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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> 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
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> 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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[1]) < min_size then
min_size := omniabs(array_y[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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 2
> if (iter >= 0) then # if number 3
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> 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 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[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, " ")
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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> 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 2;
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y_higher[1, 1]) then
tmp := omniabs(array_y_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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 2
> 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 2;
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_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 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) 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
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #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_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> 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 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #BOTTOM RADII REAL EQ = 1
> #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_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_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 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> 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 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_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 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_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;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_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 - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_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_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_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;
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_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 4
> 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_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> 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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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_y[iii]) then
array_norms[iii] := omniabs(array_y[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,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre cos 1 $eq_no = 1
> array_tmp3[1] := cos(array_x[1]);
> array_tmp3_g[1] := sin(array_x[1]);
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] - array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := -array_tmp3_g[1] * array_x[2] / 1;
> array_tmp3_g[2] := array_tmp3[1] * array_x[2] / 1;
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp2[2] - array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := -array_tmp3_g[2] * array_x[2] / 2;
> array_tmp3_g[3] := array_tmp3[2] * array_x[2] / 2;
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp2[3] - array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := -array_tmp3_g[3] * array_x[2] / 3;
> array_tmp3_g[4] := array_tmp3[3] * array_x[2] / 3;
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp2[4] - array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := -array_tmp3_g[4] * array_x[2] / 4;
> array_tmp3_g[5] := array_tmp3[4] * array_x[2] / 4;
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp2[5] - array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit cos LINEAR $eq_no = 1
> array_tmp3[kkk] := -array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp3_g[kkk] := array_tmp3[kkk - 1] * array_x[2] / (kkk - 1);
> #emit FULL - FULL sub $eq_no = 1
> array_tmp4[kkk] := array_tmp2[kkk] - array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,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_y[kkk + order_d] := temporary;
> array_y_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_y_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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := cos(array_x[1]);
array_tmp3_g[1] := sin(array_x[1]);
array_tmp4[1] := array_tmp2[1] - array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := -array_tmp1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := -array_tmp3_g[1]*array_x[2];
array_tmp3_g[2] := array_tmp3[1]*array_x[2];
array_tmp4[2] := array_tmp2[2] - array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := -1/2*array_tmp3_g[2]*array_x[2];
array_tmp3_g[3] := 1/2*array_tmp3[2]*array_x[2];
array_tmp4[3] := array_tmp2[3] - array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := -1/3*array_tmp3_g[3]*array_x[2];
array_tmp3_g[4] := 1/3*array_tmp3[3]*array_x[2];
array_tmp4[4] := array_tmp2[4] - array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := -1/4*array_tmp3_g[4]*array_x[2];
array_tmp3_g[5] := 1/4*array_tmp3[4]*array_x[2];
array_tmp4[5] := array_tmp2[5] - array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := -array_tmp3_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp3_g[kkk] := array_tmp3[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp4[kkk] := array_tmp2[kkk] - array_tmp3[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp4[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_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_y_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_y := proc(x)
> return(2.0 - cos(x) - sin(x));
> end;
exact_soln_y := proc(x) return 2.0 - cos(x) - sin(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 := 1;
> 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/subpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );");
> 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 := 0.0;");
> omniout_str(ALWAYS,"x_end := 10.0;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> 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_y := proc(x)");
> omniout_str(ALWAYS,"return(2.0 - cos(x) - sin(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_y_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..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3_g:= 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_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 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_y_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 <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) 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_y[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_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1_g[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_g[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_y_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_y_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_y_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 <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 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 <=2) 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 <=2) 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 <=2) 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 <=2) 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_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[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_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_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1_g[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_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3_g[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_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_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_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 := 0.0;
> x_end := 10.0;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 100;
> #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_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := 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 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> 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_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_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_y_higher[r_order,term_no] := array_y_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
> ;
> atomall();
> 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 4
> 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 5
> 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 5;
> 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 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> 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_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_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_y_higher[r_order,term_no] := array_y_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 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_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 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T05:15:28-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );")
> ;
> 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 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"sub diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #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_y_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_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_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 := 1;
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/subpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );");
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 := 0.0;");
omniout_str(ALWAYS, "x_end := 10.0;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
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_y := proc(x)");
omniout_str(ALWAYS, "return(2.0 - cos(x) - sin(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_y_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 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3_g := 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_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_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 <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[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_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[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_g[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_y_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_y_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_y_higher_work2[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_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 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 <= 2 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 <= 2 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 <= 2 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_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[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_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_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[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_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp3_g[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[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_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.;
x_end := 10.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
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_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 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_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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;
atomall();
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_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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;
atomall();
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_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_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 ( y , x , 1 ) = sin ( x ) - cos ( x );");
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, "2013-05-26T05:15:28-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sub");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) - cos ( x );");
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,
"sub diffeq.mxt");
logitem_str(html_log_file,
"sub maple results");
logitem_str(html_log_file, "All Tests - All Languages");
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/subpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) - cos ( x );
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 10.0;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
#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_y := proc(x)
return(2.0 - cos(x) - sin(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 10
estimated_steps = 10000000
step_error = 1.0000000000000000000000000000000e-17
est_needed_step_err = 1.0000000000000000000000000000000e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.4795963091432459590803650205169e-183
estimated_step_error = 2.4795963091432459590803650205169e-183
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6640289456673085494241237344671e-175
estimated_step_error = 1.6640289456673085494241237344671e-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 = 1.1167109634281658039768470129768e-167
estimated_step_error = 1.1167109634281658039768470129768e-167
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.4941209723208461003494033276293e-160
estimated_step_error = 7.4941209723208461003494033276293e-160
best_h = 1.60000e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.0292201963793928992805176661990e-152
estimated_step_error = 5.0292201963793928992805176661990e-152
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3750535418631942033141002227260e-144
estimated_step_error = 3.3750535418631942033141002227260e-144
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.2649614335316304211233775597983e-136
estimated_step_error = 2.2649614335316304211233775597983e-136
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5199916895423777118956430947519e-128
estimated_step_error = 1.5199916895423777118956430947519e-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 = 1.0200515736182804977695139837091e-120
estimated_step_error = 1.0200515736182804977695139837091e-120
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.8454826845994159350314380228140e-113
estimated_step_error = 6.8454826845994159350314380228140e-113
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.5939692205648102063552107208998e-105
estimated_step_error = 4.5939692205648102063552107208998e-105
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.0830190141819725294625088241667e-97
estimated_step_error = 3.0830190141819725294625088241667e-97
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0690574936827564663477631480461e-89
estimated_step_error = 2.0690574936827564663477631480461e-89
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3886262703084524939994435722306e-81
estimated_step_error = 1.3886262703084524939994435722306e-81
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.3203260310094456323386665946748e-74
estimated_step_error = 9.3203260310094456323386665946748e-74
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.2566604218990263383558127802095e-66
estimated_step_error = 6.2566604218990263383558127802095e-66
best_h = 0.065536
opt_iter = 17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.2013155974233946525901592832901e-58
estimated_step_error = 4.2013155974233946525901592832901e-58
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.8228608031194300273596148637954e-50
estimated_step_error = 2.8228608031194300273596148637954e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 1
y[1] (numeric) = 1
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
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = 0.9900501662491680575371996279787
y[1] (numeric) = 0.99005016624916805753719962797869
absolute error = 1e-32
relative error = 1.0100498278673364177533130571212e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -13.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = 0.98020132664008914222081411446952
y[1] (numeric) = 0.98020132664008914222081411446955
absolute error = 3e-32
relative error = 3.0605957352489297705151550159651e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.22
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4814
Order of pole (three term test) = -13.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 0.97045446604851682295931495160714
y[1] (numeric) = 0.97045446604851682295931495160712
absolute error = 2e-32
relative error = 2.0608900983717170713279959577505e-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
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = -13.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 0.96081055915238790023288243015498
y[1] (numeric) = 0.96081055915238790023288243015495
absolute error = 3e-32
relative error = 3.1223636870170881978952783575183e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4802
Order of pole (three term test) = -13.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = 0.95127057033435542464226418799801
y[1] (numeric) = 0.95127057033435542464226418799799
absolute error = 2e-32
relative error = 2.1024512503283203846060486802400e-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
Radius of convergence (three term test) for eq 1 = 0.4794
Order of pole (three term test) = -14.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=4001088, alloc=3145152, time=0.34
x[1] = 0.06
y[1] (analytic) = 0.94183545358535123525324717496022
y[1] (numeric) = 0.94183545358535123525324717496018
absolute error = 4e-32
relative error = 4.2470263619541171305610780571720e-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
Radius of convergence (three term test) for eq 1 = 0.4783
Order of pole (three term test) = -14.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = 0.93250615240918766140254430325241
y[1] (numeric) = 0.93250615240918766140254430325238
absolute error = 3e-32
relative error = 3.2171369510531521454100273158447e-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
Radius of convergence (three term test) for eq 1 = 0.4771
Order of pole (three term test) = -14.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 0.923283599728207927715416878052
y[1] (numeric) = 0.923283599728207927715416878052
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 = 17.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4756
Order of pole (three term test) = -14.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 0.91416871778999469721590664556776
y[1] (numeric) = 0.91416871778999469721590664556773
absolute error = 3e-32
relative error = 3.2816699386219514996549684812426e-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
Radius of convergence (three term test) for eq 1 = 0.474
Order of pole (three term test) = -15.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0.90516241807514608159762381378548
y[1] (numeric) = 0.90516241807514608159762381378552
absolute error = 4e-32
relative error = 4.4190964186362432691470777552431e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4721
Order of pole (three term test) = -15.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 0.89626560120612834097721089849675
y[1] (numeric) = 0.89626560120612834097721089849671
absolute error = 4e-32
relative error = 4.4629627586031352002385497946687e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.02
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4701
Order of pole (three term test) = -15.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0.88747915685721438778455121787143
y[1] (numeric) = 0.88747915685721438778455121787141
absolute error = 2e-32
relative error = 2.2535740524684547050771561960182e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4679
Order of pole (three term test) = -15.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0.87880396366551710086428201813989
y[1] (numeric) = 0.87880396366551710086428201813989
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 = 15.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4655
Order of pole (three term test) = -16.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0.87024088914312634638306342128323
y[1] (numeric) = 0.87024088914312634638306342128324
absolute error = 1e-32
relative error = 1.1491071178977117640498829852702e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.06
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.463
Order of pole (three term test) = -16.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 0.86179078959035849176729356265806
y[1] (numeric) = 0.86179078959035849176729356265803
absolute error = 3e-32
relative error = 3.4811233030536478583240801580004e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4602
Order of pole (three term test) = -16.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0.85345451001012708764758431629571
y[1] (numeric) = 0.85345451001012708764758431629568
absolute error = 3e-32
relative error = 3.5151258383582764271087599440139e-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 = 0.4573
Order of pole (three term test) = -16.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0.84523288402344328067044563311665
y[1] (numeric) = 0.84523288402344328067044563311665
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 = 0.4541
Order of pole (three term test) = -17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0.83712673378605440706548123568929
y[1] (numeric) = 0.83712673378605440706548123568927
absolute error = 2e-32
relative error = 2.3891245127898909754364940444395e-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 = 0.4508
Order of pole (three term test) = -17.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0.82913686990622910303927134282879
y[1] (numeric) = 0.82913686990622910303927134282879
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 = 0.4473
Order of pole (three term test) = -17.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0.82126409136369715341639085613341
y[1] (numeric) = 0.82126409136369715341639085613345
absolute error = 4e-32
relative error = 4.8705404778602432437325711358276e-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 = 0.4437
Order of pole (three term test) = -17.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0.81350918542975218447514900567296
y[1] (numeric) = 0.81350918542975218447514900567302
absolute error = 6e-32
relative error = 7.3754545215496027962695261414537e-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 = 0.4398
Order of pole (three term test) = -17.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0.80587292758852519064218601349829
y[1] (numeric) = 0.8058729275885251906421860134983
absolute error = 1e-32
relative error = 1.2408904254823102225606346236022e-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 = 0.4358
Order of pole (three term test) = -18.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0.79835608145943676762765213956833
y[1] (numeric) = 0.79835608145943676762765213956834
absolute error = 1e-32
relative error = 1.2525739118463876155113447148188e-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 = 0.4316
Order of pole (three term test) = -18.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0.79095939872083580671303266854678
y[1] (numeric) = 0.79095939872083580671303266854681
absolute error = 3e-32
relative error = 3.7928621934977870014494221817615e-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 = 0.4272
Order of pole (three term test) = -18.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0.78368361903483228625855584565641
y[1] (numeric) = 0.78368361903483228625855584565643
absolute error = 2e-32
relative error = 2.5520502807793233382279830300904e-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 = 0.4227
Order of pole (three term test) = -18.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0.77652946997333167708839388918468
y[1] (numeric) = 0.77652946997333167708839388918472
absolute error = 4e-32
relative error = 5.1511245286510141750163842069443e-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 = 0.418
Order of pole (three term test) = -18.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.76949766694527835825148076948726
y[1] (numeric) = 0.76949766694527835825148076948726
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 = 0.4131
Order of pole (three term test) = -19.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0.76258891312511531875574038794565
y[1] (numeric) = 0.76258891312511531875574038794568
absolute error = 3e-32
relative error = 3.9339674998760444898813859473780e-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 = 0.4081
Order of pole (three term test) = -19.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0.75580389938246729924593501656373
y[1] (numeric) = 0.75580389938246729924593501656377
absolute error = 4e-32
relative error = 5.2923780934025565856838393591250e-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 = 0.4029
Order of pole (three term test) = -19.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
bytes used=8002156, alloc=4259060, time=0.70
y[1] (analytic) = 0.74914330421305440525236902674697
y[1] (numeric) = 0.74914330421305440525236902674693
absolute error = 4e-32
relative error = 5.3394323589421155853784869265927e-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 = 0.3975
Order of pole (three term test) = -19.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0.74260779367084310059155123983884
y[1] (numeric) = 0.74260779367084310059155123983884
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 = 0.392
Order of pole (three term test) = -19.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0.73619802130144136576293518281675
y[1] (numeric) = 0.73619802130144136576293518281677
absolute error = 2e-32
relative error = 2.7166603850203587863562074247338e-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 = 0.3863
Order of pole (three term test) = -20.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0.72991462807674468177039372546358
y[1] (numeric) = 0.72991462807674468177039372546358
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 = 0.3805
Order of pole (three term test) = -20.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0.72375824233083937471558445294261
y[1] (numeric) = 0.72375824233083937471558445294264
absolute error = 3e-32
relative error = 4.1450305150772441168481057534884e-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 = 0.3745
Order of pole (three term test) = -20.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 0.71772947969716973077533273577867
y[1] (numeric) = 0.71772947969716973077533273577871
absolute error = 4e-32
relative error = 5.5731304246938729435138009822318e-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 = 0.3683
Order of pole (three term test) = -20.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0.71182894304697516479917419595457
y[1] (numeric) = 0.71182894304697516479917419595453
absolute error = 4e-32
relative error = 5.6193275632739074528677407730749e-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 = 0.3621
Order of pole (three term test) = -20.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0.70605722242900359875889462638195
y[1] (numeric) = 0.70605722242900359875889462638197
absolute error = 2e-32
relative error = 2.8326316004806630948045569354413e-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 = 0.3556
Order of pole (three term test) = -21.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0.7004148950105070786619837259262
y[1] (numeric) = 0.70041489501050707866198372592624
absolute error = 4e-32
relative error = 5.7109008224903542575680180083848e-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 = 0.3491
Order of pole (three term test) = -21.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 0.69490252501952553031814114927174
y[1] (numeric) = 0.69490252501952553031814114927174
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 = 0.3424
Order of pole (three term test) = -21.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 0.68952066368846442553516151115249
y[1] (numeric) = 0.6895206636884644255351615111525
absolute error = 1e-32
relative error = 1.4502828597633075487537104678756e-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 = 0.3355
Order of pole (three term test) = -21.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0.68426984919897200093056030167186
y[1] (numeric) = 0.68426984919897200093056030167185
absolute error = 1e-32
relative error = 1.4614117532295654009979258213386e-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 = 0.3285
Order of pole (three term test) = -21.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0.67915060662812154159112405224796
y[1] (numeric) = 0.679150606628121541591124052248
absolute error = 4e-32
relative error = 5.8897098242455906542627325549594e-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 = 0.3214
Order of pole (three term test) = -21.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0.67416344789590411130717084971203
y[1] (numeric) = 0.674163447895904111307170849712
absolute error = 3e-32
relative error = 4.4499594413834528784744439222112e-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 = 0.3142
Order of pole (three term test) = -22.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0.66930887171403698006474186022168
y[1] (numeric) = 0.66930887171403698006474186022173
absolute error = 5e-32
relative error = 7.4703925367005384770944732212126e-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 = 0.3068
Order of pole (three term test) = -22.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0.6645873635360928679103151422817
y[1] (numeric) = 0.66458736353609286791031514228168
absolute error = 2e-32
relative error = 3.0093861390299856695858729593255e-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 = 0.2993
Order of pole (three term test) = -22.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 0.6599993955089549922220964525707
y[1] (numeric) = 0.65999939550895499222209645257072
absolute error = 2e-32
relative error = 3.0303058057465503164676245801618e-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 = 0.2917
Order of pole (three term test) = -22.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0.65554542642560277284270592307019
y[1] (numeric) = 0.65554542642560277284270592307023
absolute error = 4e-32
relative error = 6.1017891953120905448488492127503e-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 = 0.284
Order of pole (three term test) = -22.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0.65122590167923291646340222625266
y[1] (numeric) = 0.65122590167923291646340222625265
absolute error = 1e-32
relative error = 1.5355654580406398723913717325519e-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 = 0.2762
Order of pole (three term test) = -22.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 0.64704125321872046811317350367534
y[1] (numeric) = 0.64704125321872046811317350367541
absolute error = 7e-32
relative error = 1.0818475584328435324547608672801e-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 = 0.2682
Order of pole (three term test) = -22.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0.64299189950542428361043048218063
y[1] (numeric) = 0.64299189950542428361043048218062
absolute error = 1e-32
relative error = 1.5552295460785412178629614765355e-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 = 0.2602
Order of pole (three term test) = -23.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0.63907824547134124239406128874993
y[1] (numeric) = 0.63907824547134124239406128874994
absolute error = 1e-32
relative error = 1.5647536230285339837864801067921e-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 = 0.252
Order of pole (three term test) = -23.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 0.63530068247861338527769348546375
y[1] (numeric) = 0.63530068247861338527769348546376
absolute error = 1e-32
relative error = 1.5740578084986769519187464949979e-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 = 0.2438
Order of pole (three term test) = -23.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 0.63165958828039202637964395896972
y[1] (numeric) = 0.63165958828039202637964395896974
absolute error = 2e-32
relative error = 3.1662623937123000994917948173338e-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 = 0.2354
Order of pole (three term test) = -23.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0.62815532698306275278475053812396
y[1] (numeric) = 0.62815532698306275278475053812398
absolute error = 2e-32
relative error = 3.1839258764320356383512118140085e-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 = 0.227
Order of pole (three term test) = -23.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=12005388, alloc=4324584, time=1.07
x[1] = 0.55
y[1] (analytic) = 0.62478824900983508940664009462491
y[1] (numeric) = 0.62478824900983508940664009462496
absolute error = 5e-32
relative error = 8.0027113312774431174702752295854e-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 = 0.2184
Order of pole (three term test) = -23.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 0.62155869106570047005360505502167
y[1] (numeric) = 0.62155869106570047005360505502167
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 = 0.2098
Order of pole (three term test) = -23.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 0.61846697610376201887178014300517
y[1] (numeric) = 0.61846697610376201887178014300518
absolute error = 1e-32
relative error = 1.6169012067545334327938829430969e-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 = 0.2011
Order of pole (three term test) = -23.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 0.61551341329293950915941661237354
y[1] (numeric) = 0.61551341329293950915941661237354
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 = 0.1923
Order of pole (three term test) = -24.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0.61269829798705272902946009863353
y[1] (numeric) = 0.61269829798705272902946009863357
absolute error = 4e-32
relative error = 6.5284986316128566115492793616634e-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 = 0.1834
Order of pole (three term test) = -24.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0.61002191169528634555810205538594
y[1] (numeric) = 0.61002191169528634555810205538599
absolute error = 5e-32
relative error = 8.1964268891665045480591897340711e-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 = 0.1745
Order of pole (three term test) = -24.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 0.60748452205403922090827738918248
y[1] (numeric) = 0.60748452205403922090827738918248
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 = 0.1655
Order of pole (three term test) = -24.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 0.60508638280016099547303711805709
y[1] (numeric) = 0.60508638280016099547303711805711
absolute error = 2e-32
relative error = 3.3053131864323089498883604796181e-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 = 0.1564
Order of pole (three term test) = -24.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0.60282773374557861435817894342828
y[1] (numeric) = 0.60282773374557861435817894342835
absolute error = 7e-32
relative error = 1.1611940871576300247886965335418e-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 = 0.1473
Order of pole (three term test) = -24.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 0.60070880075331533453034298153177
y[1] (numeric) = 0.60070880075331533453034298153177
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 = 0.1381
Order of pole (three term test) = -24.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0.59872979571490461070987375071416
y[1] (numeric) = 0.59872979571490461070987375071417
absolute error = 1e-32
relative error = 1.6702024972817070743475564510395e-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 = 0.1288
Order of pole (three term test) = -24.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 0.5968909165292011186010374293735
y[1] (numeric) = 0.59689091652920111860103742937347
absolute error = 3e-32
relative error = 5.0260439837891784931113816937517e-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 = 0.1195
Order of pole (three term test) = -24.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 0.59519234708259103433961394103531
y[1] (numeric) = 0.5951923470825910343396139410353
absolute error = 1e-32
relative error = 1.6801291295185897230109117606492e-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 = 0.1101
Order of pole (three term test) = -24.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0.59363425723060354911342772853545
y[1] (numeric) = 0.59363425723060354911342772853544
absolute error = 1e-32
relative error = 1.6845389022277050809193004185158e-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 = 0.1007
Order of pole (three term test) = -24.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 0.59221680278092545778903147749348
y[1] (numeric) = 0.59221680278092545778903147749352
absolute error = 4e-32
relative error = 6.7542831969927937004928804829878e-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 = 0.09131
Order of pole (three term test) = -24.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0.59094012547782052007152565840938
y[1] (numeric) = 0.59094012547782052007152565840942
absolute error = 4e-32
relative error = 6.7688752676350967017501318995912e-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 = 0.08184
Order of pole (three term test) = -24.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 0.58980435298795515224841408300756
y[1] (numeric) = 0.58980435298795515224841408300762
absolute error = 6e-32
relative error = 1.0172864899358466770946712772456e-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 = 0.07233
