345112044384
y2[1] (numeric) = -0.87796406299907808617345112044383
absolute error = 1e-32
relative error = 1.1389987838272715938342828503963e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4046
Order of pole (three term test) = -6.2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=588224716, alloc=4717728, time=71.72
x[1] = 2.08
y1[1] (analytic) = 0.48748210233435932844156884977235
y1[1] (numeric) = 0.48748210233435932844156884977234
absolute error = 1e-32
relative error = 2.0513573630937316539311885790751e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.87313297950751649487667680502462
y2[1] (numeric) = -0.87313297950751649487667680502461
absolute error = 1e-32
relative error = 1.1453009146029987423503721874535e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4097
Order of pole (three term test) = -6.396
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=592227140, alloc=4717728, time=72.21
x[1] = 2.09
y1[1] (analytic) = 0.49618891270599899883706631187045
y1[1] (numeric) = 0.49618891270599899883706631187044
absolute error = 1e-32
relative error = 2.0153614367286724927354395563966e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.86821458344561254282162205872751
y2[1] (numeric) = -0.8682145834456125428216220587275
absolute error = 1e-32
relative error = 1.1517889921076669803333046944329e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4147
Order of pole (three term test) = -6.595
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=596228280, alloc=4717728, time=72.70
x[1] = 2.1
y1[1] (analytic) = 0.50484610459985745162093852371917
y1[1] (numeric) = 0.50484610459985745162093852371916
absolute error = 1e-32
relative error = 1.9808016559672239571942225812533e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.86320936664887377068075931326902
y2[1] (numeric) = -0.86320936664887377068075931326902
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4195
Order of pole (three term test) = -6.796
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=600229596, alloc=4717728, time=73.20
x[1] = 2.11
y1[1] (analytic) = 0.51345281230395960347841015707169
y1[1] (numeric) = 0.51345281230395960347841015707168
absolute error = 1e-32
relative error = 1.9475986420501066201724483171570e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.85811782963480885223737550831068
y2[1] (numeric) = -0.85811782963480885223737550831068
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4241
Order of pole (three term test) = -6.999
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.12
y1[1] (analytic) = 0.52200817515470727670690188298389
y1[1] (numeric) = 0.52200817515470727670690188298388
absolute error = 1e-32
relative error = 1.9156788104010642135972945821173e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.85294048155287626061472733365415
y2[1] (numeric) = -0.85294048155287626061472733365415
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4286
Order of pole (three term test) = -7.204
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=604231356, alloc=4717728, time=73.69
x[1] = 2.13
y1[1] (analytic) = 0.53051133762294484181652620960972
y1[1] (numeric) = 0.53051133762294484181652620960971
absolute error = 1e-32
relative error = 1.8849738527374114560688554155413e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.8476778401335697467185299963159
y2[1] (numeric) = -0.84767784013356974671852999631589
absolute error = 1e-32
relative error = 1.1796934550541378361417484489905e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4329
Order of pole (three term test) = -7.411
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=608234052, alloc=4717728, time=74.18
x[1] = 2.14
y1[1] (analytic) = 0.5389614493995114201544499120086
y1[1] (numeric) = 0.53896144939951142015444991200859
absolute error = 1e-32
relative error = 1.8554202737768326198782713657620e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.84233043163664572130250663706891
y2[1] (numeric) = -0.8423304316366457213025066370689
absolute error = 1e-32
relative error = 1.1871825621413234937582104236738e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.437
Order of pole (three term test) = -7.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=612235068, alloc=4717728, time=74.67
x[1] = 2.15
y1[1] (analytic) = 0.54735766548027109140415388226403
y1[1] (numeric) = 0.54735766548027109140415388226402
absolute error = 1e-32
relative error = 1.8269589759422925385973718785549e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.83689879079849771787564813704379
y2[1] (numeric) = -0.83689879079849771787564813704378
absolute error = 1e-32
relative error = 1.1948876148403619587406674857067e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4409
Order of pole (three term test) = -7.832
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=616235968, alloc=4717728, time=75.16
x[1] = 2.16
y1[1] (analytic) = 0.55569914625061260300969874398337
y1[1] (numeric) = 0.55569914625061260300969874398336
absolute error = 1e-32
relative error = 1.7995348863627979696802643103276e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.83138346077868319896103812034632
y2[1] (numeric) = -0.83138346077868319896103812034632
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4447
Order of pole (three term test) = -8.045
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.17
y1[1] (analytic) = 0.56398505756941013162446999441651
y1[1] (numeric) = 0.5639850575694101316244699944165
absolute error = 1e-32
relative error = 1.7730966212290635557088100342660e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.82578499310560805298105642394338
y2[1] (numeric) = -0.82578499310560805298105642394338
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4483
Order of pole (three term test) = -8.26
NO COMPLEX POLE (six term test) for Equation 2
bytes used=620237328, alloc=4717728, time=75.66
TOP MAIN SOLVE Loop
x[1] = 2.18
y1[1] (analytic) = 0.57221457085243670057822486766249
y1[1] (numeric) = 0.57221457085243670057822486766248
absolute error = 1e-32
relative error = 1.7475961832119809106567839058896e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.82010394762137421327400974608394
y2[1] (numeric) = -0.82010394762137421327400974608394
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4517
Order of pole (three term test) = -8.476
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=624239252, alloc=4717728, time=76.14
x[1] = 2.19
y1[1] (analytic) = 0.58038686315522191209020516379695
y1[1] (numeric) = 0.58038686315522191209020516379694
absolute error = 1e-32
relative error = 1.7229886882063255820227271681440e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.814340892425795914434327645905
y2[1] (numeric) = -0.814340892425795914434327645905
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4549
Order of pole (three term test) = -8.694
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=628240904, alloc=4717728, time=76.64
x[1] = 2.2
y1[1] (analytic) = 0.58850111725534570852414261265493
y1[1] (numeric) = 0.58850111725534570852414261265492
absolute error = 1e-32
relative error = 1.6992321181373532904394435004937e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.80849640381959018430403691041612
y2[1] (numeric) = -0.80849640381959018430403691041612
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4579
Order of pole (three term test) = -8.914
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=632241692, alloc=4717728, time=77.13
x[1] = 2.21
y1[1] (analytic) = 0.59655652173415993337760917751863
y1[1] (numeric) = 0.59655652173415993337760917751863
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.80257106624674725251897404255597
y2[1] (numeric) = -0.80257106624674725251897404255597
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4608
Order of pole (three term test) = -9.135
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=636243272, alloc=4717728, time=77.63
x[1] = 2.22
y1[1] (analytic) = 0.60455227105792951991771443750015
y1[1] (numeric) = 0.60455227105792951991771443750015
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.79656547223608663852085674960916
y2[1] (numeric) = -0.79656547223608663852085674960916
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4635
Order of pole (three term test) = -9.358
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.23
y1[1] (analytic) = 0.61248756565838519341190391068563
y1[1] (numeric) = 0.61248756565838519341190391068563
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.79048022234200476337771012718854
y2[1] (numeric) = -0.79048022234200476337771012718854
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.466
Order of pole (three term test) = -9.581
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=640244448, alloc=4717728, time=78.12
x[1] = 2.24
y1[1] (analytic) = 0.62036161201267963175076226631044
y1[1] (numeric) = 0.62036161201267963175076226631044
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.7843159250844200106020886706045
y2[1] (numeric) = -0.7843159250844200106020886706045
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.24
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4683
Order of pole (three term test) = -9.806
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=644245200, alloc=4717728, time=78.61
x[1] = 2.25
y1[1] (analytic) = 0.6281736227227390889133890573964
y1[1] (numeric) = 0.6281736227227390889133890573964
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.77807319688792124141096667558776
y2[1] (numeric) = -0.77807319688792124141096667558776
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4704
Order of pole (three term test) = -10.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=648246172, alloc=4717728, time=79.10
x[1] = 2.26
y1[1] (analytic) = 0.63592281659400254617912656874484
y1[1] (numeric) = 0.63592281659400254617912656874484
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.77175266202012584952506163774032
y2[1] (numeric) = -0.77175266202012584952506163774032
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.83
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4723
Order of pole (three term test) = -10.26
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=652247152, alloc=4717728, time=79.60
x[1] = 2.27
y1[1] (analytic) = 0.6436084187135405172361343481243
y1[1] (numeric) = 0.6436084187135405172361343481243
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.76535495252925351965074260193472
y2[1] (numeric) = -0.76535495252925351965074260193472
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.14
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4741
Order of pole (three term test) = -10.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=656248716, alloc=4717728, time=80.10
x[1] = 2.28
y1[1] (analytic) = 0.6512296605275456953713983504607
y1[1] (numeric) = 0.65122966052754569537139835046069
absolute error = 1e-32
relative error = 1.5355565948730340819789574880371e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.75888070818092193221665357630092
y2[1] (numeric) = -0.75888070818092193221665357630092
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4756
Order of pole (three term test) = -10.71
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.29
y1[1] (analytic) = 0.65878577991818769374203101818895
y1[1] (numeric) = 0.65878577991818769374203101818894
absolute error = 1e-32
relative error = 1.5179441185330176815715512444306e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.75233057639417073474190827797365
y2[1] (numeric) = -0.75233057639417073474190827797366
absolute error = 1e-32
relative error = 1.3292029213977701045232408598066e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.477
Order of pole (three term test) = -10.94
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=660250848, alloc=4717728, time=80.59
x[1] = 2.3
y1[1] (analytic) = 0.66627602127982419331788057116602
y1[1] (numeric) = 0.66627602127982419331788057116601
absolute error = 1e-32
relative error = 1.5008794674602549050021477349038e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.7457052121767201773854062116435
y2[1] (numeric) = -0.74570521217672017738540621164351
absolute error = 1e-32
relative error = 1.3410124854578809564413220294695e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4781
Order of pole (three term test) = -11.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=664252260, alloc=4717728, time=81.08
x[1] = 2.31
y1[1] (analytic) = 0.67369963559456087744416432347103
y1[1] (numeric) = 0.67369963559456087744416432347103
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.73900527805947088675876419209826
y2[1] (numeric) = -0.73900527805947088675876419209827
absolute error = 1e-32
relative error = 1.3531703083716348800224786494875e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4791
Order of pole (three term test) = -11.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=668252924, alloc=4717728, time=81.57
x[1] = 2.32
y1[1] (analytic) = 0.68105588050715259709363616600823
y1[1] (numeric) = 0.68105588050715259709363616600822
absolute error = 1e-32
relative error = 1.4683082968982569152679736077002e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.73223144403025132797089867772467
y2[1] (numeric) = -0.73223144403025132797089867772469
absolute error = 2e-32
relative error = 2.7313768294241297615197433078798e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4799
Order of pole (three term test) = -11.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=672253712, alloc=4717728, time=82.07
x[1] = 2.33
y1[1] (analytic) = 0.688344020399238276754180427816
y1[1] (numeric) = 0.68834402039923827675418042781599
absolute error = 1e-32
relative error = 1.4527619480445284079444116906663e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.72538438746681958010284419247542
y2[1] (numeric) = -0.72538438746681958010284419247543
absolute error = 1e-32
relative error = 1.3785794363347003309458045492630e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 17.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4805
Order of pole (three term test) = -11.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=676254960, alloc=4717728, time=82.56
x[1] = 2.34
y1[1] (analytic) = 0.69556332646290213752310557206135
y1[1] (numeric) = 0.69556332646290213752310557206134
absolute error = 1e-32
relative error = 1.4376836183776790727046175124394e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.71846479306912612487942868679401
y2[1] (numeric) = -0.71846479306912612487942868679402
absolute error = 1e-32
relative error = 1.3918566499664046076648310495166e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4809
Order of pole (three term test) = -12.1
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.35
y1[1] (analytic) = 0.70271307677355388134712911225892
y1[1] (numeric) = 0.70271307677355388134712911225891
absolute error = 1e-32
relative error = 1.4230559143589773958804564382109e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.71147335279084442220249118201321
y2[1] (numeric) = -0.71147335279084442220249118201322
absolute error = 1e-32
relative error = 1.4055340176513613990205539733054e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 17.78
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4811
Order of pole (three term test) = -12.33
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=680257264, alloc=4717728, time=83.04
x[1] = 2.36
y1[1] (analytic) = 0.7097925563621205484503630346451
y1[1] (numeric) = 0.70979255636212054845036303464509
absolute error = 1e-32
relative error = 1.4088623373641326237051151901722e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.7044107657701761194310307129327
y2[1] (numeric) = -0.70441076577017611943103071293271
absolute error = 1e-32
relative error = 1.4196262303098644139793149698341e-30 %
Correct digits = 32
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 = 18.14
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4811
Order of pole (three term test) = -12.56
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=684258320, alloc=4717728, time=83.53
x[1] = 2.37
y1[1] (analytic) = 0.71680105728654282882471660882235
y1[1] (numeric) = 0.71680105728654282882471660882234
absolute error = 1e-32
relative error = 1.3950872279478903715491859949333e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.69727773825993781382969642028923
y2[1] (numeric) = -0.69727773825993781382969642028923
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4809
Order of pole (three term test) = -12.79
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=688259628, alloc=4717728, time=84.02
x[1] = 2.38
y1[1] (analytic) = 0.72373787870256867821114760736753
y1[1] (numeric) = 0.72373787870256867821114760736752
absolute error = 1e-32
relative error = 1.3817157142482043989095556284519e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.6900749835569363594511131070202
y2[1] (numeric) = -0.6900749835569363594511131070202
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4806
Order of pole (three term test) = -13.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=692262004, alloc=4717728, time=84.51
x[1] = 2.39
y1[1] (analytic) = 0.73060232693383715926915829261806
y1[1] (numeric) = 0.73060232693383715926915829261805
absolute error = 1e-32
relative error = 1.3687336641764614957568409192704e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.68280322193063978086250031101305
y2[1] (numeric) = -0.68280322193063978086250031101305
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.48
Order of pole (three term test) = -13.25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=696262648, alloc=4717728, time=85.01
x[1] = 2.4
y1[1] (analytic) = 0.73739371554124549960882222733478
y1[1] (numeric) = 0.73739371554124549960882222733477
absolute error = 1e-32
relative error = 1.3561276410743506504844288442144e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.67546318055115092656577152534128
y2[1] (numeric) = -0.67546318055115092656577152534129
absolute error = 1e-32
relative error = 1.4804655957472619235220928705026e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4792
Order of pole (three term test) = -13.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.41
y1[1] (analytic) = 0.74411136539159243003734439556795
y1[1] (numeric) = 0.74411136539159243003734439556794
absolute error = 1e-32
relative error = 1.3438848625484235964925226525405e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.66805559341649106468574980065472
y2[1] (numeric) = -0.66805559341649106468574980065473
absolute error = 1e-32
relative error = 1.4968814120482369301677581370305e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4783
Order of pole (three term test) = -13.72
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=700265052, alloc=4717728, time=85.30
x[1] = 2.42
y1[1] (analytic) = 0.75075460472549093874353256891074
y1[1] (numeric) = 0.75075460472549093874353256891073
absolute error = 1e-32
relative error = 1.3319931622206222665277112189853e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.66058120127920069250633410656023
y2[1] (numeric) = -0.66058120127920069250633410656024
absolute error = 1e-32
relative error = 1.5138184345293544687938366466739e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4772
Order of pole (three term test) = -13.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=704265952, alloc=4717728, time=85.51
x[1] = 2.43
y1[1] (analytic) = 0.7573227692245436502013552441779
y1[1] (numeric) = 0.75732276922454365020135524417789
absolute error = 1e-32
relative error = 1.3204409541574252711767224633132e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.6530407515722648997124970471899
y2[1] (numeric) = -0.6530407515722648997124970471899
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4758
Order of pole (three term test) = -14.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=708267080, alloc=4717728, time=85.72
x[1] = 2.44
y1[1] (analytic) = 0.7638152020777741113106750925374
y1[1] (numeric) = 0.76381520207777411131067509253739
absolute error = 1e-32
relative error = 1.3092171997621183713699516777911e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.64543499833437069274006107298253
y2[1] (numeric) = -0.64543499833437069274006107298254
absolute error = 1e-32
relative error = 1.5493426953614703268077690437558e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4743
Order of pole (three term test) = -14.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=712267772, alloc=4717728, time=85.93
x[1] = 2.45
y1[1] (analytic) = 0.77023125404730734170190306733649
y1[1] (numeric) = 0.77023125404730734170190306733648
absolute error = 1e-32
relative error = 1.2983113769343100949470174575785e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.63776470213450375443853285563378
y2[1] (numeric) = -0.63776470213450375443853285563379
absolute error = 1e-32
relative error = 1.5679763973345475110466345608186e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4726
Order of pole (three term test) = -14.63
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.46
y1[1] (analytic) = 0.7765702835332930802042763146862
y1[1] (numeric) = 0.77657028353329308020427631468619
absolute error = 1e-32
relative error = 1.2877134513184447042842961898857e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.63003062999589217930819371861593
y2[1] (numeric) = -0.63003062999589217930819371861594
absolute error = 1e-32
relative error = 1.5872244179723770466630917804731e-30 %
Correct digits = 32
h = 0.01
bytes used=716268516, alloc=4717728, time=86.14
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
Radius of convergence (three term test) for eq 2 = 0.4707
Order of pole (three term test) = -14.86
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.47
y1[1] (analytic) = 0.78283165663806523520721558406155
y1[1] (numeric) = 0.78283165663806523520721558406154
absolute error = 1e-32
relative error = 1.2774138494789314341106192185427e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.62223355531930478987454240485577
y2[1] (numeric) = -0.62223355531930478987454240485578
absolute error = 1e-32
relative error = 1.6071135853270416031045231965001e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4686
Order of pole (three term test) = -15.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=720269720, alloc=4717728, time=86.34
x[1] = 2.48
y1[1] (analytic) = 0.78901474722953112302319203359033
y1[1] (numeric) = 0.78901474722953112302319203359032
absolute error = 1e-32
relative error = 1.2674034338538053541654351058974e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.6143742578057117043045348806656
y2[1] (numeric) = -0.6143742578057117043045348806656
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4664
Order of pole (three term test) = -15.31
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=724271748, alloc=4717728, time=86.55
x[1] = 2.49
y1[1] (analytic) = 0.79511893700378415538109133257157
y1[1] (numeric) = 0.79511893700378415538109133257156
absolute error = 1e-32
relative error = 1.2576734793517322152968107255541e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.6064535233783148891434102397918
y2[1] (numeric) = -0.6064535233783148891434102397918
absolute error = 0
relative error = 0 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4639
Order of pole (three term test) = -15.53
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=728273652, alloc=4717728, time=86.76
x[1] = 2.5
y1[1] (analytic) = 0.80114361554693371483350279046735
y1[1] (numeric) = 0.80114361554693371483350279046734
absolute error = 1e-32
relative error = 1.2482156514688178309064332740749e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.59847214410395649405185470218616
y2[1] (numeric) = -0.59847214410395649405185470218617
absolute error = 1e-32
relative error = 1.6709215455586799279466768703960e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4613
Order of pole (three term test) = -15.75
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=732275112, alloc=4717728, time=86.97
x[1] = 2.51
y1[1] (analytic) = 0.80708818039614603514191750787841
y1[1] (numeric) = 0.8070881803961460351419175078784
absolute error = 1e-32
relative error = 1.2390219858122149092393174395193e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.59043091811391282764453715502405
y2[1] (numeric) = -0.59043091811391282764453715502406
absolute error = 1e-32
relative error = 1.6936782429931427171986606826110e-30 %
Correct digits = 32
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
Radius of convergence (three term test) for eq 2 = 0.4584
Order of pole (three term test) = -15.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.52
y1[1] (analytic) = 0.81295203709988998260266426045185
y1[1] (numeric) = 0.81295203709988998260266426045184
absolute error = 1e-32
relative error = 1.2300848689270543568895393433307e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.58233064952408189496642758229713
y2[1] (numeric) = -0.58233064952408189496642758229713
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4554
Order of pole (three term test) = -16.2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=736276280, alloc=4717728, time=87.17
TOP MAIN SOLVE Loop
x[1] = 2.53
y1[1] (analytic) = 0.81873459927738171378565517255499
y1[1] (numeric) = 0.81873459927738171378565517255498
absolute error = 1e-32
relative error = 1.2213970203318680090221199219169e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.5741721483545724777866405874022
y2[1] (numeric) = -0.5741721483545724777866405874022
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4522
Order of pole (three term test) = -16.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=740277184, alloc=4717728, time=87.39
x[1] = 2.54
y1[1] (analytic) = 0.82443528867722226526970435580657
y1[1] (numeric) = 0.82443528867722226526970435580655
absolute error = 2e-32
relative error = 2.4259029513510155668659391918379e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.56595623044870279873476574798203
y2[1] (numeric) = -0.56595623044870279873476574798203
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4489
Order of pole (three term test) = -16.63
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=744278868, alloc=4717728, time=87.60
x[1] = 2.55
y1[1] (analytic) = 0.83005353523522221166431047583229
y1[1] (numeric) = 0.83005353523522221166431047583227
absolute error = 2e-32
relative error = 2.4094831418713686297368098080937e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.55768371739141686934577028176624
y2[1] (numeric) = -0.55768371739141686934577028176624
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4453
Order of pole (three term test) = -16.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=748280016, alloc=4783252, time=87.81
x[1] = 2.56
y1[1] (analytic) = 0.83558877713140760950028812338244
y1[1] (numeric) = 0.83558877713140760950028812338243
absolute error = 1e-32
relative error = 1.1967609275857190065665676649005e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.54935543642712668031068338313728
y2[1] (numeric) = -0.54935543642712668031068338313728
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4416
Order of pole (three term test) = -17.06
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=752281584, alloc=4783252, time=88.02
x[1] = 2.57
y1[1] (analytic) = 0.84104046084620152644236372156713
y1[1] (numeric) = 0.84104046084620152644236372156711
absolute error = 2e-32
relative error = 2.3780068773239838550906410534134e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.54097222037698844964557254874584
y2[1] (numeric) = -0.54097222037698844964557254874584
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4377
Order of pole (three term test) = -17.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.58
y1[1] (analytic) = 0.84640804121577553771763249456923
y1[1] (numeric) = 0.84640804121577553771763249456922
absolute error = 1e-32
relative error = 1.1814632556699318156810796937003e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.53253490755562120108505876447165
y2[1] (numeric) = -0.53253490755562120108505876447165
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4336
Order of pole (three term test) = -17.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=756282728, alloc=4783252, time=88.22
x[1] = 2.59
y1[1] (analytic) = 0.85169098148656565465635974540831
y1[1] (numeric) = 0.8516909814865656546563597454083
absolute error = 1e-32
relative error = 1.1741347762712851175874594268037e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.52404434168727600077313024887591
y2[1] (numeric) = -0.52404434168727600077313024887592
absolute error = 1e-32
relative error = 1.9082354687396873512105115417111e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4293
Order of pole (three term test) = -17.69
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=760283664, alloc=4783252, time=88.43
x[1] = 2.6
y1[1] (analytic) = 0.8568887533689472337977021516452
y1[1] (numeric) = 0.85688875336894723379770215164519
absolute error = 1e-32
relative error = 1.1670126326998645031327785253268e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.51550137182146423525772693520937
y2[1] (numeric) = -0.51550137182146423525772693520937
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4249
Order of pole (three term test) = -17.89
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=764284756, alloc=4783252, time=88.64
x[1] = 2.61
y1[1] (analytic) = 0.86200083709006349911416744872265
y1[1] (numeric) = 0.86200083709006349911416744872264
absolute error = 1e-32
relative error = 1.1600916808570547640068911228112e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.5069068522480533678909866995555
y2[1] (numeric) = -0.5069068522480533678909866995555
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4203
Order of pole (three term test) = -18.1
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=768285592, alloc=4783252, time=88.85
x[1] = 2.62
y1[1] (analytic) = 0.86702672144580239454661367674835
y1[1] (numeric) = 0.86702672144580239454661367674834
absolute error = 1e-32
relative error = 1.1533669900420822601708712465435e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.49826164241183866398876000999763
y2[1] (numeric) = -0.49826164241183866398876000999764
absolute error = 1e-32
relative error = 2.0069776897926430981025624256600e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4155
Order of pole (three term test) = -18.3
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=772288216, alloc=4783252, time=89.06
x[1] = 2.63
y1[1] (analytic) = 0.87196590385191656920784839019493
y1[1] (numeric) = 0.87196590385191656920784839019492
absolute error = 1e-32
relative error = 1.1468338332754661110922812227155e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.48956660682659942750568705361163
y2[1] (numeric) = -0.48956660682659942750568705361163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4106
Order of pole (three term test) = -18.5
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.64
y1[1] (analytic) = 0.87681789039428138329890731626599
y1[1] (numeric) = 0.87681789039428138329890731626598
absolute error = 1e-32
relative error = 1.1404876781771947429276752400430e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.48082261498864834353055026953286
y2[1] (numeric) = -0.48082261498864834353055026953286
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4055
Order of pole (three term test) = -18.69
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=776289476, alloc=4783252, time=89.26
x[1] = 2.65
y1[1] (analytic) = 0.88158219587828590897930236605381
y1[1] (numeric) = 0.8815821958782859089793023660538
absolute error = 1e-32
relative error = 1.1343241783640367849402194948475e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.47203054128988257159561077839739
y2[1] (numeric) = -0.47203054128988257159561077839739
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.4003
Order of pole (three term test) = -18.89
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=780290888, alloc=4783252, time=89.47
x[1] = 2.66
y1[1] (analytic) = 0.88625834387735198713231100388259
y1[1] (numeric) = 0.88625834387735198713231100388258
absolute error = 1e-32
relative error = 1.1283391653330245615931625666865e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.46319126493034528461814059379635
y2[1] (numeric) = -0.46319126493034528461814059379635
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3948
Order of pole (three term test) = -19.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=784291956, alloc=4783252, time=89.68
x[1] = 2.67
y1[1] (analytic) = 0.89084586678057648816006285842974
y1[1] (numeric) = 0.89084586678057648816006285842973
absolute error = 1e-32
relative error = 1.1225286408005630636274489176957e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.4543056698303063972473913211913
y2[1] (numeric) = -0.4543056698303063972473913211913
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3893
Order of pole (three term test) = -19.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=788293560, alloc=4783252, time=89.89
x[1] = 2.68
y1[1] (analytic) = 0.89534430583949201262204581862066
y1[1] (numeric) = 0.89534430583949201262204581862065
absolute error = 1e-32
relative error = 1.1168887694688366829380191711037e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.44537464454187127547089883192945
y2[1] (numeric) = -0.44537464454187127547089883192946
absolute error = 1e-32
relative error = 2.2453006974131559390638199730639e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3835
Order of pole (three term test) = -19.45
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=792294532, alloc=4783252, time=90.09
x[1] = 2.69
y1[1] (analytic) = 0.89975321121394135568593488432887
y1[1] (numeric) = 0.89975321121394135568593488432886
absolute error = 1e-32
relative error = 1.1114158721932276400313009153953e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.43639908216012626653550411876099
y2[1] (numeric) = -0.436399082160126266535504118761
absolute error = 1e-32
relative error = 2.2914805298171405821646122390405e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3777
Order of pole (three term test) = -19.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.7
y1[1] (analytic) = 0.90407214201706114798252728194333
y1[1] (numeric) = 0.90407214201706114798252728194332
absolute error = 1e-32
relative error = 1.1061064195263396963425488606102e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.42737988023382993455605308585788
y2[1] (numeric) = -0.42737988023382993455605308585789
absolute error = 1e-32
relative error = 2.3398387389057146555658140918751e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3716
Order of pole (three term test) = -19.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=796295644, alloc=4783252, time=90.30
x[1] = 2.71
y1[1] (analytic) = 0.90830066635937017453818459371608
y1[1] (numeric) = 0.90830066635937017453818459371607
absolute error = 1e-32
relative error = 1.1009570256159526822865442199961e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.41831794067565893261379068110859
y2[1] (numeric) = -0.4183179406756589326137906811086
absolute error = 1e-32
relative error = 2.3905262068961699674253512918432e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3654
Order of pole (three term test) = -19.99
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=800297472, alloc=4783252, time=90.51
x[1] = 2.72
y1[1] (analytic) = 0.91243836139195796298962879998706
y1[1] (numeric) = 0.91243836139195796298962879998706
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.40921416967201748668244467400742
y2[1] (numeric) = -0.40921416967201748668244467400743
absolute error = 1e-32
relative error = 2.4437081462782521427127640082373e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3591
Order of pole (three term test) = -20.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=804298568, alloc=4783252, time=90.72
x[1] = 2.73
y1[1] (analytic) = 0.91648481334876932225826112489279
y1[1] (numeric) = 0.91648481334876932225826112489278
absolute error = 1e-32
relative error = 1.0911255543297790357577190842425e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.40006947759241951035844795789445
y2[1] (numeric) = -0.40006947759241951035844795789446
absolute error = 1e-32
relative error = 2.4995658404582772723923773162784e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3526
Order of pole (three term test) = -20.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=808300060, alloc=4783252, time=90.93
x[1] = 2.74
y1[1] (analytic) = 0.92043961758798060326537325177928
y1[1] (numeric) = 0.92043961758798060326537325177927
absolute error = 1e-32
relative error = 1.0864373728507123766068740273868e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.39088477889845241210831170164027
y2[1] (numeric) = -0.39088477889845241210831170164028
absolute error = 1e-32
relative error = 2.5582986444703416206762531667397e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.346
Order of pole (three term test) = -20.51
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.75
y1[1] (analytic) = 0.92430237863246354409665948952671
y1[1] (numeric) = 0.92430237863246354409665948952671
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.38166099205233169857656137237778
y2[1] (numeric) = -0.38166099205233169857656137237779
absolute error = 1e-32
relative error = 2.6201262922433643431964797278233e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3393
Order of pole (three term test) = -20.67
NO COMPLEX POLE (six term test) for Equation 2
bytes used=812300776, alloc=4783252, time=91.14
TOP MAIN SOLVE Loop
x[1] = 2.76
y1[1] (analytic) = 0.9280727102093326532652331971401
y1[1] (numeric) = 0.9280727102093326532652331971401
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.37239903942505551841770059244975
y2[1] (numeric) = -0.37239903942505551841770059244976
absolute error = 1e-32
relative error = 2.6852915666589622993927633959210e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3324
Order of pole (three term test) = -20.83
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=816301752, alloc=4783252, time=91.35
x[1] = 2.77
y1[1] (analytic) = 0.93175023528857217636777720782907
y1[1] (numeric) = 0.93175023528857217636777720782907
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.36309984720416833112128200917246
y2[1] (numeric) = -0.36309984720416833112128200917247
absolute error = 1e-32
relative error = 2.7540634007419658088380035492556e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3254