Order of pole (three term test) = -24.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0.58880959888763186693650920509983
y[1] (numeric) = 0.58880959888763186693650920509989
absolute error = 6e-32
relative error = 1.0190051268415270921649971805674e-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 = 0.0628
Order of pole (three term test) = -24.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 0.58795596265143173747727371068817
y[1] (numeric) = 0.58795596265143173747727371068814
absolute error = 3e-32
relative error = 5.1024229543846682678613121150027e-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 = 0.05324
Order of pole (three term test) = -24.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0.58724352964226702272469428169303
y[1] (numeric) = 0.587243529642267022724694281693
absolute error = 3e-32
relative error = 5.1086131197180144003705125477496e-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 = 0.04366
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 0.58667237110284494695491929422001
y[1] (numeric) = 0.58667237110284494695491929422002
absolute error = 1e-32
relative error = 1.7045288806087270431398370803302e-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 = 0.03406
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0.58624254414854348851255599456327
y[1] (numeric) = 0.58624254414854348851255599456327
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 = 0.02445
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0.58595409176169988960882570022349
y[1] (numeric) = 0.58595409176169988960882570022345
absolute error = 4e-32
relative error = 6.8264733641057145416245386763931e-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 = 0.01483
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 0.58580704278731245841583765111748
y[1] (numeric) = 0.58580704278731245841583765111752
absolute error = 4e-32
relative error = 6.8281869418430162065116565140752e-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 = 0.005198
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0.5858014119301560932731902639458
y[1] (numeric) = 0.58580141193015609327319026394586
absolute error = 6e-32
relative error = 1.0242378863906473059220504534705e-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
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 0.58593719975331181745207540777631
y[1] (numeric) = 0.5859371997533118174520754077763
absolute error = 1e-32
relative error = 1.7066675411989795390221195706800e-30 %
Correct digits = 32
h = 0.01
bytes used=16006292, alloc=4390108, time=1.45
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 0.58621439267811047152218390680536
y[1] (numeric) = 0.58621439267811047152218390680536
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
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 0.58663296298549056895212865687538
y[1] (numeric) = 0.58663296298549056895212865687535
absolute error = 3e-32
relative error = 5.1139301561446696560489919411712e-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
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0.58719286881877017915895685599752
y[1] (numeric) = 0.58719286881877017915895685599747
absolute error = 5e-32
relative error = 8.5150897865266619858382906595177e-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
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 0.58789405418783256082075629249945
y[1] (numeric) = 0.5878940541878325608207562924995
absolute error = 5e-32
relative error = 8.5049337791099627428087974164440e-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
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 0.58873644897472512689251244630303
y[1] (numeric) = 0.58873644897472512689251244630307
absolute error = 4e-32
relative error = 6.7942115813721647724661324859478e-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
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0.58971996894067118143338060624745
y[1] (numeric) = 0.5897199689406711814333806062475
absolute error = 5e-32
relative error = 8.4786004601160544190374552232370e-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
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 0.59084451573449372707753337079435
y[1] (numeric) = 0.59084451573449372707753337079432
absolute error = 3e-32
relative error = 5.0774779491193623029526291425618e-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
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0.59210997690245050077485626352191
y[1] (numeric) = 0.59210997690245050077485626352192
absolute error = 1e-32
relative error = 1.6888754437670097793219826197199e-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
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0.59351622589947925430611322964662
y[1] (numeric) = 0.59351622589947925430611322964657
absolute error = 5e-32
relative error = 8.4243695147886721897766690559818e-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
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 0.59506312210185215505390153287935
y[1] (numeric) = 0.59506312210185215505390153287932
absolute error = 3e-32
relative error = 5.0414819681709568230921274148259e-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
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 0.59675051082123804159986425595375
y[1] (numeric) = 0.59675051082123804159986425595378
absolute error = 3e-32
relative error = 5.0272265303492582344623293570174e-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
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0.59857822332017112793431919084398
y[1] (numeric) = 0.59857822332017112793431919084401
absolute error = 3e-32
relative error = 5.0118762813650538000412511408889e-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
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 0.60054607682892460942077369965635
y[1] (numeric) = 0.60054607682892460942077369965637
absolute error = 2e-32
relative error = 3.3303023317721760293087937431001e-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
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0.60265387456378748316879038614185
y[1] (numeric) = 0.60265387456378748316879038614184
absolute error = 1e-32
relative error = 1.6593272560038202999823925904308e-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
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0.60490140574674275514839692413694
y[1] (numeric) = 0.60490140574674275514839692413699
absolute error = 5e-32
relative error = 8.2658098534711890386271416023804e-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
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 0.60728844562654506624172705321767
y[1] (numeric) = 0.60728844562654506624172705321772
absolute error = 5e-32
relative error = 8.2333198268599595760309615552341e-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
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0.60981475550119562948685220729376
y[1] (numeric) = 0.6098147555011956294868522072938
absolute error = 4e-32
relative error = 6.5593689951179894416547826541964e-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
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0.61248008274181223103880844492095
y[1] (numeric) = 0.61248008274181223103880844492092
absolute error = 3e-32
relative error = 4.8981184605551235164627442779102e-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
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 0.61528416081789190786761417979929
y[1] (numeric) = 0.61528416081789190786761417979928
absolute error = 1e-32
relative error = 1.6252653061484772466159049081793e-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
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 0.6182267093239637759465610709267
y[1] (numeric) = 0.61822670932396377594656107092673
absolute error = 3e-32
relative error = 4.8525887910610102937689759487294e-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
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 0.62130743400762934367016985943879
y[1] (numeric) = 0.62130743400762934367016985943882
absolute error = 3e-32
relative error = 4.8285274500082056070538478123874e-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
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 0.62452602679898750649383620651082
y[1] (numeric) = 0.62452602679898750649383620651082
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
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 0.62788216584144128032022331486818
y[1] (numeric) = 0.62788216584144128032022331486823
absolute error = 5e-32
relative error = 7.9632776212067904219996055558330e-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
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 0.63137551552388319298473488689163
y[1] (numeric) = 0.63137551552388319298473488689166
absolute error = 3e-32
relative error = 4.7515304699624803249327745426371e-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
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 0.63500572651425611532774094218763
y[1] (numeric) = 0.63500572651425611532774094218763
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
bytes used=20007164, alloc=4455632, time=1.81
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 0.63877243579448617579841653804618
y[1] (numeric) = 0.63877243579448617579841653804617
absolute error = 1e-32
relative error = 1.5655027423909262975568119674194e-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
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 0.64267526669678426532784367404728
y[1] (numeric) = 0.64267526669678426532784367404726
absolute error = 2e-32
relative error = 3.1119915510045679172392879804066e-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
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 0.64671382894131250235114022384924
y[1] (numeric) = 0.64671382894131250235114022384921
absolute error = 3e-32
relative error = 4.6388369410796096213879685965478e-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
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 0.65088771867521189136350229748885
y[1] (numeric) = 0.65088771867521189136350229748881
absolute error = 4e-32
relative error = 6.1454531791465097757807699461233e-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
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 0.6551965185129872722768273703436
y[1] (numeric) = 0.65519651851298727227682737034358
absolute error = 2e-32
relative error = 3.0525192724453649566797706618982e-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
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 0.65963979757824552211563652872703
y[1] (numeric) = 0.65963979757824552211563652872706
absolute error = 3e-32
relative error = 4.5479366330139356450836254570644e-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
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 0.66421711154678283526690795869975
y[1] (numeric) = 0.66421711154678283526690795869973
absolute error = 2e-32
relative error = 3.0110636495686454553257250528822e-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
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 0.6689280026910167735917026419351
y[1] (numeric) = 0.66892800269101677359170264193507
absolute error = 3e-32
relative error = 4.4847875824174819856827273295008e-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
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 0.6737719999257586432305976810752
y[1] (numeric) = 0.67377199992575864323059768107522
absolute error = 2e-32
relative error = 2.9683631854995091963985274223468e-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
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 0.67874861885532162090339023143642
y[1] (numeric) = 0.67874861885532162090339023143641
absolute error = 1e-32
relative error = 1.4732994988431123178704677247712e-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
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 0.68385736182195991892969870973167
y[1] (numeric) = 0.68385736182195991892969870973166
absolute error = 1e-32
relative error = 1.4622932439240842854255882469048e-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
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 0.68909771795563414509432505598747
y[1] (numeric) = 0.68909771795563414509432505598747
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
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 0.69446916322509788086286250741244
y[1] (numeric) = 0.69446916322509788086286250741247
absolute error = 3e-32
relative error = 4.3198462348825872443734614153192e-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
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 0.69997116049030036933229933004683
y[1] (numeric) = 0.69997116049030036933229933004686
absolute error = 3e-32
relative error = 4.2858908614158133711250334653787e-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
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 0.70560315955610007269149220888207
y[1] (numeric) = 0.7056031595561000726914922088821
absolute error = 3e-32
relative error = 4.2516816419690087156199244020202e-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
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 0.71136459722728372788052439779159
y[1] (numeric) = 0.71136459722728372788052439779161
absolute error = 2e-32
relative error = 2.8114977998560593241342067605974e-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
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 0.71725489736488539858923175367643
y[1] (numeric) = 0.71725489736488539858923175367644
absolute error = 1e-32
relative error = 1.3942044922577574791066650405764e-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
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 0.72327347094379989173662918911306
y[1] (numeric) = 0.7232734709437998917366291891131
absolute error = 4e-32
relative error = 5.5304116087382523824824379844546e-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
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 0.72941971611168477713760062122081
y[1] (numeric) = 0.72941971611168477713760062122084
absolute error = 3e-32
relative error = 4.1128583910400583786772503587086e-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
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 0.73569301824914512020397060052595
y[1] (numeric) = 0.73569301824914512020397060052592
absolute error = 3e-32
relative error = 4.0777877804788940830566689621729e-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
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 0.74209275003119490925684128939808
y[1] (numeric) = 0.7420927500311949092568412893981
absolute error = 2e-32
relative error = 2.6950809045310403527635978844535e-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
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 0.74861827148998903135868124172911
y[1] (numeric) = 0.74861827148998903135868124172916
absolute error = 5e-32
relative error = 6.6789713668735414680698678448081e-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
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 0.75526893007881952351985924724711
y[1] (numeric) = 0.75526893007881952351985924724713
absolute error = 2e-32
relative error = 2.6480633855695360137468171102714e-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
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 0.76204406073736969970783261865343
y[1] (numeric) = 0.76204406073736969970783261865345
absolute error = 2e-32
relative error = 2.6245201597198439653872845010460e-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
bytes used=24008616, alloc=4455632, time=2.18
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 0.76894298595821962830066726066755
y[1] (numeric) = 0.76894298595821962830066726066758
absolute error = 3e-32
relative error = 3.9014596072575456622490773130695e-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
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 0.7759650158545963094925652154463
y[1] (numeric) = 0.77596501585459630949256521544631
absolute error = 1e-32
relative error = 1.2887178926470885352566601108070e-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
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 0.78310944822936177769011742459983
y[1] (numeric) = 0.78310944822936177769011742459988
absolute error = 5e-32
relative error = 6.3848035690351805118355367188103e-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
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 0.7903755686452322301465319762256
y[1] (numeric) = 0.79037556864523223014653197622563
absolute error = 3e-32
relative error = 3.7956638831109659601897840624702e-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
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 0.79776265049622115997949015961035
y[1] (numeric) = 0.79776265049622115997949015961031
absolute error = 4e-32
relative error = 5.0140226513637055630228655702393e-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
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 0.80526995508029934931886428772418
y[1] (numeric) = 0.80526995508029934931886428772416
absolute error = 2e-32
relative error = 2.4836391664464439021464597887795e-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
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 0.81289673167326445664553230818147
y[1] (numeric) = 0.81289673167326445664553230818152
absolute error = 5e-32
relative error = 6.1508427887365389982472489501841e-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
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 0.82064221760381281142411310546277
y[1] (numeric) = 0.82064221760381281142411310546277
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
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 0.82850563832980590891271884119575
y[1] (numeric) = 0.82850563832980590891271884119576
absolute error = 1e-32
relative error = 1.2069923893528492536085183823267e-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
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 0.83648620751572397856379855775309
y[1] (numeric) = 0.83648620751572397856379855775305
absolute error = 4e-32
relative error = 4.7819078952653375133633494538146e-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
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 0.8445831271112988807237773859903
y[1] (numeric) = 0.84458312711129888072377738599027
absolute error = 3e-32
relative error = 3.5520482279356037951654347981636e-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
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 0.85279558743131846840734858869686
y[1] (numeric) = 0.85279558743131846840734858869686
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
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 0.8611227672365944337767444236884
y[1] (numeric) = 0.8611227672365944337767444236884
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 0.86956383381608554260881087994327
y[1] (numeric) = 0.86956383381608554260881087994326
absolute error = 1e-32
relative error = 1.1500018297811382557143845922614e-30 %
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 0.87811794307016804449487537991282
y[1] (numeric) = 0.87811794307016804449487537991286
absolute error = 4e-32
relative error = 4.5551967495559656862566186023716e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.35
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
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 0.88678423959504493180177923842899
y[1] (numeric) = 0.88678423959504493180177923842898
absolute error = 1e-32
relative error = 1.1276700186469886849886734351772e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.67
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
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 0.89556185676828560653851958962657
y[1] (numeric) = 0.89556185676828560653851958962661
absolute error = 4e-32
relative error = 4.4664698141950292372827266426438e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 0.90444991683548740123309693580203
y[1] (numeric) = 0.90444991683548740123309693580204
absolute error = 1e-32
relative error = 1.1056444158885277847506688142278e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 0.91344753099805028773969832678951
y[1] (numeric) = 0.91344753099805028773969832678949
absolute error = 2e-32
relative error = 2.1895072591796943716816966943488e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.66
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
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 0.9225537995020559965784807983926
y[1] (numeric) = 0.9225537995020559965784807983926
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
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
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 0.93176781172824265897008677742421
y[1] (numeric) = 0.93176781172824265897008677742426
absolute error = 5e-32
relative error = 5.3661437292258481144428705847985e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.35
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
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 0.94108864628306597417566662024709
y[1] (numeric) = 0.94108864628306597417566662024711
absolute error = 2e-32
relative error = 2.1251983093189168815624634705694e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.7
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
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 0.95051537109083779610155833573045
y[1] (numeric) = 0.95051537109083779610155833573044
absolute error = 1e-32
relative error = 1.0520608402706547203275686256139e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.06
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
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 0.96004704348693292538674592421492
y[1] (numeric) = 0.96004704348693292538674592421492
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 = 18.43
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
bytes used=28012144, alloc=4455632, time=2.55
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 0.96968271031205478637155965448357
y[1] (numeric) = 0.96968271031205478637155965448359
absolute error = 2e-32
relative error = 2.0625303294893002048539711290692e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 0.97942140800755056245847587766993
y[1] (numeric) = 0.97942140800755056245847587766999
absolute error = 6e-32
relative error = 6.1260658087981519365420446374042e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 0.98926216271176625843090931282562
y[1] (numeric) = 0.98926216271176625843090931282563
absolute error = 1e-32
relative error = 1.0108543899615034028145123662168e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.41
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 0.99920399035743205430406154253127
y[1] (numeric) = 0.99920399035743205430406154253134
absolute error = 7e-32
relative error = 7.0055765064508823645860245888743e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.03
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
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 1.009245896770068212253594824731
y[1] (numeric) = 1.009245896770068212253594824731
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 = 18.65
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
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 1.0193868777674016961134430024979
y[1] (numeric) = 1.0193868777674016961134430024979
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 = 18.28
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
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 1.0296259192597835618636566374003
y[1] (numeric) = 1.0296259192597835618636566374003
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 = 17.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 1.0399619973515970774529144617567
y[1] (numeric) = 1.0399619973515970774529144617568
absolute error = 1e-31
relative error = 9.6157359840709019008911403935397e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.57
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
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 1.0503940784436464312282253834655
y[1] (numeric) = 1.0503940784436464312282253834656
absolute error = 1e-31
relative error = 9.5202364571750575609447045594885e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.22
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
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 1.0609211193365157901863017124867
y[1] (numeric) = 1.0609211193365157901863017124868
absolute error = 1e-31
relative error = 9.4257714525033213817523788632264e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.87
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 1.0715420673348883722269107330887
y[1] (numeric) = 1.0715420673348883722269107330888
absolute error = 1e-31
relative error = 9.3323447626015659293682456143318e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.54
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
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 1.0822558603528151005879115571391
y[1] (numeric) = 1.0822558603528151005879115571392
absolute error = 1e-31
relative error = 9.2399592058942539367208595232290e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.21
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
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 1.0930614270199223136842573410376
y[1] (numeric) = 1.0930614270199223136842573410378
absolute error = 2e-31
relative error = 1.8297233353597680999839701671377e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.88
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
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 1.1039576867885479096684850959144
y[1] (numeric) = 1.1039576867885479096684850959145
absolute error = 1e-31
relative error = 9.0583181943235115288233869929807e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.56
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 1.1149435500417952121875168649792
y[1] (numeric) = 1.1149435500417952121875168649794
absolute error = 2e-31
relative error = 1.7938127898269174379496633633752e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 1.1260179182024937520392411758875
y[1] (numeric) = 1.1260179182024937520392411758876
absolute error = 1e-31
relative error = 8.8808533490864775777335527750618e-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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 1.137179683843056068741509458687
y[1] (numeric) = 1.1371796838430560687415094586871
absolute error = 1e-31
relative error = 8.7936850632130317798306016079694e-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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 1.14842773079621954642493755919
y[1] (numeric) = 1.1484277307962195464249375591901
absolute error = 1e-31
relative error = 8.7075570641845028105388523373559e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.33
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
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 1.1597609342666622099582076232457
y[1] (numeric) = 1.1597609342666622099582076232458
absolute error = 1e-31
relative error = 8.6224666692391916545532577064503e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.03
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 1.1711781609434813198192706751205
y[1] (numeric) = 1.1711781609434813198192706751206
absolute error = 1e-31
relative error = 8.5384105796031656850544253172223e-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
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 1.1826782691135235179466946196796
y[1] (numeric) = 1.1826782691135235179466946196796
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
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 1.1942601087755551916510140069746
y[1] (numeric) = 1.1942601087755551916510140069747
absolute error = 1e-31
relative error = 8.3733852671783101913220302538852e-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
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 1.2059225217552616386448320770481
y[1] (numeric) = 1.2059225217552616386448320770482
absolute error = 1e-31
relative error = 8.2924067007593959072226937593134e-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
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 1.217664341821063533371004392832
y[1] (numeric) = 1.217664341821063533371004392832
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
bytes used=32014540, alloc=4455632, time=2.92
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 1.229484394800739113078784643007
y[1] (numeric) = 1.2294843948007391130787846430071
absolute error = 1e-31
relative error = 8.1334907887307399199060372558986e-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
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 1.241381498698840421526509831356
y[1] (numeric) = 1.2413814986988404215265098313561
absolute error = 1e-31
relative error = 8.0555413549191322681563612804121e-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
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 1.2533544638148918687843011276872
y[1] (numeric) = 1.2533544638148918687843011276873
absolute error = 1e-31
relative error = 7.9785888898201599887810726844995e-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
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 1.2654020928623592873792985817516
y[1] (numeric) = 1.2654020928623592873792985817517
absolute error = 1e-31
relative error = 7.9026264113249914869786358991413e-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
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 1.2775231810883775879769557263328
y[1] (numeric) = 1.2775231810883775879769557263329
absolute error = 1e-31
relative error = 7.8276466118450898566584531975853e-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
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 1.2897165163942250419325986538757
y[1] (numeric) = 1.2897165163942250419325986538758
absolute error = 1e-31
relative error = 7.7536418839993518414010930543888e-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
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 1.3019808794565321433853893115545
y[1] (numeric) = 1.3019808794565321433853893115546
absolute error = 1e-31
relative error = 7.6806043451069431840966328378021e-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
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 1.3143150438492129301094906668387
y[1] (numeric) = 1.3143150438492129301094906668388
absolute error = 1e-31
relative error = 7.6085258605221194749516208807010e-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
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 1.3267177761661065700919577223859
y[1] (numeric) = 1.326717776166106570091957722386
absolute error = 1e-31
relative error = 7.5373980658475692722340551246979e-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
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 1.3391878361443169497808975726373
y[1] (numeric) = 1.3391878361443169497808975726373
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
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 1.3517239767882379301478563337071
y[1] (numeric) = 1.3517239767882379301478563337072
absolute error = 1e-31
relative error = 7.3979600656048785440579557244744e-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
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 1.3643249444942518681421807434129
y[1] (numeric) = 1.364324944494251868142180743413
absolute error = 1e-31
relative error = 7.3296321674357040916565415608896e-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
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 1.3769894791760889337891240834453
y[1] (numeric) = 1.3769894791760889337891240834454
absolute error = 1e-31
relative error = 7.2622196111356080243026050530038e-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
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 1.3897163143908346871044523624493
y[1] (numeric) = 1.3897163143908346871044523624494
absolute error = 1e-31
relative error = 7.1957131800552970199784990833319e-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
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 1.402504177465573314172865263472
y[1] (numeric) = 1.4025041774655733141728652634721
absolute error = 1e-31
relative error = 7.1301035395635859590667757022759e-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
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 1.4153517896246538581721596919631
y[1] (numeric) = 1.4153517896246538581721596919632
absolute error = 1e-31
relative error = 7.0653812524248572813409339493135e-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
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 1.428257866117566718826088346975
y[1] (numeric) = 1.4282578661175667188260883469751
absolute error = 1e-31
relative error = 7.0015367933404067052880744792473e-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
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 1.4412211163474176327425314240392
y[1] (numeric) = 1.4412211163474176327425314240393
absolute error = 1e-31
relative error = 6.9385605626870524666046992747490e-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
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 1.4542402439999862873460089259574
y[1] (numeric) = 1.4542402439999862873460089259575
absolute error = 1e-31
relative error = 6.8764428994856604272891859433392e-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
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 1.4673139471733566626506888167261
y[1] (numeric) = 1.4673139471733566626506888167262
absolute error = 1e-31
relative error = 6.8151740936314729677578773954084e-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
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 1.4804409185081061379477386425052
y[1] (numeric) = 1.4804409185081061379477386425053
absolute error = 1e-31
relative error = 6.7547443974173327404641175952158e-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
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 1.4936198453180403446048424450727
y[1] (numeric) = 1.4936198453180403446048424450728
absolute error = 1e-31
relative error = 6.6951440363800697114402807262858e-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
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 1.5068494097214606916015483635891
y[1] (numeric) = 1.5068494097214606916015483635891
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
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 1.5201282887729514371572826298917
y[1] (numeric) = 1.5201282887729514371572826298918
absolute error = 1e-31
relative error = 6.5783921487784472664306570506797e-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
TOP MAIN SOLVE Loop
bytes used=36015800, alloc=4521156, time=3.29
x[1] = 2.02
y[1] (analytic) = 1.5334551545956731278546893495365
y[1] (numeric) = 1.5334551545956731278546893495366
absolute error = 1e-31
relative error = 6.5212210282319634583074953665302e-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
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 1.5468286745141491760246278997285
y[1] (numeric) = 1.5468286745141491760246278997286
absolute error = 1e-31
relative error = 6.4648400723117884247922198352298e-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
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 1.5602475111875322968457445567072
y[1] (numeric) = 1.5602475111875322968457445567072
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
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 1.5737103227433374786259633894871
y[1] (numeric) = 1.5737103227433374786259633894871
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
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 1.587215762911628113080312041288
y[1] (numeric) = 1.587215762911628113080312041288
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
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 1.6007624811596418671038760185679
y[1] (numeric) = 1.6007624811596418671038760185679
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
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 1.6143491228268428335648920447478
y[1] (numeric) = 1.6143491228268428335648920447477
absolute error = 1e-31
relative error = 6.1944469499195267202933663818424e-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
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 1.6279743292603864560154442531429
y[1] (numeric) = 1.6279743292603864560154442531429
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
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 1.6416367379509836809401792104502
y[1] (numeric) = 1.6416367379509836809401792104501
absolute error = 1e-31
relative error = 6.0914816102870268526829592852521e-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
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 1.655334982669150751241034648761
y[1] (numeric) = 1.655334982669150751241034648761
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
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 1.6690676936018310160921745493298
y[1] (numeric) = 1.6690676936018310160921745493297
absolute error = 1e-31
relative error = 5.9913687373698440312485383932696e-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
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 1.6828334974893750950979962132938
y[1] (numeric) = 1.6828334974893750950979962132938
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
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 1.6966310177628656988519432749397
y[1] (numeric) = 1.6966310177628656988519432749397
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
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 1.7104588746817733735285057452202
y[1] (numeric) = 1.7104588746817733735285057452202
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
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 1.7243156854719294040486606236371
y[1] (numeric) = 1.724315685471929404048660623637
absolute error = 1e-31
relative error = 5.7994020957149105937238567582193e-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
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 1.7382000644638020786434135704731
y[1] (numeric) = 1.7382000644638020786434135704731
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
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 1.7521106232310624873042151215786
y[1] (numeric) = 1.7521106232310624873042151215785
absolute error = 1e-31
relative error = 5.7074021853477646856365372782358e-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
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 1.766045970729425997655877517892
y[1] (numeric) = 1.7660459707294259976558775178919
absolute error = 1e-31