Order of pole (three term test) = -20.99
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=820304172, alloc=4783252, time=91.56
x[1] = 2.78
y1[1] (analytic) = 0.93533458612073878346935166911759
y1[1] (numeric) = 0.93533458612073878346935166911759
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.35376434530114292438633931722734
y2[1] (numeric) = -0.35376434530114292438633931722735
absolute error = 1e-32
relative error = 2.8267404934455650167981703294397e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3182
Order of pole (three term test) = -21.15
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=824305772, alloc=4783252, time=91.77
x[1] = 2.79
y1[1] (analytic) = 0.93882540427373620697953961962409
y1[1] (numeric) = 0.93882540427373620697953961962409
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.34439346725839004176626159556229
y2[1] (numeric) = -0.3443934672583900417662615955623
absolute error = 1e-32
relative error = 2.9036555424836915477923452310660e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3109
Order of pole (three term test) = -21.3
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=828306468, alloc=4783252, time=91.98
x[1] = 2.8
y1[1] (analytic) = 0.94222234066865815258678811736615
y1[1] (numeric) = 0.94222234066865815258678811736615
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.33498815015590491954385375271242
y2[1] (numeric) = -0.33498815015590491954385375271243
absolute error = 1e-32
relative error = 2.9851802206573447982399170446714e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.3035
Order of pole (three term test) = -21.44
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.81
y1[1] (analytic) = 0.94552505561469589898972047835884
y1[1] (numeric) = 0.94552505561469589898972047835883
absolute error = 1e-32
relative error = 1.0576134329405891418234074231371e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.32554933451756006810510128120633
y2[1] (numeric) = -0.32554933451756006810510128120634
absolute error = 1e-32
relative error = 3.0717310526280931270504447516423e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.296
Order of pole (three term test) = -21.59
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=832307476, alloc=4783252, time=92.18
x[1] = 2.82
y1[1] (analytic) = 0.94873321884310709569453606376004
y1[1] (numeric) = 0.94873321884310709569453606376003
absolute error = 1e-32
relative error = 1.0540370887607456486683317706204e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.31607796421705366845541285602457
y2[1] (numeric) = -0.31607796421705366845541285602458
absolute error = 1e-32
relative error = 3.1637763881359686586138345258726e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2884
Order of pole (three term test) = -21.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=836308136, alloc=4783252, time=92.39
x[1] = 2.83
y1[1] (analytic) = 0.95184650954024236202702511272453
y1[1] (numeric) = 0.95184650954024236202702511272452
absolute error = 1e-32
relative error = 1.0505895540689817435563597689260e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.3065749863835229889603130778681
y2[1] (numeric) = -0.30657498638352298896031307786811
absolute error = 1e-32
relative error = 3.2618447179803754903727107270218e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2806
Order of pole (three term test) = -21.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=840309216, alloc=4783252, time=92.60
x[1] = 2.84
y1[1] (analytic) = 0.95486461637962638472681949358624
y1[1] (numeric) = 0.95486461637962638472681949358623
absolute error = 1e-32
relative error = 1.0472688827778587411748286751844e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.29704135130683226089025606809731
y2[1] (numeric) = -0.29704135130683226089025606809732
absolute error = 1e-32
relative error = 3.3665346444207310506307682570007e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2728
Order of pole (three term test) = -22
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=844310004, alloc=4783252, time=92.81
x[1] = 2.85
y1[1] (analytic) = 0.95778723755309030604085410717493
y1[1] (numeric) = 0.95778723755309030604085410717492
absolute error = 1e-32
relative error = 1.0440732145844340857680869364712e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.28747801234254448390307892669172
y2[1] (numeric) = -0.28747801234254448390307892669173
absolute error = 1e-32
relative error = 3.4785269031582484896781683663001e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2648
Order of pole (three term test) = -22.13
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=848310872, alloc=4783252, time=93.02
x[1] = 2.86
y1[1] (analytic) = 0.96061408080095228910317316639277
y1[1] (numeric) = 0.96061408080095228910317316639276
absolute error = 1e-32
relative error = 1.0410007723041161841650780220451e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.27788592581658666420435690975324
y2[1] (numeric) = -0.27788592581658666420435690975324
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2567
Order of pole (three term test) = -22.25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.87
y1[1] (analytic) = 0.96334486344124324256969375873794
y1[1] (numeric) = 0.96334486344124324256969375873793
absolute error = 1e-32
relative error = 1.0380498593492448136008015252841e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.26826605092961801878239892098714
y2[1] (numeric) = -0.26826605092961801878239892098714
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2485
Order of pole (three term test) = -22.37
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=852311536, alloc=4783252, time=93.22
x[1] = 2.88
y1[1] (analytic) = 0.96597931239797478195981790476552
y1[1] (numeric) = 0.96597931239797478195981790476552
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.25861934966111070881776692011768
y2[1] (numeric) = -0.25861934966111070881776692011768
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2402
Order of pole (three term test) = -22.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=856312532, alloc=4783252, time=93.44
x[1] = 2.89
y1[1] (analytic) = 0.96851716422844660093231550720928
y1[1] (numeric) = 0.96851716422844660093231550720928
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.24894678667315269411404584058049
y2[1] (numeric) = -0.24894678667315269411404584058049
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2319
Order of pole (three term test) = -22.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=860314768, alloc=4783252, time=93.64
x[1] = 2.9
y1[1] (analytic) = 0.97095816514959052178110666934553
y1[1] (numeric) = 0.97095816514959052178110666934553
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.23924932921398232818425691873958
y2[1] (numeric) = -0.23924932921398232818425691873958
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2234
Order of pole (three term test) = -22.72
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=864317016, alloc=4783252, time=93.85
x[1] = 2.91
y1[1] (analytic) = 0.97330207106334859076784710660275
y1[1] (numeric) = 0.97330207106334859076784710660275
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.22952794702126434045301822382699
y2[1] (numeric) = -0.229527947021264340453018223827
absolute error = 1e-32
relative error = 4.3567679360080548419401459949694e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2148
Order of pole (three term test) = -22.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=868318304, alloc=4783252, time=94.06
x[1] = 2.92
y1[1] (analytic) = 0.97554864758108268050293173515827
y1[1] (numeric) = 0.97554864758108268050293173515826
absolute error = 1e-32
relative error = 1.0250642061567565716677397753355e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.21978361222511687789562909306458
y2[1] (numeric) = -0.21978361222511687789562909306459
absolute error = 1e-32
relative error = 4.5499297689935772634393913813968e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2062
Order of pole (three term test) = -22.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.93
y1[1] (analytic) = 0.97769767004701315843501960467633
y1[1] (numeric) = 0.97769767004701315843501960467632
absolute error = 1e-32
relative error = 1.0228110699618568397721468468929e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.21001729925089930332910403425911
y2[1] (numeric) = -0.21001729925089930332910403425912
absolute error = 1e-32
relative error = 4.7615125209535230985898698723305e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1974
Order of pole (three term test) = -23.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=872319072, alloc=4783252, time=94.27
x[1] = 2.94
y1[1] (analytic) = 0.97974892356068427760176338132832
y1[1] (numeric) = 0.97974892356068427760176338132832
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.20022998472177047149431709442312
y2[1] (numeric) = -0.20022998472177047149431709442313
absolute error = 1e-32
relative error = 4.9942569859831421674745800189863e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1886
Order of pole (three term test) = -23.11
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=876320132, alloc=4783252, time=94.48
x[1] = 2.95
y1[1] (analytic) = 0.98170220299845404312138940470197
y1[1] (numeric) = 0.98170220299845404312138940470197
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.19042264736102722702044731405738
y2[1] (numeric) = -0.19042264736102722702044731405739
absolute error = 1e-32
relative error = 5.2514761970726838536540501288232e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1798
Order of pole (three term test) = -23.2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=880321836, alloc=4783252, time=94.68
x[1] = 2.96
y1[1] (analytic) = 0.98355731303400640545638732297616
y1[1] (numeric) = 0.98355731303400640545638732297616
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.18059626789423289034054450880135
y2[1] (numeric) = -0.18059626789423289034054450880136
absolute error = 1e-32
relative error = 5.5372129870682322915499384819863e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1708
Order of pole (three term test) = -23.28
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=884323956, alloc=4783252, time=94.89
x[1] = 2.97
y1[1] (analytic) = 0.98531406815788372924707637480614
y1[1] (numeric) = 0.98531406815788372924707637480614
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.17075182895114551862806449866797
y2[1] (numeric) = -0.17075182895114551862806449866798
absolute error = 1e-32
relative error = 5.8564526432458533522652748324000e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1618
Order of pole (three term test) = -23.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.98
y1[1] (analytic) = 0.9869722926960375844844419643954
y1[1] (numeric) = 0.9869722926960375844844419643954
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.16089031496745574884655395454133
y2[1] (numeric) = -0.16089031496745574884655395454134
absolute error = 1e-32
relative error = 6.2154145213916450546258508174006e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1527
Order of pole (three term test) = -23.44
NO COMPLEX POLE (six term test) for Equation 2
bytes used=888324836, alloc=4783252, time=95.10
TOP MAIN SOLVE Loop
x[1] = 2.99
y1[1] (analytic) = 0.98853182082739600495858418721084
y1[1] (numeric) = 0.98853182082739600495858418721084
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.15101271208634404904629503561052
y2[1] (numeric) = -0.15101271208634404904629503561053
absolute error = 1e-32
relative error = 6.6219590800291914525142806545476e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1435
Order of pole (three term test) = -23.51
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=892327932, alloc=4783252, time=95.31
x[1] = 3
y1[1] (analytic) = 0.98999249660044545727157279473126
y1[1] (numeric) = 0.98999249660044545727157279473126
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.14112000805986722210074480280811
y2[1] (numeric) = -0.14112000805986722210074480280812
absolute error = 1e-32
relative error = 7.0861673957371859182175322724613e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1343
Order of pole (three term test) = -23.58
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=896329988, alloc=4783252, time=95.52
x[1] = 3.01
y1[1] (analytic) = 0.99135417394882586223162557418242
y1[1] (numeric) = 0.99135417394882586223162557418242
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.13121319215018402315021812468485
y2[1] (numeric) = -0.13121319215018402315021812468486
absolute error = 1e-32
relative error = 7.6211849099396940900082969487215e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1251
Order of pole (three term test) = -23.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=900331892, alloc=4783252, time=95.73
x[1] = 3.02
y1[1] (analytic) = 0.99261671670593710913946653326304
y1[1] (numeric) = 0.99261671670593710913946653326304
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.12129325503062976810875799633911
y2[1] (numeric) = -0.12129325503062976810875799633912
absolute error = 1e-32
relative error = 8.2444815232922345332773777793007e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1158
Order of pole (three term test) = -23.7
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=904332608, alloc=4783252, time=95.94
x[1] = 3.03
y1[1] (analytic) = 0.99377999861855560232760730870843
y1[1] (numeric) = 0.99377999861855560232760730870843
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.11136118868664982569090503291726
y2[1] (numeric) = -0.11136118868664982569090503291727
absolute error = 1e-32
relative error = 8.9797892047813759655275720827597e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1064
Order of pole (three term test) = -23.75
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.04
y1[1] (analytic) = 0.99484390335945947830924495484319
y1[1] (numeric) = 0.99484390335945947830924495484319
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.10141798631660189952660831260879
y2[1] (numeric) = -0.1014179863166018995266083126088
absolute error = 1e-32
relative error = 9.8601839409258929143111130003625e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.09702
Order of pole (three term test) = -23.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=908334932, alloc=4783252, time=96.14
x[1] = 3.05
y1[1] (analytic) = 0.99580832453906123102558220156492
y1[1] (numeric) = 0.99580832453906123102558220156492
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.091464642232437020053401588696418
y2[1] (numeric) = -0.091464642232437020053401588696432
absolute error = 1.4e-32
relative error = 1.5306461227303680527854692922925e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.08758
Order of pole (three term test) = -23.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=912337068, alloc=4783252, time=96.35
x[1] = 3.06
y1[1] (analytic) = 0.99667316571604658193873927179315
y1[1] (numeric) = 0.99667316571604658193873927179316
absolute error = 1e-32
relative error = 1.0033379390540361325077898799425e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.081502151760269178003890088835723
y2[1] (numeric) = -0.081502151760269178003890088835737
absolute error = 1.4e-32
relative error = 1.7177460591690471528306899937744e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.07811
Order of pole (three term test) = -23.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=916337752, alloc=4783252, time=96.56
x[1] = 3.07
y1[1] (analytic) = 0.99743834040701853109211366272677
y1[1] (numeric) = 0.99743834040701853109211366272678
absolute error = 1e-32
relative error = 1.0025682385458896118104345192173e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.071531511140843542442340790318903
y2[1] (numeric) = -0.071531511140843542442340790318917
absolute error = 1.4e-32
relative error = 1.9571793992209100716264011646757e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.0686
Order of pole (three term test) = -23.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=920338444, alloc=4783252, time=96.77
x[1] = 3.08
y1[1] (analytic) = 0.99810377209514562474111853735979
y1[1] (numeric) = 0.9981037720951456247411185373598
absolute error = 1e-32
relative error = 1.0018998304163042625061034377805e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.061553717429913216445629637135705
y2[1] (numeric) = -0.061553717429913216445629637135719
absolute error = 1.4e-32
relative error = 2.2744361485463150792054329356661e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.05907
Order of pole (three term test) = -23.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=924340020, alloc=4783252, time=96.98
x[1] = 3.09
y1[1] (analytic) = 0.99866939423781357473474351808576
y1[1] (numeric) = 0.99866939423781357473474351808576
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.051569768398534492669958510574615
y2[1] (numeric) = -0.051569768398534492669958510574628
absolute error = 1.3e-32
relative error = 2.5208567739795072277317365266868e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.04952
Order of pole (three term test) = -23.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.1
y1[1] (analytic) = 0.99913515027327946449237605454147
y1[1] (numeric) = 0.99913515027327946449237605454147
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.041580662433290579194698271596673
y2[1] (numeric) = -0.041580662433290579194698271596686
absolute error = 1.3e-32
relative error = 3.1264533172977676815935366476197e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.03995
Order of pole (three term test) = -24
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=928341168, alloc=4783252, time=97.19
x[1] = 3.11
y1[1] (analytic) = 0.99950099362632787616083083671683
y1[1] (numeric) = 0.99950099362632787616083083671684
absolute error = 1e-32
relative error = 1.0004992555053513850774541731279e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.031587398436453773187626872703365
y2[1] (numeric) = -0.031587398436453773187626872703378
absolute error = 1.3e-32
relative error = 4.1155652708002732215949975315208e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.03036
Order of pole (three term test) = -24.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=932342520, alloc=4783252, time=97.40
x[1] = 3.12
y1[1] (analytic) = 0.99976688771292837334358497397559
y1[1] (numeric) = 0.9997668877129283733435849739756
absolute error = 1e-32
relative error = 1.0002331666410805977636579275351e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.021590975726096066090998104201892
y2[1] (numeric) = -0.021590975726096066090998104201905
absolute error = 1.3e-32
relative error = 6.0210340490946269518832671844294e-29 %
Correct digits = 31
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.02076
Order of pole (three term test) = -24.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=936343384, alloc=4783252, time=97.61
x[1] = 3.13
y1[1] (analytic) = 0.99993280594389387365782723913921
y1[1] (numeric) = 0.99993280594389387365782723913922
absolute error = 1e-32
relative error = 1.0000671985714507066524953955073e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.011592393936158169184681483118307