relative error = 5.6623667592694217792792924702701e-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
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 1.7800047134357555242201057022388
y[1] (numeric) = 1.7800047134357555242201057022388
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
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 1.7939854554874126808586351349626
y[1] (numeric) = 1.7939854554874126808586351349627
absolute error = 1e-31
relative error = 5.5741812005287821006656160831340e-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
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 1.807986798821842881396857687891
y[1] (numeric) = 1.807986798821842881396857687891
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
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 1.8220073433163804300341937834971
y[1] (numeric) = 1.8220073433163804300341937834971
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
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 1.8360456869282596211486735957059
y[1] (numeric) = 1.836045686928259621148673595706
absolute error = 1e-31
relative error = 5.4464875635693988486352444323244e-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
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 1.8501004258348178475024223818086
y[1] (numeric) = 1.8501004258348178475024223818087
absolute error = 1e-31
relative error = 5.4051119930355759150017557986075e-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
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 1.8641701545738766966540649310045
y[1] (numeric) = 1.8641701545738766966540649310046
absolute error = 1e-31
relative error = 5.3643171871753630558442989244401e-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
TOP MAIN SOLVE Loop
bytes used=40016880, alloc=4521156, time=3.65
x[1] = 2.27
y[1] (analytic) = 1.8782534661842869975853917461896
y[1] (numeric) = 1.8782534661842869975853917461897
absolute error = 1e-31
relative error = 5.3240950596062089239908552635253e-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
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 1.8923489523466237631547447741598
y[1] (numeric) = 1.8923489523466237631547447741599
absolute error = 1e-31
relative error = 5.2844376231980962594104898859920e-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
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 1.9064552035240169590001227402154
y[1] (numeric) = 1.9064552035240169590001227402154
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
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 1.9205708091031040159324743595225
y[1] (numeric) = 1.9205708091031040159324743595226
absolute error = 1e-31
relative error = 5.2067853747448889387786839429134e-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
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 1.9346943575350899906854001313727
y[1] (numeric) = 1.9346943575350899906854001313729
absolute error = 2e-31
relative error = 1.0337550177941869280789569541256e-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
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 1.9488244364769012691227374882835
y[1] (numeric) = 1.9488244364769012691227374882837
absolute error = 2e-31
relative error = 1.0262597094767624527574428059977e-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
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 1.9629596329324186966513362353406
y[1] (numeric) = 1.9629596329324186966513362353407
absolute error = 1e-31
relative error = 5.0943482648500712675891137698272e-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
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 1.9770985333937760126436768852674
y[1] (numeric) = 1.9770985333937760126436768852675
absolute error = 1e-31
relative error = 5.0579168569988077917246479543899e-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
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 1.9912397239827094591446379302457
y[1] (numeric) = 1.9912397239827094591446379302459
absolute error = 2e-31
relative error = 1.0043994080229420980552526169725e-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
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 2.0053817905919444290193323217124
y[1] (numeric) = 2.0053817905919444290193323217126
absolute error = 2e-31
relative error = 9.9731632618926102682035409101823e-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 = 0.00367
Order of pole (three term test) = -0.8932
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 2.0195233190266050149950201885332
y[1] (numeric) = 2.0195233190266050149950201885333
absolute error = 1e-31
relative error = 4.9516635464352669438509191471921e-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 = 0.01331
Order of pole (three term test) = -0.8975
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 2.0336628951456323187600345003473
y[1] (numeric) = 2.0336628951456323187600345003475
absolute error = 2e-31
relative error = 9.8344716067447270291716874023276e-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 = 0.02295
Order of pole (three term test) = -0.9066
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 2.047799105003197378406657981605
y[1] (numeric) = 2.0477991050031973784066579816052
absolute error = 2e-31
relative error = 9.7665830359705975837380568920863e-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 = 0.03257
Order of pole (three term test) = -0.9205
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 2.0619305349900945730430507019935
y[1] (numeric) = 2.0619305349900945730430507019937
absolute error = 2e-31
relative error = 9.6996478109268987341997287752460e-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 = 0.04219
Order of pole (three term test) = -0.9392
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 2.0760557719751013653515945949133
y[1] (numeric) = 2.0760557719751013653515945949134
absolute error = 1e-31
relative error = 4.8168262794242178950943045893511e-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 = 0.05178
Order of pole (three term test) = -0.9628
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 2.0901734034462902462371984623505
y[1] (numeric) = 2.0901734034462902462371984623507
absolute error = 2e-31
relative error = 9.5685841026509484508480110670117e-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 = 0.06136
Order of pole (three term test) = -0.9912
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 2.104282017652278750488858196988
y[1] (numeric) = 2.1042820176522787504888581969882
absolute error = 2e-31
relative error = 9.5044294596566248315496976832314e-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 = 0.07091
Order of pole (three term test) = -1.024
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 2.1183802037434034185706140195549
y[1] (numeric) = 2.1183802037434034185706140195551
absolute error = 2e-31
relative error = 9.4411758402282414102828717475271e-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 = 0.08043
Order of pole (three term test) = -1.062
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 2.1324665519128035872633702117027
y[1] (numeric) = 2.1324665519128035872633702117029
absolute error = 2e-31
relative error = 9.3788106463194826439158944393724e-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 = 0.08992
Order of pole (three term test) = -1.105
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 2.1465396535374009008960825960703
y[1] (numeric) = 2.1465396535374009008960825960705
absolute error = 2e-31
relative error = 9.3173214699485745060732980065317e-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 = 0.09938
Order of pole (three term test) = -1.152
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 2.1605981013187604453326731792058
y[1] (numeric) = 2.160598101318760445332673179206
absolute error = 2e-31
relative error = 9.2566960916019667609305844681363e-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 = 0.1088
Order of pole (three term test) = -1.205
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 2.1746404894238194187186571529247
y[1] (numeric) = 2.174640489423819418718657152925
absolute error = 3e-31
relative error = 1.3795383717861627882021402701993e-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 = 0.1182
Order of pole (three term test) = -1.262
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 2.1886654136254692662376810927798
y[1] (numeric) = 2.18866541362546926623768109278
absolute error = 2e-31
relative error = 9.1379887832514804129412796148077e-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 = 0.1275
Order of pole (three term test) = -1.323
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 2.2026714714429772207816480882812
y[1] (numeric) = 2.2026714714429772207816480882814
absolute error = 2e-31
relative error = 9.0798833413400207027204072317109e-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 = 0.1368
Order of pole (three term test) = -1.389
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=44018456, alloc=4521156, time=4.03
x[1] = 2.51
y[1] (analytic) = 2.2166572622822332074973803528544
y[1] (numeric) = 2.2166572622822332074973803528546
absolute error = 2e-31
relative error = 9.0225946700521193006708595042928e-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 = 0.146
Order of pole (three term test) = -1.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 2.2306213875758080876362366781547
y[1] (numeric) = 2.230621387575808087636236678155
absolute error = 3e-31
relative error = 1.3449167199371006817406695786482e-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 = 0.1551
Order of pole (three term test) = -1.536
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 2.2445624509228092359990145851528
y[1] (numeric) = 2.2445624509228092359990145851531
absolute error = 3e-31
relative error = 1.3365633906807123849825071044416e-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 = 0.1642
Order of pole (three term test) = -1.616
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 2.2584790582285194665349386078246
y[1] (numeric) = 2.2584790582285194665349386078248
absolute error = 2e-31
relative error = 8.8555171353624931191794807193730e-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 = 0.1733
Order of pole (three term test) = -1.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 2.2723698178438053423185401940661
y[1] (numeric) = 2.2723698178438053423185401940663
absolute error = 2e-31
relative error = 8.8013842830290263982069398022494e-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 = 0.1822
Order of pole (three term test) = -1.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 2.2862333407042809291896047402451
y[1] (numeric) = 2.2862333407042809291896047402454
absolute error = 3e-31
relative error = 1.3122020165604973394764244959145e-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 = 0.1911
Order of pole (three term test) = -1.883
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 2.3000682404692130767967911728213
y[1] (numeric) = 2.3000682404692130767967911728215
absolute error = 2e-31
relative error = 8.6953941835743131434935924012761e-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 = 0.1999
Order of pole (three term test) = -1.981
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 2.3138731336601543366325737300976
y[1] (numeric) = 2.3138731336601543366325737300978
absolute error = 2e-31
relative error = 8.6435162365031640966455585864638e-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 = 0.2087
Order of pole (three term test) = -2.084
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 2.3276466397992896538832294965324
y[1] (numeric) = 2.3276466397992896538832294965326
absolute error = 2e-31
relative error = 8.5923695023247074378844613403058e-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 = 0.2173
Order of pole (three term test) = -2.191
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 2.3413873815474829985399752164358
y[1] (numeric) = 2.341387381547482998539975216436
absolute error = 2e-31
relative error = 8.5419440446379645287244004630221e-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 = 0.2259
Order of pole (three term test) = -2.302
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 2.3550939848420101312231807491671
y[1] (numeric) = 2.3550939848420101312231807491673
absolute error = 2e-31
relative error = 8.4922300887884465117642609748298e-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 = 0.2343
Order of pole (three term test) = -2.417
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 2.3687650790339637305578536667508
y[1] (numeric) = 2.3687650790339637305578536667509
absolute error = 1e-31
relative error = 4.2216090099057975892538696529306e-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 = 0.2427
Order of pole (three term test) = -2.537
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 2.3823992970253171417021613365833
y[1] (numeric) = 2.3823992970253171417021613365835
absolute error = 2e-31
relative error = 8.3948983803731642757149654666691e-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 = 0.251
Order of pole (three term test) = -2.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 2.3959952754056330397683570467331
y[1] (numeric) = 2.3959952754056330397683570467333
absolute error = 2e-31
relative error = 8.3472618687088499347951062704016e-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 = 0.2592
Order of pole (three term test) = -2.788
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 2.4095516545884033373836915876564
y[1] (numeric) = 2.4095516545884033373836915876566
absolute error = 2e-31
relative error = 8.3002993365653227739774874030733e-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 = 0.2673
Order of pole (three term test) = -2.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 2.4230670789470067025141704100862
y[1] (numeric) = 2.4230670789470067025141704100864
absolute error = 2e-31
relative error = 8.2540017871446664857909723581547e-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 = 0.2752
Order of pole (three term test) = -3.056
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 2.4365401969502700909126715372384
y[1] (numeric) = 2.4365401969502700909126715372386
absolute error = 2e-31
relative error = 8.2083603730540879786306309562712e-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 = 0.2831
Order of pole (three term test) = -3.196
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 2.4499696612976207371511469866912
y[1] (numeric) = 2.4499696612976207371511469866914
absolute error = 2e-31
relative error = 8.1633663942626320041212357933867e-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 = 0.2908
Order of pole (three term test) = -3.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 2.4633541290538150891504307655679
y[1] (numeric) = 2.4633541290538150891504307655681
absolute error = 2e-31
relative error = 8.1190112960665083015714572563229e-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 = 0.2985
Order of pole (three term test) = -3.488
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 2.4766922617832312134264741960854
y[1] (numeric) = 2.4766922617832312134264741960857
absolute error = 3e-31
relative error = 1.2112930000596781909790382187759e-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 = 0.306
Order of pole (three term test) = -3.639
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 2.4899827256837112419243939126075
y[1] (numeric) = 2.4899827256837112419243939126077
absolute error = 2e-31
relative error = 8.0321842371449807306820029098578e-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 = 0.3134
Order of pole (three term test) = -3.795
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 2.5032241917199404763071841259797
y[1] (numeric) = 2.5032241917199404763071841259799
absolute error = 2e-31
relative error = 7.9896958754853670019736240257554e-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 = 0.3206
Order of pole (three term test) = -3.954
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 2.5164153357563498118998131669984
y[1] (numeric) = 2.5164153357563498118998131669986
absolute error = 2e-31
relative error = 7.9478135885659243478077850938922e-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 = 0.3277
Order of pole (three term test) = -4.116
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 2.529554838689528191157061550139
y[1] (numeric) = 2.5295548386895281911570615501393
absolute error = 3e-31
relative error = 1.1859794277297394374369462716706e-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 = 0.3347
Order of pole (three term test) = -4.282
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 2.5426413865801318455200981171489
y[1] (numeric) = 2.5426413865801318455200981171492
absolute error = 3e-31
relative error = 1.1798753909354941617287293406282e-29 %
Correct digits = 31
h = 0.01
bytes used=48019912, alloc=4521156, time=4.40
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3416
Order of pole (three term test) = -4.452
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 2.5556736707842771348475326046904
y[1] (numeric) = 2.5556736707842771348475326046906
absolute error = 2e-31
relative error = 7.8257252593060766696115259692610e-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 = 0.3483
Order of pole (three term test) = -4.625
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 2.5686503880844038452464951986566
y[1] (numeric) = 2.5686503880844038452464951986569
absolute error = 3e-31
relative error = 1.1679285020322595740715097308078e-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 = 0.3549
Order of pole (three term test) = -4.801
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 2.5815702408195958590830123518903
y[1] (numeric) = 2.5815702408195958590830123518905
absolute error = 2e-31
relative error = 7.7472228660531848320305950099490e-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 = 0.3614
Order of pole (three term test) = -4.981
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 2.5944319370153461652132780240618
y[1] (numeric) = 2.594431937015346165213278024062
absolute error = 2e-31
relative error = 7.7088166063081034400482461491237e-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 = 0.3677
Order of pole (three term test) = -5.163
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 2.6072341905127532330429343646538
y[1] (numeric) = 2.6072341905127532330429343646539
absolute error = 1e-31
relative error = 3.8354820738344736750951992272932e-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 = 0.3738
Order of pole (three term test) = -5.349
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 2.6199757210971358308846191971525
y[1] (numeric) = 2.6199757210971358308846191971527
absolute error = 2e-31
relative error = 7.6336585255167325409098610229342e-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 = 0.3798
Order of pole (three term test) = -5.538
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 2.6326552546260534272391232077354
y[1] (numeric) = 2.6326552546260534272391232077357
absolute error = 3e-31
relative error = 1.1395339343153476467172084573210e-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 = 0.3857
Order of pole (three term test) = -5.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 2.6452715231567193730667120348564
y[1] (numeric) = 2.6452715231567193730667120348567
absolute error = 3e-31
relative error = 1.1340990797118503223050890339480e-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 = 0.3914
Order of pole (three term test) = -5.925
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 2.6578232650727941238365634254889
y[1] (numeric) = 2.6578232650727941238365634254892
absolute error = 3e-31
relative error = 1.1287432236085246721628645437893e-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 = 0.3969
Order of pole (three term test) = -6.122
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 2.6703092252105458221377751804832
y[1] (numeric) = 2.6703092252105458221377751804835
absolute error = 3e-31
relative error = 1.1234653918268432209136676166267e-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 = 0.4023
Order of pole (three term test) = -6.323
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 2.6827281549843656248988162566396
y[1] (numeric) = 2.6827281549843656248988162566398
absolute error = 2e-31
relative error = 7.4550975143870124220453596875746e-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 = 0.4075
Order of pole (three term test) = -6.526
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 2.6950788125116252237872948377508
y[1] (numeric) = 2.6950788125116252237872948377511
absolute error = 3e-31
relative error = 1.1131399891063703349565965641007e-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 = 0.4126
Order of pole (three term test) = -6.731
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 2.7073599627368640731420509846478
y[1] (numeric) = 2.7073599627368640731420509846481
absolute error = 3e-31
relative error = 1.1080905536356188018554392796205e-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 = 0.4175
Order of pole (three term test) = -6.939
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 2.7195703775552939068182696666288
y[1] (numeric) = 2.7195703775552939068182696666291
absolute error = 3e-31
relative error = 1.1031154129192982942572308016503e-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 = 0.4222
Order of pole (three term test) = -7.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 2.7317088359356081935968497506059
y[1] (numeric) = 2.7317088359356081935968497506063
absolute error = 4e-31
relative error = 1.4642849001255300511126432983314e-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 = 0.4268
Order of pole (three term test) = -7.363
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 2.7437741240420842503148288827758
y[1] (numeric) = 2.7437741240420842503148288827761
absolute error = 3e-31
relative error = 1.0933844640171939075134872137335e-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 = 0.4312
Order of pole (three term test) = -7.578
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 2.7557650353559658026073026420937
y[1] (numeric) = 2.755765035355965802607302642094
absolute error = 3e-31
relative error = 1.0886269190263117062260294953674e-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 = 0.4354
Order of pole (three term test) = -7.795
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 2.7676803707961138551059155704172
y[1] (numeric) = 2.7676803707961138551059155704175
absolute error = 3e-31
relative error = 1.0839401947042967945354562563950e-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 = 0.4394
Order of pole (three term test) = -8.014
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 2.7795189388389138061074462869052
y[1] (numeric) = 2.7795189388389138061074462869055
absolute error = 3e-31
relative error = 1.0793234606464626461228362038554e-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 = 0.4433
Order of pole (three term test) = -8.235
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 2.7912795556374268161009420906446
y[1] (numeric) = 2.7912795556374268161009420906449
absolute error = 3e-31
relative error = 1.0747759012317592887093743901530e-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 = 0.447
Order of pole (three term test) = -8.459
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 2.8029610451397735151158428141748
y[1] (numeric) = 2.8029610451397735151158428141751
absolute error = 3e-31
relative error = 1.0702967153974131901900772770055e-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 = 0.4505
Order of pole (three term test) = -8.684
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 2.8145622392067382106190118761381
y[1] (numeric) = 2.8145622392067382106190118761385
absolute error = 4e-31
relative error = 1.4211801552227773484820043681157e-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 = 0.4538
Order of pole (three term test) = -8.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 2.8260819777285818356378880098541
y[1] (numeric) = 2.8260819777285818356378880098544
absolute error = 3e-31
relative error = 1.0615403316825232336631170325852e-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 = 0.457
Order of pole (three term test) = -9.138
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 2.8375191087410519559122891516003
y[1] (numeric) = 2.8375191087410519559122891516007
absolute error = 4e-31
relative error = 1.4096821366516599666963978405083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.96
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4599
Order of pole (three term test) = -9.368
NO COMPLEX POLE (six term test) for Equation 1
bytes used=52022856, alloc=4521156, time=4.78
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 2.8488724885405782351708279919232
y[1] (numeric) = 2.8488724885405782351708279919235
absolute error = 3e-31
relative error = 1.0530481838226608165550512193167e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.26
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4627
Order of pole (three term test) = -9.599
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = 2.8601409817986418390814074494976
y[1] (numeric) = 2.8601409817986418390814074494979
absolute error = 3e-31
relative error = 1.0488993441551981660069820225772e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4653
Order of pole (three term test) = -9.832
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 2.8713234616753073410307085369239
y[1] (numeric) = 2.8713234616753073410307085369243
absolute error = 4e-31
relative error = 1.3930858203158180926572178613410e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.86
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4677
Order of pole (three term test) = -10.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 2.8824188099319057766367022757911
y[1] (numeric) = 2.8824188099319057766367022757915
absolute error = 4e-31
relative error = 1.3877233891956512545900160900929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.17
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4699
Order of pole (three term test) = -10.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 2.8934259170428575787826366422344
y[1] (numeric) = 2.8934259170428575787826366422347
absolute error = 3e-31
relative error = 1.0368331818448848988534967289263e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.472
Order of pole (three term test) = -10.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 2.9043436823066242109721806128685
y[1] (numeric) = 2.9043436823066242109721806128688
absolute error = 3e-31
relative error = 1.0329356054781387731733306817433e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4738
Order of pole (three term test) = -10.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 2.9151710139557774039348491829575
y[1] (numeric) = 2.9151710139557774039348491829577
absolute error = 2e-31
relative error = 6.8606609712617690835999971602896e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.13
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4755
Order of pole (three term test) = -11.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 2.9259068292661749886497728724079
y[1] (numeric) = 2.9259068292661749886497728724081
absolute error = 2e-31
relative error = 6.8354876511963478355951263558810e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4769
Order of pole (three term test) = -11.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 2.9365500546652324082954889002241
y[1] (numeric) = 2.9365500546652324082954889002243
absolute error = 2e-31
relative error = 6.8107131251607444609693080491456e-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
Radius of convergence (three term test) for eq 1 = 0.4782
Order of pole (three term test) = -11.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 2.9470996258392790820647850075112
y[1] (numeric) = 2.9470996258392790820647850075114
absolute error = 2e-31
relative error = 6.7863331882797726972513752618410e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.13
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4793
Order of pole (three term test) = -11.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 2.9575544878399888852976777829448
y[1] (numeric) = 2.957554487839988885297677782945
absolute error = 2e-31
relative error = 6.7623437141158936293774635250370e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4802
Order of pole (three term test) = -11.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 2.9679135951898741029732039640134
y[1] (numeric) = 2.9679135951898741029732039640137
absolute error = 3e-31
relative error = 1.0108110980259427496867424067419e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = -12.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 2.9781759119868323072525868697737
y[1] (numeric) = 2.9781759119868323072525868697739
absolute error = 2e-31
relative error = 6.7155200334211916439807628821886e-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
Radius of convergence (three term test) for eq 1 = 0.4814
Order of pole (three term test) = -12.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 2.9883404120077357044731457560209
y[1] (numeric) = 2.9883404120077357044731457560211
absolute error = 2e-31
relative error = 6.6926779558433476825730718059629e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -12.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 2.9984060788110525927445728700206
y[1] (numeric) = 2.9984060788110525927445728700208
absolute error = 2e-31
relative error = 6.6702105966682570209957684495449e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.94
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 3.0083719058384906680873361733658
y[1] (numeric) = 3.008371905838490668087336173366
absolute error = 2e-31
relative error = 6.6481142046251154173848653294643e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -13.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 3.0182368965156520148672963654614
y[1] (numeric) = 3.0182368965156520148672963654615
absolute error = 1e-31
relative error = 3.3131925501090771855347893052905e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -13.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 3.028000064351689715111373625032
y[1] (numeric) = 3.0280000643516897151113736250322
absolute error = 2e-31
relative error = 6.6050196746881847200330490539139e-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
Radius of convergence (three term test) for eq 1 = 0.481
Order of pole (three term test) = -13.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 3.0376604330379561111263794005864
y[1] (numeric) = 3.0376604330379561111263794005866
absolute error = 2e-31
relative error = 6.5840143889941158601494212398467e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4804
Order of pole (three term test) = -13.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 3.0472170365456328566769579781507
y[1] (numeric) = 3.0472170365456328566769579781508
absolute error = 1e-31
relative error = 3.2816828864071124837272018405310e-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
Radius of convergence (three term test) for eq 1 = 0.4795
Order of pole (three term test) = -14.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 3.0566689192223329937988781369027
y[1] (numeric) = 3.0566689192223329937988781369028
absolute error = 1e-31
relative error = 3.2715352117834747355723458512057e-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
Radius of convergence (three term test) for eq 1 = 0.4785
Order of pole (three term test) = -14.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 3.0660151358876653951204950258811
y[1] (numeric) = 3.0660151358876653951204950258812
absolute error = 1e-31
relative error = 3.2615625027254876327634271073866e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4773
Order of pole (three term test) = -14.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 3.0752547519277520153277868853919
y[1] (numeric) = 3.075254751927752015327786885392
absolute error = 1e-31
relative error = 3.2517631242521963697005094532748e-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
Radius of convergence (three term test) for eq 1 = 0.4758
Order of pole (three term test) = -14.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=56023544, alloc=4521156, time=5.15
x[1] = 3.23
y[1] (analytic) = 3.0843868433886885001265842231147
y[1] (numeric) = 3.0843868433886885001265842231148
absolute error = 1e-31
relative error = 3.2421354738413463091877851927773e-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
Radius of convergence (three term test) for eq 1 = 0.4742
Order of pole (three term test) = -15.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 3.0934104970689388067189788031801
y[1] (numeric) = 3.0934104970689388067189788031802
absolute error = 1e-31
relative error = 3.2326779809776869188288270702613e-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
Radius of convergence (three term test) for eq 1 = 0.4724
Order of pole (three term test) = -15.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 3.1023248106106545964088600677324
y[1] (numeric) = 3.1023248106106545964088600677325
absolute error = 1e-31
relative error = 3.2233891067104680847306259766689e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4705
Order of pole (three term test) = -15.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 3.1111288925899102674734176775078
y[1] (numeric) = 3.1111288925899102674734176775078
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 = 15.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4683
Order of pole (three term test) = -15.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 3.1198218626058446048725186312483
y[1] (numeric) = 3.1198218626058446048725186312484
absolute error = 1e-31
relative error = 3.2053112133932727388613636904586e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4659
Order of pole (three term test) = -16.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 3.128402851368700132705272486717
y[1] (numeric) = 3.128402851368700132705272486717
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 = 15.11
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4634
Order of pole (three term test) = -16.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 3.1368710007867513655519049092821
y[1] (numeric) = 3.1368710007867513655519049092822
absolute error = 1e-31
relative error = 3.1878900973268977629933357599924e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4607
Order of pole (three term test) = -16.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 3.1452254640521132659482453287053
y[1] (numeric) = 3.1452254640521132659482453287054
absolute error = 1e-31
relative error = 3.1794223066974094419862849859685e-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 = 0.4577
Order of pole (three term test) = -16.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 3.1534654057254213272185880649025
y[1] (numeric) = 3.1534654057254213272185880649026
absolute error = 1e-31
relative error = 3.1711145401639837813638803171833e-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 = 0.4546
Order of pole (three term test) = -16.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 3.1615900018193748137292101370396
y[1] (numeric) = 3.1615900018193748137292101370397
absolute error = 1e-31
relative error = 3.1629654680857986932744207984064e-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 = 0.4514
Order of pole (three term test) = -17.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 3.1695984398811348043081395389952
y[1] (numeric) = 3.1695984398811348043081395389953
absolute error = 1e-31
relative error = 3.1549737891639726377615412111293e-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 = 0.4479
Order of pole (three term test) = -17.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 3.1774899190735687990954968116626
y[1] (numeric) = 3.1774899190735687990954968116627
absolute error = 1e-31
relative error = 3.1471382300767792993982191143252e-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 = 0.4443
Order of pole (three term test) = -17.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 3.185263650255333765431428491297
y[1] (numeric) = 3.1852636502553337654314284912971
absolute error = 1e-31
relative error = 3.1394575451229572420454572127086e-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 = 0.4404
Order of pole (three term test) = -17.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 3.1929188560597896145437792896838
y[1] (numeric) = 3.1929188560597896145437792896839
absolute error = 1e-31
relative error = 3.1319305158730106737413601429584e-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 = 0.4364
Order of pole (three term test) = -18.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 3.2004547709727352177535952502794
y[1] (numeric) = 3.2004547709727352177535952502795
absolute error = 1e-31
relative error = 3.1245559508283987987081116103383e-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 = 0.4323
Order of pole (three term test) = -18.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 3.2078706414089591886616171275802
y[1] (numeric) = 3.2078706414089591886616171275803
absolute error = 1e-31
relative error = 3.1173326850885126306805653606183e-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 = 0.4279
Order of pole (three term test) = -18.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 3.2151657257875977763013374462304
y[1] (numeric) = 3.2151657257875977763013374462305
absolute error = 1e-31
relative error = 3.1102595800253395868270867557882e-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 = 0.4234
Order of pole (three term test) = -18.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 3.2223392946062923335321039691294
y[1] (numeric) = 3.2223392946062923335321039691295
absolute error = 1e-31
relative error = 3.1033355229657176703404104053729e-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 = 0.4187
Order of pole (three term test) = -18.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 3.2293906305141389449872279485271
y[1] (numeric) = 3.2293906305141389449872279485271
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 = 0.4139
Order of pole (three term test) = -19.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = 3.2363190283834229196750935032676
y[1] (numeric) = 3.2363190283834229196750935032676
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 = 0.4089
Order of pole (three term test) = -19.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 3.243123795380130974843786555817
y[1] (numeric) = 3.2431237953801309748437865558169
absolute error = 1e-31
relative error = 3.0834468959356780660816319591105e-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 = 0.4037
Order of pole (three term test) = -19.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 3.2498042510332340599496168235328
y[1] (numeric) = 3.2498042510332340599496168235328
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 = 0.3984
Order of pole (three term test) = -19.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 3.2563597273027338925048715061677
y[1] (numeric) = 3.2563597273027338925048715061676
absolute error = 1e-31
relative error = 3.0709137925259478907815771584411e-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 = 0.3929
Order of pole (three term test) = -19.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 3.2627895686464664012079211517569
y[1] (numeric) = 3.2627895686464664012079211517569
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 = 0.3872
Order of pole (three term test) = -20.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 3.269093132085655396067034040684
y[1] (numeric) = 3.2690931320856553960670340406839
absolute error = 1e-31
relative error = 3.0589523136711861129144253470793e-30 %
bytes used=60024792, alloc=4521156, time=5.52
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 = 0.3814
Order of pole (three term test) = -20.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 3.275269787269209910205514582825
y[1] (numeric) = 3.275269787269209910205514582825
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 = 0.3754
Order of pole (three term test) = -20.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 3.2813189165367587836675661535043
y[1] (numeric) = 3.2813189165367587836675661535042
absolute error = 1e-31
relative error = 3.0475550394090977970294951458743e-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 = 0.3693
Order of pole (three term test) = -20.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 3.2872399149804161858190264267154
y[1] (numeric) = 3.2872399149804161858190264267153
absolute error = 1e-31
relative error = 3.0420657629607710730867434545865e-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 = 0.3631
Order of pole (three term test) = -20.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 3.293032190505271899842206229175
y[1] (numeric) = 3.2930321905052718998422062291749
absolute error = 1e-31
relative error = 3.0367149245709721655599251545516e-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 = 0.3567
Order of pole (three term test) = -21.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 3.2986951638886003203467908337052
y[1] (numeric) = 3.2986951638886003203467908337051
absolute error = 1e-31
relative error = 3.0315017008760826249981292062951e-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 = 0.3501
Order of pole (three term test) = -21.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 3.3042282688377822432463832686906
y[1] (numeric) = 3.3042282688377822432463832686905
absolute error = 1e-31
relative error = 3.0264252909855302499035923843293e-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 = 0.3434
Order of pole (three term test) = -21.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 3.3096309520469336557699699866143
y[1] (numeric) = 3.3096309520469336557699699866141
absolute error = 2e-31
relative error = 6.0429698325217926998804877627289e-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 = 0.3366
Order of pole (three term test) = -21.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 3.3149026732522358637764982461474
y[1] (numeric) = 3.3149026732522358637764982461472
absolute error = 2e-31
relative error = 6.0333596402026764179689130920707e-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 = 0.3297
Order of pole (three term test) = -21.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 3.3200429052859614234059420357896
y[1] (numeric) = 3.3200429052859614234059420357894
absolute error = 2e-31
relative error = 6.0240185354705116634548655515815e-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 = 0.3226
Order of pole (three term test) = -21.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 3.325051134129190474518712892103
y[1] (numeric) = 3.3250511341291904745187128921028
absolute error = 2e-31
relative error = 6.0149450920362677313809488567285e-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 = 0.3154
Order of pole (three term test) = -22.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 3.3299268589632122043340018028928
y[1] (numeric) = 3.3299268589632122043340018028926
absolute error = 2e-31
relative error = 6.0061379264729828033682016062014e-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 = 0.308
Order of pole (three term test) = -22.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 3.3346695922196063011635227713918
y[1] (numeric) = 3.3346695922196063011635227713917
absolute error = 1e-31
relative error = 2.9987978489178741689446565912956e-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 = 0.3005
Order of pole (three term test) = -22.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 3.3392788596289993901370190727586
y[1] (numeric) = 3.3392788596289993901370190727585
absolute error = 1e-31
relative error = 2.9946585536468254555219639938405e-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 = 0.293
Order of pole (three term test) = -22.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 3.3437542002684915753165898799309
y[1] (numeric) = 3.3437542002684915753165898799308
absolute error = 1e-31
relative error = 2.9906504488867738991571579671191e-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 = 0.2852
Order of pole (three term test) = -22.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 3.3480951666077483455851478128628
y[1] (numeric) = 3.3480951666077483455851478128627
absolute error = 1e-31
relative error = 2.9867729268077781081489315934235e-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 = 0.2774
Order of pole (three term test) = -22.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 3.3523013245537532351568283589299
y[1] (numeric) = 3.3523013245537532351568283589298
absolute error = 1e-31
relative error = 2.9830254001200698849017066863953e-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 = 0.2695
Order of pole (three term test) = -22.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 3.356372253494216763480593883007
y[1] (numeric) = 3.3563722534942167634805938830069
absolute error = 1e-31
relative error = 2.9794073019133396363940030027700e-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 = 0.2615
Order of pole (three term test) = -23.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 3.3603075463396373136792158628236
y[1] (numeric) = 3.3603075463396373136792158628235
absolute error = 1e-31
relative error = 2.9759180855017093651792800527691e-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 = 0.2533
Order of pole (three term test) = -23.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 3.3641068095640097434708420665702
y[1] (numeric) = 3.3641068095640097434708420665702
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 = 0.2451
Order of pole (three term test) = -23.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 3.3677696632441776577459802453937
y[1] (numeric) = 3.3677696632441776577459802453936
absolute error = 1e-31
relative error = 2.9693242115516251590318142936899e-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 = 0.2367
Order of pole (three term test) = -23.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 3.3712957410978254076054340935802
y[1] (numeric) = 3.3712957410978254076054340935801
absolute error = 1e-31
relative error = 2.9662185604469128833623370925104e-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 = 0.2283
Order of pole (three term test) = -23.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 3.3746846905201060166909475764969
y[1] (numeric) = 3.3746846905201060166909475764967
absolute error = 2e-31
relative error = 5.9264796074674467730376243498012e-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 = 0.2198
Order of pole (three term test) = -23.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 3.3779361726189013720464477320556
y[1] (numeric) = 3.3779361726189013720464477320555
absolute error = 1e-31
relative error = 2.9603874937184017692411674373936e-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 = 0.2112
Order of pole (three term test) = -23.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 3.3810498622487111535201832158602
y[1] (numeric) = 3.38104986224871115352018321586
absolute error = 2e-31
relative error = 5.9153224042363422978109856078553e-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 = 0.2025
Order of pole (three term test) = -23.92
NO COMPLEX POLE (six term test) for Equation 1
bytes used=64026680, alloc=4521156, time=5.89
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 3.3840254480431671128430590565459
y[1] (numeric) = 3.3840254480431671128430590565458
absolute error = 1e-31
relative error = 2.9550605199445410816773164015988e-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 = 0.1937
Order of pole (three term test) = -24.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 3.3868626324461694509823549300873
y[1] (numeric) = 3.3868626324461694509823549300873
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 = 0.1848
Order of pole (three term test) = -24.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 3.389561131741642180159038475882
y[1] (numeric) = 3.389561131741642180159038475882
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 = 0.1759
Order of pole (three term test) = -24.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 3.392120676081904495017267975641
y[1] (numeric) = 3.392120676081904495017267975641
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 = 0.1669
Order of pole (three term test) = -24.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 3.394541009514655315832610175317
y[1] (numeric) = 3.394541009514655315832610175317
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 = 0.1578
Order of pole (three term test) = -24.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 3.3968218900085683053271394726706
y[1] (numeric) = 3.3968218900085683053271394726706
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 = 0.1487
Order of pole (three term test) = -24.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 3.3989630894774947996110660701379
y[1] (numeric) = 3.3989630894774947996110660701379
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 = 0.1395
Order of pole (three term test) = -24.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 3.4009643938032722329779679720729
y[1] (numeric) = 3.4009643938032722329779679720728
absolute error = 1e-31
relative error = 2.9403424564574982744553132399115e-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 = 0.1303
Order of pole (three term test) = -24.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 3.4028256028571357757301542604696
y[1] (numeric) = 3.4028256028571357757301542604696
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 = 0.121
Order of pole (three term test) = -24.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 3.4045465305197310438882200848828
y[1] (numeric) = 3.4045465305197310438882200848828
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 = 0.1116
Order of pole (three term test) = -24.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 3.4061270046997258795304996135461
y[1] (numeric) = 3.4061270046997258795304996135461
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 = 0.1022
Order of pole (three term test) = -24.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 3.4075668673510193405998927656458
y[1] (numeric) = 3.4075668673510193405998927656458
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 = 0.09282
Order of pole (three term test) = -24.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 3.4088659744885461792934258191104
y[1] (numeric) = 3.4088659744885461792934258191105
absolute error = 1e-31
relative error = 2.9335268898333157659419927388195e-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 = 0.08335
Order of pole (three term test) = -24.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 3.4100241962026752285998772926148
y[1] (numeric) = 3.4100241962026752285998772926149
absolute error = 1e-31
relative error = 2.9325305114068606181304935995132e-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 = 0.07385
Order of pole (three term test) = -24.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 3.4110414166722002571588139546605
y[1] (numeric) = 3.4110414166722002571588139546606
absolute error = 1e-31
relative error = 2.9316559896115140250416599048393e-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 = 0.06432
Order of pole (three term test) = -24.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 3.4119175341759219933663767324308
y[1] (numeric) = 3.4119175341759219933663767324309
absolute error = 1e-31
relative error = 2.9309031944159496991155780151698e-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 = 0.05476
Order of pole (three term test) = -24.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 3.4126524611028201605350575964098
y[1] (numeric) = 3.4126524611028201605350575964099
absolute error = 1e-31
relative error = 2.9302720139185919175604866409125e-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 = 0.04518
Order of pole (three term test) = -24.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 3.4132461239608145059124281107904
y[1] (numeric) = 3.4132461239608145059124281107904
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 = 0.03559
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 3.4136984633841139474632186099931
y[1] (numeric) = 3.4136984633841139474632186099931
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 = 0.02598
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 3.4140094341391531035061940619509
y[1] (numeric) = 3.4140094341391531035061940619509
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 = 0.01636
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 3.4141790051291156115578100221132
y[1] (numeric) = 3.4141790051291156115578100221133
absolute error = 1e-31
relative error = 2.9289618338631384389264839160841e-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 = 0.006732
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 3.4142071593970437840545337323786
y[1] (numeric) = 3.4142071593970437840545337323786
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
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 3.4140938941275342899908495039764
y[1] (numeric) = 3.4140938941275342899908495039765
absolute error = 1e-31
relative error = 2.9290348508576922049752538104495e-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
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 3.413839220647019692906197647083
y[1] (numeric) = 3.4138392206470196929061976470832
absolute error = 2e-31
relative error = 5.8585067155592145268077330273460e-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
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 3.4134431644226358170672828674832
y[1] (numeric) = 3.4134431644226358170672828674833
absolute error = 1e-31
relative error = 2.9295932342530865616506462337819e-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
bytes used=68028600, alloc=4586680, time=6.27
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 3.4129057650596750551081900410706
y[1] (numeric) = 3.4129057650596750551081900410708
absolute error = 2e-31
relative error = 5.8601090615375656786740321684543e-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
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 3.4122270762976258717954211180514
y[1] (numeric) = 3.4122270762976258717954211180516
absolute error = 2e-31
relative error = 5.8612746317283876531490991452792e-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
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 3.4114071660047988999641762506302
y[1] (numeric) = 3.4114071660047988999641762506304
absolute error = 2e-31
relative error = 5.8626833522843885499039682051353e-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
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 3.4104461161715401660118072776096
y[1] (numeric) = 3.4104461161715401660118072776098
absolute error = 2e-31
relative error = 5.8643354325889108773547837463886e-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
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 3.4093440229020321236202385939827
y[1] (numeric) = 3.4093440229020321236202385939829
absolute error = 2e-31
relative error = 5.8662311182595204488135511963386e-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
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 3.4081009964046833155971507143099
y[1] (numeric) = 3.40810099640468331559715071431
absolute error = 1e-31
relative error = 2.9341853456072239432434639773374e-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
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 3.4067171609811076248617338230849
y[1] (numeric) = 3.4067171609811076248617338230851
absolute error = 2e-31
relative error = 5.8707544697488646301468372714598e-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
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 3.4051926550136942166407288098392
y[1] (numeric) = 3.4051926550136942166407288098393
absolute error = 1e-31
relative error = 2.9366914043105100940911097305748e-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
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 3.4035276309517694148701778379018
y[1] (numeric) = 3.4035276309517694148701778379019
absolute error = 1e-31
relative error = 2.9381280495741354053421238957428e-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
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 3.4017222552963518966037125405356
y[1] (numeric) = 3.4017222552963518966037125405358
absolute error = 2e-31
relative error = 5.8793747693130332112520067313937e-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
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 3.3997767085835027288952350533153
y[1] (numeric) = 3.3997767085835027288952350533154
absolute error = 1e-31
relative error = 2.9413696419393502084192726737801e-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
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 3.397691185366271913138428691628
y[1] (numeric) = 3.3976911853662719131384286916281
absolute error = 1e-31
relative error = 2.9431750722577801418355829074065e-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
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 3.395465894195243242193619825997
y[1] (numeric) = 3.3954658941952432421936198259971
absolute error = 1e-31
relative error = 2.9451039449683803412655198124380e-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
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 3.3931010575976794158000657040182
y[1] (numeric) = 3.3931010575976794158000657040183
absolute error = 1e-31
relative error = 2.9471565480221844144463282732420e-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
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 3.3905969120552694997447479775705
y[1] (numeric) = 3.3905969120552694997447479775706
absolute error = 1e-31
relative error = 2.9493331880427878564989067617105e-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
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 3.3879537079804809540232113337315
y[1] (numeric) = 3.3879537079804809540232113337316
absolute error = 1e-31
relative error = 2.9516341904095500361155658977343e-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
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 3.3851717096915185947699245680268
y[1] (numeric) = 3.385171709691518594769924568027
absolute error = 2e-31
relative error = 5.9081197986918498434952631152066e-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
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 3.3822511953858929940411036017382
y[1] (numeric) = 3.3822511953858929940411036017383
absolute error = 1e-31
relative error = 2.9566106780129512684665294105784e-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
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 3.3791924571126009605879919008749
y[1] (numeric) = 3.3791924571126009605879919008751
absolute error = 2e-31
relative error = 5.9185738172158694845448854822513e-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
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 3.3759958007429208835493381133559
y[1] (numeric) = 3.3759958007429208835493381133561
absolute error = 2e-31
relative error = 5.9241779849367124381870617667461e-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
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 3.3726615459398258595043645441707
y[1] (numeric) = 3.3726615459398258595043645441709
absolute error = 2e-31
relative error = 5.9300347003620845212446293822306e-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
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 3.3691900261260176615480321958476
y[1] (numeric) = 3.3691900261260176615480321958478
absolute error = 2e-31
relative error = 5.9361448433932710770244842765483e-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
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 3.3655815884505847469650565774149
y[1] (numeric) = 3.3655815884505847469650565774152
absolute error = 3e-31
relative error = 8.9137639993482142569432947992424e-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
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 3.3618365937542876376741219792859
y[1] (numeric) = 3.3618365937542876376741219792862
absolute error = 3e-31
relative error = 8.9236936904473060945425416040697e-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
TOP MAIN SOLVE Loop
bytes used=72029828, alloc=4586680, time=6.64
x[1] = 4.21
y[1] (analytic) = 3.357955416533475144875321039439
y[1] (numeric) = 3.3579554165334751448753210394393
absolute error = 3e-31
relative error = 8.9340078347347327842090787312247e-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
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 3.3539384449026350462482851443764
y[1] (numeric) = 3.3539384449026350462482851443767
absolute error = 3e-31
relative error = 8.9447079881845896785956627785738e-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
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 3.3497860805555829606020781868441
y[1] (numeric) = 3.3497860805555829606020781868444
absolute error = 3e-31
relative error = 8.9557957668223137619944076694676e-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
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 3.3454987387252933010570461942881
y[1] (numeric) = 3.3454987387252933010570461942884
absolute error = 3e-31
relative error = 8.9672728471661725299385330215454e-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
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 3.3410768481423763236298305489831
y[1] (numeric) = 3.3410768481423763236298305489834
absolute error = 3e-31
relative error = 8.9791409666855956495524768934940e-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
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 3.3365208509922054234820839543391
y[1] (numeric) = 3.3365208509922054234820839543394
absolute error = 3e-31
relative error = 8.9914019242765056439031709194689e-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
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 3.3318312028706989660675371417556
y[1] (numeric) = 3.3318312028706989660675371417559
absolute error = 3e-31
relative error = 9.0040575807538092603603297617585e-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
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 3.3270083727387610749574532601354
y[1] (numeric) = 3.3270083727387610749574532601357
absolute error = 3e-31
relative error = 9.0171098593612166081104341245106e-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
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 3.3220528428753859322277215190272
y[1] (numeric) = 3.3220528428753859322277215190275
absolute error = 3e-31
relative error = 9.0305607462985605821866592643711e-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
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 3.3169651088294302809384717566206
y[1] (numeric) = 3.3169651088294302809384717566209
absolute error = 3e-31
relative error = 9.0444122912667945291908134139965e-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
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 3.3117456793700589524157725238352
y[1] (numeric) = 3.3117456793700589524157725238355
absolute error = 3e-31
relative error = 9.0586666080308515516140765871109e-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
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 3.3063950764358683737413892584141
y[1] (numeric) = 3.3063950764358683737413892584143
absolute error = 2e-31
relative error = 6.0488839166670361942832429351389e-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
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 3.3009138350826931430574566374359
y[1] (numeric) = 3.3009138350826931430574566374361
absolute error = 2e-31
relative error = 6.0589282238865129848526600282380e-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
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 3.2953025034301008919850402654125
y[1] (numeric) = 3.2953025034301008919850402654128
absolute error = 3e-31
relative error = 9.1038683000340069609812818538790e-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
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 3.2895616426065807856257583757773
y[1] (numeric) = 3.2895616426065807856257583757776
absolute error = 3e-31
relative error = 9.1197561436266684051040497085102e-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
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 3.2836918266934311412507872858484
y[1] (numeric) = 3.2836918266934311412507872858487
absolute error = 3e-31
relative error = 9.1360583097741562120999012830842e-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
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 3.2776936426673517768686215428311
y[1] (numeric) = 3.2776936426673517768686215428314
absolute error = 3e-31
relative error = 9.1527773094700587027109213760315e-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
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 3.2715676903417468303888924347823
y[1] (numeric) = 3.2715676903417468303888924347826
absolute error = 3e-31
relative error = 9.1699157222286329545561361441924e-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
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 3.2653145823067439190514143303698
y[1] (numeric) = 3.2653145823067439190514143303702
absolute error = 4e-31
relative error = 1.2249968262397082795662128511521e-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
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 3.2589349438679356371545320755981
y[1] (numeric) = 3.2589349438679356371545320755984
absolute error = 3e-31
relative error = 9.2054614518919692191752536545101e-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
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 3.2524294129838495178819480310268
y[1] (numeric) = 3.2524294129838495178819480310271
absolute error = 3e-31
relative error = 9.2238742769446753913515154017759e-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
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 3.2457986402021527121797378753321
y[1] (numeric) = 3.2457986402021527121797378753324
absolute error = 3e-31
relative error = 9.2427175328816945905235667520383e-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
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 3.2390432885945977641625048832341
y[1] (numeric) = 3.2390432885945977641625048832344
absolute error = 3e-31
relative error = 9.2619941529144636071905645299208e-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
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 3.2321640336907159884169203892412
y[1] (numeric) = 3.2321640336907159884169203892415
absolute error = 3e-31
relative error = 9.2817071433543102223740502299143e-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
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 3.2251615634102650798096647484362
bytes used=76031912, alloc=4586680, time=7.02
y[1] (numeric) = 3.2251615634102650798096647484364
absolute error = 2e-31
relative error = 6.2012397229651120861193442715779e-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
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 3.2180365779944377109824945293591
y[1] (numeric) = 3.2180365779944377109824945293594
absolute error = 3e-31
relative error = 9.3224546312325521947536725101087e-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
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 3.2107897899358379966173604546018
y[1] (numeric) = 3.210789789935837996617360454602
absolute error = 2e-31
relative error = 6.2289970096110418138588622077742e-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
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 3.2034219239072328267667968253815
y[1] (numeric) = 3.2034219239072328267667968253818
absolute error = 3e-31
relative error = 9.3649855412766923536963524630373e-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
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 3.1959337166890851940568757001753
y[1] (numeric) = 3.1959337166890851940568757001755
absolute error = 2e-31
relative error = 6.2579520643874761410455141325753e-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
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 3.1883259170958767613696168392924
y[1] (numeric) = 3.1883259170958767613696168392927
absolute error = 3e-31
relative error = 9.4093266435339346252753617661886e-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
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 3.1805992859012270376866875187885
y[1] (numeric) = 3.1805992859012270376866875187887
absolute error = 2e-31
relative error = 6.2881231498273990843433049373302e-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
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 3.172754595761816650114407364941
y[1] (numeric) = 3.1727545957618166501144073649413
absolute error = 3e-31
relative error = 9.4555059632012409462690346604121e-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
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 3.1647926311401223196994586468184
y[1] (numeric) = 3.1647926311401223196994586468187
absolute error = 3e-31
relative error = 9.4792940633182798025588980842936e-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
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 3.1567141882259712674733331503803
y[1] (numeric) = 3.1567141882259712674733331503807
absolute error = 4e-31
relative error = 1.2671403749250873527012967051634e-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
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 3.148520074856922895219540079033
y[1] (numeric) = 3.1485200748569228952195400790334
absolute error = 4e-31
relative error = 1.2704381439212423034764714359529e-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
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 3.140211110437485702729149881648
y[1] (numeric) = 3.1402111104374857027291498816484
absolute error = 4e-31
relative error = 1.2737997094223167814304022448481e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.67
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 3.1317881258571775197856294424397
y[1] (numeric) = 3.1317881258571775197856294424401
absolute error = 4e-31
relative error = 1.2772256101792297712540437694363e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.98
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 3.1232519634074372467874872367796
y[1] (numeric) = 3.12325196340743724678748723678
absolute error = 4e-31
relative error = 1.2807163965202600074332182411802e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 3.1146034766973964127654262030843
y[1] (numeric) = 3.1146034766973964127654262030847
absolute error = 4e-31
relative error = 1.2842726305055831365393970462893e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.62
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 3.105843530568518973568012481138
y[1] (numeric) = 3.1058435305685189735680124811384
absolute error = 4e-31
relative error = 1.2878948860852006029097510244003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.94
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
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 3.0969730010081178861649081855758
y[1] (numeric) = 3.0969730010081178861649081855762
absolute error = 4e-31
relative error = 1.2915837492603039551493524743056e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.27
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
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 3.0879927750617571073381686100673
y[1] (numeric) = 3.0879927750617571073381686100677
absolute error = 4e-31
relative error = 1.2953398182481186536471242611169e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.61
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 3.0789037507445477764887366413833
y[1] (numeric) = 3.0789037507445477764887366413837
absolute error = 4e-31
relative error = 1.2991637036502718063701465626012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 3.0697068369513474528659341326429
y[1] (numeric) = 3.0697068369513474528659341326433
absolute error = 4e-31
relative error = 1.3030560286247285687792841465881e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 3.0604029533658713872213935670731
y[1] (numeric) = 3.0604029533658713872213935670735
absolute error = 4e-31
relative error = 1.3070174290613422108101028768033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 3.0509930303687249166845242646285
y[1] (numeric) = 3.0509930303687249166845242646289
absolute error = 4e-31
relative error = 1.3110485537610630763207892303698e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.01
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 3.0414780089443661795433861693787
y[1] (numeric) = 3.0414780089443661795433861693791
absolute error = 4e-31
relative error = 1.3151500646188518348641163166914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.37
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
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 3.0318588405870084535819623177043
y[1] (numeric) = 3.0318588405870084535819623177047
absolute error = 4e-31
relative error = 1.3193226368103425485304863028086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.74
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
TOP MAIN SOLVE Loop
x[1] = 4.69
bytes used=80034044, alloc=4586680, time=7.40
y[1] (analytic) = 3.0221364872054715276615818033849
y[1] (numeric) = 3.0221364872054715276615818033854
absolute error = 5e-31
relative error = 1.6544586987278764301949247148249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.12
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
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 3.0123119210269916213300448379021
y[1] (numeric) = 3.0123119210269916213300448379026
absolute error = 5e-31
relative error = 1.6598546668086561117355791290462e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.48
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
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 3.0023861244999994713863308603183
y[1] (numeric) = 3.0023861244999994713863308603188
absolute error = 5e-31
relative error = 1.6653420954750355196436012112354e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.09
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
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 2.992360090195876307511215234787
y[1] (numeric) = 2.9923600901958763075112152347875
absolute error = 5e-31
relative error = 1.6709218975289521350929378623153e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.71
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 2.9822348207096975412843617266149
y[1] (numeric) = 2.9822348207096975412843617266153
absolute error = 4e-31
relative error = 1.3412760028897052843630400993789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.34
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 2.9720113285599740941362757308538
y[1] (numeric) = 2.9720113285599740941362757308542
absolute error = 4e-31
relative error = 1.3458898899749875139285083356928e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.98
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
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 2.9616906360874013900187744432238
y[1] (numeric) = 2.9616906360874013900187744432242
absolute error = 4e-31
relative error = 1.3505799529704686667277189658948e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 2.9512737753526261378103313681589
y[1] (numeric) = 2.9512737753526261378103313681594
absolute error = 5e-31
relative error = 1.6941837256025447981692774043547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.27
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 2.9407617880330411266928605655122
y[1] (numeric) = 2.9407617880330411266928605655127
absolute error = 5e-31
relative error = 1.7002397203155654455861079721793e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.93
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
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 2.9301557253186183549343989069881
y[1] (numeric) = 2.9301557253186183549343989069886
absolute error = 5e-31
relative error = 1.7063939492350057835321125320103e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.59
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
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 2.9194566478067909086780026374151
y[1] (numeric) = 2.9194566478067909086780026374156
absolute error = 5e-31
relative error = 1.7126474557367357964199595206041e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.26
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
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 2.9086656253963941024613812088541
y[1] (numeric) = 2.9086656253963941024613812088546
absolute error = 5e-31
relative error = 1.7190013029835968241876796398533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.93
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 2.8977837371806764872648343358656
y[1] (numeric) = 2.8977837371806764872648343358661
absolute error = 5e-31
relative error = 1.7254565742247626421961160283437e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.61