y2[1] (numeric) = -0.01159239393615816918468148311832
absolute error = 1.3e-32
relative error = 1.1214249680949269913695389085879e-28 %
Correct digits = 30
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.01115
Order of pole (three term test) = -24.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=940344988, alloc=4783252, time=97.82
x[1] = 3.14
y1[1] (analytic) = 0.99999873172753954528511430634505
y1[1] (numeric) = 0.99999873172753954528511430634506
absolute error = 1e-32
relative error = 1.0000012682740689717888714570959e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = -0.0015926529164869525405414363244433
y2[1] (numeric) = -0.0015926529164869525405414363244558
absolute error = 1.25e-32
relative error = 7.8485399239228426744706254548376e-28 %
Correct digits = 30
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.001531
Order of pole (three term test) = -24.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=944346112, alloc=4783252, time=98.03
x[1] = 3.15
y1[1] (analytic) = 0.99996465847134196162819465679473
y1[1] (numeric) = 0.99996465847134196162819465679474
absolute error = 1e-32
relative error = 1.0000353427777258302239144347070e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.008407247367148706459141516571067
y2[1] (numeric) = 0.0084072473671487064591415165710546
absolute error = 1.24e-32
relative error = 1.4749179438270083881842796911264e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.16
y1[1] (analytic) = 0.99983058958259834815991709427395
y1[1] (numeric) = 0.99983058958259834815991709427397
absolute error = 2e-32
relative error = 2.0003388782443081202577655560834e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.01840630693305366670737927118737
y2[1] (numeric) = 0.018406306933053666707379271187358
absolute error = 1.2e-32
relative error = 6.5195044522758920605196154816803e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=948347132, alloc=4783252, time=98.23
x[1] = 3.17
y1[1] (analytic) = 0.99959653846808585554008835013528
y1[1] (numeric) = 0.9995965384680858555400883501353
absolute error = 2e-32
relative error = 2.0008072487576486856484747461864e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.028403525883603859571285274896733
y2[1] (numeric) = 0.028403525883603859571285274896721
absolute error = 1.2e-32
relative error = 4.2248275968185649291008109297936e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=952348208, alloc=4783252, time=98.44
x[1] = 3.18
y1[1] (analytic) = 0.99926252853272089307268415386031
y1[1] (numeric) = 0.99926252853272089307268415386033
absolute error = 2e-32
relative error = 2.0014760314656489361062559609102e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.03839790450523521805369524672612
y2[1] (numeric) = 0.038397904505235218053695246726108
absolute error = 1.2e-32
relative error = 3.1251705411069776154664952509576e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=956349916, alloc=4783252, time=98.65
x[1] = 3.19
y1[1] (analytic) = 0.99882859317721865656895082969948
y1[1] (numeric) = 0.9988285931772186565689508296995
absolute error = 2e-32
relative error = 2.0023455612520165505996040115299e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.048388443368414200108007148451169
y2[1] (numeric) = 0.048388443368414200108007148451158
absolute error = 1.1e-32
relative error = 2.2732700691050345608598019668675e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=960351584, alloc=4783252, time=98.86
x[1] = 3.2
y1[1] (analytic) = 0.99829477579475308466166072228358
y1[1] (numeric) = 0.9982947757947530846616607222836
absolute error = 2e-32
relative error = 2.0034162739234799024546068656658e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.058374143427579909137217414619095
y2[1] (numeric) = 0.058374143427579909137217414619084
absolute error = 1.1e-32
relative error = 1.8843959592566549021970197939579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.21
y1[1] (analytic) = 0.99766112976661757757210666520424
y1[1] (numeric) = 0.99766112976661757757210666520426
absolute error = 2e-32
relative error = 2.0046887067434000426513713834122e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.068354006121047817548388360676863
y2[1] (numeric) = 0.068354006121047817548388360676852
absolute error = 1.1e-32
relative error = 1.6092692475873538374885266650403e-29 %
Correct digits = 31
h = 0.01
bytes used=964352404, alloc=4783252, time=99.07
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.22
y1[1] (analytic) = 0.99692771845688691225434273747586
y1[1] (numeric) = 0.99692771845688691225434273747588
absolute error = 2e-32
relative error = 2.0061634990907235999060378923184e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.078327033470865103073444147916042
y2[1] (numeric) = 0.078327033470865103073444147916031
absolute error = 1.1e-32
relative error = 1.4043682637478684113731991349273e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=968353408, alloc=4783252, time=99.28
x[1] = 3.23
y1[1] (analytic) = 0.99609461520608088772070849458495
y1[1] (numeric) = 0.99609461520608088772070849458496
absolute error = 1e-32
relative error = 1.0039206966228917236328623211591e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.088292228182607612405875728529723
y2[1] (numeric) = 0.088292228182607612405875728529713
absolute error = 1.0e-32
relative error = 1.1326025184592482851296365408645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=972354952, alloc=4783252, time=99.48
x[1] = 3.24
y1[1] (analytic) = 0.99516190332383033417882384374247
y1[1] (numeric) = 0.99516190332383033417882384374249
absolute error = 2e-32
relative error = 2.0097232353047488526139009096253e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.098248593745108472540154959437637
y2[1] (numeric) = 0.098248593745108472540154959437627
absolute error = 1.0e-32
relative error = 1.0178262730094162305888199498389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=976356744, alloc=4783252, time=99.69
x[1] = 3.25
y1[1] (analytic) = 0.9941296760805462193730292251716
y1[1] (numeric) = 0.99412967608054621937302922517162
absolute error = 2e-32
relative error = 2.0118099762248283515863440190997e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.10819513453010837703583084256083
y2[1] (numeric) = 0.10819513453010837703583084256082
absolute error = 1e-32
relative error = 9.2425597910941321028953286566179e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=980357408, alloc=4783252, time=99.90
x[1] = 3.26
y1[1] (analytic) = 0.99299803669809268521269456717166
y1[1] (numeric) = 0.99299803669809268521269456717168
absolute error = 2e-32
relative error = 2.0141026730026378991846493446658e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.11813085589181758226072311033608
y2[1] (numeric) = 0.11813085589181758226072311033607
absolute error = 1e-32
relative error = 8.4651888149848384458040674739664e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.27
y1[1] (analytic) = 0.99176709833946494737596174049474
y1[1] (numeric) = 0.99176709833946494737596174049476
absolute error = 2e-32
relative error = 2.0166024899884651566227217823812e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.12805476426637965749655689075362
y2[1] (numeric) = 0.12805476426637965749655689075361
absolute error = 1e-32
relative error = 7.8091588839271839286141847664172e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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
bytes used=984358496, alloc=4783252, time=100.11
TOP MAIN SOLVE Loop
x[1] = 3.28
y1[1] (analytic) = 0.99043698409747309009035841613171
y1[1] (numeric) = 0.99043698409747309009035841613173
absolute error = 2e-32
relative error = 2.0193107003394892876752512439983e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.13796586727122704261491407058525
y2[1] (numeric) = 0.13796586727122704261491407058524
absolute error = 1e-32
relative error = 7.2481695638103039271032128979851e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=988359848, alloc=4783252, time=100.32
x[1] = 3.29
y1[1] (analytic) = 0.98900782698243288770137512553948
y1[1] (numeric) = 0.9890078269824328877013751255395
absolute error = 2e-32
relative error = 2.0222286876153556653792182312660e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.14786317380431847785052978374264
y2[1] (numeric) = 0.14786317380431847785052978374263
absolute error = 1e-32
relative error = 6.7630091676741358753823081802124e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=992360764, alloc=4783252, time=100.52
x[1] = 3.3
y1[1] (analytic) = 0.98747976990886488393659105110285
y1[1] (numeric) = 0.98747976990886488393659105110287
absolute error = 2e-32
relative error = 2.0253579475198577805975407169415e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.15774569414324838201165427760248
y2[1] (numeric) = 0.15774569414324838201165427760247
absolute error = 1e-32
relative error = 6.3393172500284100361868555679349e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=996362008, alloc=4783252, time=100.74
x[1] = 3.31
y1[1] (analytic) = 0.98585296568120305894633807058553
y1[1] (numeric) = 0.98585296568120305894633807058555
absolute error = 2e-32
relative error = 2.0287000897928458257955360596540e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.16761244004421826827224999431698
y2[1] (numeric) = 0.16761244004421826827224999431696
absolute error = 2e-32
relative error = 1.1932288554909020258741742172114e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1000363624, alloc=4783252, time=100.95
x[1] = 3.32
y1[1] (analytic) = 0.98412757697851451324228958473119
y1[1] (numeric) = 0.98412757697851451324228958473122
absolute error = 3e-32
relative error = 3.0483852603852966119497410512131e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.17746242484086030048692055230841
y2[1] (numeric) = 0.17746242484086030048692055230839
absolute error = 2e-32
relative error = 1.1269991389971725244457202316317e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.33
y1[1] (analytic) = 0.98230377633823169655284671485927
y1[1] (numeric) = 0.98230377633823169655284671485929
absolute error = 2e-32
relative error = 2.0360300430234222211883489835665e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.18729466354290310775529282413595
y2[1] (numeric) = 0.18729466354290310775529282413593
absolute error = 2e-32
relative error = 1.0678360836169072881224613658003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1004364896, alloc=4783252, time=101.15
x[1] = 3.34
y1[1] (analytic) = 0.98038174613889880835887990106991
y1[1] (numeric) = 0.98038174613889880835887990106994
absolute error = 3e-32
relative error = 3.0600324942963239678707661732179e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.19710817293466999073661691059272
y2[1] (numeric) = 0.1971081729346699907366169105927
absolute error = 2e-32
relative error = 1.0146712691933301183593687562886e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1008366772, alloc=4783252, time=101.36
x[1] = 3.35
y1[1] (analytic) = 0.97836167858193409545539437527153
y1[1] (numeric) = 0.97836167858193409545539437527156
absolute error = 3e-32
relative error = 3.0663506816296069087620608186982e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.20690197167339966997603411602551
y2[1] (numeric) = 0.20690197167339966997603411602549
absolute error = 2e-32
relative error = 9.6664134412264268803230680025431e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1012369116, alloc=4783252, time=101.57
x[1] = 3.36
y1[1] (analytic) = 0.97624377567240987029416530777832
y1[1] (numeric) = 0.97624377567240987029416530777835
absolute error = 3e-32
relative error = 3.0730029473772393444869677080355e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.21667508038737974424961398190553
y2[1] (numeric) = 0.21667508038737974424961398190551
absolute error = 2e-32
relative error = 9.2304107903148152926906480455249e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1016369876, alloc=4783252, time=101.78
x[1] = 3.37
y1[1] (analytic) = 0.97402824919885217208949176597085
y1[1] (numeric) = 0.97402824919885217208949176597088
absolute error = 3e-32
relative error = 3.0799928056168078761574911558517e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.22642652177388304566410348430857
y2[1] (numeric) = 0.22642652177388304566410348430855
absolute error = 2e-32
relative error = 8.8328875271831699364184321568232e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1020371136, alloc=4783252, time=101.99
x[1] = 3.38
y1[1] (analytic) = 0.97171532071206209070412534999057
y1[1] (numeric) = 0.9717153207120620907041253499906
absolute error = 3e-32
relative error = 3.0873239683013679772491094393227e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.23615532069689709795749177758963
y2[1] (numeric) = 0.23615532069689709795749177758961
absolute error = 2e-32
relative error = 8.4690024941973644260865989969192e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.39
y1[1] (analytic) = 0.96930522150296087116533607467248
y1[1] (numeric) = 0.9693052215029608711653360746725
absolute error = 2e-32
relative error = 2.0633335667983820255708760103271e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.24586050428463690513600137155794
y2[1] (numeric) = 0.24586050428463690513600137155792
absolute error = 2e-32
relative error = 8.1346941259201430733668415489387e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1024371776, alloc=4783252, time=102.19
x[1] = 3.4
y1[1] (analytic) = 0.96679819257946101428220153976569
y1[1] (numeric) = 0.96679819257946101428220153976572
absolute error = 3e-32
relative error = 3.1030260741343187821538765664552e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.25554110202683131924990242936374
y2[1] (numeric) = 0.25554110202683131924990242936372
absolute error = 2e-32
relative error = 7.8265296037973722347871080744204e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1028373468, alloc=4783252, time=102.40
x[1] = 3.41
y1[1] (analytic) = 0.96419448464236568623478364095296
y1[1] (numeric) = 0.96419448464236568623478364095299
absolute error = 3e-32
relative error = 3.1114054765753460646068306985358e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.26519614587177325875244430757411
y2[1] (numeric) = 0.26519614587177325875244430757409
absolute error = 2e-32
relative error = 7.5415877309432438681495770677803e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1032374232, alloc=4783252, time=102.61
x[1] = 3.42
y1[1] (analytic) = 0.96149435806029884717415014560141
y1[1] (numeric) = 0.96149435806029884717415014560144
absolute error = 3e-32
relative error = 3.1201431135302189336775747581903e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.2748246703231240725009433576662
y2[1] (numeric) = 0.27482467032312407250094335766618
absolute error = 2e-32
relative error = 7.2773670487751609857863149091906e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1036375540, alloc=4783252, time=102.82
x[1] = 3.43
y1[1] (analytic) = 0.95869808284366860579948964122556
y1[1] (numeric) = 0.95869808284366860579948964122559
absolute error = 3e-32
relative error = 3.1292437668191301065322891083732e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.28442571253646236904429691459137
y2[1] (numeric) = 0.28442571253646236904429691459135
absolute error = 2e-32
relative error = 7.0317130689919853257458521080857e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1040377244, alloc=4783252, time=103.03
x[1] = 3.44
y1[1] (analytic) = 0.95580593861766640355516501297249
y1[1] (numeric) = 0.95580593861766640355516501297252
absolute error = 3e-32
relative error = 3.1387124507080879516123252767506e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.29399831241556765639445181056032
y2[1] (numeric) = 0.2939983124155676563944518105603
absolute error = 2e-32
relative error = 6.8027601368438908347139897698201e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.45
y1[1] (analytic) = 0.95281821459430472850678513994775
y1[1] (numeric) = 0.95281821459430472850678513994778
absolute error = 3e-32
relative error = 3.1485544189322132551799144753866e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.30354151270842916399808636621989
y2[1] (numeric) = 0.30354151270842916399808636621988
absolute error = 1e-32
relative error = 3.2944423023962567395839057338678e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1044378192, alloc=4783252, time=103.24
x[1] = 3.46
y1[1] (analytic) = 0.94973520954349615510160537578203
y1[1] (numeric) = 0.94973520954349615510160537578206
absolute error = 3e-32
relative error = 3.1587751721261266192765087526678e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.31305435910297024610631577597493
y2[1] (numeric) = 0.31305435910297024610631577597491
absolute error = 2e-32
relative error = 6.3886668300381576996974977141096e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1048379480, alloc=4783252, time=103.45
x[1] = 3.47
y1[1] (analytic) = 0.94655723176317660188518005352668
y1[1] (numeric) = 0.94655723176317660188518005352671
absolute error = 3e-32
relative error = 3.1693804656817449066846084915797e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.32253590032247879418185398715726
y2[1] (numeric) = 0.32253590032247879418185398715725
absolute error = 1e-32
relative error = 3.1004300575538321582027428502563e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1052380336, alloc=4783252, time=103.66
x[1] = 3.48
y1[1] (analytic) = 0.94328459904847579482359814738228
y1[1] (numeric) = 0.94328459904847579482359814738231
absolute error = 3e-32
relative error = 3.1803763180552349187078415428792e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.33198518822073411538191643544275
y2[1] (numeric) = 0.33198518822073411538191643544274
absolute error = 1e-32
relative error = 3.0121825776609905359728894020887e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1056381928, alloc=4783252, time=103.87
x[1] = 3.49
y1[1] (analytic) = 0.93991763865993801915927867276677
y1[1] (numeric) = 0.9399176386599380191592786727668
absolute error = 3e-32
relative error = 3.1917690195464022940556779489570e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.3414012778768207645082874807375
y2[1] (numeric) = 0.34140127787682076450828748073749
absolute error = 1e-32
relative error = 2.9291044433665091494158517668943e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.5
y1[1] (analytic) = 0.93645668729079633769865762667176
y1[1] (numeric) = 0.93645668729079633769865762667179
absolute error = 3e-32
relative error = 3.2035651415754319764399127552571e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.35078322768961984812036880004364
y2[1] (numeric) = 0.35078322768961984812036880004362
absolute error = 2e-32
relative error = 5.7015268750809282632903349024746e-30 %
Correct digits = 32
h = 0.01
bytes used=1060383916, alloc=4783252, time=104.08
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.51
y1[1] (analytic) = 0.93290209103330354808266630575758
y1[1] (numeric) = 0.93290209103330354808266630575761
absolute error = 3e-32
relative error = 3.2157715464836528034738979738615e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.36013009947196835175953992341737
y2[1] (numeric) = 0.36013009947196835175953992341736
absolute error = 1e-32
relative error = 2.7767742864765391820343105316800e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1064386772, alloc=4783252, time=104.29