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 2.8868120713393914248975302821285
y[1] (numeric) = 2.886812071339391424897530282129
absolute error = 5e-31
relative error = 1.7320143731005512945876833462933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 2.8757517250299800194747633623156
y[1] (numeric) = 2.875751725029980019474763362316
absolute error = 4e-31
relative error = 1.3909406591621881308095459498095e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.98
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 2.8646038042778562876023623453078
y[1] (numeric) = 2.8646038042778562876023623453083
absolute error = 5e-31
relative error = 1.7454420721403950022856616725271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.68
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 2.8533694238658055386598025978259
y[1] (numeric) = 2.8533694238658055386598025978264
absolute error = 5e-31
relative error = 1.7523142843613617104101296458298e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.38
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
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 2.8420497072225070252518259480575
y[1] (numeric) = 2.842049707222507025251825948058
absolute error = 5e-31
relative error = 1.7592936489792874701544369108849e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 2.8306457863101920114706256256645
y[1] (numeric) = 2.830645786310192011470625625665
absolute error = 5e-31
relative error = 1.7663813763563854851896897117625e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.79
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
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 2.8191588015114484930681520952868
y[1] (numeric) = 2.8191588015114484930681520952873
absolute error = 5e-31
relative error = 1.7735786991918749478634077611029e-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
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 2.8075899015151838889721934675351
y[1] (numeric) = 2.8075899015151838889721934675356
absolute error = 5e-31
relative error = 1.7808868728661649987240358107017e-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
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 2.7959402432017571077820481057964
y[1] (numeric) = 2.795940243201757107782048105797
absolute error = 6e-31
relative error = 2.1459686109489699775618117906271e-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
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 2.7842109915272914759414169027503
y[1] (numeric) = 2.7842109915272914759414169027509
absolute error = 6e-31
relative error = 2.1550090917171018650580842744490e-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
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 2.7724033194071800961992923655293
y[1] (numeric) = 2.77240331940718009619929236553
absolute error = 7e-31
relative error = 2.5248851604667686582974312896447e-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
TOP MAIN SOLVE Loop
bytes used=84037276, alloc=4586680, time=7.77
x[1] = 4.93
y[1] (analytic) = 2.7605184075987952857259198762633
y[1] (numeric) = 2.760518407598795285725919876264
absolute error = 7e-31
relative error = 2.5357555960254828698727168926178e-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
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 2.7485574445834138228422777227835
y[1] (numeric) = 2.7485574445834138228422777227841
absolute error = 6e-31
relative error = 2.1829632892789666004438818354967e-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
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 2.7365216264473698097400076517426
y[1] (numeric) = 2.7365216264473698097400076517433
absolute error = 7e-31
relative error = 2.5579918434949841962839132667498e-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
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 2.7244121567624470358064850001614
y[1] (numeric) = 2.7244121567624470358064850001621
absolute error = 7e-31
relative error = 2.5693616080169177816766859304329e-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
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 2.7122302464655228022190232000654
y[1] (numeric) = 2.712230246465522802219023200066
absolute error = 6e-31
relative error = 2.2122015665222287059766308760571e-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
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 2.6999771137374752433254567572481
y[1] (numeric) = 2.6999771137374752433254567572488
absolute error = 7e-31
relative error = 2.5926145686139417805362371536206e-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
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 2.6876539838813662539780544167141
y[1] (numeric) = 2.6876539838813662539780544167148
absolute error = 7e-31
relative error = 2.6045019343937176330353581243562e-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
TOP MAIN SOLVE Loop
x[1] = 5
y[1] (analytic) = 2.6752620891999122044265152346424
y[1] (numeric) = 2.6752620891999122044265152346431
absolute error = 7e-31
relative error = 2.6165660659040260895116775986339e-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
TOP MAIN SOLVE Loop
x[1] = 5.01
y[1] (analytic) = 2.662802668872254695596450860034
y[1] (numeric) = 2.6628026688722546955964508600347
absolute error = 7e-31
relative error = 2.6288091422728771585509033497490e-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
TOP MAIN SOLVE Loop
x[1] = 5.02
y[1] (analytic) = 2.6502769688300436775751354828495
y[1] (numeric) = 2.6502769688300436775751354828502
absolute error = 7e-31
relative error = 2.6412333813888620454470849647545e-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
TOP MAIN SOLVE Loop
x[1] = 5.03
y[1] (analytic) = 2.6376862416328453228894111499265
y[1] (numeric) = 2.6376862416328453228894111499272
absolute error = 7e-31
relative error = 2.6538410404971775829304910875063e-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
TOP MAIN SOLVE Loop
x[1] = 5.04
y[1] (analytic) = 2.6250317463428871136845942319657
y[1] (numeric) = 2.6250317463428871136845942319663
absolute error = 6e-31
relative error = 2.2856866429745141467721660154636e-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
TOP MAIN SOLVE Loop
x[1] = 5.05
y[1] (analytic) = 2.6123147483991526681912864048498
y[1] (numeric) = 2.6123147483991526681912864048505
absolute error = 7e-31
relative error = 2.6796158480863210992018976103066e-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
TOP MAIN SOLVE Loop
x[1] = 5.06
y[1] (analytic) = 2.5995365194908388968925228359918
y[1] (numeric) = 2.5995365194908388968925228359925
absolute error = 7e-31
relative error = 2.6927877133155500975789355178739e-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
TOP MAIN SOLVE Loop
x[1] = 5.07
y[1] (analytic) = 2.5866983374301881425701888425363
y[1] (numeric) = 2.5866983374301881425701888425369
absolute error = 6e-31
relative error = 2.3195592285263657027273615742938e-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
TOP MAIN SOLVE Loop
x[1] = 5.08
y[1] (analytic) = 2.573801486024708020910727516367
y[1] (numeric) = 2.5738014860247080209107275163676
absolute error = 6e-31
relative error = 2.3311821181932448008062760295164e-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
TOP MAIN SOLVE Loop
x[1] = 5.09
y[1] (analytic) = 2.5608472549487917395795946339389
y[1] (numeric) = 2.5608472549487917395795946339396
absolute error = 7e-31
relative error = 2.7334703334892874197171793963835e-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
TOP MAIN SOLVE Loop
x[1] = 5.1
y[1] (analytic) = 2.5478369396147517336255706946159
y[1] (numeric) = 2.5478369396147517336255706946166
absolute error = 7e-31
relative error = 2.7474285701574144276441494040077e-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
TOP MAIN SOLVE Loop
x[1] = 5.11
y[1] (analytic) = 2.5347718410432795137439180440519
y[1] (numeric) = 2.5347718410432795137439180440526
absolute error = 7e-31
relative error = 2.7615897757168116407786781555340e-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
TOP MAIN SOLVE Loop
x[1] = 5.12
y[1] (analytic) = 2.5216532657333446813056070002912
y[1] (numeric) = 2.5216532657333446813056070002919
absolute error = 7e-31
relative error = 2.7759565897194303592702721154474e-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
TOP MAIN SOLVE Loop
x[1] = 5.13
y[1] (analytic) = 2.5084825255315461201426909338882
y[1] (numeric) = 2.5084825255315461201426909338889
absolute error = 7e-31
relative error = 2.7905316974519101754891594015295e-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
TOP MAIN SOLVE Loop
x[1] = 5.14
y[1] (analytic) = 2.4952609375009284298617781206076
y[1] (numeric) = 2.4952609375009284298617781206083
absolute error = 7e-31
relative error = 2.8053178306116113193689914702730e-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
TOP MAIN SOLVE Loop
x[1] = 5.15
y[1] (analytic) = 2.4819898237892767189329497450112
y[1] (numeric) = 2.481989823789276718932949745012
absolute error = 8e-31
relative error = 3.2232203062727817044183591242526e-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
TOP MAIN SOLVE Loop
x[1] = 5.16
y[1] (analytic) = 2.468670511496902927965061189887
y[1] (numeric) = 2.4686705114969029279650611898877
absolute error = 7e-31
relative error = 2.8355343361538678362815656485016e-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
TOP MAIN SOLVE Loop
x[1] = 5.17
y[1] (analytic) = 2.4553043325439369044249213847113
y[1] (numeric) = 2.4553043325439369044249213847121
absolute error = 8e-31
relative error = 3.2582518973162128356222003249578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
bytes used=88038680, alloc=4586680, time=8.14
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.18
y[1] (analytic) = 2.441892623537135499582287892781
y[1] (numeric) = 2.4418926235371354995822878927818
absolute error = 8e-31
relative error = 3.2761473305127655348667830563469e-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
TOP MAIN SOLVE Loop
x[1] = 5.19
y[1] (analytic) = 2.4284367256362230066599911882643
y[1] (numeric) = 2.428436725636223006659991188265
absolute error = 7e-31
relative error = 2.8825128223862118645094477937345e-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
TOP MAIN SOLVE Loop
x[1] = 5.2
y[1] (analytic) = 2.4149379844197763060339905138132
y[1] (numeric) = 2.4149379844197763060339905138139
absolute error = 7e-31
relative error = 2.8986251593876233626772406939691e-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
TOP MAIN SOLVE Loop
x[1] = 5.21
y[1] (analytic) = 2.4013977497506681288570793066914
y[1] (numeric) = 2.4013977497506681288570793066922
absolute error = 8e-31
relative error = 3.3313931441930527694357803283761e-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
TOP MAIN SOLVE Loop
x[1] = 5.22
y[1] (analytic) = 2.3878173756410818946677475829961
y[1] (numeric) = 2.3878173756410818946677475829969
absolute error = 8e-31
relative error = 3.3503399722318201587005940548195e-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
TOP MAIN SOLVE Loop
x[1] = 5.23
y[1] (analytic) = 2.3741982201171116213879531333671
y[1] (numeric) = 2.374198220117111621387953133368
absolute error = 9e-31
relative error = 3.7907534104528385678850163858081e-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
TOP MAIN SOLVE Loop
x[1] = 5.24
y[1] (analytic) = 2.3605416450829604476059687208406
y[1] (numeric) = 2.3605416450829604476059687208414
absolute error = 8e-31
relative error = 3.3890526848632838554744209637335e-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
TOP MAIN SOLVE Loop
x[1] = 5.25
y[1] (analytic) = 2.3468490161847513471789094752536
y[1] (numeric) = 2.3468490161847513471789094752544
absolute error = 8e-31
relative error = 3.4088260236721657086047678764700e-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
TOP MAIN SOLVE Loop
x[1] = 5.26
y[1] (analytic) = 2.3331217026739636549699895386006
y[1] (numeric) = 2.3331217026739636549699895386014
absolute error = 8e-31
relative error = 3.4288824242778647253229878437617e-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
TOP MAIN SOLVE Loop
x[1] = 5.27
y[1] (analytic) = 2.3193610772705090599541317197985
y[1] (numeric) = 2.3193610772705090599541317197993
absolute error = 8e-31
relative error = 3.4492257710104502107734551404002e-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
TOP MAIN SOLVE Loop
x[1] = 5.28
y[1] (analytic) = 2.3055685160254607579785166391619
y[1] (numeric) = 2.3055685160254607579785166391628
absolute error = 9e-31
relative error = 3.9035925141426643144491414164335e-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
TOP MAIN SOLVE Loop
x[1] = 5.29
y[1] (analytic) = 2.2917453981834494911484033162804
y[1] (numeric) = 2.2917453981834494911484033162813
absolute error = 9e-31
relative error = 3.9271378082110884498060721879100e-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
TOP MAIN SOLVE Loop
x[1] = 5.3
y[1] (analytic) = 2.2778931060447402341196130342938
y[1] (numeric) = 2.2778931060447402341196130342946
absolute error = 8e-31
relative error = 3.5120173017648491551679111099898e-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
TOP MAIN SOLVE Loop
x[1] = 5.31
y[1] (analytic) = 2.2640130248270033195141115205415
y[1] (numeric) = 2.2640130248270033195141115205424
absolute error = 9e-31
relative error = 3.9752421480383063148403131947883e-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
TOP MAIN SOLVE Loop
x[1] = 5.32
y[1] (analytic) = 2.2501065425267938252309575405181
y[1] (numeric) = 2.250106542526793825230957540519
absolute error = 9e-31
relative error = 3.9998106000319892736038349020887e-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
TOP MAIN SOLVE Loop
x[1] = 5.33
y[1] (analytic) = 2.2361750497807530755984533511439
y[1] (numeric) = 2.2361750497807530755984533511448
absolute error = 9e-31
relative error = 4.0247296386221685081477224882558e-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
TOP MAIN SOLVE Loop
x[1] = 5.34
y[1] (analytic) = 2.2222199397265461361017167681517
y[1] (numeric) = 2.2222199397265461361017167681526
absolute error = 9e-31
relative error = 4.0500041598526423475058123123467e-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
TOP MAIN SOLVE Loop
x[1] = 5.35
y[1] (analytic) = 2.2082426078635492078203170556062
y[1] (numeric) = 2.208242607863549207820317055607
absolute error = 8e-31
relative error = 3.6227903453687605925075396204308e-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
TOP MAIN SOLVE Loop
x[1] = 5.36
y[1] (analytic) = 2.1942444519133008527204374229757
y[1] (numeric) = 2.1942444519133008527204374229766
absolute error = 9e-31
relative error = 4.1016396291453896123579974594020e-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
TOP MAIN SOLVE Loop
x[1] = 5.37
y[1] (analytic) = 2.1802268716797310045627446555546
y[1] (numeric) = 2.1802268716797310045627446555555
absolute error = 9e-31
relative error = 4.1280107666345990534989779452325e-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
TOP MAIN SOLVE Loop
x[1] = 5.38
y[1] (analytic) = 2.166191268909181742408399655278
y[1] (numeric) = 2.1661912689091817424083996552789
absolute error = 9e-31
relative error = 4.1547577673194508019887694466635e-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
TOP MAIN SOLVE Loop
x[1] = 5.39
y[1] (analytic) = 2.1521390471502338245292093242972
y[1] (numeric) = 2.1521390471502338245292093242982
absolute error = 1.0e-30
relative error = 4.6465399218705465626495527751790e-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
TOP MAIN SOLVE Loop
x[1] = 5.4
y[1] (analytic) = 2.1380716116133529999517179437535
y[1] (numeric) = 2.1380716116133529999517179437544
absolute error = 9e-31
relative error = 4.2094006351867470225764770568734e-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
TOP MAIN SOLVE Loop
x[1] = 5.41
y[1] (analytic) = 2.1239903690303701328871226214372
y[1] (numeric) = 2.1239903690303701328871226214381
absolute error = 9e-31
relative error = 4.2373073490482067306990810012955e-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
TOP MAIN SOLVE Loop
bytes used=92040572, alloc=4586680, time=8.52
x[1] = 5.42
y[1] (analytic) = 2.1098967275138091919174703108124
y[1] (numeric) = 2.1098967275138091919174703108132
absolute error = 8e-31
relative error = 3.7916547742252661091621749714624e-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
TOP MAIN SOLVE Loop
x[1] = 5.43
y[1] (analytic) = 2.0957920964160771710219914967793
y[1] (numeric) = 2.0957920964160771710219914967802
absolute error = 9e-31
relative error = 4.2943190860345872128038528684259e-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
TOP MAIN SOLVE Loop
x[1] = 5.44
y[1] (analytic) = 2.08167788618853002333412657347
y[1] (numeric) = 2.0816778861885300233341265734708
absolute error = 8e-31
relative error = 3.8430537467291272303283021417660e-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
TOP MAIN SOLVE Loop
x[1] = 5.45
y[1] (analytic) = 2.0675555082404287009184245477154
y[1] (numeric) = 2.0675555082404287009184245477162
absolute error = 8e-31
relative error = 3.8693036139127967531442841154888e-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
TOP MAIN SOLVE Loop
x[1] = 5.46
y[1] (analytic) = 2.0534263747977994048458001365863
y[1] (numeric) = 2.0534263747977994048458001365872
absolute error = 9e-31
relative error = 4.3829182825638093234516994899285e-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
TOP MAIN SOLVE Loop
x[1] = 5.47
y[1] (analytic) = 2.0392918987622121594245256670798
y[1] (numeric) = 2.0392918987622121594245256670807
absolute error = 9e-31
relative error = 4.4132965984235630349837551015297e-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
TOP MAIN SOLVE Loop
x[1] = 5.48
y[1] (analytic) = 2.0251534935694918326118505495682
y[1] (numeric) = 2.0251534935694918326118505495691
absolute error = 9e-31
relative error = 4.4441075842289831941806360578409e-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
TOP MAIN SOLVE Loop
x[1] = 5.49
y[1] (analytic) = 2.011012573048375731386466739209
y[1] (numeric) = 2.0110125730483757313864667392098
absolute error = 8e-31
relative error = 3.9780954665406543543678322995612e-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
TOP MAIN SOLVE Loop
x[1] = 5.5
y[1] (analytic) = 1.9968705512791319062044979941963
y[1] (numeric) = 1.9968705512791319062044979941971
absolute error = 8e-31
relative error = 4.0062687062390969074189390826848e-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 = 0.002134
Order of pole (three term test) = -0.893
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.51
y[1] (analytic) = 1.9827288424521523025907496450351
y[1] (numeric) = 1.982728842452152302590749645036
absolute error = 9e-31
relative error = 4.5391986071424641624615108216988e-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 = 0.01178
Order of pole (three term test) = -0.8965
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.52
y[1] (analytic) = 1.9685888607265349004322211023162
y[1] (numeric) = 1.9685888607265349004322211023171
absolute error = 9e-31
relative error = 4.5718027667180976184568645721083e-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 = 0.02141
Order of pole (three term test) = -0.9048
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.53
y[1] (analytic) = 1.954452020088668982642103927312
y[1] (numeric) = 1.9544520200886689826421039273129
absolute error = 9e-31
relative error = 4.6048712925639846340615316670258e-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 = 0.03104
Order of pole (three term test) = -0.9179
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.54
y[1] (analytic) = 1.9403197342108376745495538489584
y[1] (numeric) = 1.9403197342108376745495538489593
absolute error = 9e-31
relative error = 4.6384107945283868635209615826851e-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 = 0.04066
Order of pole (three term test) = -0.9359
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.55
y[1] (analytic) = 1.9261934163098518936434669256154
y[1] (numeric) = 1.9261934163098518936434669256164
absolute error = 1.0e-30
relative error = 5.1915866367966949013672811434957e-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 = 0.05026
Order of pole (three term test) = -0.9587
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.56
y[1] (analytic) = 1.912074479005729846157480824793
y[1] (numeric) = 1.912074479005729846157480824794
absolute error = 1.0e-30
relative error = 5.2299217994897119029395657100998e-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 = 0.05984
Order of pole (three term test) = -0.9863
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.57
y[1] (analytic) = 1.8979643341804362024287760270908
y[1] (numeric) = 1.8979643341804362024287760270917
absolute error = 9e-31
relative error = 4.7419226156777640959695588519678e-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 = 0.06939
Order of pole (three term test) = -1.019
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.58
y[1] (analytic) = 1.8838643928366950769954241127546
y[1] (numeric) = 1.8838643928366950769954241127555
absolute error = 9e-31
relative error = 4.7774139339445412059676852204283e-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 = 0.07892
Order of pole (three term test) = -1.056
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.59
y[1] (analytic) = 1.8697760649568909320166179382882
y[1] (numeric) = 1.8697760649568909320166179382891
absolute error = 9e-31
relative error = 4.8134106370687238668793901674680e-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 = 0.08842
Order of pole (three term test) = -1.098
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.6
y[1] (analytic) = 1.8557007593620715138078594915594
y[1] (numeric) = 1.8557007593620715138078594915603
absolute error = 9e-31
relative error = 4.8499198777576089615715211708184e-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 = 0.09788
Order of pole (three term test) = -1.145
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.61
y[1] (analytic) = 1.8416398835710669220799547453862
y[1] (numeric) = 1.8416398835710669220799547453871
absolute error = 9e-31
relative error = 4.8869488982549500608917469575606e-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 = 0.1073
Order of pole (three term test) = -1.196
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.62
y[1] (analytic) = 1.8275948436597388998574912258192
y[1] (numeric) = 1.8275948436597388998574912258201
absolute error = 9e-31
relative error = 4.9245050297786994080017322440952e-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 = 0.1167
Order of pole (three term test) = -1.252
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.63
y[1] (analytic) = 1.8135670441203744190305145799346
y[1] (numeric) = 1.8135670441203744190305145799356
absolute error = 1.0e-30
relative error = 5.5139952131465044584701061188010e-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 = 0.126
Order of pole (three term test) = -1.313
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.64
y[1] (analytic) = 1.7995578877212376220636773540144
y[1] (numeric) = 1.7995578877212376220636773540153
absolute error = 9e-31
relative error = 5.0012283913781796159608904208097e-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 = 0.1353
Order of pole (three term test) = -1.379
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.65
y[1] (analytic) = 1.7855687753662941645516494087916
y[1] (numeric) = 1.7855687753662941645516494087925
absolute error = 9e-31
relative error = 5.0404107218741697393503786418654e-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 = 0.1445
Order of pole (three term test) = -1.449
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.66
y[1] (analytic) = 1.7716011059551219860696384391713
y[1] (numeric) = 1.7716011059551219860696384391723
absolute error = 1.0e-30
relative error = 5.6446115134979594859963023071491e-29 %
Correct digits = 31
h = 0.01
bytes used=96041248, alloc=4586680, time=8.90
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1537
Order of pole (three term test) = -1.523
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.67
y[1] (analytic) = 1.7576562762430225181251949112187
y[1] (numeric) = 1.7576562762430225181251949112197
absolute error = 1.0e-30
relative error = 5.6893945279078837455362185827617e-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 = 0.1628
Order of pole (three term test) = -1.603
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.68
y[1] (analytic) = 1.7437356807013463179739326311258
y[1] (numeric) = 1.7437356807013463179739326311268
absolute error = 1.0e-30
relative error = 5.7348141181454228395290863222950e-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 = 0.1718
Order of pole (three term test) = -1.687
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.69
y[1] (analytic) = 1.7298407113780470956193884569321
y[1] (numeric) = 1.7298407113780470956193884569331
absolute error = 1.0e-30
relative error = 5.7808790914821725740609625610224e-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 = 0.1808
Order of pole (three term test) = -1.775
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.7
y[1] (analytic) = 1.7159727577584780784781165768751
y[1] (numeric) = 1.715972757758478078478116576876
absolute error = 9e-31
relative error = 5.2448385088329843256901588394742e-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 = 0.1897
Order of pole (three term test) = -1.868
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.71
y[1] (analytic) = 1.702133206626444633957548202174
y[1] (numeric) = 1.7021332066264446339575482021749
absolute error = 9e-31
relative error = 5.2874827686592260702482456612175e-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 = 0.1985
Order of pole (three term test) = -1.965
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.72
y[1] (analytic) = 1.6883234419255270445685697930567
y[1] (numeric) = 1.6883234419255270445685697930576
absolute error = 9e-31
relative error = 5.3307321195135045548656326173832e-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 = 0.2073
Order of pole (three term test) = -2.067
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.73
y[1] (analytic) = 1.674544844620687303179744591348
y[1] (numeric) = 1.674544844620687303179744591349
absolute error = 1.0e-30
relative error = 5.9717719905346392431343687109038e-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 = 0.2159
Order of pole (three term test) = -2.173
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.74
y[1] (analytic) = 1.6607987925601737676183247512693
y[1] (numeric) = 1.6607987925601737676183247512702
absolute error = 9e-31
relative error = 5.4190790843038944432973950224410e-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 = 0.2245
Order of pole (three term test) = -2.284
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.75
y[1] (analytic) = 1.6470866603377374840375148963345
y[1] (numeric) = 1.6470866603377374840375148963354
absolute error = 9e-31
relative error = 5.4641933643944011305482561135338e-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 = 0.233
Order of pole (three term test) = -2.398
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.76
y[1] (analytic) = 1.6334098191551739573028310281927
y[1] (numeric) = 1.6334098191551739573028310281936
absolute error = 9e-31
relative error = 5.5099460615799076845756964448462e-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 = 0.2414
Order of pole (three term test) = -2.517
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.77
y[1] (analytic) = 1.619769636685204114105968008674
y[1] (numeric) = 1.6197696366852041141059680086749
absolute error = 9e-31
relative error = 5.5563456655590555165611662104365e-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 = 0.2497
Order of pole (three term test) = -2.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.78
y[1] (analytic) = 1.6061674769347081705955987451057
y[1] (numeric) = 1.6061674769347081705955987451066
absolute error = 9e-31
relative error = 5.6034007220567424576416246538883e-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 = 0.2579
Order of pole (three term test) = -2.768
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.79
y[1] (analytic) = 1.592604700108326081024370601911
y[1] (numeric) = 1.5926047001083260810243706019119
absolute error = 9e-31
relative error = 5.6511198286604556269123783011356e-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 = 0.266
Order of pole (three term test) = -2.899
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.8
y[1] (analytic) = 1.5790826624724382072535684249411
y[1] (numeric) = 1.579082662472438207253568424942
absolute error = 9e-31
relative error = 5.6995116303210559493498240346765e-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 = 0.274
Order of pole (three term test) = -3.034
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.81
y[1] (analytic) = 1.5656027162195398109351446479906
y[1] (numeric) = 1.5656027162195398109351446479915
absolute error = 9e-31
relative error = 5.7485848145002558724993743930118e-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 = 0.2818
Order of pole (three term test) = -3.174
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.82
y[1] (analytic) = 1.5521662093330229308088773987068
y[1] (numeric) = 1.5521662093330229308088773987076
absolute error = 8e-31
relative error = 5.1540872052856104750127631862737e-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 = 0.2896
Order of pole (three term test) = -3.317
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.83
y[1] (analytic) = 1.5387744854523791668142454947682
y[1] (numeric) = 1.5387744854523791668142454947691
absolute error = 9e-31
relative error = 5.8488102610787181639800843278164e-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 = 0.2972
Order of pole (three term test) = -3.464
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.84
y[1] (analytic) = 1.5254288837388368506262785040301
y[1] (numeric) = 1.525428883738836850626278504031
absolute error = 9e-31
relative error = 5.8999800619619428775836301097711e-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 = 0.3048
Order of pole (three term test) = -3.615
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.85
y[1] (analytic) = 1.5121307387414460387863596323048
y[1] (numeric) = 1.5121307387414460387863596323057
absolute error = 9e-31
relative error = 5.9518663098474837703997492386328e-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 = 0.3122
Order of pole (three term test) = -3.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.86
y[1] (analytic) = 1.4988813802636247198170728914176
y[1] (numeric) = 1.4988813802636247198170728914185
absolute error = 9e-31
relative error = 6.0044778182627575355647232231952e-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 = 0.3195
Order of pole (three term test) = -3.928
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.87
y[1] (analytic) = 1.4856821332301795805891719394539
y[1] (numeric) = 1.4856821332301795805891719394549
absolute error = 1.0e-30
relative error = 6.7309148951383942048494933316839e-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 = 0.3266
Order of pole (three term test) = -4.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.88
y[1] (analytic) = 1.4725343175548146297532182376728
y[1] (numeric) = 1.4725343175548146297532182376739
absolute error = 1.1e-30
relative error = 7.4701145289882376122479559863855e-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 = 0.3336
Order of pole (three term test) = -4.256
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.89
y[1] (analytic) = 1.4594392480081409272631362478279
y[1] (numeric) = 1.4594392480081409272631362478289
absolute error = 1.0e-30
relative error = 6.8519467416325224110770839145719e-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 = 0.3405
Order of pole (three term test) = -4.425
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.9
y[1] (analytic) = 1.4463982340862006189087417889509
y[1] (numeric) = 1.446398234086200618908741788952
absolute error = 1.1e-30
relative error = 7.6050977806603405078864193620040e-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 = 0.3473
Order of pole (three term test) = -4.597
NO COMPLEX POLE (six term test) for Equation 1
bytes used=100042976, alloc=4586680, time=9.28
TOP MAIN SOLVE Loop
x[1] = 5.91
y[1] (analytic) = 1.4334125798795184233442273614185
y[1] (numeric) = 1.4334125798795184233442273614196
absolute error = 1.1e-30
relative error = 7.6739943226426650554716327912667e-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 = 0.3539
Order of pole (three term test) = -4.773
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.92
y[1] (analytic) = 1.4204835839426936663547781927022
y[1] (numeric) = 1.4204835839426936663547781927033
absolute error = 1.1e-30
relative error = 7.7438416919035448534208498653995e-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 = 0.3604
Order of pole (three term test) = -4.952
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.93
y[1] (analytic) = 1.4076125391645459030492194006656
y[1] (numeric) = 1.4076125391645459030492194006667
absolute error = 1.1e-30
relative error = 7.8146504765642267984369856136148e-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 = 0.3667
Order of pole (three term test) = -5.134
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.94
y[1] (analytic) = 1.394800732638827113308263388891
y[1] (numeric) = 1.3948007326388271133082633888921
absolute error = 1.1e-30
relative error = 7.8864311887684999647496335968893e-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 = 0.3729
Order of pole (three term test) = -5.319
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.95
y[1] (analytic) = 1.3820494455355133991610731713017
y[1] (numeric) = 1.3820494455355133991610731713029
absolute error = 1.2e-30
relative error = 8.6827573635401062587596493411723e-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 = 0.3789
Order of pole (three term test) = -5.508
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.96
y[1] (analytic) = 1.3693599529726890548131474084177
y[1] (numeric) = 1.3693599529726890548131474084189
absolute error = 1.2e-30
relative error = 8.7632181545470767616929620667295e-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 = 0.3848
Order of pole (three term test) = -5.699
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.97
y[1] (analytic) = 1.3567335238890358208117614476402
y[1] (numeric) = 1.3567335238890358208117614476414
absolute error = 1.2e-30
relative error = 8.8447729703047073617944893444809e-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 = 0.3905
Order of pole (three term test) = -5.894
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.98
y[1] (analytic) = 1.3441714209169400733172892227959
y[1] (numeric) = 1.3441714209169400733172892227972
absolute error = 1.3e-30
relative error = 9.6713855076102712134528715592819e-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 = 0.3961
Order of pole (three term test) = -6.091
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 5.99
y[1] (analytic) = 1.3316749002562306376557352242898
y[1] (numeric) = 1.331674900256230637655735224291
absolute error = 1.2e-30
relative error = 9.0112083645122787361332138099873e-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 = 0.4015
Order of pole (three term test) = -6.291
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6
y[1] (analytic) = 1.319245211548559852265903148689
y[1] (numeric) = 1.3192452115485598522659031486902
absolute error = 1.2e-30
relative error = 9.0961103326000544865760812357355e-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 = 0.4067
Order of pole (three term test) = -6.493
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.01
y[1] (analytic) = 1.3068835977524404448301244131061
y[1] (numeric) = 1.3068835977524404448301244131073
absolute error = 1.2e-30
relative error = 9.1821490610467733003534336139966e-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 = 0.4118
Order of pole (three term test) = -6.698
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.02
y[1] (analytic) = 1.2945912950189507167967978720894
y[1] (numeric) = 1.2945912950189507167967978720905
absolute error = 1.1e-30
relative error = 8.4968901322938200673204692068936e-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 = 0.4167
Order of pole (three term test) = -6.906
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.03
y[1] (analytic) = 1.2823695325681204656727098154137
y[1] (numeric) = 1.2823695325681204656727098154148
absolute error = 1.1e-30
relative error = 8.5778706688164953385306208868518e-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 = 0.4215
Order of pole (three term test) = -7.116
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.04
y[1] (analytic) = 1.2702195325660100063898936267222
y[1] (numeric) = 1.2702195325660100063898936267233
absolute error = 1.1e-30
relative error = 8.6599203665043299129641428534697e-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 = 0.4261
Order of pole (three term test) = -7.329
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.05
y[1] (analytic) = 1.2581425100024945837424586096369
y[1] (numeric) = 1.2581425100024945837424586096381
absolute error = 1.2e-30
relative error = 9.5378702369544821945243814247381e-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 = 0.4305
Order of pole (three term test) = -7.543
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.06
y[1] (analytic) = 1.2461396725697663973502983149748
y[1] (numeric) = 1.2461396725697663973502983149759
absolute error = 1.1e-30
relative error = 8.8272608938900095959846107052018e-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 = 0.4347
Order of pole (three term test) = -7.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.07
y[1] (analytic) = 1.2342122205415663888459340231986
y[1] (numeric) = 1.2342122205415663888459340231997
absolute error = 1.1e-30
relative error = 8.9125677228939224754779281207779e-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 = 0.4388
Order of pole (three term test) = -7.979
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.08
y[1] (analytic) = 1.222361346653157868005134855879
y[1] (numeric) = 1.2223613466531578680051348558801
absolute error = 1.1e-30
relative error = 8.9989756548815543509729501251310e-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 = 0.4427
Order of pole (three term test) = -8.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.09
y[1] (analytic) = 1.2105882359820539803586798093356
y[1] (numeric) = 1.2105882359820539803586798093366
absolute error = 1.0e-30
relative error = 8.2604470312631074870854211621672e-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 = 0.4464
Order of pole (three term test) = -8.423
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.1
y[1] (analytic) = 1.1988940658295109434391070885767
y[1] (numeric) = 1.1988940658295109434391070885777
absolute error = 1.0e-30
relative error = 8.3410205163381405197359125436321e-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 = 0.4499
Order of pole (three term test) = -8.648
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.11
y[1] (analytic) = 1.1872800056027989022400707593291
y[1] (numeric) = 1.1872800056027989022400707593301
absolute error = 1.0e-30
relative error = 8.4226129917203971902129240239991e-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 = 0.4533
Order of pole (three term test) = -8.874
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.12
y[1] (analytic) = 1.175747216698262176704651489065
y[1] (numeric) = 1.175747216698262176704651489066
absolute error = 1.0e-30
relative error = 8.5052295748418084144527383818166e-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 = 0.4565
Order of pole (three term test) = -9.102
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.13
y[1] (analytic) = 1.1642968523851805951204230770255
y[1] (numeric) = 1.1642968523851805951204230770265
absolute error = 1.0e-30
relative error = 8.5888748900368340585711331485744e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4595
Order of pole (three term test) = -9.332
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.14
y[1] (analytic) = 1.1529300576904435271911533670237
y[1] (numeric) = 1.1529300576904435271911533670247
absolute error = 1.0e-30
relative error = 8.6735530341121130558296325878345e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.21
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4623
Order of pole (three term test) = -9.563
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=104045800, alloc=4586680, time=9.65
x[1] = 6.15
y[1] (analytic) = 1.141647969284048149285727720845
y[1] (numeric) = 1.141647969284048149285727720846
absolute error = 1.0e-30
relative error = 8.7592675404759085294087446079592e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4649
Order of pole (three term test) = -9.795
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.16
y[1] (analytic) = 1.1304517153654333919423523656643
y[1] (numeric) = 1.1304517153654333919423523656653
absolute error = 1.0e-30
relative error = 8.8460213418026159709710651860020e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.81
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4673
Order of pole (three term test) = -10.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.17
y[1] (analytic) = 1.1193424155506609361385658004711
y[1] (numeric) = 1.119342415550660936138565800472
absolute error = 9e-31
relative error = 8.0404350580893930513221471471953e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4696
Order of pole (three term test) = -10.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.18
y[1] (analytic) = 1.1083211807604545401334157373048
y[1] (numeric) = 1.1083211807604545401334157373058
absolute error = 1.0e-30
relative error = 9.0226553219335579207975616675968e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4717
Order of pole (three term test) = -10.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.19
y[1] (analytic) = 1.0973891131091088928558171096453
y[1] (numeric) = 1.0973891131091088928558171096462
absolute error = 9e-31
relative error = 8.2012842049264680106267582319702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4735
Order of pole (three term test) = -10.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.2
y[1] (analytic) = 1.0865473057942791028611766652291
y[1] (numeric) = 1.08654730579427910286117666523
absolute error = 9e-31
relative error = 8.2831184173991321386005626814191e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4752
Order of pole (three term test) = -10.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.21
y[1] (analytic) = 1.0757968429876618438155466944416
y[1] (numeric) = 1.0757968429876618438155466944426
absolute error = 1.0e-30
relative error = 9.2954353465366030388212028284193e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4767
Order of pole (three term test) = -11.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.22
y[1] (analytic) = 1.0651387997265790883016607371408
y[1] (numeric) = 1.0651387997265790883016607371418
absolute error = 1.0e-30
relative error = 9.3884477802958618646891316914353e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.478
Order of pole (three term test) = -11.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.23
y[1] (analytic) = 1.0545742418064752714831240770046
y[1] (numeric) = 1.0545742418064752714831240770056
absolute error = 1.0e-30
relative error = 9.4824997649004764831566068885266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4791
Order of pole (three term test) = -11.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.24
y[1] (analytic) = 1.0441042256743386348208072060246
y[1] (numeric) = 1.0441042256743386348208072060256
absolute error = 1.0e-30
relative error = 9.5775879017647519331201612808035e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.48
Order of pole (three term test) = -11.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.25
y[1] (analytic) = 1.0337297983230574076182553689473
y[1] (numeric) = 1.0337297983230574076182553689482
absolute error = 9e-31
relative error = 8.7063370085684163824026779404038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.78
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4808
Order of pole (three term test) = -12.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.26
y[1] (analytic) = 1.0234519971867213906899234247838
y[1] (numeric) = 1.0234519971867213906899234247847
absolute error = 9e-31
relative error = 8.7937685643677680998808182935304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.14
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -12.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.27
y[1] (analytic) = 1.0132718500368794119066208124552
y[1] (numeric) = 1.0132718500368794119066208124561
absolute error = 9e-31
relative error = 8.8821178637030454529071744082077e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -12.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.28
y[1] (analytic) = 1.0031903748797630277861602438701
y[1] (numeric) = 1.0031903748797630277861602438709
absolute error = 8e-31
relative error = 7.9745581699374226243911228715130e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.88
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.29
y[1] (analytic) = 0.99320857985448674867340442971298
y[1] (numeric) = 0.99320857985448674867340442971383
absolute error = 8.5e-31
relative error = 8.5581218008057483036284921393537e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.26
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.3
y[1] (analytic) = 0.9833274631322349674023599703662
y[1] (numeric) = 0.98332746313223496740235997036708
absolute error = 8.8e-31
relative error = 8.9492059664122307145961134572851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -13.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.31
y[1] (analytic) = 0.97354801281644567266344158982794
y[1] (numeric) = 0.97354801281644567266344158982877
absolute error = 8.3e-31
relative error = 8.5255168627876348127737076006084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.96
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -13.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.32
y[1] (analytic) = 0.96387120684400092862139002461076
y[1] (numeric) = 0.96387120684400092862139002461163
absolute error = 8.7e-31
relative error = 9.0261021786161349231304151170952e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = -13.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.33
y[1] (analytic) = 0.95429801288743400165354078331755
y[1] (numeric) = 0.95429801288743400165354078331847
absolute error = 9.2e-31
relative error = 9.6405943172441700598760351479191e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.21
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4797
Order of pole (three term test) = -14.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.34
y[1] (analytic) = 0.94482938825816291341427616061244
y[1] (numeric) = 0.9448293882581629134142761606133
absolute error = 8.6e-31
relative error = 9.1021724206255919820015408410728e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.85
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4787
Order of pole (three term test) = -14.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.35
y[1] (analytic) = 0.93546627981076009678971562340151
y[1] (numeric) = 0.93546627981076009678971562340237
absolute error = 8.6e-31
relative error = 9.1932763217715712011740832630431e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4775
Order of pole (three term test) = -14.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.36
y[1] (analytic) = 0.92620962384826772769727407939828
y[1] (numeric) = 0.92620962384826772769727407939916
absolute error = 8.8e-31
relative error = 9.5010889256767448704929431056188e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4761
Order of pole (three term test) = -14.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.37
y[1] (analytic) = 0.91706034602856820111800444509109
y[1] (numeric) = 0.91706034602856820111800444509199
absolute error = 9.0e-31
relative error = 9.8139670295150158156934967529377e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4745
Order of pole (three term test) = -15.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.38
y[1] (analytic) = 0.90801936127181911423609693563169
y[1] (numeric) = 0.9080193612718191142360969356326
absolute error = 9.1e-31
relative error = 1.0021812736739519520949321782590e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4727
Order of pole (three term test) = -15.3
NO COMPLEX POLE (six term test) for Equation 1
bytes used=108048880, alloc=4586680, time=10.02
TOP MAIN SOLVE Loop
x[1] = 6.39
y[1] (analytic) = 0.89908757366896201311008386978999
y[1] (numeric) = 0.89908757366896201311008386979087
absolute error = 8.8e-31
relative error = 9.7877006175152641011846995112710e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.13
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4708
Order of pole (three term test) = -15.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.4
y[1] (analytic) = 0.89026587639131405192484041252885
y[1] (numeric) = 0.89026587639131405192484041252977
absolute error = 9.2e-31
relative error = 1.0333991500710023747220766516926e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4686
Order of pole (three term test) = -15.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.41
y[1] (analytic) = 0.88155515160125160558311602230258
y[1] (numeric) = 0.88155515160125160558311602230348
absolute error = 9.0e-31
relative error = 1.0209230793617906718542495111111e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4663
Order of pole (three term test) = -16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.42
y[1] (analytic) = 0.87295627036399476720090737519323
y[1] (numeric) = 0.87295627036399476720090737519411
absolute error = 8.8e-31
relative error = 1.0080688230042361955291074829573e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.16
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4638
Order of pole (three term test) = -16.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.43
y[1] (analytic) = 0.86447009256050155198341055488262
y[1] (numeric) = 0.86447009256050155198341055488351
absolute error = 8.9e-31
relative error = 1.0295324357189507858211330931441e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.85
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4611
Order of pole (three term test) = -16.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.44
y[1] (analytic) = 0.85609746680148051798857699176355
y[1] (numeric) = 0.85609746680148051798857699176446
absolute error = 9.1e-31
relative error = 1.0629630798931202538152692421969e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4582
Order of pole (three term test) = -16.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.45
y[1] (analytic) = 0.84783923034253040244454088508621
y[1] (numeric) = 0.84783923034253040244454088508708
absolute error = 8.7e-31
relative error = 1.0261379384963309128350197118172e-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 = 0.4551
Order of pole (three term test) = -16.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.46
y[1] (analytic) = 0.8396962090004152595865696313847
y[1] (numeric) = 0.83969620900041525958656963138557
absolute error = 8.7e-31
relative error = 1.0360889934654566888879739945831e-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 = 0.4519
Order of pole (three term test) = -17.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.47
y[1] (analytic) = 0.83166921707048347242998307824102
y[1] (numeric) = 0.83166921707048347242998307824187
absolute error = 8.5e-31
relative error = 1.0220409539673547934126896319034e-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 = 0.4485
Order of pole (three term test) = -17.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.48
y[1] (analytic) = 0.823759057245238896509047050662
y[1] (numeric) = 0.8237590572452388965090470506629
absolute error = 9.0e-31
relative error = 1.0925524788883306149788431104655e-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 = 0.4448
Order of pole (three term test) = -17.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.49
y[1] (analytic) = 0.81596652053407227839961010669111
y[1] (numeric) = 0.81596652053407227839961010669195
absolute error = 8.4e-31
relative error = 1.0294540019242421315089293098189e-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 = 0.4411
Order of pole (three term test) = -17.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.5
y[1] (analytic) = 0.80829238618416097581674099698117
y[1] (numeric) = 0.80829238618416097581674099698207
absolute error = 9.0e-31
relative error = 1.1134584655050114531960790314553e-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 = 0.4371
Order of pole (three term test) = -18.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.51
y[1] (analytic) = 0.80073742160254488924944038438876
y[1] (numeric) = 0.8007374216025448892494403843896
absolute error = 8.4e-31
relative error = 1.0490330254815336173007754984154e-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 = 0.433
Order of pole (three term test) = -18.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.52
y[1] (analytic) = 0.79330238227938639747432684523248
y[1] (numeric) = 0.79330238227938639747432684523331
absolute error = 8.3e-31
relative error = 1.0462593060859980900052862132130e-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 = 0.4286
Order of pole (three term test) = -18.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.53
y[1] (analytic) = 0.78598801171242197089079594304616
y[1] (numeric) = 0.78598801171242197089079594304705
absolute error = 8.9e-31
relative error = 1.1323327922788140853976066849666e-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 = 0.4242
Order of pole (three term test) = -18.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.54
y[1] (analytic) = 0.7787950413326130174533620798865
y[1] (numeric) = 0.77879504133261301745336207988734
absolute error = 8.4e-31
relative error = 1.0785893019589054595463621548703e-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 = 0.4195
Order of pole (three term test) = -18.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.55
y[1] (analytic) = 0.77172419043100339605463246914531
y[1] (numeric) = 0.77172419043100339605463246914614
absolute error = 8.3e-31
relative error = 1.0755137784866506633266269003723e-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 = 0.4147
Order of pole (three term test) = -19.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.56
y[1] (analytic) = 0.76477616608679091154662306346296
y[1] (numeric) = 0.76477616608679091154662306346386
absolute error = 9.0e-31
relative error = 1.1768149164547358039387833309523e-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 = 0.4097
Order of pole (three term test) = -19.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.57
y[1] (analytic) = 0.75795166309661998419097408513452
y[1] (numeric) = 0.75795166309661998419097408513535
absolute error = 8.3e-31
relative error = 1.0950566380566086902862949950767e-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 = 0.4045
Order of pole (three term test) = -19.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.58
y[1] (analytic) = 0.75125136390510256421219755840566
y[1] (numeric) = 0.75125136390510256421219755840647
absolute error = 8.1e-31
relative error = 1.0782010375189395512688820052810e-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 = 0.3992
Order of pole (three term test) = -19.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.59
y[1] (analytic) = 0.74467593853657423930460247403209
y[1] (numeric) = 0.74467593853657423930460247403294
absolute error = 8.5e-31
relative error = 1.1414361012797150325555781820767e-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 = 0.3938
Order of pole (three term test) = -19.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.6
y[1] (analytic) = 0.73822604452809235942527717273921
y[1] (numeric) = 0.73822604452809235942527717274008
absolute error = 8.7e-31
relative error = 1.1785008215961054884412680107463e-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 = 0.3881
Order of pole (three term test) = -20.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.61
y[1] (analytic) = 0.73190232686368287900481493945434
y[1] (numeric) = 0.73190232686368287900481493945526
absolute error = 9.2e-31
relative error = 1.2569983264602332559038642701257e-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 = 0.3823
Order of pole (three term test) = -20.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.62
y[1] (analytic) = 0.72570541790984249183676762024235
y[1] (numeric) = 0.72570541790984249183676762024324
absolute error = 8.9e-31
relative error = 1.2263929385608755801925578106783e-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 = 0.3764
Order of pole (three term test) = -20.5
NO COMPLEX POLE (six term test) for Equation 1
bytes used=112050004, alloc=4586680, time=10.40
TOP MAIN SOLVE Loop
x[1] = 6.63
y[1] (analytic) = 0.7196359373523025083785902748168
y[1] (numeric) = 0.71963593735230250837859027481767
absolute error = 8.7e-31
relative error = 1.2089446271970792022128396127290e-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 = 0.3703
Order of pole (three term test) = -20.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.64
y[1] (analytic) = 0.71369449213406079902365017690234
y[1] (numeric) = 0.7136944921340607990236501769032
absolute error = 8.6e-31
relative error = 1.2049973896091902123402954060623e-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 = 0.3641
Order of pole (three term test) = -20.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.65
y[1] (analytic) = 0.70788167639468800009833308640711
y[1] (numeric) = 0.70788167639468800009833308640798
absolute error = 8.7e-31
relative error = 1.2290189575622253648458999916954e-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 = 0.3577
Order of pole (three term test) = -21.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.66
y[1] (analytic) = 0.70219807141091405191306908970309
y[1] (numeric) = 0.70219807141091405191306908970392
absolute error = 8.3e-31
relative error = 1.1820026767266617722368449562401e-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 = 0.3512
Order of pole (three term test) = -21.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.67
y[1] (analytic) = 0.69664424553850101016396185217604
y[1] (numeric) = 0.69664424553850101016396185217689
absolute error = 8.5e-31
relative error = 1.2201349619172639407524083446746e-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 = 0.3445
Order of pole (three term test) = -21.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.68
y[1] (analytic) = 0.69122075415540794335544195775286
y[1] (numeric) = 0.69122075415540794335544195775378
absolute error = 9.2e-31
relative error = 1.3309785542017382195692987442326e-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 = 0.3377
Order of pole (three term test) = -21.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.69
y[1] (analytic) = 0.68592813960625359970683964246542
y[1] (numeric) = 0.68592813960625359970683964246634
absolute error = 9.2e-31
relative error = 1.3412483711895997123765318277071e-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 = 0.3308
Order of pole (three term test) = -21.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.7
y[1] (analytic) = 0.68076693114808239722990530813655
y[1] (numeric) = 0.68076693114808239722990530813737
absolute error = 8.2e-31
relative error = 1.2045238428622074503034086930359e-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 = 0.3237
Order of pole (three term test) = -21.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.71
y[1] (analytic) = 0.67573764489743916033307520651799
y[1] (numeric) = 0.67573764489743916033307520651887
absolute error = 8.8e-31
relative error = 1.3022805620568364042030896505791e-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 = 0.3165
Order of pole (three term test) = -22.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.72
y[1] (analytic) = 0.6708407837787578954347176281642
y[1] (numeric) = 0.67084078377875789543471762816506
absolute error = 8.6e-31
relative error = 1.2819733397181565509526753108682e-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 = 0.3092
Order of pole (three term test) = -22.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.73
y[1] (analytic) = 0.66607683747406976666478906112911
y[1] (numeric) = 0.66607683747406976666478906112995
absolute error = 8.4e-31
relative error = 1.2611157643395774530773082675600e-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 = 0.3017
Order of pole (three term test) = -22.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.74
y[1] (analytic) = 0.66144628237403530081542027332393
y[1] (numeric) = 0.66144628237403530081542027332476
absolute error = 8.3e-31
relative error = 1.2548260109966885799289135911098e-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 = 0.2942
Order of pole (three term test) = -22.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.75
y[1] (analytic) = 0.65694958153030571827913090007311
y[1] (numeric) = 0.65694958153030571827913090007397
absolute error = 8.6e-31
relative error = 1.3090806725178306090967795360423e-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 = 0.2865
Order of pole (three term test) = -22.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.76
y[1] (analytic) = 0.65258718460921815380187995685478
y[1] (numeric) = 0.65258718460921815380187995685569
absolute error = 9.1e-31
relative error = 1.3944496941736997577106915906439e-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 = 0.2787
Order of pole (three term test) = -22.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.77
y[1] (analytic) = 0.64835952784682939749028978475927
y[1] (numeric) = 0.64835952784682939749028978476019
absolute error = 9.2e-31
relative error = 1.4189658059861871073537780250011e-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 = 0.2708
Order of pole (three term test) = -22.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.78
y[1] (analytic) = 0.64426703400529265266147094868322
y[1] (numeric) = 0.6442670340052926526614709486841
absolute error = 8.8e-31
relative error = 1.3658932609498855739950033747908e-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 = 0.2628
Order of pole (three term test) = -23.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.79
y[1] (analytic) = 0.64031011233058167282331052515318
y[1] (numeric) = 0.6403101123305816728233105251541
absolute error = 9.2e-31
relative error = 1.4368037959785008011970059927428e-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 = 0.2546
Order of pole (three term test) = -23.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.8
y[1] (analytic) = 0.63648915851156650533629598253336
y[1] (numeric) = 0.63648915851156650533629598253426
absolute error = 9.0e-31
relative error = 1.4140068027311809785848080152680e-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 = 0.2464
Order of pole (three term test) = -23.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.81
y[1] (analytic) = 0.63280455464044493414840503795799
y[1] (numeric) = 0.63280455464044493414840503795891
absolute error = 9.2e-31
relative error = 1.4538454144388032790417940054841e-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 = 0.2381
Order of pole (three term test) = -23.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.82
y[1] (analytic) = 0.62925666917453357842581431419592
y[1] (numeric) = 0.6292566691745335784258143141968
absolute error = 8.8e-31
relative error = 1.3984754442958777388283983452848e-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 = 0.2297
Order of pole (three term test) = -23.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.83
y[1] (analytic) = 0.62584585689942246793772308057454
y[1] (numeric) = 0.62584585689942246793772308057546
absolute error = 9.2e-31
relative error = 1.4700105303211267103510726273575e-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 = 0.2211
Order of pole (three term test) = -23.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.84
y[1] (analytic) = 0.62257245889349677970704917742639
y[1] (numeric) = 0.62257245889349677970704917742727
absolute error = 8.8e-31
relative error = 1.4134900884694310679010655760734e-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 = 0.2125
Order of pole (three term test) = -23.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.85
y[1] (analytic) = 0.61943680249382928372376693355664
y[1] (numeric) = 0.61943680249382928372376693355755
absolute error = 9.1e-31
relative error = 1.4690764196385720136053652297773e-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 = 0.2039
Order of pole (three term test) = -23.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.86
y[1] (analytic) = 0.61643920126344690844789287577948
y[1] (numeric) = 0.61643920126344690844789287578041
absolute error = 9.3e-31
relative error = 1.5086645983803145181091820385079e-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 = 0.1951
Order of pole (three term test) = -24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=116052648, alloc=4586680, time=10.77
x[1] = 6.87
y[1] (analytic) = 0.61357995495997469941829116079586
y[1] (numeric) = 0.61357995495997469941829116079669
absolute error = 8.3e-31
relative error = 1.3527169414361701274660325922438e-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 = 0.1863
Order of pole (three term test) = -24.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.88
y[1] (analytic) = 0.61085934950566030654530790147714
y[1] (numeric) = 0.61085934950566030654530790147798
absolute error = 8.4e-31
relative error = 1.3751119642840408792794155934695e-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 = 0.1773
Order of pole (three term test) = -24.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.89
y[1] (analytic) = 0.60827765695878199761352561346565
y[1] (numeric) = 0.60827765695878199761352561346651
absolute error = 8.6e-31
relative error = 1.4138280276473728296379523080803e-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 = 0.1683
Order of pole (three term test) = -24.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.9
y[1] (analytic) = 0.60583513548644305716946093065304
y[1] (numeric) = 0.60583513548644305716946093065396
absolute error = 9.2e-31
relative error = 1.5185649463220792320021344465732e-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 = 0.1593
Order of pole (three term test) = -24.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.91
y[1] (analytic) = 0.60353202933875529133164556107738
y[1] (numeric) = 0.60353202933875529133164556107828
absolute error = 9.0e-31
relative error = 1.4912216025818255149758594191928e-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 = 0.1502
Order of pole (three term test) = -24.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.92
y[1] (analytic) = 0.60136856882441422015109580086292
y[1] (numeric) = 0.60136856882441422015109580086376
absolute error = 8.4e-31
relative error = 1.3968139399803927314253727177016e-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 = 0.141
Order of pole (three term test) = -24.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.93
y[1] (analytic) = 0.59934497028766839998258062073236
y[1] (numeric) = 0.59934497028766839998258062073324
absolute error = 8.8e-31
relative error = 1.4682696003565780043542538132054e-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 = 0.1318
Order of pole (three term test) = -24.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.94
y[1] (analytic) = 0.59746143608668517891525903089959
y[1] (numeric) = 0.59746143608668517891525903090046
absolute error = 8.7e-31
relative error = 1.4561609293118835360499979067543e-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 = 0.1225
Order of pole (three term test) = -24.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.95
y[1] (analytic) = 0.59571815457331504866911518355922
y[1] (numeric) = 0.59571815457331504866911518356006
absolute error = 8.4e-31
relative error = 1.4100627848108012936259910694910e-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 = 0.1131
Order of pole (three term test) = -24.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.96
y[1] (analytic) = 0.59411530007425661650513858558769
y[1] (numeric) = 0.59411530007425661650513858558855
absolute error = 8.6e-31
relative error = 1.4475304707562846554423827263180e-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 = 0.1037
Order of pole (three term test) = -24.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.97
y[1] (analytic) = 0.59265303287362408063636259901217
y[1] (numeric) = 0.59265303287362408063636259901307
absolute error = 9.0e-31
relative error = 1.5185951139676591407384067847765e-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 = 0.09432
Order of pole (three term test) = -24.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.98
y[1] (analytic) = 0.59133149919691895237769306999634
y[1] (numeric) = 0.59133149919691895237769306999721
absolute error = 8.7e-31
relative error = 1.4712559726338572997098484614449e-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 = 0.08486
Order of pole (three term test) = -24.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 6.99
y[1] (analytic) = 0.59015083119640762784895524979462
y[1] (numeric) = 0.59015083119640762784895524979549
absolute error = 8.7e-31
relative error = 1.4741993978662312402788692177593e-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 = 0.07536
Order of pole (three term test) = -24.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7
y[1] (analytic) = 0.58911114693790627146180338668716
y[1] (numeric) = 0.58911114693790627146180338668807
absolute error = 9.1e-31
relative error = 1.5447000192239040821725211560241e-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 = 0.06584
Order of pole (three term test) = -24.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.01
y[1] (analytic) = 0.58821255038897433269113173754996
y[1] (numeric) = 0.58821255038897433269113173755082
absolute error = 8.6e-31
relative error = 1.4620565294489169554456047045201e-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 = 0.05628
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.02
y[1] (analytic) = 0.58745513140851787676947115473058
y[1] (numeric) = 0.5874551314085178767694711547315
absolute error = 9.2e-31
relative error = 1.5660770513556541361161319648420e-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 = 0.04671
Order of pole (three term test) = -24.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.03
y[1] (analytic) = 0.58683896573780376896263794636405
y[1] (numeric) = 0.58683896573780376896263794636497
absolute error = 9.2e-31
relative error = 1.5677213915802766242843474636332e-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 = 0.03712
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.04
y[1] (analytic) = 0.58636411499288561100071929043072
y[1] (numeric) = 0.58636411499288561100071929043163
absolute error = 9.1e-31
relative error = 1.5519367177014935191114062591395e-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 = 0.02751
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.05
y[1] (analytic) = 0.58603062665844218706444040541493
y[1] (numeric) = 0.58603062665844218706444040541585
absolute error = 9.2e-31
relative error = 1.5698838220211417121249849848054e-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 = 0.01789
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.06
y[1] (analytic) = 0.58583853408302903547718022961729
y[1] (numeric) = 0.58583853408302903547718022961814
absolute error = 8.5e-31
relative error = 1.4509117283151131854967184262082e-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 = 0.008265
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.07
y[1] (analytic) = 0.58578785647574362094150939715216
y[1] (numeric) = 0.58578785647574362094150939715302
absolute error = 8.6e-31
relative error = 1.4681082758765092134315483250034e-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
TOP MAIN SOLVE Loop
x[1] = 7.08
y[1] (analytic) = 0.58587859890430444080024784296141
y[1] (numeric) = 0.58587859890430444080024784296231
absolute error = 9.0e-31
relative error = 1.5361544212114208943054404669357e-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
TOP MAIN SOLVE Loop
x[1] = 7.09
y[1] (analytic) = 0.58611075229454425740981519163572
y[1] (numeric) = 0.58611075229454425740981519163663
absolute error = 9.1e-31
relative error = 1.5526075855757178664720248786028e-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
TOP MAIN SOLVE Loop
x[1] = 7.1
y[1] (analytic) = 0.58648429343131750730221429005751
y[1] (numeric) = 0.58648429343131750730221429005838
absolute error = 8.7e-31
relative error = 1.4834156852009280398002568597754e-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
TOP MAIN SOLVE Loop
x[1] = 7.11
y[1] (analytic) = 0.58699918496082179639548785729313
y[1] (numeric) = 0.58699918496082179639548785729404
absolute error = 9.1e-31
relative error = 1.5502576891324581845616905550713e-28 %
Correct digits = 30
h = 0.01
bytes used=120053792, alloc=4586680, time=11.15
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.12
y[1] (analytic) = 0.58765537539433324910506177896328
y[1] (numeric) = 0.58765537539433324910506177896419
absolute error = 9.1e-31
relative error = 1.5485266332999412476489500558707e-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
TOP MAIN SOLVE Loop
x[1] = 7.13
y[1] (analytic) = 0.58845279911335533782417669231118
y[1] (numeric) = 0.58845279911335533782417669231208
absolute error = 9.0e-31
relative error = 1.5294344786124986007534253890261e-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
TOP MAIN SOLVE Loop
x[1] = 7.14
y[1] (analytic) = 0.58939137637618067789475049574267
y[1] (numeric) = 0.58939137637618067789475049574356
absolute error = 8.9e-31
relative error = 1.5100322734141176774600889062053e-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
TOP MAIN SOLVE Loop
x[1] = 7.15
y[1] (analytic) = 0.59047101332586513189464284083519
y[1] (numeric) = 0.59047101332586513189464284083607
absolute error = 8.8e-31
relative error = 1.4903356475423656023675443106288e-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
TOP MAIN SOLVE Loop
x[1] = 7.16
y[1] (analytic) = 0.59169160199961342583753794512227
y[1] (numeric) = 0.59169160199961342583753794512314
absolute error = 8.7e-31
relative error = 1.4703605680051014200554663328915e-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
TOP MAIN SOLVE Loop
x[1] = 7.17
y[1] (analytic) = 0.59305302033957533873164705813445
y[1] (numeric) = 0.5930530203395753387316470581354
absolute error = 9.5e-31
relative error = 1.6018803840777017305623594094291e-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
TOP MAIN SOLVE Loop
x[1] = 7.18
y[1] (analytic) = 0.59455513220505138588727150509341
y[1] (numeric) = 0.59455513220505138588727150509433
absolute error = 9.2e-31
relative error = 1.5473754243579694216607880740422e-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
TOP MAIN SOLVE Loop
x[1] = 7.19
y[1] (analytic) = 0.59619778738610677541506692080511
y[1] (numeric) = 0.596197787386106775415066920806
absolute error = 8.9e-31
relative error = 1.4927931951945041906737158255953e-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
TOP MAIN SOLVE Loop
x[1] = 7.2
y[1] (analytic) = 0.59798082161859227653070377326272
y[1] (numeric) = 0.59798082161859227653070377326359
absolute error = 8.7e-31
relative error = 1.4548961581161019768478255677634e-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
TOP MAIN SOLVE Loop
x[1] = 7.21
y[1] (analytic) = 0.59990405660057049759161105943477
y[1] (numeric) = 0.59990405660057049759161105943562
absolute error = 8.5e-31
relative error = 1.4168932359228051698114422102222e-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
TOP MAIN SOLVE Loop
x[1] = 7.22
y[1] (analytic) = 0.60196730001014593125168801827152
y[1] (numeric) = 0.60196730001014593125168801827241
absolute error = 8.9e-31
relative error = 1.4784856253570574124018336677784e-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
TOP MAIN SOLVE Loop
x[1] = 7.23
y[1] (analytic) = 0.60417034552469698374432671119311
y[1] (numeric) = 0.60417034552469698374432671119398
absolute error = 8.7e-31
relative error = 1.4399912316855620315431199453567e-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
TOP MAIN SOLVE Loop
x[1] = 7.24
y[1] (analytic) = 0.60651297284150806510684380544745
y[1] (numeric) = 0.60651297284150806510684380544831
absolute error = 8.6e-31
relative error = 1.4179416410021823461441655567624e-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
TOP MAIN SOLVE Loop
x[1] = 7.25
y[1] (analytic) = 0.60899494769979967715449246836974
y[1] (numeric) = 0.60899494769979967715449246837067
absolute error = 9.3e-31
relative error = 1.5271062650234625489527716795241e-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
TOP MAIN SOLVE Loop
x[1] = 7.26
y[1] (analytic) = 0.61161602190415429621361531680418
y[1] (numeric) = 0.6116160219041542962136153168051
absolute error = 9.2e-31
relative error = 1.5042117391492602736010446515144e-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
TOP MAIN SOLVE Loop
x[1] = 7.27
y[1] (analytic) = 0.61437593334933570804518661026465
y[1] (numeric) = 0.61437593334933570804518661026555
absolute error = 9.0e-31