x[1] = 3.52
y1[1] (analytic) = 0.92925420534412324591621651227224
y1[1] (numeric) = 0.92925420534412324591621651227227
absolute error = 3e-32
relative error = 3.2283953978868829510200500241719e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.36944095854447707443057432143296
y2[1] (numeric) = 0.36944095854447707443057432143295
absolute error = 1e-32
relative error = 2.7067924572841042756477628875396e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1068388312, alloc=4783252, time=104.49
x[1] = 3.53
y1[1] (analytic) = 0.92551339500878445462153901468401
y1[1] (numeric) = 0.92551339500878445462153901468405
absolute error = 4e-32
relative error = 4.3219255621492482461819263374475e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.37871487382899778862484425400664
y2[1] (numeric) = 0.37871487382899778862484425400662
absolute error = 2e-32
relative error = 5.2810178268917574299183980839462e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1072390728, alloc=4783252, time=104.70
x[1] = 3.54
y1[1] (analytic) = 0.92168003410520337652276888612977
y1[1] (numeric) = 0.9216800341052033765227688861298
absolute error = 3e-32
relative error = 3.2549256672490432069778069602331e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.38795091794173027924720110048451
y2[1] (numeric) = 0.38795091794173027924720110048449
absolute error = 2e-32
relative error = 5.1552913203839805983861661454303e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1076392416, alloc=4783252, time=104.92
x[1] = 3.55
y1[1] (analytic) = 0.91775450596627591295627082271047
y1[1] (numeric) = 0.91775450596627591295627082271051
absolute error = 4e-32
relative error = 4.3584640271403747487873891249449e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.39714816728595995082022742343695
y2[1] (numeric) = 0.39714816728595995082022742343693
absolute error = 2e-32
relative error = 5.0359038886359336304585698354206e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.56
y1[1] (analytic) = 0.91373720314154469412352061310366
y1[1] (numeric) = 0.9137372031415446941235206131037
absolute error = 4e-32
relative error = 4.3776262871288280315333366313346e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.40630570214441672928242142268591
y2[1] (numeric) = 0.4063057021444167292824214226859
absolute error = 1e-32
relative error = 2.4612009989575814558071788733097e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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
bytes used=1080393428, alloc=4783252, time=105.12
TOP MAIN SOLVE Loop
x[1] = 3.57
y1[1] (analytic) = 0.90962852735794445195161343603674
y1[1] (numeric) = 0.90962852735794445195161343603678
absolute error = 4e-32
relative error = 4.3973994654918900298651116988602e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.41542260677124602256709945606629
y2[1] (numeric) = 0.41542260677124602256709945606627
absolute error = 2e-32
relative error = 4.8143744885345330113528478794894e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1084394700, alloc=4783252, time=105.33
x[1] = 3.58
y1[1] (analytic) = 0.90542888947962966139140085454902
y1[1] (numeric) = 0.90542888947962966139140085454906
absolute error = 4e-32
relative error = 4.4177958605881130299232047275343e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.42449796948358254294260094834376
y2[1] (numeric) = 0.42449796948358254294260094834375
absolute error = 1e-32
relative error = 2.3557238712273157186325818437360e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1088395344, alloc=4783252, time=105.54
x[1] = 3.59
y1[1] (analytic) = 0.90113870946688846735564983934783
y1[1] (numeric) = 0.90113870946688846735564983934788
absolute error = 5e-32
relative error = 5.5485353669447716804922396964309e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.43353088275271783380787293204403
y2[1] (numeric) = 0.43353088275271783380787293204402
absolute error = 1e-32
relative error = 2.3066407487523584818720126263562e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1092397672, alloc=4783252, time=105.75
x[1] = 3.6
y1[1] (analytic) = 0.89675841633414700587029172526594
y1[1] (numeric) = 0.89675841633414700587029172526599
absolute error = 5e-32
relative error = 5.5756376621916391017857263551022e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.44252044329485238426672734749269
y2[1] (numeric) = 0.44252044329485238426672734749269
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1096398728, alloc=4783252, time=105.96
x[1] = 3.61
y1[1] (analytic) = 0.89228844810706831897164969353841
y1[1] (numeric) = 0.89228844810706831897164969353847
absolute error = 6e-32
relative error = 6.7242829521424470218226855619390e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.45146575216142325634494018639253
y2[1] (numeric) = 0.45146575216142325634494018639252
absolute error = 1e-32
relative error = 2.2150074401268122907060729334685e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.62
y1[1] (analytic) = 0.887729251778750153422404272068
y1[1] (numeric) = 0.88772925177875015342240427206805
absolute error = 5e-32
relative error = 5.6323479146163768770126261726770e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.46036591482899819216274354079485
y2[1] (numeric) = 0.46036591482899819216274354079484
absolute error = 1e-32
relative error = 2.1721851418375480430853532160604e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1100400896, alloc=4783252, time=106.17
x[1] = 3.63
y1[1] (analytic) = 0.88308128326502602342992354439801
y1[1] (numeric) = 0.88308128326502602342992354439806
absolute error = 5e-32
relative error = 5.6619929498601144327620307950744e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.46922004128872721172690481453191
y2[1] (numeric) = 0.4692200412887272117269048145319
absolute error = 1e-32
relative error = 2.1311962661557877584986803289582e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1104401964, alloc=4783252, time=106.37
x[1] = 3.64
y1[1] (analytic) = 0.87834500735887400722343724413409
y1[1] (numeric) = 0.87834500735887400722343724413414
absolute error = 5e-32
relative error = 5.6925239605273934403660845502851e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.47802724613534275625715663887291
y2[1] (numeric) = 0.4780272461353427562571566388729
absolute error = 1e-32
relative error = 2.0919309685474963425349997549629e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1108404240, alloc=4783252, time=106.58
x[1] = 3.65
y1[1] (analytic) = 0.87352089768393783657240447452827
y1[1] (numeric) = 0.87352089768393783657240447452832
absolute error = 5e-32
relative error = 5.7239615139798609139683912980158e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.48678664865569947710681138829532
y2[1] (numeric) = 0.48678664865569947710681138829531
absolute error = 1e-32
relative error = 2.0542880597928897864245366054038e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1112404960, alloc=4783252, time=106.79
x[1] = 3.66
y1[1] (analytic) = 0.86860943664716492709839092015993
y1[1] (numeric) = 0.86860943664716492709839092015997
absolute error = 4e-32
relative error = 4.6050616436312414376255882253501e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.49549737291684481637245114641035
y2[1] (numeric) = 0.49549737291684481637245114641034
absolute error = 1e-32
relative error = 2.0181741713650248632342090941543e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1116406860, alloc=4783252, time=107.00
x[1] = 3.67
y1[1] (analytic) = 0.86361111539056608553795618647981
y1[1] (numeric) = 0.86361111539056608553795618647985
absolute error = 4e-32
relative error = 4.6317143546618311590046727388390e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.50415854785361157220802405891391
y2[1] (numeric) = 0.5041585478536115722080240589139
absolute error = 1e-32
relative error = 1.9835030155838236188588021195751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.68
y1[1] (analytic) = 0.85852643374210171794562486853616
y1[1] (numeric) = 0.8585264337421017179456248685362
absolute error = 4e-32
relative error = 4.6591460003916265545546539244775e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.51276930735572368965980922504404
y2[1] (numeric) = 0.51276930735572368965980922504403
absolute error = 1e-32
relative error = 1.9501947282236016043783828662545e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1120409040, alloc=4783252, time=107.21
x[1] = 3.69
y1[1] (analytic) = 0.85335590016569945017519302837216
y1[1] (numeric) = 0.8533559001656994501751930283722
absolute error = 4e-32
relative error = 4.6873760399656279020433582684154e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.52132879035440656651575454812466
y2[1] (numeric) = 0.52132879035440656651575454812465
absolute error = 1e-32
relative error = 1.9181752830496587076247694350921e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1124410788, alloc=4783252, time=107.42
x[1] = 3.7
y1[1] (analytic) = 0.8481000317104081588356701063544
y1[1] (numeric) = 0.84810003171040815883567010635444
absolute error = 4e-32
relative error = 4.7164247735411453608845494722616e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.52983614090849321321077762570121
y2[1] (numeric) = 0.5298361409084932132107776257012
absolute error = 1e-32
relative error = 1.8873759692672752393665846131690e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1128411864, alloc=4783252, time=107.62
x[1] = 3.71
y1[1] (analytic) = 0.84275935395869349727638917260975
y1[1] (numeric) = 0.84275935395869349727638917260978
absolute error = 3e-32
relative error = 3.5597350369451256247924205429640e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.53829050829001765624379404325037
y2[1] (numeric) = 0.53829050829001765624379404325037
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1132412524, alloc=4783252, time=107.83
x[1] = 3.72
y1[1] (analytic) = 0.83733440097388008700560008948967
y1[1] (numeric) = 0.8373344009738800870056000894897
absolute error = 3e-32
relative error = 3.5827979795297845066105551811822e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.54669104706928702583745896705622
y2[1] (numeric) = 0.54669104706928702583745896705622
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.73
y1[1] (analytic) = 0.83182571524674563027960569792163
y1[1] (numeric) = 0.83182571524674563027960569792166
absolute error = 3e-32
relative error = 3.6065247142667449109327873797439e-30 %
Correct digits = 32
h = 0.01
bytes used=1136414596, alloc=4783252, time=108.04
y2[1] (analytic) = 0.55503691719942382070274923216573
y2[1] (numeric) = 0.55503691719942382070274923216573
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 3.74
y1[1] (analytic) = 0.82623384764127228440667735620253
y1[1] (numeric) = 0.82623384764127228440667735620257
absolute error = 4e-32
relative error = 4.8412444145433854816585550698792e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.56332728410036989575236111967948
y2[1] (numeric) = 0.56332728410036989575236111967948
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1140415792, alloc=4783252, time=108.25
x[1] = 3.75
y1[1] (analytic) = 0.82055935733956072258311240229071
y1[1] (numeric) = 0.82055935733956072258311240229075
absolute error = 4e-32
relative error = 4.8747235214877153105826287371072e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.57156131874234377243415557335029
y2[1] (numeric) = 0.57156131874234377243415557335029
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1144416596, alloc=4783252, time=108.46
x[1] = 3.76
y1[1] (analytic) = 0.81480281178591238980944513756309
y1[1] (numeric) = 0.81480281178591238980944513756313
absolute error = 4e-32
relative error = 4.9091632259253801189308114356384e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.57973819772874292602316503775395
y2[1] (numeric) = 0.57973819772874292602316503775395
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1148417768, alloc=4783252, time=108.67
x[1] = 3.77
y1[1] (analytic) = 0.80896478663008554561462174619622
y1[1] (numeric) = 0.80896478663008554561462174619625
absolute error = 3e-32
relative error = 3.7084432469516213445706500905239e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.58785710337848275971251772647441
y2[1] (numeric) = 0.58785710337848275971251772647441
absolute error = 0
relative error = 0 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1152419796, alloc=4783252, time=108.88
x[1] = 3.78
y1[1] (analytic) = 0.80304586566973076793658025923771
y1[1] (numeric) = 0.80304586566973076793658025923775
absolute error = 4e-32
relative error = 4.9810355435477489698553701171814e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.59591722380776403167448581090021
y2[1] (numeric) = 0.59591722380776403167448581090021
absolute error = 0
relative error = 0 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.79
y1[1] (analytic) = 0.79704664079201167456087725184016
y1[1] (numeric) = 0.79704664079201167456087725184019
absolute error = 3e-32
relative error = 3.7638951680656367675908407364283e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.60391775301126055841709072023268
y2[1] (numeric) = 0.60391775301126055841709072023269
absolute error = 1e-32
relative error = 1.6558546176425354270845997327108e-30 %
Correct digits = 32
h = 0.01
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1156421364, alloc=4783252, time=109.09
TOP MAIN SOLVE Loop
x[1] = 3.8
y1[1] (analytic) = 0.79096771191441669999656817435073
y1[1] (numeric) = 0.79096771191441669999656817435076
absolute error = 3e-32
relative error = 3.7928223299266636200212290530847e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.61185789094271907573358608611888
y2[1] (numeric) = 0.61185789094271907573358608611889
absolute error = 1e-32
relative error = 1.6343664350871598385445951448472e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1160422948, alloc=4783252, time=109.30
x[1] = 3.81
y1[1] (analytic) = 0.78480968692476784656233037436496
y1[1] (numeric) = 0.78480968692476784656233037436499
absolute error = 3e-32
relative error = 3.8225827866056667757849837176074e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.61973684359496319732588971051781
y2[1] (numeric) = 0.61973684359496319732588971051781
absolute error = 0
relative error = 0 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1164425252, alloc=4783252, time=109.51
x[1] = 3.82
y1[1] (analytic) = 0.7785731816204324087577276566562
y1[1] (numeric) = 0.77857318162043240875772765665623
absolute error = 3e-32
relative error = 3.8532023332169572830062673734720e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.62755382307929347077277195688991
y2[1] (numeric) = 0.62755382307929347077277195688992
absolute error = 1e-32
relative error = 1.5934888183664953005220038049735e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1168427504, alloc=4783252, time=109.72
x[1] = 3.83
y1[1] (analytic) = 0.77225881964674374969652252702348
y1[1] (numeric) = 0.77225881964674374969652252702352
absolute error = 4e-32
relative error = 5.1796106411963411866775573372135e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.63530804770427559090337023862228
y2[1] (numeric) = 0.63530804770427559090337023862229
absolute error = 1e-32
relative error = 1.5740395602000652112546247382985e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1172428360, alloc=4783252, time=109.93
x[1] = 3.84
y1[1] (analytic) = 0.76586723243463728747307694024768
y1[1] (numeric) = 0.76586723243463728747307694024772
absolute error = 4e-32
relative error = 5.2228373673649483592679319449829e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.64299874205390889182034887886274
y2[1] (numeric) = 0.64299874205390889182034887886275
absolute error = 1e-32
relative error = 1.5552129959161882634687231225976e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.85
y1[1] (analytic) = 0.75939905913750792781123507395279
y1[1] (numeric) = 0.75939905913750792781123507395283
absolute error = 4e-32
relative error = 5.2673228283203618675604036053148e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.650625137065167300788642218662
y2[1] (numeric) = 0.65062513706516730078864221866201
absolute error = 1e-32
relative error = 1.5369833457569576565559634340774e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1176429060, alloc=4783252, time=110.13
x[1] = 3.86
y1[1] (analytic) = 0.75285494656729525719980460936484
y1[1] (numeric) = 0.75285494656729525719980460936488
absolute error = 4e-32
relative error = 5.3131084789152713608170922317323e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.6581864701049049999590093452957
y2[1] (numeric) = 0.65818647010490499995900934529571
absolute error = 1e-32
relative error = 1.5193262782211476891123098907326e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1180429852, alloc=4783252, time=110.34
x[1] = 3.87
y1[1] (analytic) = 0.74623554912980288794206080932728
y1[1] (numeric) = 0.74623554912980288794206080932733
absolute error = 5e-32
relative error = 6.7002972531000155642241600406925e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.66568198504611910542431592310351
y2[1] (numeric) = 0.66568198504611910542431592310352
absolute error = 1e-32
relative error = 1.5022188108796710373507403052542e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1184430596, alloc=4783252, time=110.54
x[1] = 3.88
y1[1] (analytic) = 0.73954152875925842313086807704128
y1[1] (numeric) = 0.73954152875925842313086807704133
absolute error = 5e-32
relative error = 6.7609455393108027747553392791551e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.67311093234356173740418951936854
y2[1] (numeric) = 0.67311093234356173740418951936855
absolute error = 1e-32
relative error = 1.4856392192566428391871432796665e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1188431368, alloc=4783252, time=110.75
x[1] = 3.89
y1[1] (analytic) = 0.73277355485212058549838830263169
y1[1] (numeric) = 0.73277355485212058549838830263173
absolute error = 4e-32
relative error = 5.4587122768195847016188239762821e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.68047256910869392041403980815868
y2[1] (numeric) = 0.6804725691086939204140398081587
absolute error = 2e-32
relative error = 2.9391339060436600981196707933377e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1192432752, alloc=4783252, time=110.96
x[1] = 3.9
y1[1] (analytic) = 0.72593230420014012937233048461435
y1[1] (numeric) = 0.72593230420014012937233048461439
absolute error = 4e-32
relative error = 5.5101556672110802385544401960560e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.68776615918397381809088812537869
y2[1] (numeric) = 0.68776615918397381809088812537871
absolute error = 2e-32
relative error = 2.9079651176396577465695190128444e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.91
y1[1] (analytic) = 0.71901846092268122959176361387439
y1[1] (numeric) = 0.71901846092268122959176361387443
absolute error = 4e-32
relative error = 5.5631394983475050241049681273074e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.69499097321647187391443044807649
y2[1] (numeric) = 0.69499097321647187391443044807651
absolute error = 2e-32
relative error = 2.8777352182631173033567307721590e-30 %
Correct digits = 32
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