relative error = 1.4649011316142452571809034936376e-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
TOP MAIN SOLVE Loop
x[1] = 7.28
y[1] (analytic) = 0.61727440604649931304593404377702
y[1] (numeric) = 0.6172744060464993130459340437779
absolute error = 8.8e-31
relative error = 1.4256220432598165334029379234397e-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
TOP MAIN SOLVE Loop
x[1] = 7.29
y[1] (analytic) = 0.62031115015079078071836187641728
y[1] (numeric) = 0.62031115015079078071836187641816
absolute error = 8.8e-31
relative error = 1.4186428855681245318976336205714e-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
TOP MAIN SOLVE Loop
x[1] = 7.3
y[1] (analytic) = 0.62348586199033029356722719529539
y[1] (numeric) = 0.6234858619903302935672271952963
absolute error = 9.1e-31
relative error = 1.4595359020572519152021860394460e-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
TOP MAIN SOLVE Loop
x[1] = 7.31
y[1] (analytic) = 0.62679822409657948202223312342711
y[1] (numeric) = 0.62679822409657948202223312342802
absolute error = 9.1e-31
relative error = 1.4518228753944007644577813470086e-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
TOP MAIN SOLVE Loop
x[1] = 7.32
y[1] (analytic) = 0.63024790523608801371875239692257
y[1] (numeric) = 0.63024790523608801371875239692349
absolute error = 9.2e-31
relative error = 1.4597430508799107592083311257182e-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
TOP MAIN SOLVE Loop
x[1] = 7.33
y[1] (analytic) = 0.63383456044361666250410864201688
y[1] (numeric) = 0.63383456044361666250410864201778
absolute error = 9.0e-31
relative error = 1.4199288839190085935400327617849e-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
TOP MAIN SOLVE Loop
x[1] = 7.34
y[1] (analytic) = 0.63755783105663354489011718931125
y[1] (numeric) = 0.63755783105663354489011718931217
absolute error = 9.2e-31
relative error = 1.4430063520281306606454193404253e-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
TOP MAIN SOLVE Loop
x[1] = 7.35
y[1] (analytic) = 0.64141734475118007435698693903173
y[1] (numeric) = 0.64141734475118007435698693903264
absolute error = 9.1e-31
relative error = 1.4187330720733924922167251491769e-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
TOP MAIN SOLVE Loop
bytes used=124054720, alloc=4586680, time=11.52
x[1] = 7.36
y[1] (analytic) = 0.64541271557910304694304108274388
y[1] (numeric) = 0.64541271557910304694304108274482
absolute error = 9.4e-31
relative error = 1.4564324149650128148267879940247e-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
TOP MAIN SOLVE Loop
x[1] = 7.37
y[1] (analytic) = 0.64954354400664913494272434402149
y[1] (numeric) = 0.64954354400664913494272434402233
absolute error = 8.4e-31
relative error = 1.2932158401860757057552005213690e-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
TOP MAIN SOLVE Loop
x[1] = 7.38
y[1] (analytic) = 0.65380941695441792929568890821861
y[1] (numeric) = 0.65380941695441792929568890821948
absolute error = 8.7e-31
relative error = 1.3306629997050874153073998688460e-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
TOP MAIN SOLVE Loop
x[1] = 7.39
y[1] (analytic) = 0.65820990783866953539601422376479
y[1] (numeric) = 0.65820990783866953539601422376567
absolute error = 8.8e-31
relative error = 1.3369595162880658124633908525539e-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
TOP MAIN SOLVE Loop
x[1] = 7.4
y[1] (analytic) = 0.66274457661398259159640263476514
y[1] (numeric) = 0.662744576613982591596402634766
absolute error = 8.6e-31
relative error = 1.2976341570289595509618265403246e-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
TOP MAIN SOLVE Loop
x[1] = 7.41
y[1] (analytic) = 0.66741296981725844464104865560316
y[1] (numeric) = 0.66741296981725844464104865560403
absolute error = 8.7e-31
relative error = 1.3035407451524519567591344315492e-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
TOP MAIN SOLVE Loop
x[1] = 7.42
y[1] (analytic) = 0.6722146206130670816463086245788
y[1] (numeric) = 0.67221462061306708164630862457965
absolute error = 8.5e-31
relative error = 1.2644771088507279253586042282783e-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
TOP MAIN SOLVE Loop
x[1] = 7.43
y[1] (analytic) = 0.67714904884033028407376082030574
y[1] (numeric) = 0.67714904884033028407376082030662
absolute error = 8.8e-31
relative error = 1.2995661760244181663956937647689e-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
TOP MAIN SOLVE Loop
x[1] = 7.44
y[1] (analytic) = 0.68221576106033733541916123349283
y[1] (numeric) = 0.68221576106033733541916123349375
absolute error = 9.2e-31
relative error = 1.3485469737170617330817410389161e-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
TOP MAIN SOLVE Loop
x[1] = 7.45
y[1] (analytic) = 0.68741425060608848108653905489578
y[1] (numeric) = 0.68741425060608848108653905489669
absolute error = 9.1e-31
relative error = 1.3238014766171332261107537060162e-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
TOP MAIN SOLVE Loop
x[1] = 7.46
y[1] (analytic) = 0.69274399763296120614256388272073
y[1] (numeric) = 0.69274399763296120614256388272164
absolute error = 9.1e-31
relative error = 1.3136165785764747175649167259307e-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
TOP MAIN SOLVE Loop
x[1] = 7.47
y[1] (analytic) = 0.69820446917069426436563097014857
y[1] (numeric) = 0.69820446917069426436563097014946
absolute error = 8.9e-31
relative error = 1.2746982285248253310647056091002e-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
TOP MAIN SOLVE Loop
x[1] = 7.48
y[1] (analytic) = 0.70379511917668426023007948426229
y[1] (numeric) = 0.70379511917668426023007948426323
absolute error = 9.4e-31
relative error = 1.3356159688911080393340916622573e-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
TOP MAIN SOLVE Loop
x[1] = 7.49
y[1] (analytic) = 0.7095153885905894542117590248268
y[1] (numeric) = 0.70951538859058945421175902482774
absolute error = 9.4e-31
relative error = 1.3248479386292870352959213816056e-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
TOP MAIN SOLVE Loop
x[1] = 7.5
y[1] (analytic) = 0.71536470539023533107991686567905
y[1] (numeric) = 0.71536470539023533107991686567996
absolute error = 9.1e-31
relative error = 1.2720784141895707013936580234745e-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
TOP MAIN SOLVE Loop
x[1] = 7.51
y[1] (analytic) = 0.72134248464881634066516454828915
y[1] (numeric) = 0.72134248464881634066516454829006
absolute error = 9.1e-31
relative error = 1.2615366755266481581166694413858e-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
TOP MAIN SOLVE Loop
x[1] = 7.52
y[1] (analytic) = 0.72744812859338809097711498924585
y[1] (numeric) = 0.7274481285933880909771149892468
absolute error = 9.5e-31
relative error = 1.3059350387455718360425012062349e-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
TOP MAIN SOLVE Loop
x[1] = 7.53
y[1] (analytic) = 0.73368102666464414450112166974221
y[1] (numeric) = 0.73368102666464414450112166974312
absolute error = 9.1e-31
relative error = 1.2403210208895710166070087413375e-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
TOP MAIN SOLVE Loop
x[1] = 7.54
y[1] (analytic) = 0.74004055557797144004430406400985
y[1] (numeric) = 0.74004055557797144004430406401072
absolute error = 8.7e-31
relative error = 1.1756112464951738691278953622945e-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
TOP MAIN SOLVE Loop
x[1] = 7.55
y[1] (analytic) = 0.74652607938577823463955405276666
y[1] (numeric) = 0.7465260793857782346395540527676
absolute error = 9.4e-31
relative error = 1.2591656553692095415100819633983e-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
TOP MAIN SOLVE Loop
x[1] = 7.56
y[1] (analytic) = 0.75313694954108833276527269949021
y[1] (numeric) = 0.75313694954108833276527269949106
absolute error = 8.5e-31
relative error = 1.1286127981344343560016860092201e-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
TOP MAIN SOLVE Loop
x[1] = 7.57
y[1] (analytic) = 0.7598725049623952435109104302038
y[1] (numeric) = 0.75987250496239524351091043020471
absolute error = 9.1e-31
relative error = 1.1975693212442715014464105532258e-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
TOP MAIN SOLVE Loop
x[1] = 7.58
y[1] (analytic) = 0.76673207209976978032663901358165
y[1] (numeric) = 0.76673207209976978032663901358257
absolute error = 9.2e-31
relative error = 1.1998976350115252209515587491195e-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
TOP MAIN SOLVE Loop
x[1] = 7.59
y[1] (analytic) = 0.77371496500221449265226985699767
y[1] (numeric) = 0.77371496500221449265226985699853
absolute error = 8.6e-31
relative error = 1.1115204421534467103760923761298e-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
TOP MAIN SOLVE Loop
bytes used=128056564, alloc=4586680, time=11.88
x[1] = 7.6
y[1] (analytic) = 0.78082048538625819403838423261938
y[1] (numeric) = 0.78082048538625819403838423262028
absolute error = 9.0e-31
relative error = 1.1526336934600093018516852001249e-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
TOP MAIN SOLVE Loop
x[1] = 7.61
y[1] (analytic) = 0.78804792270578372736402523675188
y[1] (numeric) = 0.78804792270578372736402523675274
absolute error = 8.6e-31
relative error = 1.0913041900385535958136960905662e-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
TOP MAIN SOLVE Loop
x[1] = 7.62
y[1] (analytic) = 0.79539655422308198443261932361648
y[1] (numeric) = 0.79539655422308198443261932361742
absolute error = 9.4e-31
relative error = 1.1818004428220864683453238639485e-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
TOP MAIN SOLVE Loop
x[1] = 7.63
y[1] (analytic) = 0.80286564508112507460337930703817
y[1] (numeric) = 0.80286564508112507460337930703902
absolute error = 8.5e-31
relative error = 1.0587076495396838943680605367010e-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
TOP MAIN SOLVE Loop
x[1] = 7.64
y[1] (analytic) = 0.81045444837705141520155312950598
y[1] (numeric) = 0.81045444837705141520155312950687
absolute error = 8.9e-31
relative error = 1.0981493183018982523144205570579e-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
TOP MAIN SOLVE Loop
x[1] = 7.65
y[1] (analytic) = 0.81816220523685539525971474495037
y[1] (numeric) = 0.81816220523685539525971474495127
absolute error = 9.0e-31
relative error = 1.1000263691469991815859773525949e-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
TOP MAIN SOLVE Loop
x[1] = 7.66
y[1] (analytic) = 0.82598814489127414368596416512567
y[1] (numeric) = 0.82598814489127414368596416512653
absolute error = 8.6e-31
relative error = 1.0411771710273188963197172624590e-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
TOP MAIN SOLVE Loop
x[1] = 7.67
y[1] (analytic) = 0.83393148475286381324545861227259
y[1] (numeric) = 0.83393148475286381324545861227352
absolute error = 9.3e-31
relative error = 1.1151995301815546145970558913462e-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
TOP MAIN SOLVE Loop
x[1] = 7.68
y[1] (analytic) = 0.84199143049425767279110664749629
y[1] (numeric) = 0.8419914304942576727911066474972
absolute error = 9.1e-31
relative error = 1.0807710946248236682775236120006e-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
TOP MAIN SOLVE Loop
x[1] = 7.69
y[1] (analytic) = 0.85016717612759818199941706492118
y[1] (numeric) = 0.8501671761275981819994170649221
absolute error = 9.2e-31
relative error = 1.0821401082437472151000163524485e-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
TOP MAIN SOLVE Loop
x[1] = 7.7
y[1] (analytic) = 0.85845790408513510547022214170434
y[1] (numeric) = 0.85845790408513510547022214170518
absolute error = 8.4e-31
relative error = 9.7849876622103464765267042908599e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.71
y[1] (analytic) = 0.86686278530098160644603014278012
y[1] (numeric) = 0.86686278530098160644603014278105
absolute error = 9.3e-31
relative error = 1.0728341506517627860638522168475e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.93
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.72
y[1] (analytic) = 0.87538097929402014460976499608769
y[1] (numeric) = 0.87538097929402014460976499608855
absolute error = 8.6e-31
relative error = 9.8242938828026096416809932405051e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.73
y[1] (analytic) = 0.88401163425194988744020138218134
y[1] (numeric) = 0.8840116342519498874402013821823
absolute error = 9.6e-31
relative error = 1.0859585584666557266480530707297e-28 %
Correct digits = 30
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.74
y[1] (analytic) = 0.89275388711646723045399897071758
y[1] (numeric) = 0.89275388711646723045399897071846
absolute error = 8.8e-31
relative error = 9.8571399430400533340233284481625e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.89
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
TOP MAIN SOLVE Loop
x[1] = 7.75
y[1] (analytic) = 0.90160686366957090835329513064641
y[1] (numeric) = 0.90160686366957090835329513064729
absolute error = 8.8e-31
relative error = 9.7603516062241337543733444436912e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.22
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
TOP MAIN SOLVE Loop
x[1] = 7.76
y[1] (analytic) = 0.91056967862098306663966204106089
y[1] (numeric) = 0.91056967862098306663966204106182
absolute error = 9.3e-31
relative error = 1.0213386430881855010962788704901e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.55
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
TOP MAIN SOLVE Loop
x[1] = 7.77
y[1] (analytic) = 0.9196414356966775516601174571664
y[1] (numeric) = 0.9196414356966775516601174571673
absolute error = 9.0e-31
relative error = 9.7864228933769375660326053289296e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.89
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
TOP MAIN SOLVE Loop
x[1] = 7.78
y[1] (analytic) = 0.92882122772850656632995785942085
y[1] (numeric) = 0.92882122772850656632995785942173
absolute error = 8.8e-31
relative error = 9.4743743330683549144292847257773e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.24
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
TOP MAIN SOLVE Loop
x[1] = 7.79
y[1] (analytic) = 0.93810813674491672894153033333811
y[1] (numeric) = 0.93810813674491672894153033333904
absolute error = 9.3e-31
relative error = 9.9135692738680356188435837422778e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.59
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
TOP MAIN SOLVE Loop
x[1] = 7.8
y[1] (analytic) = 0.94750123406274546352865876645141
y[1] (numeric) = 0.94750123406274546352865876645234
absolute error = 9.3e-31
relative error = 9.8152906462432480998045420402575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.95
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
TOP MAIN SOLVE Loop
x[1] = 7.81
y[1] (analytic) = 0.95699958038008854222418465679748
y[1] (numeric) = 0.95699958038008854222418465679842
absolute error = 9.4e-31
relative error = 9.8223658533545346818290822927232e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.31
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
TOP MAIN SOLVE Loop
x[1] = 7.82
y[1] (analytic) = 0.96660222587022949293377613950805
y[1] (numeric) = 0.96660222587022949293377613950892
absolute error = 8.7e-31
relative error = 9.0006000060339323351437025735535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.68
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
TOP MAIN SOLVE Loop
x[1] = 7.83
y[1] (analytic) = 0.97630821027662147946351209608496
y[1] (numeric) = 0.97630821027662147946351209608587
absolute error = 9.1e-31
relative error = 9.3208270751115152710424226187371e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.06
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
TOP MAIN SOLVE Loop
bytes used=132057800, alloc=4586680, time=12.25
x[1] = 7.84
y[1] (analytic) = 0.98611656300891215599237989088459
y[1] (numeric) = 0.98611656300891215599237989088551
absolute error = 9.2e-31
relative error = 9.3295258847780389730457372882958e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.45
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
TOP MAIN SOLVE Loop
x[1] = 7.85
y[1] (analytic) = 0.99602630324000189348425993036111
y[1] (numeric) = 0.99602630324000189348425993036202
absolute error = 9.1e-31
relative error = 9.1363049052001486383461827169894e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.86
y[1] (analytic) = 1.0060364400041256722976374323518
y[1] (numeric) = 1.0060364400041256722976374323527
absolute error = 9e-31
relative error = 8.9459980196771915575896023024287e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.87
y[1] (analytic) = 1.016145972295948832885515072286
y[1] (numeric) = 1.0161459722959488328855150722869
absolute error = 9e-31
relative error = 8.8569952008615378415655617405107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.88
y[1] (analytic) = 1.0263538891706667750930360320368
y[1] (numeric) = 1.0263538891706667750930360320377
absolute error = 9e-31
relative error = 8.7689052430758989612673656414938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.04
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
TOP MAIN SOLVE Loop
x[1] = 7.89
y[1] (analytic) = 1.0366591698450985961663038271389
y[1] (numeric) = 1.0366591698450985961663038271398
absolute error = 9e-31
relative error = 8.6817348090836961483097002478905e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.68
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
TOP MAIN SOLVE Loop
x[1] = 7.9
y[1] (analytic) = 1.0470607837997645581928424479146
y[1] (numeric) = 1.0470607837997645581928424479155
absolute error = 9e-31
relative error = 8.5954895257743906133554804737785e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.33
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
TOP MAIN SOLVE Loop
x[1] = 7.91
y[1] (analytic) = 1.0575576908819371773120170411462
y[1] (numeric) = 1.0575576908819371773120170411471
absolute error = 9e-31
relative error = 8.5101740336213347702610697333535e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.92
y[1] (analytic) = 1.0681488414096556296723697116501
y[1] (numeric) = 1.068148841409655629672369711651
absolute error = 9e-31
relative error = 8.4257920348652298528018034646867e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.93
y[1] (analytic) = 1.0788331762766930727819530928743
y[1] (numeric) = 1.0788331762766930727819530928752
absolute error = 9e-31
relative error = 8.3423463403870428961178219359683e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.31
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
TOP MAIN SOLVE Loop
x[1] = 7.94
y[1] (analytic) = 1.0896096270584663856069991293797
y[1] (numeric) = 1.0896096270584663856069991293806
absolute error = 9e-31
relative error = 8.2598389152421439398036407160172e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.95
y[1] (analytic) = 1.1004771161188777365331710268819
y[1] (numeric) = 1.1004771161188777365331710268828
absolute error = 9e-31
relative error = 8.1782709228346967861332279060057e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.96
y[1] (analytic) = 1.1114345567180772951216365878451
y[1] (numeric) = 1.111434556718077295121636587846
absolute error = 9e-31
relative error = 8.0976427677180001091272309900849e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.35
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
TOP MAIN SOLVE Loop
x[1] = 7.97
y[1] (analytic) = 1.1224808531211363114785892857504
y[1] (numeric) = 1.1224808531211363114785892857514
absolute error = 1.0e-30
relative error = 8.9088379300139529717194732199917e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.98
y[1] (analytic) = 1.1336149007076196960208407235378
y[1] (numeric) = 1.1336149007076196960208407235388
absolute error = 1.0e-30
relative error = 8.8213378227102057421763415899236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.73
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 7.99
y[1] (analytic) = 1.144835586082047142470818095744
y[1] (numeric) = 1.144835586082047142470818095745
absolute error = 1.0e-30
relative error = 8.7348787210771837075882640753020e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.43
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
TOP MAIN SOLVE Loop
x[1] = 8
y[1] (analytic) = 1.1561417871852317480607177835859
y[1] (numeric) = 1.1561417871852317480607177835869
absolute error = 1.0e-30
relative error = 8.6494581467781907511783926472596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.13
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
TOP MAIN SOLVE Loop
x[1] = 8.01
y[1] (analytic) = 1.1675323734064849971765765418579
y[1] (numeric) = 1.1675323734064849971765765418589
absolute error = 1.0e-30
relative error = 8.5650729930710249595745919660623e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.84
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
TOP MAIN SOLVE Loop
x[1] = 8.02
y[1] (analytic) = 1.1790062056966768880373997118827
y[1] (numeric) = 1.1790062056966768880373997118836
absolute error = 9e-31
relative error = 7.6335476068863300075245081169665e-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
TOP MAIN SOLVE Loop
x[1] = 8.03
y[1] (analytic) = 1.1905621366821398964908950058704
y[1] (numeric) = 1.1905621366821398964908950058714
absolute error = 1.0e-30
relative error = 8.3993936073492249161336628513780e-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
TOP MAIN SOLVE Loop
x[1] = 8.04
y[1] (analytic) = 1.2021990107794053866243519427395
y[1] (numeric) = 1.2021990107794053866243519427404
absolute error = 9e-31
relative error = 7.4862813222289644138614532074901e-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
TOP MAIN SOLVE Loop
x[1] = 8.05
y[1] (analytic) = 1.213915664310760994645219204251
y[1] (numeric) = 1.213915664310760994645219204252
absolute error = 1.0e-30
relative error = 8.2378045641892398053277161833465e-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
TOP MAIN SOLVE Loop
x[1] = 8.06
y[1] (analytic) = 1.2257109256206174303892893526318
y[1] (numeric) = 1.2257109256206174303892893526327
absolute error = 9e-31
relative error = 7.3426774713972679777853027451650e-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
TOP MAIN SOLVE Loop
x[1] = 8.07
y[1] (analytic) = 1.2375836151926730598733121025612
y[1] (numeric) = 1.2375836151926730598733121025622
absolute error = 1.0e-30
relative error = 8.0802621150112359670521208782739e-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
TOP MAIN SOLVE Loop
bytes used=136060088, alloc=4586680, time=12.63
x[1] = 8.08
y[1] (analytic) = 1.2495325457678645525314177128683
y[1] (numeric) = 1.2495325457678645525314177128693
absolute error = 1.0e-30
relative error = 8.0029928262931202760519432766732e-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
TOP MAIN SOLVE Loop
x[1] = 8.09
y[1] (analytic) = 1.2615565224630917981689187339872
y[1] (numeric) = 1.2615565224630917981689187339882
absolute error = 1.0e-30
relative error = 7.9267157847797190759974590057409e-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
TOP MAIN SOLVE Loop
x[1] = 8.1
y[1] (analytic) = 1.2736543428907052212407318320024
y[1] (numeric) = 1.2736543428907052212407318320032
absolute error = 8e-31
relative error = 6.2811390269694983486652596894840e-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
TOP MAIN SOLVE Loop
x[1] = 8.11
y[1] (analytic) = 1.2858247972787435438225642770893
y[1] (numeric) = 1.2858247972787435438225642770903
absolute error = 1.0e-30
relative error = 7.7771093084870574250224739969178e-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
TOP MAIN SOLVE Loop
x[1] = 8.12
y[1] (analytic) = 1.2980666685919099735987657795216
y[1] (numeric) = 1.2980666685919099735987657795225
absolute error = 9e-31
relative error = 6.9333881053758468664392095713166e-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
TOP MAIN SOLVE Loop
x[1] = 8.13
y[1] (analytic) = 1.3103787326532747193488600420006
y[1] (numeric) = 1.3103787326532747193488600420014
absolute error = 8e-31
relative error = 6.1051051887888005810511942111464e-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
TOP MAIN SOLVE Loop
x[1] = 8.14
y[1] (analytic) = 1.3227597582666916637826258000013
y[1] (numeric) = 1.3227597582666916637826258000022
absolute error = 9e-31
relative error = 6.8039566094703052581945653330902e-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
TOP MAIN SOLVE Loop
x[1] = 8.15
y[1] (analytic) = 1.335208507339916952158457396012
y[1] (numeric) = 1.3352085073399169521584573960128
absolute error = 8e-31
relative error = 5.9915735677404297531340537254277e-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
TOP MAIN SOLVE Loop
x[1] = 8.16
y[1] (analytic) = 1.3477237350084171849287415334612
y[1] (numeric) = 1.347723735008417184928741533462
absolute error = 8e-31
relative error = 5.9359346371903408975978646099696e-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
TOP MAIN SOLVE Loop
x[1] = 8.17
y[1] (analytic) = 1.360304189759854833696158822621
y[1] (numeric) = 1.3603041897598548336961588226218
absolute error = 8e-31
relative error = 5.8810375357384606284709340851751e-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
TOP MAIN SOLVE Loop
x[1] = 8.18
y[1] (analytic) = 1.3729486135592384320430519891663
y[1] (numeric) = 1.3729486135592384320430519891671
absolute error = 8e-31
relative error = 5.8268750345002078690291806914054e-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
TOP MAIN SOLVE Loop
x[1] = 8.19
y[1] (analytic) = 1.3856557419747250263190692866238
y[1] (numeric) = 1.3856557419747250263190692866245
absolute error = 7e-31
relative error = 5.0517598188018644940328912047032e-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
TOP MAIN SOLVE Loop
x[1] = 8.2
y[1] (analytic) = 1.398424304304062306246839374574
y[1] (numeric) = 1.3984243043040623062468393745748
absolute error = 8e-31
relative error = 5.7207243719789808187240782413057e-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
TOP MAIN SOLVE Loop
x[1] = 8.21
y[1] (analytic) = 1.4112530237016577712379851860634
y[1] (numeric) = 1.4112530237016577712379851860643
absolute error = 9e-31
relative error = 6.3773114025955286791716811023440e-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
TOP MAIN SOLVE Loop
x[1] = 8.22
y[1] (analytic) = 1.4241406173062622256087358017996
y[1] (numeric) = 1.4241406173062622256087358018005
absolute error = 9e-31
relative error = 6.3196006704895104004307908341889e-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
TOP MAIN SOLVE Loop
x[1] = 8.23
y[1] (analytic) = 1.4370857963692548344520173279467
y[1] (numeric) = 1.4370857963692548344520173279475
absolute error = 8e-31
relative error = 5.5668214244491943169209846296718e-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
TOP MAIN SOLVE Loop
x[1] = 8.24
y[1] (analytic) = 1.4500872663835169117673394253125
y[1] (numeric) = 1.4500872663835169117673394253134
absolute error = 9e-31
relative error = 6.2065230201253925489671935437201e-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
TOP MAIN SOLVE Loop
x[1] = 8.25
y[1] (analytic) = 1.4631437272128815535770589667361
y[1] (numeric) = 1.4631437272128815535770589667369
absolute error = 8e-31
relative error = 5.4676788419406127376762267481989e-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
TOP MAIN SOLVE Loop
x[1] = 8.26
y[1] (analytic) = 1.4762538732221461711735835309881
y[1] (numeric) = 1.4762538732221461711735835309889
absolute error = 8e-31
relative error = 5.4191221070524925713750634333240e-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
TOP MAIN SOLVE Loop
x[1] = 8.27
y[1] (analytic) = 1.4894163934076349233525334293992
y[1] (numeric) = 1.4894163934076349233525334294001
absolute error = 9e-31
relative error = 6.0426352495079667376935492503849e-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
TOP MAIN SOLVE Loop
x[1] = 8.28
y[1] (analytic) = 1.5026299715282979914974406131996
y[1] (numeric) = 1.5026299715282979914974406132004
absolute error = 8e-31
relative error = 5.3239986900190360873135667745035e-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
TOP MAIN SOLVE Loop
x[1] = 8.29
y[1] (analytic) = 1.515893286237334587697725023419
y[1] (numeric) = 1.5158932862373345876977250234198
absolute error = 8e-31
relative error = 5.2774163409992743833550435072058e-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
TOP MAIN SOLVE Loop
x[1] = 8.3
y[1] (analytic) = 1.5292050112143265337088220601935
y[1] (numeric) = 1.5292050112143265337088220601944
absolute error = 9e-31
relative error = 5.8854110037562519209618018940285e-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
TOP MAIN SOLVE Loop
x[1] = 8.31
y[1] (analytic) = 1.542563815297869197506676107493
y[1] (numeric) = 1.5425638152978691975066761074938
absolute error = 8e-31
relative error = 5.1861711785681938564775937394080e-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
TOP MAIN SOLVE Loop
x[1] = 8.32
y[1] (analytic) = 1.555968362618686524453470075961
y[1] (numeric) = 1.5559683626186865244534700759619
absolute error = 9e-31
relative error = 5.7841793035258426481334221625475e-29 %
Correct digits = 31
bytes used=140061116, alloc=4586680, time=13.01
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.33
y[1] (analytic) = 1.5694173127332168516824032137891
y[1] (numeric) = 1.56941731273321685168240321379
absolute error = 9e-31
relative error = 5.7346124112305481833621461203385e-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
TOP MAIN SOLVE Loop
x[1] = 8.34
y[1] (analytic) = 1.582909320757656147231399848758
y[1] (numeric) = 1.5829093207576561472313998487589
absolute error = 9e-31
relative error = 5.6857331509629176525763261538315e-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
TOP MAIN SOLVE Loop
x[1] = 8.35
y[1] (analytic) = 1.5964430375024452697135380175099
y[1] (numeric) = 1.5964430375024452697135380175109
absolute error = 1.0e-30
relative error = 6.2639253422060685413417641207109e-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
TOP MAIN SOLVE Loop
x[1] = 8.36
y[1] (analytic) = 1.6100171096071877999103032820059
y[1] (numeric) = 1.6100171096071877999103032820069
absolute error = 1.0e-30
relative error = 6.2111141181846206601942742081693e-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
TOP MAIN SOLVE Loop
x[1] = 8.37
y[1] (analytic) = 1.6236301796759849526169395593417
y[1] (numeric) = 1.6236301796759849526169395593427
absolute error = 1.0e-30
relative error = 6.1590380156616828805674767211809e-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
TOP MAIN SOLVE Loop
x[1] = 8.38
y[1] (analytic) = 1.6372808864131740353614911471161
y[1] (numeric) = 1.6372808864131740353614911471171
absolute error = 1.0e-30
relative error = 6.1076874975968308652758495761542e-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
TOP MAIN SOLVE Loop
x[1] = 8.39
y[1] (analytic) = 1.6509678647594568802647790453627
y[1] (numeric) = 1.6509678647594568802647790453636
absolute error = 9e-31
relative error = 5.4513477773301688104757032417327e-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
TOP MAIN SOLVE Loop
x[1] = 8.4
y[1] (analytic) = 1.6646897460284046363115655591631
y[1] (numeric) = 1.664689746028404636311565559164
absolute error = 9e-31
relative error = 5.4064128294609155415732227268356e-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
TOP MAIN SOLVE Loop
x[1] = 8.41
y[1] (analytic) = 1.6784451580433252716674336798615
y[1] (numeric) = 1.6784451580433252716674336798625
absolute error = 1.0e-30
relative error = 5.9578949911343320643325199951202e-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
TOP MAIN SOLVE Loop
x[1] = 8.42
y[1] (analytic) = 1.6922327252744800994052054286866
y[1] (numeric) = 1.6922327252744800994052054286876
absolute error = 1.0e-30
relative error = 5.9093526857412595465539891405841e-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
TOP MAIN SOLVE Loop
x[1] = 8.43
y[1] (analytic) = 1.7060510689766356051026732445605
y[1] (numeric) = 1.7060510689766356051026732445614
absolute error = 9e-31
relative error = 5.2753403246003623204328327026828e-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
TOP MAIN SOLVE Loop
x[1] = 8.44
y[1] (analytic) = 1.7198988073269368212435107838682
y[1] (numeric) = 1.7198988073269368212435107838691
absolute error = 9e-31
relative error = 5.2328660044760316078894606459215e-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
TOP MAIN SOLVE Loop
x[1] = 8.45
y[1] (analytic) = 1.7337745555630884611988171367941
y[1] (numeric) = 1.7337745555630884611988171367951
absolute error = 1.0e-30
relative error = 5.7677625778469447231448388402820e-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
TOP MAIN SOLVE Loop
x[1] = 8.46
y[1] (analytic) = 1.747676926121829994791046866951
y[1] (numeric) = 1.747676926121829994791046866952
absolute error = 1.0e-30
relative error = 5.7218813446203862198212200370002e-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
TOP MAIN SOLVE Loop
x[1] = 8.47
y[1] (analytic) = 1.7616045287776908180481649929499
y[1] (numeric) = 1.7616045287776908180481649929509
absolute error = 1.0e-30
relative error = 5.6766429903189524891431661262211e-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
TOP MAIN SOLVE Loop
x[1] = 8.48
y[1] (analytic) = 1.7755559707820116417466804191106
y[1] (numeric) = 1.7755559707820116417466804191117
absolute error = 1.1e-30
relative error = 6.1952426062667279130910037576817e-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
TOP MAIN SOLVE Loop
x[1] = 8.49
y[1] (analytic) = 1.7895298570022181967205542829194
y[1] (numeric) = 1.7895298570022181967205542829205
absolute error = 1.1e-30
relative error = 6.1468658692439826905258256028958e-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
TOP MAIN SOLVE Loop
x[1] = 8.5
y[1] (analytic) = 1.8035247900613333286815133626179
y[1] (numeric) = 1.803524790061333328681513362619
absolute error = 1.1e-30
relative error = 6.0991676192185402384886685890953e-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
TOP MAIN SOLVE Loop
x[1] = 8.51
y[1] (analytic) = 1.8175393704777135314575462050684
y[1] (numeric) = 1.8175393704777135314575462050695
absolute error = 1.1e-30
relative error = 6.0521385003664660887757043124453e-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
TOP MAIN SOLVE Loop
x[1] = 8.52
y[1] (analytic) = 1.8315721968049959451127048471569
y[1] (numeric) = 1.831572196804995945112704847158
absolute error = 1.1e-30
relative error = 6.0057692616149432403359366312604e-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
TOP MAIN SOLVE Loop
x[1] = 8.53
y[1] (analytic) = 1.8456218657722418243650222602545
y[1] (numeric) = 1.8456218657722418243650222602556
absolute error = 1.1e-30
relative error = 5.9600507579581582001718744250558e-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
TOP MAIN SOLVE Loop
x[1] = 8.54
y[1] (analytic) = 1.859686972424262463072489560388
y[1] (numeric) = 1.8596869724242624630724895603891
absolute error = 1.1e-30
relative error = 5.9149739515895789059111549375247e-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
TOP MAIN SOLVE Loop
x[1] = 8.55
y[1] (analytic) = 1.8737661102621135423115822670094
y[1] (numeric) = 1.8737661102621135423115822670106
absolute error = 1.2e-30
relative error = 6.4042144503944351222597849505065e-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
TOP MAIN SOLVE Loop
x[1] = 8.56
y[1] (analytic) = 1.8878578713837438527306059908769
y[1] (numeric) = 1.8878578713837438527306059908781
absolute error = 1.2e-30
relative error = 6.3564107139084340863002794241492e-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
TOP MAIN SOLVE Loop
bytes used=144063948, alloc=4586680, time=13.39
x[1] = 8.57
y[1] (analytic) = 1.901960846624784326422833094414
y[1] (numeric) = 1.9019608466247843264228330944152
absolute error = 1.2e-30
relative error = 6.3092781438141455329952551572316e-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
TOP MAIN SOLVE Loop
x[1] = 8.58
y[1] (analytic) = 1.9160736256994632995335668130314
y[1] (numeric) = 1.9160736256994632995335668130326
absolute error = 1.2e-30
relative error = 6.2628073572169733830441500787742e-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
TOP MAIN SOLVE Loop
x[1] = 8.59
y[1] (analytic) = 1.9301947973416339141923011250723
y[1] (numeric) = 1.9301947973416339141923011250735
absolute error = 1.2e-30
relative error = 6.2169890917367682045923206494122e-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
TOP MAIN SOLVE Loop
x[1] = 8.6
y[1] (analytic) = 1.944322949445899557147305597597
y[1] (numeric) = 1.9443229494458995571473055975982
absolute error = 1.2e-30
relative error = 6.1718142057726598272283836323161e-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
TOP MAIN SOLVE Loop
x[1] = 8.61
y[1] (analytic) = 1.9584566692088232226763758897024
y[1] (numeric) = 1.9584566692088232226763758897036
absolute error = 1.2e-30
relative error = 6.1272736786399040642784231391572e-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
TOP MAIN SOLVE Loop
x[1] = 8.62
y[1] (analytic) = 1.9725945432702066789551329151711
y[1] (numeric) = 1.9725945432702066789551329151724
absolute error = 1.3e-30
relative error = 6.5903051614693914972563546953417e-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
TOP MAIN SOLVE Loop
x[1] = 8.63
y[1] (analytic) = 1.9867351578544253100839660807336
y[1] (numeric) = 1.9867351578544253100839660807348
absolute error = 1.2e-30
relative error = 6.0400602227019530571945551659687e-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
TOP MAIN SOLVE Loop
x[1] = 8.64
y[1] (analytic) = 2.0008770989118045004071965480436
y[1] (numeric) = 2.0008770989118045004071965480449
absolute error = 1.3e-30
relative error = 6.4971506781052020276959599592029e-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 = 0.0005981
Order of pole (three term test) = -0.8929
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.65
y[1] (analytic) = 2.0150189522600234236038418639322
y[1] (numeric) = 2.0150189522600234236038418639334
absolute error = 1.2e-30
relative error = 5.9552789746919898808398957749299e-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 = 0.01024
Order of pole (three term test) = -0.8956
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.66
y[1] (analytic) = 2.0291593037255320962889089805942
y[1] (numeric) = 2.0291593037255320962889089805954
absolute error = 1.2e-30
relative error = 5.9137791586732623377564987014418e-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 = 0.01988
Order of pole (three term test) = -0.9031
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.67
y[1] (analytic) = 2.0432967392849675545377026882523
y[1] (numeric) = 2.0432967392849675545377026882536
absolute error = 1.3e-30
relative error = 6.3622672860277883750811558201418e-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 = 0.02951
Order of pole (three term test) = -0.9155