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1196433844, alloc=4783252, time=111.17
x[1] = 3.92
y1[1] (analytic) = 0.71203271639831011518720258429259
y1[1] (numeric) = 0.71203271639831011518720258429263
absolute error = 4e-32
relative error = 5.6177193938970713546924655947707e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.70214628873080549637060743782065
y2[1] (numeric) = 0.70214628873080549637060743782067
absolute error = 2e-32
relative error = 2.8484092732515689767411345177547e-30 %
Correct digits = 32
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 = 18.25
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=1200436140, alloc=4783252, time=111.37
x[1] = 3.93
y1[1] (analytic) = 0.70497576919565778890458983952695
y1[1] (numeric) = 0.70497576919565778890458983952699
absolute error = 4e-32
relative error = 5.6739538786755757696853768695737e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.70923139020138599514994389285155
y2[1] (numeric) = 0.70923139020138599514994389285157
absolute error = 2e-32
relative error = 2.8199541470268267847307086814027e-30 %
Correct digits = 32
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 = 17.89
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=1204439096, alloc=4783252, time=111.58
x[1] = 3.94
y1[1] (analytic) = 0.69784832500356374624360614943559
y1[1] (numeric) = 0.69784832500356374624360614943563
absolute error = 4e-32
relative error = 5.7319045653359889437816948699444e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.71624556912397054374724335454079
y2[1] (numeric) = 0.71624556912397054374724335454081
absolute error = 2e-32
relative error = 2.7923383909322757588324056936659e-30 %
Correct digits = 32
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 = 17.54
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=1208440812, alloc=4783252, time=111.79
x[1] = 3.95
y1[1] (analytic) = 0.69065109656050767958019331164023
y1[1] (numeric) = 0.69065109656050767958019331164026
absolute error = 3e-32
relative error = 4.3437272668359126283592945040719e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.72318812408651201332600433544282
y2[1] (numeric) = 0.72318812408651201332600433544285
absolute error = 3e-32
relative error = 4.1482982091131827962000111752156e-30 %
Correct digits = 32
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 = 17.19
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
bytes used=1212441772, alloc=4783252, time=112.00
x[1] = 3.96
y1[1] (analytic) = 0.68338480358333622414406980875151
y1[1] (numeric) = 0.68338480358333622414406980875154
absolute error = 3e-32
relative error = 4.3899132440017174100431284466408e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.73005836083929959292321305873169
y2[1] (numeric) = 0.73005836083929959292321305873171
absolute error = 2e-32
relative error = 2.7395070137964489284258773417777e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.85
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] = 3.97
y1[1] (analytic) = 0.67605017269529187311724748931934
y1[1] (numeric) = 0.67605017269529187311724748931937
absolute error = 3e-32
relative error = 4.4375404683938371599095772151617e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.73685559236438318199094255175134
y2[1] (numeric) = 0.73685559236438318199094255175136
absolute error = 2e-32
relative error = 2.7142360331181120188580302083677e-30 %
Correct digits = 32
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 = 16.51
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
bytes used=1216442920, alloc=4783252, time=112.20
x[1] = 3.98
y1[1] (analytic) = 0.66864793735335125890206371667484
y1[1] (numeric) = 0.66864793735335125890206371667487
absolute error = 3e-32
relative error = 4.4866660501109583217335839694484e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.7435791389442746128933574013766
y2[1] (numeric) = 0.74357913894427461289335740137662
absolute error = 2e-32
relative error = 2.6896935312622913876929294727838e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 16.19
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
bytes used=1220445436, alloc=4783252, time=112.41
x[1] = 3.99
y1[1] (analytic) = 0.66117883777488006667005095201013
y1[1] (numeric) = 0.66117883777488006667005095201016
absolute error = 3e-32
relative error = 4.5373503031284978871857231880547e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.75022832822991883329412529862008
y2[1] (numeric) = 0.75022832822991883329412529862011
absolute error = 3e-32
relative error = 3.9987826200567096759904483175361e-30 %
Correct digits = 32
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 = 15.86
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
bytes used=1224446800, alloc=4783252, time=112.61
x[1] = 4
y1[1] (analytic) = 0.65364362086361191463916818309775
y1[1] (numeric) = 0.65364362086361191463916818309778
absolute error = 3e-32
relative error = 4.5896569693991927238885327688121e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.75680249530792825137263909451183
y2[1] (numeric) = 0.75680249530792825137263909451186
absolute error = 3e-32
relative error = 3.9640461264327071330903752691186e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.55
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=1228447480, alloc=4783252, time=112.82
x[1] = 4.01
y1[1] (analytic) = 0.64604304013495860312968241468503
y1[1] (numeric) = 0.64604304013495860312968241468506
absolute error = 3e-32
relative error = 4.6436534621180951277398302543607e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.7633009827670735204905561792977
y2[1] (numeric) = 0.76330098276707352049055617929773
absolute error = 3e-32
relative error = 3.9302975729502897510244952033511e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 15.23
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=1232448648, alloc=4783252, time=113.03
x[1] = 4.02
y1[1] (analytic) = 0.63837785564065920131155338076535
y1[1] (numeric) = 0.63837785564065920131155338076539
absolute error = 4e-32
relative error = 6.2658815067852022503978614369740e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.76972314076402411428559733354449
y2[1] (numeric) = 0.76972314076402411428559733354452
absolute error = 3e-32
relative error = 3.8975052731586216646046771930873e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (ratio test) for eq 2 = 14.93
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] = 4.03
y1[1] (analytic) = 0.63064883389277550667185452185245
y1[1] (numeric) = 0.63064883389277550667185452185248
absolute error = 3e-32
relative error = 4.7570055453556384587875678172840e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.7760683270883321181898793012325
y2[1] (numeric) = 0.77606832708833211818987930123253
absolute error = 3e-32
relative error = 3.8656390104921005467677122484934e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.63
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=1236449432, alloc=4783252, time=113.23
x[1] = 4.04
y1[1] (analytic) = 0.62285674778704147759294657917268
y1[1] (numeric) = 0.62285674778704147759294657917271
absolute error = 3e-32
relative error = 4.8165168165212176594979803302127e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.78233590722665273904778223066649
y2[1] (numeric) = 0.78233590722665273904778223066653
absolute error = 4e-32
relative error = 5.1128932764697309674029135156845e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.33
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=1240450472, alloc=4783252, time=113.44
x[1] = 4.05
y1[1] (analytic) = 0.61500237652557430403427072848237
y1[1] (numeric) = 0.6150023765255743040342707284824
absolute error = 3e-32
relative error = 4.8780299304668585772041615152127e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.78852525442619511083590710941938
y2[1] (numeric) = 0.78852525442619511083590710941942
absolute error = 4e-32
relative error = 5.0727607994125374567271993125513e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 14.04
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=1244452172, alloc=4783252, time=113.65
x[1] = 4.06
y1[1] (analytic) = 0.60708650553895484514628584778934
y1[1] (numeric) = 0.60708650553895484514628584778937
absolute error = 3e-32
relative error = 4.9416351255191907225089079122630e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.79463574975739705145742669274634
y2[1] (numeric) = 0.79463574975739705145742669274638
absolute error = 4e-32
relative error = 5.0337528876862176069820282344369e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.75
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=1248453952, alloc=4783252, time=113.86
x[1] = 4.07
y1[1] (analytic) = 0.59910992640768522570785577303961
y1[1] (numeric) = 0.59910992640768522570785577303964
absolute error = 3e-32
relative error = 5.0074282994913114884796287958635e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.80066678217581750318737928027569
y2[1] (numeric) = 0.80066678217581750318737928027573
absolute error = 4e-32
relative error = 4.9958360819340755087563146388017e-30 %
Correct digits = 32
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
Radius of convergence (ratio test) for eq 2 = 13.47
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] = 4.08
y1[1] (analytic) = 0.59107343678303144556199101824792
y1[1] (numeric) = 0.59107343678303144556199101824795
absolute error = 3e-32
relative error = 5.0755114564575270936107778784018e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.80661774858324046757643767338011
y2[1] (numeric) = 0.80661774858324046757643767338015
absolute error = 4e-32
relative error = 4.9589784095696876653662672944968e-30 %
Correct digits = 32
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
bytes used=1252454796, alloc=4783252, time=114.07
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.19
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] = 4.09
y1[1] (analytic) = 0.58297784030725891772303711364428
y1[1] (numeric) = 0.58297784030725891772303711364431
absolute error = 3e-32
relative error = 5.1459931966176410749972099668250e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.81248805388798432447058271235272
y2[1] (numeric) = 0.81248805388798432447058271235276
absolute error = 4e-32
relative error = 4.9231493076838147523488210562858e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1256456116, alloc=4783252, time=114.27
x[1] = 4.1
y1[1] (analytic) = 0.57482394653326891153502867965979
y1[1] (numeric) = 0.57482394653326891153502867965982
absolute error = 3e-32
relative error = 5.2189892541757042270342562840468e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.81827711106441050426503702435845
y2[1] (numeric) = 0.8182771110644105042650370243585
absolute error = 5e-32
relative error = 6.1103994385178715953405970226515e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1260457868, alloc=4783252, time=114.48
x[1] = 4.11
y1[1] (analytic) = 0.56661257084364393716992399387447
y1[1] (numeric) = 0.5666125708436439371699239938745
absolute error = 3e-32
relative error = 5.2946230888122078398714042348155e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.82398434121162556257482398369604
y2[1] (numeric) = 0.82398434121162556257482398369609
absolute error = 5e-32
relative error = 6.0680764790357100989823430845784e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1264459724, alloc=4783252, time=114.69
x[1] = 4.12
y1[1] (analytic) = 0.5583445343691101668598082727593
y1[1] (numeric) = 0.55834453436911016685980827275932
absolute error = 2e-32
relative error = 3.5820176913880934531311371463441e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.82960917361137078716340306097222
y2[1] (numeric) = 0.82960917361137078716340306097226
absolute error = 4e-32
relative error = 4.8215474553971050858283709615162e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1268460648, alloc=4783252, time=114.90
x[1] = 4.13
y1[1] (analytic) = 0.55002066390642504655299469207052
y1[1] (numeric) = 0.55002066390642504655299469207054
absolute error = 2e-32
relative error = 3.6362270206274645968173257745338e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.83515104578509354821692987595635
y2[1] (numeric) = 0.8351510457850935482169298759564
absolute error = 5e-32
relative error = 5.9869409554527843311485256468253e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.14
y1[1] (analytic) = 0.54164179183569830916443077359731
y1[1] (numeric) = 0.54164179183569830916443077359733
absolute error = 2e-32
relative error = 3.6924772610727206540335417561348e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.84060940355019468487667282814088
y2[1] (numeric) = 0.84060940355019468487667282814092
absolute error = 4e-32
relative error = 4.7584525977303690385808762993197e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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
bytes used=1272462392, alloc=4783252, time=115.10
TOP MAIN SOLVE Loop
x[1] = 4.15
y1[1] (analytic) = 0.53320875603715465725018617166272
y1[1] (numeric) = 0.53320875603715465725018617166274
absolute error = 2e-32
relative error = 3.7508761387643782103914058422479e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.84598370107544630333780572921222
y2[1] (numeric) = 0.84598370107544630333780572921226
absolute error = 4e-32
relative error = 4.7282234810375773622625658636071e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1276463692, alloc=4783252, time=115.31
x[1] = 4.16
y1[1] (analytic) = 0.52472239980734643876839021070922
y1[1] (numeric) = 0.52472239980734643876839021070924
absolute error = 2e-32
relative error = 3.8115392076540025776076108914687e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.85127340093557444478094790264673
y2[1] (numeric) = 0.85127340093557444478094790264677
absolute error = 4e-32
relative error = 4.6988429282576932819496359093661e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1280465888, alloc=4783252, time=115.52
x[1] = 4.17
y1[1] (analytic) = 0.51618357177482469458922054275779
y1[1] (numeric) = 0.51618357177482469458922054275781
absolute error = 2e-32
relative error = 3.8745905707988361069370766912611e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.85647797416500116491514400141294
y2[1] (numeric) = 0.85647797416500116491514400141298
absolute error = 4e-32
relative error = 4.6702893952406495970139792893957e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1284467440, alloc=4783252, time=115.73
x[1] = 4.18
y1[1] (analytic) = 0.50759312581527701057891803304672
y1[1] (numeric) = 0.50759312581527701057891803304674
absolute error = 2e-32
relative error = 3.9401636828467192723642713130950e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.86159690031074065096911416280091
y2[1] (numeric) = 0.86159690031074065096911416280095
absolute error = 4e-32
relative error = 4.6425422358847546961572918477634e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1288468300, alloc=4783252, time=115.94
x[1] = 4.19
y1[1] (analytic) = 0.49895192096614066040190125149245
y1[1] (numeric) = 0.49895192096614066040190125149246
absolute error = 1e-32
relative error = 2.0042011223519488692871578243948e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.86662966748444408656315532592254
y2[1] (numeric) = 0.86662966748444408656315532592258
absolute error = 4e-32
relative error = 4.6155816608618462611967465927719e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.2
y1[1] (analytic) = 0.49026082134069957765554488137713
y1[1] (numeric) = 0.49026082134069957765554488137715
absolute error = 2e-32
relative error = 4.0794612029789940956405236822714e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.87157577241358806001857709790882
y2[1] (numeric) = 0.87157577241358806001857709790886
absolute error = 4e-32
relative error = 4.5893886987279444837779720315225e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1292470164, alloc=4783252, time=116.15
x[1] = 4.21
y1[1] (analytic) = 0.48152069604167374756882294948685
y1[1] (numeric) = 0.48152069604167374756882294948687
absolute error = 2e-32
relative error = 4.1535078688017757840058343124216e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.8764347204918013973064980899522
y2[1] (numeric) = 0.87643472049180139730649808995224
absolute error = 4e-32
relative error = 4.5639451592646231466542429649931e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1296472304, alloc=4783252, time=116.36
x[1] = 4.22
y1[1] (analytic) = 0.47273241907430965925363841315521
y1[1] (numeric) = 0.47273241907430965925363841315522
absolute error = 1e-32
relative error = 2.1153615864936231532481864793789e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.88120602582832538699464673122123
y2[1] (numeric) = 0.88120602582832538699464673122127
absolute error = 4e-32
relative error = 4.5392335989078576403577651210616e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1300473228, alloc=4783252, time=116.57
x[1] = 4.23
y1[1] (analytic) = 0.46389686925898050939118958954484
y1[1] (numeric) = 0.46389686925898050939118958954485
absolute error = 1e-32
relative error = 2.1556515386650050152561719058495e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.88588921129660245121088859729926
y2[1] (numeric) = 0.8858892112966024512108885972993
absolute error = 4e-32
relative error = 4.5152372881316979404339230878253e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1304474688, alloc=4783252, time=116.78
x[1] = 4.24
y1[1] (analytic) = 0.45501493014330489726017186970594
y1[1] (numeric) = 0.45501493014330489726017186970595
absolute error = 1e-32
relative error = 2.1977300825822451942620043560178e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.89048380858198840379687432458221
y2[1] (numeric) = 0.89048380858198840379687432458225
absolute error = 4e-32
relative error = 4.4919401806638385324850391160610e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1308476220, alloc=4783252, time=116.99
x[1] = 4.25
y1[1] (analytic) = 0.44608748991379279916407772054484
y1[1] (numeric) = 0.44608748991379279916407772054485
absolute error = 1e-32
relative error = 2.2417127191646907170552393918760e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.89498935822858352446575282843828
y2[1] (numeric) = 0.89498935822858352446575282843832
absolute error = 4e-32
relative error = 4.4693268844190944098018437771026e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.26
y1[1] (analytic) = 0.43711544130702765758652413548598
y1[1] (numeric) = 0.43711544130702765758652413548599
absolute error = 1e-32
relative error = 2.2877251762369224974101511493109e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.89940540968517776589555981885312
y2[1] (numeric) = 0.89940540968517776589555981885316
absolute error = 4e-32
relative error = 4.4473826340450130678748540310834e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1312478780, alloc=4783252, time=117.19
x[1] = 4.27
y1[1] (analytic) = 0.42809968152039346679167732209429
y1[1] (numeric) = 0.4280996815203934667916773220943
absolute error = 1e-32
relative error = 2.3359045642092186603069729504190e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.90373152135030549927585981966133
y2[1] (numeric) = 0.90373152135030549927585981966137
absolute error = 4e-32
relative error = 4.4260932649814205041644917624577e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1316480168, alloc=4783252, time=117.40
x[1] = 4.28
y1[1] (analytic) = 0.41904111212235578208682073683604
y1[1] (numeric) = 0.41904111212235578208682073683605
absolute error = 1e-32
relative error = 2.3864006921306806692079899168699e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.90796726061640529287063252329942
y2[1] (numeric) = 0.90796726061640529287063252329947
absolute error = 5e-32
relative error = 5.5068064861783401034805390208186e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1320480920, alloc=4783252, time=117.62
x[1] = 4.29
y1[1] (analytic) = 0.40994063896230562457137463377925
y1[1] (numeric) = 0.40994063896230562457137463377926
absolute error = 1e-32
relative error = 2.4393775706924992473406648051432e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.91211220391308030765634688524802
y2[1] (numeric) = 0.91211220391308030765634688524807
absolute error = 5e-32
relative error = 5.4817817134222609086214205991799e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1324482204, alloc=4783252, time=117.83
x[1] = 4.3
y1[1] (analytic) = 0.40079917207997529690676239633603
y1[1] (numeric) = 0.40079917207997529690676239633605
absolute error = 2e-32
relative error = 4.9900302678292979301779116876909e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.91616593674945498403170936028464
y2[1] (numeric) = 0.91616593674945498403170936028468
absolute error = 4e-32
relative error = 4.3660213063497523133926511091642e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1328482956, alloc=4783252, time=118.03
x[1] = 4.31
y1[1] (analytic) = 0.39161762561443516845006009684425
y1[1] (numeric) = 0.39161762561443516845006009684426
absolute error = 1e-32
relative error = 2.5535112175582825336333077853388e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.92012805375562378396571242699099
y2[1] (numeric) = 0.92012805375562378396571242699104
absolute error = 5e-32
relative error = 5.4340262527501925003561202236560e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.32
y1[1] (analytic) = 0.38239691771268052999708015943008
y1[1] (numeric) = 0.38239691771268052999708015943009
absolute error = 1e-32
relative error = 2.6150838400621327783291715359200e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.92399815872318784374430909898398
y2[1] (numeric) = 0.92399815872318784374430909898403
absolute error = 5e-32
relative error = 5.4112661944144677276888335209132e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1332484664, alloc=4783252, time=118.24
x[1] = 4.33
y1[1] (analytic) = 0.37313797043781765937323745066286
y1[1] (numeric) = 0.37313797043781765937323745066287
absolute error = 1e-32
relative error = 2.6799738413827467775104792430524e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.92777586464487548368421918677298
y2[1] (numeric) = 0.92777586464487548368421918677303
absolute error = 5e-32
relative error = 5.3892326698041974234557391724278e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1336486948, alloc=4783252, time=118.45
x[1] = 4.34
y1[1] (analytic) = 0.36384170967685827918912735442367
y1[1] (numeric) = 0.36384170967685827918912735442368
absolute error = 1e-32
relative error = 2.7484479470155804818466931725000e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.93146079375324261279591291098884
y2[1] (numeric) = 0.93146079375324261279591291098889
absolute error = 5e-32
relative error = 5.3679124591523838771046633103813e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1340488432, alloc=4783252, time=118.66
x[1] = 4.35
y1[1] (analytic) = 0.35450906504813162723820257743587
y1[1] (numeric) = 0.35450906504813162723820257743588
absolute error = 1e-32
relative error = 2.8208023393258792784069342753200e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.93505257755844915838755579834142
y2[1] (numeric) = 0.93505257755844915838755579834147
absolute error = 5e-32
relative error = 5.3472928902625855078319284276965e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1344490880, alloc=4783252, time=118.87
x[1] = 4.36
y1[1] (analytic) = 0.34514096980832339825235256696343
y1[1] (numeric) = 0.34514096980832339825235256696343
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.93855085688510774299843471888496
y2[1] (numeric) = 0.93855085688510774299843471888501
absolute error = 5e-32
relative error = 5.3273618188301037620056795064106e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.37
y1[1] (analytic) = 0.33573836075915085304374269242283
y1[1] (numeric) = 0.33573836075915085304374269242283
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.94195528190820092382487885040826
y2[1] (numeric) = 0.94195528190820092382487885040831
absolute error = 5e-32
relative error = 5.3081076098124999683572217997629e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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
bytes used=1348491964, alloc=4783252, time=119.08
TOP MAIN SOLVE Loop
x[1] = 4.38
y1[1] (analytic) = 0.32630217815368342744422852384408
y1[1] (numeric) = 0.32630217815368342744422852384408
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.94526551218806340294466391093816
y2[1] (numeric) = 0.94526551218806340294466391093821
absolute error = 5e-32
relative error = 5.2895191197933338272377404633819e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1352492644, alloc=4783252, time=119.28
x[1] = 4.39
y1[1] (analytic) = 0.31683336560231820890338536675574
y1[1] (numeric) = 0.31683336560231820890338536675574
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.94848121670442571014802896361413
y2[1] (numeric) = 0.94848121670442571014802896361418
absolute error = 5e-32
relative error = 5.2715856802867454083116275412932e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1356494932, alloc=4783252, time=119.49
x[1] = 4.4
y1[1] (analytic) = 0.30733286997841968311913974221771
y1[1] (numeric) = 0.30733286997841968311913974221771
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.95160207388951595403539233338039
y2[1] (numeric) = 0.95160207388951595403539233338044
absolute error = 5e-32
relative error = 5.2542970819339723300267806413692e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1360496220, alloc=4783252, time=119.70
x[1] = 4.41
y1[1] (analytic) = 0.29780164132363318664770646649064
y1[1] (numeric) = 0.29780164132363318664770646649063
absolute error = 1e-32
relative error = 3.3579398540428433181964241724346e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.95462777166021633123424156453615
y2[1] (numeric) = 0.95462777166021633123424156453621
absolute error = 6e-32
relative error = 6.2851722714553488741577422114757e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1364497712, alloc=4783252, time=119.91
x[1] = 4.42
y1[1] (analytic) = 0.28824063275288153406866514349322
y1[1] (numeric) = 0.28824063275288153406866514349321
absolute error = 1e-32
relative error = 3.4693234970009724492882803113689e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.95755800744927117811107273183889
y2[1] (numeric) = 0.95755800744927117811107273183895
absolute error = 6e-32
relative error = 6.2659389335406541416515476414429e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.43
y1[1] (analytic) = 0.27865080035905431996329034893364
y1[1] (numeric) = 0.27865080035905431996329034893364
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96039248823554344419921453430048
y2[1] (numeric) = 0.96039248823554344419921453430053
absolute error = 5e-32
relative error = 5.2062048186009057849067596221068e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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
bytes used=1368499044, alloc=4783252, time=120.11
TOP MAIN SOLVE Loop
x[1] = 4.44
y1[1] (analytic) = 0.26903310311739942669651235616339
y1[1] (numeric) = 0.26903310311739942669651235616338
absolute error = 1e-32
relative error = 3.7170147034419946633608241631069e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96313093057331656172040803307784
y2[1] (numeric) = 0.9631309305733165617204080330779
absolute error = 6e-32
relative error = 6.2296826002965347514989885407114e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1372499700, alloc=4783252, time=120.32
x[1] = 4.45
y1[1] (analytic) = 0.25938850278962629877205672974446
y1[1] (numeric) = 0.25938850278962629877205672974445
absolute error = 1e-32
relative error = 3.8552209879982117337591946524116e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96577306062063878103760801869169
y2[1] (numeric) = 0.96577306062063878103760801869175
absolute error = 6e-32
relative error = 6.2126396403562912663802694134309e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1376501744, alloc=4783252, time=120.53
x[1] = 4.46
y1[1] (analytic) = 0.24971796382773057335341360111266
y1[1] (numeric) = 0.24971796382773057335341360111265
absolute error = 1e-32
relative error = 4.0045176753477613806281067805341e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96831861416670713762908092824644
y2[1] (numeric) = 0.9683186141667071376290809282465
absolute error = 6e-32
relative error = 6.1963076122040046770186173204906e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1380502936, alloc=4783252, time=120.74
x[1] = 4.47
y1[1] (analytic) = 0.24002245327754968440743865533016
y1[1] (numeric) = 0.24002245327754968440743865533015
absolute error = 1e-32
relative error = 4.1662768892860667673646637117370e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97076733665828831220992179927159
y2[1] (numeric) = 0.97076733665828831220992179927165
absolute error = 6e-32
relative error = 6.1806776695372166174808263991622e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1384503668, alloc=4783252, time=120.95
x[1] = 4.48
y1[1] (analytic) = 0.23030294068205908482980140684885
y1[1] (numeric) = 0.23030294068205908482980140684884
absolute error = 1e-32
relative error = 4.3421069528614202905886570075463e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97311898322517374193699541853268
y2[1] (numeric) = 0.97311898322517374193699541853275
absolute error = 7e-32
relative error = 7.1933649642720443095871478089705e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.49
y1[1] (analytic) = 0.2205603979844187568494820065161
y1[1] (numeric) = 0.22056039798441875684948200651608
absolute error = 2e-32
relative error = 9.0678109863643235165973944524780e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97537331870466643720739369365918
y2[1] (numeric) = 0.97537331870466643720739369365925
absolute error = 7e-32
relative error = 7.1767392707607290804592711788314e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1388506456, alloc=4783252, time=121.16
x[1] = 4.5
y1[1] (analytic) = 0.21079579943077970598048182479383
y1[1] (numeric) = 0.21079579943077970598048182479381
absolute error = 2e-32
relative error = 9.4878550967366506722573236959487e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97753011766509705538913501449863
y2[1] (numeric) = 0.9775301176650970553891350144987
absolute error = 7e-32
relative error = 7.1609046856991142500208612472957e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1392508936, alloc=4783252, time=121.37
x[1] = 4.51
y1[1] (analytic) = 0.20101012147286015779035832174077
y1[1] (numeric) = 0.20101012147286015779035832174075
absolute error = 2e-32
relative error = 9.9497477308376960681588136420416e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97958916442836687989632919704766
y2[1] (numeric) = 0.97958916442836687989632919704773
absolute error = 7e-32
relative error = 7.1458528270724657794077074953538e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1396509740, alloc=4783252, time=121.58
x[1] = 4.52
y1[1] (analytic) = 0.19120434267030119978472111819888
y1[1] (numeric) = 0.19120434267030119978472111819887
absolute error = 1e-32
relative error = 5.2300067353821923687859766195964e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.98155025309151545032968624674211
y2[1] (numeric) = 0.98155025309151545032968624674217
absolute error = 6e-32
relative error = 6.1127792296953197932989379045282e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1400511008, alloc=4783252, time=121.79
x[1] = 4.53
y1[1] (analytic) = 0.1813794435928116327621307913814
y1[1] (numeric) = 0.18137944359281163276213079138139
absolute error = 1e-32
relative error = 5.5133039345128504593960921109290e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.98341318754731068693732785543696
y2[1] (numeric) = 0.98341318754731068693732785543702
absolute error = 6e-32
relative error = 6.1011994510306971685084201831205e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1404511664, alloc=4783252, time=122.00
x[1] = 4.54
y1[1] (analytic) = 0.1715364067221118170727192195978
y1[1] (numeric) = 0.17153640672211181707271921959779
absolute error = 1e-32
relative error = 5.8296662446707034023631287904177e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.98517778150385945040061393078254
y2[1] (numeric) = 0.9851777815038594504006139307826
absolute error = 6e-32
relative error = 6.0902713323894575670212290206752e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.55
y1[1] (analytic) = 0.16167621635368631931419242500794
y1[1] (numeric) = 0.16167621635368631931419242500793
absolute error = 1e-32
relative error = 6.1852016490315359343761647364504e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.98684385850323657590534765402509
y2[1] (numeric) = 0.98684385850323657590534765402515
absolute error = 6e-32
relative error = 6.0799891981901832481803540053891e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1408512512, alloc=4783252, time=122.20
x[1] = 4.56
y1[1] (analytic) = 0.1517998584983551841186737926099
y1[1] (numeric) = 0.15179985849835518411867379260989
absolute error = 1e-32
relative error = 6.5876214239740903601587833413468e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.98841125193913051861047608903809
y2[1] (numeric) = 0.98841125193913051861047608903815
absolute error = 6e-32
relative error = 6.0703477304905255350219664978212e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1412513360, alloc=4783252, time=122.41
x[1] = 4.57
y1[1] (analytic) = 0.14190832078367367382118531437459
y1[1] (numeric) = 0.14190832078367367382118531437458
absolute error = 1e-32
relative error = 7.0468031365434098387633243681115e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.98987980507350384596444412806507
y2[1] (numeric) = 0.98987980507350384596444412806513
absolute error = 6e-32
relative error = 6.0613419621733449285538145993670e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1416514512, alloc=4783252, time=122.62
x[1] = 4.58
y1[1] (analytic) = 0.1320025923551703359536334006823
y1[1] (numeric) = 0.13200259235517033595363340068229
absolute error = 1e-32
relative error = 7.5756087979648799485203494353145e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.99124937105226691083385383609731
y2[1] (numeric) = 0.99124937105226691083385383609737
absolute error = 6e-32
relative error = 6.0529672706179503839366128228515e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1420515780, alloc=4783252, time=122.83
x[1] = 4.59
y1[1] (analytic) = 0.1220836637774332746752485243965
y1[1] (numeric) = 0.1220836637774332746752485243965
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.99251981291996313809017767868781
y2[1] (numeric) = 0.99251981291996313809017767868787
absolute error = 6e-32
relative error = 6.0452193718412353629041758892717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1424517404, alloc=4783252, time=123.04
x[1] = 4.6
y1[1] (analytic) = 0.11215252693505451742990782122919
y1[1] (numeric) = 0.11215252693505451742990782122918
absolute error = 1e-32
relative error = 8.9164286113596152761366411596562e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.99369100363346445613810465990883
y2[1] (numeric) = 0.99369100363346445613810465990889
absolute error = 6e-32
relative error = 6.0380943150947315848626379343855e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.61
y1[1] (analytic) = 0.10221017493344238231112882817269
y1[1] (numeric) = 0.10221017493344238231112882817268
absolute error = 1e-32
relative error = 9.7837617502482886281334189202740e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.99476282607467550385377935740314
y2[1] (numeric) = 0.9947628260746755038537793574032
absolute error = 6e-32
relative error = 6.0315884779047705300698592246970e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1428519336, alloc=4783252, time=123.24
x[1] = 4.62
y1[1] (analytic) = 0.09225760199951176481534177561582
y1[1] (numeric) = 0.092257601999511764815341775615812
absolute error = 8e-33
relative error = 8.6713721434493134666528310430633e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.99573517306224534252282683445147
y2[1] (numeric) = 0.99573517306224534252282683445153
absolute error = 6e-32
relative error = 6.0256985615440626090019468163775e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1432520024, alloc=4783252, time=123.45
x[1] = 4.63
y1[1] (analytic) = 0.082295803382262274872007287402623
y1[1] (numeric) = 0.082295803382262274872007287402614
absolute error = 9e-33
relative error = 1.0936159111534751531162479916746e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.9966079473622855016167293539807
y2[1] (numeric) = 0.99660794736228550161672935398077
absolute error = 7e-32
relative error = 7.0238251847447589836211974996759e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1436521696, alloc=4783252, time=123.66
x[1] = 4.64
y1[1] (analytic) = 0.072325775253254166254025200760118
y1[1] (numeric) = 0.072325775253254166254025200760109
absolute error = 9e-33
relative error = 1.2443696550069211219570507968708e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99738106169809328661190893188283
y2[1] (numeric) = 0.9973810616980932866119089318829
absolute error = 7e-32
relative error = 7.0183807060484333241425357927588e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1440523244, alloc=4783252, time=123.88
x[1] = 4.65
y1[1] (analytic) = 0.062348514606992010692557016177074
y1[1] (numeric) = 0.062348514606992010692557016177064
absolute error = 1.0e-32
relative error = 1.6038874483272068491530378967730e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99805443875887937652883655089603
y2[1] (numeric) = 0.99805443875887937652883655089609
absolute error = 6e-32
relative error = 6.0116961229702460321302792321874e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.66
y1[1] (analytic) = 0.052365019161226078245837166795957
y1[1] (numeric) = 0.052365019161226078245837166795946
absolute error = 1.1e-32
relative error = 2.1006389716257377237734581876828e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99862801120749883843868709783252
y2[1] (numeric) = 0.99862801120749883843868709783259
absolute error = 7e-32
relative error = 7.0096171161230451310708612605621e-30 %
Correct digits = 32
h = 0.01
bytes used=1444524348, alloc=4783252, time=124.08
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.67
y1[1] (analytic) = 0.042376287257181393700854320105276
y1[1] (numeric) = 0.042376287257181393700854320105265
absolute error = 1.1e-32
relative error = 2.5957913521873863627510073009947e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99910172168718478584253184927338
y2[1] (numeric) = 0.99910172168718478584253184927345
absolute error = 7e-32
relative error = 7.0062936015955292622678557694555e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1448526420, alloc=4783252, time=124.29
x[1] = 4.68
y1[1] (analytic) = 0.032383317759724446019120367944567
y1[1] (numeric) = 0.032383317759724446019120367944555
absolute error = 1.2e-32
relative error = 3.7056116637080825175316674686596e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99947552282728400756284194975967
y2[1] (numeric) = 0.99947552282728400756284194975974
absolute error = 7e-32
relative error = 7.0036732667535734929377917493953e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1452527508, alloc=4783252, time=124.50
x[1] = 4.69
y1[1] (analytic) = 0.022387109957477534072388396442007
y1[1] (numeric) = 0.022387109957477534072388396441995
absolute error = 1.2e-32
relative error = 5.3602273910268045584797562760735e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99974937724799399358919340694292
y2[1] (numeric) = 0.99974937724799399358919340694298
absolute error = 6e-32
relative error = 6.0015041134770949973363608729398e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1456529116, alloc=4783252, time=124.71
x[1] = 4.7
y1[1] (analytic) = 0.012388663462890737150508296327111
y1[1] (numeric) = 0.012388663462890737150508296327098
absolute error = 1.3e-32
relative error = 1.0493464479796769973014688957839e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.99992325756410088417953654157497
y2[1] (numeric) = 0.99992325756410088417953654157503
absolute error = 6e-32
relative error = 6.0004604899545155115161830423735e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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=1460529908, alloc=4783252, time=124.92
x[1] = 4.71
y1[1] (analytic) = 0.0023889781122815029610961477246958
y1[1] (numeric) = 0.0023889781122815029610961477246826
absolute error = 1.32e-32
relative error = 5.5253750263094041143425920190249e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.99999714638771796842523471259357
y2[1] (numeric) = 0.99999714638771796842523471259363
absolute error = 6e-32
relative error = 6.0000171217225509472095116666056e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 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] = 4.72
y1[1] (analytic) = -0.0076109461341481509210826531746326
y1[1] (numeric) = -0.0076109461341481509210826531746464
absolute error = 1.38e-32
relative error = 1.8131779882245289335742057384004e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.99997103633002445843229788796164
y2[1] (numeric) = 0.9999710363300244584322978879617
absolute error = 6e-32
relative error = 6.0001737870533641090660986277635e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.007329
Order of pole (three term test) = -0.8902
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1464530644, alloc=4783252, time=125.13
TOP MAIN SOLVE Loop
x[1] = 4.73
y1[1] (analytic) = -0.017610109292306823958480184942845
y1[1] (numeric) = -0.017610109292306823958480184942859
absolute error = 1.4e-32
relative error = 7.9499790532907475130413165459613e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99984493000200436524284191155768
y2[1] (numeric) = 0.99984493000200436524284191155774
absolute error = 6e-32
relative error = 6.0009305642905764830474544380700e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.01696
Order of pole (three term test) = -0.8961
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1468531912, alloc=4783252, time=125.34
x[1] = 4.74
y1[1] (analytic) = -0.027607511454211308473521317218995
y1[1] (numeric) = -0.02760751145421130847352131721901
absolute error = 1.5e-32
relative error = 5.4333039125523456477223259770513e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99961884001418540260979704807277
y2[1] (numeric) = 0.99961884001418540260979704807283
absolute error = 6e-32
relative error = 6.0022878319448792406953594877485e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.02657
Order of pole (three term test) = -0.9066
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1472533812, alloc=4783252, time=125.54
x[1] = 4.75
y1[1] (analytic) = -0.037602152887976554715496312373334
y1[1] (numeric) = -0.03760215288797655471549631237335
absolute error = 1.6e-32
relative error = 4.2550755132736207669448847940431e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99929278897537794473427075559708
y2[1] (numeric) = 0.99929278897537794473427075559714
absolute error = 6e-32
relative error = 6.0042462691560930331782970071647e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.03618
Order of pole (three term test) = -0.9217
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1476535192, alloc=4783252, time=125.75
x[1] = 4.76
y1[1] (analytic) = -0.047593034137788026258408716410526
y1[1] (numeric) = -0.047593034137788026258408716410543
absolute error = 1.7e-32
relative error = 3.5719512966504274752345865674988e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99886680949041416406874008456944
y2[1] (numeric) = 0.9988668094904141640687400845695
absolute error = 6e-32
relative error = 6.0068068565227266819074279962207e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.04578
Order of pole (three term test) = -0.9414
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1480537228, alloc=4783252, time=125.96
x[1] = 4.77
y1[1] (analytic) = -0.057579156123846448577548772787261
y1[1] (numeric) = -0.057579156123846448577548772787278
absolute error = 1.7e-32
relative error = 2.9524573030273081537218111722566e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99834094415688757527040933829949
y2[1] (numeric) = 0.99834094415688757527040933829955
absolute error = 6e-32
relative error = 6.0099708773009215993994969486846e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.05535
Order of pole (three term test) = -0.9658
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.78
y1[1] (analytic) = -0.067559520242274956413221714659554
y1[1] (numeric) = -0.067559520242274956413221714659572
absolute error = 1.8e-32
relative error = 2.6643173212968747722276302394925e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99771524556089331134762062164767
y2[1] (numeric) = 0.99771524556089331134762062164774
absolute error = 7e-32
relative error = 7.0160299054714311334454905501766e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.06491
Order of pole (three term test) = -0.9947
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1484538344, alloc=4783252, time=126.17
x[1] = 4.79
y1[1] (analytic) = -0.077533128464978649290150241347593
y1[1] (numeric) = -0.077533128464978649290150241347612
absolute error = 1.9e-32
relative error = 2.4505653745910963649682874901239e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99698977627176955796815287876274
y2[1] (numeric) = 0.99698977627176955796815287876281
absolute error = 7e-32
relative error = 7.0211351877412524174098609369303e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.07444
Order of pole (three term test) = -1.028
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1488539608, alloc=4783252, time=126.37
x[1] = 4.8
y1[1] (analytic) = -0.087498983439446569320215257649488
y1[1] (numeric) = -0.087498983439446569320215257649507
absolute error = 1.9e-32
relative error = 2.1714537990202934996762627797288e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99616460883584067178159646650363
y2[1] (numeric) = 0.99616460883584067178159646650371
absolute error = 8e-32
relative error = 8.0308012642098700984750584521554e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.08393
Order of pole (three term test) = -1.066
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1492540716, alloc=4783252, time=126.58
x[1] = 4.81
y1[1] (analytic) = -0.097456088588486121173922639538394
y1[1] (numeric) = -0.097456088588486121173922639538414
absolute error = 2.0e-32
relative error = 2.0522063105211556252161332319848e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99523982576916260843875697540403
y2[1] (numeric) = 0.9952398257691626084387569754041
absolute error = 7e-32
relative error = 7.0334805930722373580952535833995e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.0934
Order of pole (three term test) = -1.109
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1496542348, alloc=4783252, time=126.80
x[1] = 4.82
y1[1] (analytic) = -0.10740344820987996086171061916977
y1[1] (numeric) = -0.10740344820987996086171061916979
absolute error = 2e-32
relative error = 1.8621376066918692590613198706732e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99421551954927138575924090129834
y2[1] (numeric) = 0.99421551954927138575924090129841
absolute error = 7e-32
relative error = 7.0407269473860728911603538749756e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1028
Order of pole (three term test) = -1.156
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1500543312, alloc=4783252, time=127.01
x[1] = 4.83
y1[1] (analytic) = -0.11734006757595538771926678895382
y1[1] (numeric) = -0.11734006757595538771926678895384
absolute error = 2e-32
relative error = 1.7044476292851801834054597978547e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.9930917926059354071940301512694
y2[1] (numeric) = 0.99309179260593540719403015126947
absolute error = 7e-32
relative error = 7.0486938388963613834221295250664e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1122
Order of pole (three term test) = -1.208
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.84
y1[1] (analytic) = -0.12726495303305628274063040973268
y1[1] (numeric) = -0.1272649530330562827406304097327
absolute error = 2e-32
relative error = 1.5715245653534421187727174574801e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99186875731091257034299275504052
y2[1] (numeric) = 0.99186875731091257034299275504058
absolute error = 6e-32
relative error = 6.0491874109098806845344917968352e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1216
Order of pole (three term test) = -1.264
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1504545380, alloc=4783252, time=127.22
x[1] = 4.85
y1[1] (analytic) = -0.13717711210090764614813971846528
y1[1] (numeric) = -0.1371771121009076461481397184653
absolute error = 2e-32
relative error = 1.4579691680116414981777981573388e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.99054653596671318480794231629118
y2[1] (numeric) = 0.99054653596671318480794231629124
absolute error = 6e-32
relative error = 6.0572621094922762562752759695056e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1308
Order of pole (three term test) = -1.325
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1508546896, alloc=4783252, time=127.43
x[1] = 4.86
y1[1] (analytic) = -0.1470755535718627978282707459854
y1[1] (numeric) = -0.14707555357186279782827074598542
absolute error = 2e-32
relative error = 1.3598452981669568373244533066068e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.98912526079436982308009669404291
y2[1] (numeric) = 0.98912526079436982308009669404297
absolute error = 6e-32
relative error = 6.0659657960624520131777365496702e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1401
Order of pole (three term test) = -1.39
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1512547612, alloc=4783252, time=127.64
x[1] = 4.87
y1[1] (analytic) = -0.15695928761002331599602978562804
y1[1] (numeric) = -0.15695928761002331599602978562805
absolute error = 1e-32
relative error = 6.3710788652696501108340620463256e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.98760507392021532746665541129251
y2[1] (numeric) = 0.98760507392021532746665541129257
absolute error = 6e-32
relative error = 6.0753029307388066891096838899294e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1493
Order of pole (three term test) = -1.46
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1516548728, alloc=4783252, time=127.85
x[1] = 4.88
y1[1] (analytic) = -0.16682732585022180217663274703162
y1[1] (numeric) = -0.16682732585022180217663274703164
absolute error = 2e-32
relative error = 1.1988443678559035879299005793817e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.98598612736167029524478484231842
y2[1] (numeric) = 0.98598612736167029524478484231848
absolute error = 6e-32
relative error = 6.0852783152791110164030908504765e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1584
Order of pole (three term test) = -1.534
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1520549712, alloc=4783252, time=128.06
x[1] = 4.89
y1[1] (analytic) = -0.17667868149685757431045858971384
y1[1] (numeric) = -0.17667868149685757431045858971386
absolute error = 2e-32
relative error = 1.1319984862098782479514253635421e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.9842685830120414632826520572489
y2[1] (numeric) = 0.98426858301204146328265205724896
absolute error = 6e-32
relative error = 6.0958970991829335661172510667959e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1675
Order of pole (three term test) = -1.613
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.9
y1[1] (analytic) = -0.18651236942257540449432914412192
y1[1] (numeric) = -0.18651236942257540449432914412194
absolute error = 2e-32
relative error = 1.0723149387849235939823868584558e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.98245261262433251227637724991833
y2[1] (numeric) = 0.98245261262433251227637724991839
absolute error = 6e-32
relative error = 6.1071647862717458642179643179974e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1764
Order of pole (three term test) = -1.695
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1524551868, alloc=4783252, time=128.26
x[1] = 4.91
y1[1] (analytic) = -0.1963274062667774335675731995194
y1[1] (numeric) = -0.19632740626677743356757319951942
absolute error = 2e-32
relative error = 1.0187064750818950922164329369779e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.98053839779406890950899010226969
y2[1] (numeric) = 0.98053839779406890950899010226975
absolute error = 6e-32
relative error = 6.1190872417625712486435357518926e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1854
Order of pole (three term test) = -1.782
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1528553668, alloc=4783252, time=128.47
x[1] = 4.92
y1[1] (analytic) = -0.20612281053395841143350924081177
y1[1] (numeric) = -0.2061228105339584114335092408118
absolute error = 3e-32
relative error = 1.4554429915973587410080426737934e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.97852612994113850763280160634113
y2[1] (numeric) = 0.97852612994113850763280160634119
absolute error = 6e-32
relative error = 6.1316706998523578395372370828605e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.1942
Order of pole (three term test) = -1.874
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1532554356, alloc=4783252, time=128.68
x[1] = 4.93
y1[1] (analytic) = -0.21589760269185442967426044648577
y1[1] (numeric) = -0.21589760269185442967426044648579
absolute error = 2e-32
relative error = 9.2636508004887528057229078526246e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97641601029064971540018032274914
y2[1] (numeric) = 0.9764160102906497154001803227492
absolute error = 6e-32
relative error = 6.1449217718316399132586550412144e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.203
Order of pole (three term test) = -1.969
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1536555044, alloc=4783252, time=128.89
x[1] = 4.94
y1[1] (analytic) = -0.22565080526939533166743080403972
y1[1] (numeric) = -0.22565080526939533166743080403974
absolute error = 2e-32
relative error = 8.8632522166817939312687887323304e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97420824985280915450970852682316
y2[1] (numeric) = 0.97420824985280915450970852682322
absolute error = 6e-32
relative error = 6.1588474547475100566126551058651e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2117
Order of pole (three term test) = -2.069
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1540555904, alloc=4783252, time=129.10
x[1] = 4.95
y1[1] (analytic) = -0.23538144295445100504525741163474
y1[1] (numeric) = -0.23538144295445100504525741163476
absolute error = 2e-32
relative error = 8.4968465436207850095753093699717e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97190306940182081478526506337735
y2[1] (numeric) = 0.97190306940182081478526506337742
absolute error = 7e-32
relative error = 7.2023643307437072165889346092849e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2203
Order of pole (three term test) = -2.173
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.96
y1[1] (analytic) = -0.24508854269136178194844802293532
y1[1] (numeric) = -0.24508854269136178194844802293534
absolute error = 2e-32
relative error = 8.1603161781356113572270331873118e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96950069945380881775493302309673
y2[1] (numeric) = 0.9695006994538088177549330230968
absolute error = 7e-32
relative error = 7.2202113974168515806274480166017e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2288
Order of pole (three term test) = -2.281
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1544557432, alloc=4783252, time=129.30
x[1] = 4.97
y1[1] (analytic) = -0.25477113377824319411595351401254
y1[1] (numeric) = -0.25477113377824319411595351401256
absolute error = 2e-32
relative error = 7.8501829086368610638002805666221e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96700138024376599633497671407791
y2[1] (numeric) = 0.96700138024376599633497671407797
absolute error = 6e-32
relative error = 6.2047481240280064455944575163143e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2372
Order of pole (three term test) = -2.394
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1548559596, alloc=4783252, time=129.51
x[1] = 4.98
y1[1] (analytic) = -0.26442824796405535241625332068078
y1[1] (numeric) = -0.2644282479640553524162533206808
absolute error = 2e-32
relative error = 7.5634884525342652761140772259340e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96440536170153059574171007792892
y2[1] (numeric) = 0.96440536170153059574171007792899
absolute error = 7e-32
relative error = 7.2583586508163752644110335513589e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2455
Order of pole (three term test) = -2.51
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1552561024, alloc=4783252, time=129.72
x[1] = 4.99
y1[1] (analytic) = -0.27405891954542724396309159769695
y1[1] (numeric) = -0.27405891954542724396309159769697
absolute error = 2e-32
relative error = 7.2977008130855072016523539894619e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96171290342679349794114601441111
y2[1] (numeric) = 0.96171290342679349794114601441117
absolute error = 6e-32
relative error = 6.2388681472617110558166000535117e-30 %
Correct digits = 32
h = 0.01
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
Radius of convergence (three term test) for eq 2 = 0.2538
Order of pole (three term test) = -2.63
NO COMPLEX POLE (six term test) for Equation 2
Finished!
diff ( y1 , x , 1 ) = m1 * y2 ;
diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;
Iterations = 450
Total Elapsed Time = 2 Minutes 9 Seconds
Elapsed Time(since restart) = 2 Minutes 2 Seconds
Time to Timeout = 50 Seconds
Percent Done = 100.2 %
> quit
bytes used=1554142840, alloc=4783252, time=129.80