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.68
y[1] (analytic) = 2.057429845206555011833343450402
y[1] (numeric) = 2.0574298452065550118333434504033
absolute error = 1.3e-30
relative error = 6.3185629538172025274108737284528e-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 = 0.03913
Order of pole (three term test) = -0.9327
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.69
y[1] (analytic) = 2.0715572081914798584395337953625
y[1] (numeric) = 2.0715572081914798584395337953637
absolute error = 1.2e-30
relative error = 5.7927437159586307950476559614531e-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 = 0.04873
Order of pole (three term test) = -0.9548
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.7
y[1] (analytic) = 2.0856774155152163651164455942737
y[1] (numeric) = 2.0856774155152163651164455942749
absolute error = 1.2e-30
relative error = 5.7535263654545969465699220758227e-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 = 0.05831
Order of pole (three term test) = -0.9816
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.71
y[1] (analytic) = 2.0997890551687989584271301639961
y[1] (numeric) = 2.0997890551687989584271301639973
absolute error = 1.2e-30
relative error = 5.7148597714903974594797160757763e-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 = 0.06787
Order of pole (three term test) = -1.013
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.72
y[1] (analytic) = 2.113890716000021940624646224237
y[1] (numeric) = 2.1138907160000219406246462242382
absolute error = 1.2e-30
relative error = 5.6767362234821771405430142175079e-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 = 0.0774
Order of pole (three term test) = -1.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.73
y[1] (analytic) = 2.1279809878545535342655830371279
y[1] (numeric) = 2.127980987854553534265583037129
absolute error = 1.1e-30
relative error = 5.1692191155759727356019563632546e-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 = 0.08691
Order of pole (three term test) = -1.091
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.74
y[1] (analytic) = 2.1420584617169501402631120221331
y[1] (numeric) = 2.1420584617169501402631120221342
absolute error = 1.1e-30
relative error = 5.1352473317572464261566530695822e-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 = 0.09637
Order of pole (three term test) = -1.137
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.75
y[1] (analytic) = 2.1561217298515567080712730311345
y[1] (numeric) = 2.1561217298515567080712730311356
absolute error = 1.1e-30
relative error = 5.1017527664160784536285399542936e-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 = 0.1058
Order of pole (three term test) = -1.188
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.76
y[1] (analytic) = 2.1701693859432791280808934388279
y[1] (numeric) = 2.170169385943279128080893438829
absolute error = 1.1e-30
relative error = 5.0687287689383628210925483734842e-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 = 0.1152
Order of pole (three term test) = -1.243
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.77
y[1] (analytic) = 2.1842000252382145691052103924856
y[1] (numeric) = 2.1842000252382145691052103924867
absolute error = 1.1e-30
relative error = 5.0361687908140698888395617004853e-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 = 0.1245
Order of pole (three term test) = -1.303
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.78
y[1] (analytic) = 2.1982122446841256980386392161264
y[1] (numeric) = 2.1982122446841256980386392161275
absolute error = 1.1e-30
relative error = 5.0040663846728121452288765829357e-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 = 0.1338
Order of pole (three term test) = -1.368
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.79
y[1] (analytic) = 2.212204643070744734383783551761
y[1] (numeric) = 2.2122046430707447343837835517621
absolute error = 1.1e-30
relative error = 4.9724152032928482589741858516958e-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 = 0.143
Order of pole (three term test) = -1.437
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.8
y[1] (analytic) = 2.2261758211698933093581541924069
y[1] (numeric) = 2.2261758211698933093581541924081
absolute error = 1.2e-30
relative error = 5.3904098166396379333662751053290e-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 = 0.1522
Order of pole (three term test) = -1.511
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.81
y[1] (analytic) = 2.2401243818754041177114520950235
y[1] (numeric) = 2.2401243818754041177114520950247
bytes used=148065040, alloc=4586680, time=13.77
absolute error = 1.2e-30
relative error = 5.3568454042510577340905946206033e-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 = 0.1613
Order of pole (three term test) = -1.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.82
y[1] (analytic) = 2.2540489303428303702048348329082
y[1] (numeric) = 2.2540489303428303702048348329094
absolute error = 1.2e-30
relative error = 5.3237531086669248794331087827643e-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 = 0.1704
Order of pole (three term test) = -1.673
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.83
y[1] (analytic) = 2.2679480741289290759233427165629
y[1] (numeric) = 2.2679480741289290759233427165641
absolute error = 1.2e-30
relative error = 5.2911264313707651309347363906210e-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 = 0.1794
Order of pole (three term test) = -1.761
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.84
y[1] (analytic) = 2.2818204233309042062094890215573
y[1] (numeric) = 2.2818204233309042062094890215585
absolute error = 1.2e-30
relative error = 5.2589589773602391646699464713607e-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 = 0.1883
Order of pole (three term test) = -1.853
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.85
y[1] (analytic) = 2.2956645907253958160176565475257
y[1] (numeric) = 2.2956645907253958160176565475269
absolute error = 1.2e-30
relative error = 5.2272444539505567508896264205149e-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 = 0.1971
Order of pole (three term test) = -1.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.86
y[1] (analytic) = 2.3094791919072012238929889503568
y[1] (numeric) = 2.309479191907201223892988950358
absolute error = 1.2e-30
relative error = 5.1959766695668848769677030647382e-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 = 0.2059
Order of pole (three term test) = -2.051
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.87
y[1] (analytic) = 2.3232628454277143785723795564228
y[1] (numeric) = 2.3232628454277143785723795564239
absolute error = 1.1e-30
relative error = 4.7347204048170847428757873628941e-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 = 0.2146
Order of pole (three term test) = -2.156
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.88
y[1] (analytic) = 2.3370141729330695683862633142472
y[1] (numeric) = 2.3370141729330695683862633142483
absolute error = 1.1e-30
relative error = 4.7068606290027117492559834981758e-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 = 0.2232
Order of pole (three term test) = -2.266
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.89
y[1] (analytic) = 2.35073179930197565920539107852
y[1] (numeric) = 2.350731799301975659205391078521
absolute error = 1.0e-30
relative error = 4.2539944382295724520717888837353e-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 = 0.2317
Order of pole (three term test) = -2.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.9
y[1] (analytic) = 2.3644143527832270776236530311141
y[1] (numeric) = 2.3644143527832270776236530311151
absolute error = 1.0e-30
relative error = 4.2293771344386752846208812267677e-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 = 0.2401
Order of pole (three term test) = -2.498
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.91
y[1] (analytic) = 2.3780604651328777883932250607736
y[1] (numeric) = 2.3780604651328777883932250607746
absolute error = 1.0e-30
relative error = 4.2051075431512354795025767399070e-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 = 0.2484
Order of pole (three term test) = -2.621
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.92
y[1] (analytic) = 2.391668771751064548828605853659
y[1] (numeric) = 2.39166877175106454882860585366
absolute error = 1.0e-30
relative error = 4.1811809888199870579240725154873e-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 = 0.2566
Order of pole (three term test) = -2.747
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.93
y[1] (analytic) = 2.4052379118184657579681232896477
y[1] (numeric) = 2.4052379118184657579681232896487
absolute error = 1.0e-30
relative error = 4.1575928729809350647195880019040e-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 = 0.2647
Order of pole (three term test) = -2.878
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.94
y[1] (analytic) = 2.418766528432382254721709322332
y[1] (numeric) = 2.4187665284323822547217093223331
absolute error = 1.1e-30
relative error = 4.5477725405474206458659204783306e-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 = 0.2727
Order of pole (three term test) = -3.013
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.95
y[1] (analytic) = 2.4322532687424264570385288523496
y[1] (numeric) = 2.4322532687424264570385288523507
absolute error = 1.1e-30
relative error = 4.5225553363887330440804328624571e-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 = 0.2806
Order of pole (three term test) = -3.151
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.96
y[1] (analytic) = 2.4456967840858062732936197368834
y[1] (numeric) = 2.4456967840858062732936197368845
absolute error = 1.1e-30
relative error = 4.4976957370910414094863599559188e-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 = 0.2884
Order of pole (three term test) = -3.294
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.97
y[1] (analytic) = 2.4590957301221902576151414883655
y[1] (numeric) = 2.4590957301221902576151414883666
absolute error = 1.1e-30
relative error = 4.4731890122282550920596365806863e-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 = 0.296
Order of pole (three term test) = -3.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.98
y[1] (analytic) = 2.4724487669681405227490871923298
y[1] (numeric) = 2.4724487669681405227490871923309
absolute error = 1.1e-30
relative error = 4.4490305105447484430480485694542e-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 = 0.3036
Order of pole (three term test) = -3.591
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 8.99
y[1] (analytic) = 2.4857545593310999672821992271839
y[1] (numeric) = 2.485754559331099967282199227185
absolute error = 1.1e-30
relative error = 4.4252156588460716326657212761834e-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 = 0.311
Order of pole (three term test) = -3.745
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9
y[1] (analytic) = 2.4990117766429204186120221448288
y[1] (numeric) = 2.4990117766429204186120221448298
absolute error = 1.0e-30
relative error = 4.0015817826331448888695659680150e-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 = 0.3183
Order of pole (three term test) = -3.903
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.01
y[1] (analytic) = 2.5122190931929183389610687884018
y[1] (numeric) = 2.5122190931929183389610687884029
absolute error = 1.1e-30
relative error = 4.3785989963238003122097159786335e-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 = 0.3255
Order of pole (three term test) = -4.064
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.02
y[1] (analytic) = 2.5253751882604447889753776159455
y[1] (numeric) = 2.5253751882604447889753776159466
absolute error = 1.1e-30
relative error = 4.3557884195326772190704751227642e-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 = 0.3325
Order of pole (three term test) = -4.229
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.03
y[1] (analytic) = 2.5384787462469563920215759756844
y[1] (numeric) = 2.5384787462469563920215759756855
absolute error = 1.1e-30
relative error = 4.3333039586260388129501009880259e-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 = 0.3394
Order of pole (three term test) = -4.397
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.04
y[1] (analytic) = 2.5515284568075740921960783966351
y[1] (numeric) = 2.5515284568075740921960783966363
absolute error = 1.2e-30
relative error = 4.7030633610938367977284308594682e-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 = 0.3462
Order of pole (three term test) = -4.569
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.05
y[1] (analytic) = 2.5645230149821165502802509076205
y[1] (numeric) = 2.5645230149821165502802509076216
absolute error = 1.1e-30
relative error = 4.2892966589643600531827073125584e-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 = 0.3528
Order of pole (three term test) = -4.745
NO COMPLEX POLE (six term test) for Equation 1
bytes used=152065916, alloc=4586680, time=14.14
TOP MAIN SOLVE Loop
x[1] = 9.06
y[1] (analytic) = 2.5774611213255950744111400009037
y[1] (numeric) = 2.5774611213255950744111400009048
absolute error = 1.1e-30
relative error = 4.2677656353329088801392148531145e-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 = 0.3593
Order of pole (three term test) = -4.923
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.07
y[1] (analytic) = 2.590341482038157036083444580621
y[1] (numeric) = 2.5903414820381570360834445806221
absolute error = 1.1e-30
relative error = 4.2465443557445081496741088296701e-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 = 0.3657
Order of pole (three term test) = -5.105
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.08
y[1] (analytic) = 2.6031628090944647772494165178653
y[1] (numeric) = 2.6031628090944647772494165178664
absolute error = 1.1e-30
relative error = 4.2256289009547027940550979449673e-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 = 0.3719
Order of pole (three term test) = -5.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.09
y[1] (analytic) = 2.615923820372497070733795218897
y[1] (numeric) = 2.6159238203724970707337952188981
absolute error = 1.1e-30
relative error = 4.2050154191545394750732809789438e-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 = 0.3779
Order of pole (three term test) = -5.478
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.1
y[1] (analytic) = 2.62862323978176025392506890559
y[1] (numeric) = 2.6286232397817602539250689055911
absolute error = 1.1e-30
relative error = 4.1847001249647583168564093172072e-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 = 0.3839
Order of pole (three term test) = -5.669
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.11
y[1] (analytic) = 2.6412597973908962147365357372524
y[1] (numeric) = 2.6412597973908962147365357372536
absolute error = 1.2e-30
relative error = 4.5432865073908693207574435689172e-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 = 0.3896
Order of pole (three term test) = -5.862
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.12
y[1] (analytic) = 2.6538322295546744691449083015452
y[1] (numeric) = 2.6538322295546744691449083015464
absolute error = 1.2e-30
relative error = 4.5217628553759995762698052094255e-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 = 0.3952
Order of pole (three term test) = -6.059
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.13
y[1] (analytic) = 2.6663392790403556312045339925759
y[1] (numeric) = 2.6663392790403556312045339925771
absolute error = 1.2e-30
relative error = 4.5005525344542536597807564212296e-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 = 0.4006
Order of pole (three term test) = -6.259
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.14
y[1] (analytic) = 2.6787796951534136392955323947999
y[1] (numeric) = 2.6787796951534136392955323948011
absolute error = 1.2e-30
relative error = 4.4796516942811754181240825019871e-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 = 0.4059
Order of pole (three term test) = -6.461
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.15
y[1] (analytic) = 2.6911522338626041664879930316364
y[1] (numeric) = 2.6911522338626041664879930316377
absolute error = 1.3e-30
relative error = 4.8306445976640764206192912569652e-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 = 0.411
Order of pole (three term test) = -6.666
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.16
y[1] (analytic) = 2.7034556579243667082854203869158
y[1] (numeric) = 2.703455657924366708285420386917
absolute error = 1.2e-30
relative error = 4.4387633896733653348137000813654e-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 = 0.416
Order of pole (three term test) = -6.873
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.17
y[1] (analytic) = 2.7156887370065479076423199155477
y[1] (numeric) = 2.715688737006547907642319915549
absolute error = 1.3e-30
relative error = 4.7869992694117268310856639611807e-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 = 0.4207
Order of pole (three term test) = -7.083
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.18
y[1] (analytic) = 2.7278502478114337450265257119842
y[1] (numeric) = 2.7278502478114337450265257119854
absolute error = 1.2e-30
relative error = 4.3990684641239572421175548526108e-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 = 0.4254
Order of pole (three term test) = -7.295
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.19
y[1] (analytic) = 2.7399389741980782904097900870034
y[1] (numeric) = 2.7399389741980782904097900870046
absolute error = 1.2e-30
relative error = 4.3796595884082214292964229332374e-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 = 0.4298
Order of pole (three term test) = -7.509
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.2
y[1] (analytic) = 2.7519537073039167844133762807175
y[1] (numeric) = 2.7519537073039167844133762807187
absolute error = 1.2e-30
relative error = 4.3605384669629397842228273791942e-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 = 0.4341
Order of pole (three term test) = -7.726
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.21
y[1] (analytic) = 2.7638932456656508874018836490052
y[1] (numeric) = 2.7638932456656508874018836490064
absolute error = 1.2e-30
relative error = 4.3417016987969600147713150229358e-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 = 0.4382
Order of pole (three term test) = -7.944
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.22
y[1] (analytic) = 2.775756395339394008101133312638
y[1] (numeric) = 2.7757563953393940081011333126391
absolute error = 1.1e-30
relative error = 3.9628837813251335370938009901642e-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 = 0.4421
Order of pole (three term test) = -8.165
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.23
y[1] (analytic) = 2.7875419700200646973073732539797
y[1] (numeric) = 2.7875419700200646973073732539809
absolute error = 1.2e-30
relative error = 4.3048679191415453838903825119810e-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 = 0.4458
Order of pole (three term test) = -8.387
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.24
y[1] (analytic) = 2.7992487911600161674479261038611
y[1] (numeric) = 2.7992487911600161674479261038623
absolute error = 1.2e-30
relative error = 4.2868644037271042221365202683843e-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 = 0.4494
Order of pole (three term test) = -8.612
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.25
y[1] (analytic) = 2.8108756880868900751401811572893
y[1] (numeric) = 2.8108756880868900751401811572906
absolute error = 1.3e-30
relative error = 4.6248932512728548235540414658901e-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 = 0.4528
Order of pole (three term test) = -8.838
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.26
y[1] (analytic) = 2.8224214981206827814688858768887
y[1] (numeric) = 2.8224214981206827814688858768899
absolute error = 1.2e-30
relative error = 4.2516682954655190357468515342914e-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 = 0.456
Order of pole (three term test) = -9.066
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.27
y[1] (analytic) = 2.8338850666900123834532640466342
y[1] (numeric) = 2.8338850666900123834532640466354
absolute error = 1.2e-30
relative error = 4.2344695418491483658386370527842e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.459
Order of pole (three term test) = -9.295
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.28
y[1] (analytic) = 2.8452652474475748900977027339896
y[1] (numeric) = 2.8452652474475748900977027339909
absolute error = 1.3e-30
relative error = 4.5689940548291640480761053353039e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.16
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4618
Order of pole (three term test) = -9.526
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.29
y[1] (analytic) = 2.8565609023847779975046161510853
y[1] (numeric) = 2.8565609023847779975046161510866
absolute error = 1.3e-30
relative error = 4.5509269517576360921265980110899e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4645
Order of pole (three term test) = -9.758
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=156067188, alloc=4586680, time=14.52
x[1] = 9.3
y[1] (analytic) = 2.8677709019455409997675029560489
y[1] (numeric) = 2.8677709019455409997675029560501
absolute error = 1.2e-30
relative error = 4.1844346742827367347699074506531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = -9.991
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.31
y[1] (analytic) = 2.8788941251392494557479406317273
y[1] (numeric) = 2.8788941251392494557479406317286
absolute error = 1.3e-30
relative error = 4.5156228172757836241481665335796e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4692
Order of pole (three term test) = -10.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.32
y[1] (analytic) = 2.8899294596528533163639678175814
y[1] (numeric) = 2.8899294596528533163639678175827
absolute error = 1.3e-30
relative error = 4.4983796945554503578438873057380e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4713
Order of pole (three term test) = -10.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.33
y[1] (analytic) = 2.900875801962097302670540551208
y[1] (numeric) = 2.9008758019620973026705405512093
absolute error = 1.3e-30
relative error = 4.4814052332771526721734361010486e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4732
Order of pole (three term test) = -10.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.34
y[1] (analytic) = 2.9117320574418724117869460466285
y[1] (numeric) = 2.9117320574418724117869460466297
absolute error = 1.2e-30
relative error = 4.1212583312156492294952593445818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.02
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.475
Order of pole (three term test) = -10.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.35
y[1] (analytic) = 2.9224971404756775156125405497065
y[1] (numeric) = 2.9224971404756775156125405497077
absolute error = 1.2e-30
relative error = 4.1060775847489216757879503065765e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4765
Order of pole (three term test) = -11.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.36
y[1] (analytic) = 2.93316997456418010626215739178
y[1] (numeric) = 2.9331699745641801062621573917812
absolute error = 1.2e-30
relative error = 4.0911369283271757414503445346406e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4778
Order of pole (three term test) = -11.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.37
y[1] (analytic) = 2.9437494924328653322371086870076
y[1] (numeric) = 2.9437494924328653322371086870088
absolute error = 1.2e-30
relative error = 4.0764338238858040433017538949793e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.02
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = -11.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.38
y[1] (analytic) = 2.9542346361387625605178708043778
y[1] (numeric) = 2.954234636138762560517870804379
absolute error = 1.2e-30
relative error = 4.0619657806477465006409689765620e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -11.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.39
y[1] (analytic) = 2.9646243571762387920111828511153
y[1] (numeric) = 2.9646243571762387920111828511164
absolute error = 1.1e-30
relative error = 3.7104194915531688559738572802604e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -12.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.4
y[1] (analytic) = 2.9749176165818483510981743433053
y[1] (numeric) = 2.9749176165818483510981743433065
absolute error = 1.2e-30
relative error = 4.0337251469127687179911352755996e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -12.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.41
y[1] (analytic) = 2.9851133850382283644019417010112
y[1] (numeric) = 2.9851133850382283644019417010124
absolute error = 1.2e-30
relative error = 4.0199478050467164986538320138040e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.42
y[1] (analytic) = 2.9952106429770296393132760872758
y[1] (numeric) = 2.9952106429770296393132760872769
absolute error = 1.1e-30
relative error = 3.6725296852800877722787873627465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.82
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.43
y[1] (analytic) = 3.0052083806808726492724654644099
y[1] (numeric) = 3.005208380680872649272465464411
absolute error = 1.1e-30
relative error = 3.6603119007367448306469313497659e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.44
y[1] (analytic) = 3.0151055983843184302936057252201
y[1] (numeric) = 3.0151055983843184302936057252212
absolute error = 1.1e-30
relative error = 3.6482967647615678348528588111941e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.45
y[1] (analytic) = 3.0249013063738442917259106013581
y[1] (numeric) = 3.0249013063738442917259106013592
absolute error = 1.1e-30
relative error = 3.6364822802058461135070901010046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.02
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -13.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.46
y[1] (analytic) = 3.034594525086814343764257032392
y[1] (numeric) = 3.0345945250868143437642570323931
absolute error = 1.1e-30
relative error = 3.6248664884430678904532618778488e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -13.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.47
y[1] (analytic) = 3.0441842852094349447386901057381
y[1] (numeric) = 3.0441842852094349447386901057392
absolute error = 1.1e-30
relative error = 3.6134474688161718268157755154884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.27
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = -14.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.48
y[1] (analytic) = 3.0536696277736852727197878842677
y[1] (numeric) = 3.0536696277736852727197878842688
absolute error = 1.1e-30
relative error = 3.6022233380955761309892150634772e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4788
Order of pole (three term test) = -14.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.49
y[1] (analytic) = 3.0630496042532133284635007921944
y[1] (numeric) = 3.0630496042532133284635007921955
absolute error = 1.1e-30
relative error = 3.5911922499478602166438745127458e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4777
Order of pole (three term test) = -14.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.5
y[1] (analytic) = 3.072323276658187780175084144712
y[1] (numeric) = 3.0723232766581877801750841447131
absolute error = 1.1e-30
relative error = 3.5803523944149736036031193965873e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = -14.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.51
y[1] (analytic) = 3.0814897176290961649866903686239
y[1] (numeric) = 3.081489717629096164986690368625
absolute error = 1.1e-30
relative error = 3.5697019974038466548898470755042e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4748
Order of pole (three term test) = -15.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.52
y[1] (analytic) = 3.0905480105294800674066380620896
y[1] (numeric) = 3.0905480105294800674066380620907
absolute error = 1.1e-30
relative error = 3.5592393201862778131802628076058e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.473
Order of pole (three term test) = -15.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.53
y[1] (analytic) = 3.0994972495375980012997920243597
y[1] (numeric) = 3.0994972495375980012997920243608
absolute error = 1.1e-30
relative error = 3.5489626589089722298646702197376e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.18
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4711
Order of pole (three term test) = -15.49
NO COMPLEX POLE (six term test) for Equation 1
bytes used=160068520, alloc=4586680, time=14.89
TOP MAIN SOLVE Loop
x[1] = 9.54
y[1] (analytic) = 3.1083365397370068291872416978607
y[1] (numeric) = 3.1083365397370068291872416978618
absolute error = 1.1e-30
relative error = 3.5388703441136070590649989955627e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.469
Order of pole (three term test) = -15.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.55
y[1] (analytic) = 3.1170649972060526607988323192548
y[1] (numeric) = 3.1170649972060526607988323192559
absolute error = 1.1e-30
relative error = 3.5289607402667992070790332066306e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4667
Order of pole (three term test) = -15.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.56
y[1] (analytic) = 3.1256817491062622818632690265674
y[1] (numeric) = 3.1256817491062622818632690265686
absolute error = 1.2e-30
relative error = 3.8391624494180203365550841324601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.21
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4642
Order of pole (three term test) = -16.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.57
y[1] (analytic) = 3.1341859337696262740665741904323
y[1] (numeric) = 3.1341859337696262740665741904335
absolute error = 1.2e-30
relative error = 3.8287454074452630560378418715083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = -16.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.58
y[1] (analytic) = 3.1425767007847650979396378145668
y[1] (numeric) = 3.142576700784765097939637814568
absolute error = 1.2e-30
relative error = 3.8185225509383292940242847170347e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4587
Order of pole (three term test) = -16.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.59
y[1] (analytic) = 3.1508532110819695221383770801613
y[1] (numeric) = 3.1508532110819695221383770801624
absolute error = 1.1e-30
relative error = 3.4911178855655788705008791032596e-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 = 0.4556
Order of pole (three term test) = -16.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.6
y[1] (analytic) = 3.1590146370171068951444438064041
y[1] (numeric) = 3.1590146370171068951444438064053
absolute error = 1.2e-30
relative error = 3.7986528645308764499264740802632e-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 = 0.4524
Order of pole (three term test) = -17.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.61
y[1] (analytic) = 3.1670601624543848688292314164094
y[1] (numeric) = 3.1670601624543848688292314164106
absolute error = 1.2e-30
relative error = 3.7890028557905034310421946629083e-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 = 0.449
Order of pole (three term test) = -17.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.62
y[1] (analytic) = 3.1749889828479642975777945475861
y[1] (numeric) = 3.1749889828479642975777945475873
absolute error = 1.2e-30
relative error = 3.7795406739446393604057646062250e-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 = 0.4454
Order of pole (three term test) = -17.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.63
y[1] (analytic) = 3.1828003053224131517507794370578
y[1] (numeric) = 3.182800305322413151750779437059
absolute error = 1.2e-30
relative error = 3.7702648136400807082677581007111e-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 = 0.4417
Order of pole (three term test) = -17.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.64
y[1] (analytic) = 3.1904933487519934001600635934959
y[1] (numeric) = 3.1904933487519934001600635934971
absolute error = 1.2e-30
relative error = 3.7611738023819951633868156128590e-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 = 0.4377
Order of pole (three term test) = -18.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.65
y[1] (analytic) = 3.1980673438387729329359293732203
y[1] (numeric) = 3.1980673438387729329359293732215
absolute error = 1.2e-30
relative error = 3.7522662001219467985941532355528e-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 = 0.4336
Order of pole (three term test) = -18.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.66
y[1] (analytic) = 3.2055215331895547136585777952904
y[1] (numeric) = 3.2055215331895547136585777952916
absolute error = 1.2e-30
relative error = 3.7435405988553046583807558789463e-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 = 0.4293
Order of pole (three term test) = -18.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.67
y[1] (analytic) = 3.2128551713916154679028768572878
y[1] (numeric) = 3.2128551713916154679028768572891
absolute error = 1.3e-30
relative error = 4.0462452574135741427941840918111e-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 = 0.4249
Order of pole (three term test) = -18.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.68
y[1] (analytic) = 3.2200675250872463343906052403635
y[1] (numeric) = 3.2200675250872463343906052403647
absolute error = 1.2e-30
relative error = 3.7266299251519159367318422192976e-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 = 0.4203
Order of pole (three term test) = -18.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.69
y[1] (analytic) = 3.2271578730470880247471931814128
y[1] (numeric) = 3.227157873047088024747193181414
absolute error = 1.2e-30
relative error = 3.7184421934305864378686171734960e-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 = 0.4155
Order of pole (three term test) = -19.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.7
y[1] (analytic) = 3.2341255062422531584080972677162
y[1] (numeric) = 3.2341255062422531584080972677174
absolute error = 1.2e-30
relative error = 3.7104311433921007320541183579344e-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 = 0.4105
Order of pole (three term test) = -19.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.71
y[1] (analytic) = 3.2409697279152285605014202619804
y[1] (numeric) = 3.2409697279152285605014202619815
absolute error = 1.1e-30
relative error = 3.3940458947377487372264539710937e-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 = 0.4054
Order of pole (three term test) = -19.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.72
y[1] (analytic) = 3.2476898536495504325360727470818
y[1] (numeric) = 3.247689853649550432536072747083
absolute error = 1.2e-30
relative error = 3.6949341041648886644618309534316e-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 = 0.4001
Order of pole (three term test) = -19.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.73
y[1] (analytic) = 3.2542852114382454284364702230493
y[1] (numeric) = 3.2542852114382454284364702230504
absolute error = 1.1e-30
relative error = 3.3801585556597549757883499472812e-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 = 0.3946
Order of pole (three term test) = -19.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.74
y[1] (analytic) = 3.2607551417510307918731962264869
y[1] (numeric) = 3.260755141751030791873196226488
absolute error = 1.1e-30
relative error = 3.3734517072916374167350506316909e-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 = 0.389
Order of pole (three term test) = -20.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.75
y[1] (analytic) = 3.2670989976002668349318983339047
y[1] (numeric) = 3.2670989976002668349318983339059
absolute error = 1.2e-30
relative error = 3.6729832823597264109288794767778e-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 = 0.3833
Order of pole (three term test) = -20.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.76
y[1] (analytic) = 3.2733161446056551629275103750451
y[1] (numeric) = 3.2733161446056551629275103750462
absolute error = 1.1e-30
relative error = 3.3605064448564586683019496528940e-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 = 0.3774
Order of pole (three term test) = -20.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.77
y[1] (analytic) = 3.2794059610576761755952344416098
y[1] (numeric) = 3.279405961057676175595234441611
absolute error = 1.2e-30
relative error = 3.6591993008787945478106531804508e-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 = 0.3713
Order of pole (three term test) = -20.66
NO COMPLEX POLE (six term test) for Equation 1
bytes used=164069328, alloc=4586680, time=15.27
TOP MAIN SOLVE Loop
x[1] = 9.78
y[1] (analytic) = 3.2853678379797595009610280013021
y[1] (numeric) = 3.2853678379797595009610280013033
absolute error = 1.2e-30
relative error = 3.6525590411145705072679499303701e-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 = 0.3651
Order of pole (three term test) = -20.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.79
y[1] (analytic) = 3.2912011791891811449000175906641
y[1] (numeric) = 3.2912011791891811449000175906653
absolute error = 1.2e-30
relative error = 3.6460852274476623302973148936348e-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 = 0.3587
Order of pole (three term test) = -21.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.8
y[1] (analytic) = 3.2969054013566812667186307008181
y[1] (numeric) = 3.2969054013566812667186307008192
absolute error = 1.1e-30
relative error = 3.3364621245952293136604436518961e-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 = 0.3522
Order of pole (three term test) = -21.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.81
y[1] (analytic) = 3.3024799340647966190325689569673
y[1] (numeric) = 3.3024799340647966190325689569684
absolute error = 1.1e-30
relative error = 3.3308302304991911155976095832448e-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 = 0.3456
Order of pole (three term test) = -21.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.82
y[1] (analytic) = 3.3079242198649018187452449988707
y[1] (numeric) = 3.3079242198649018187452449988719
absolute error = 1.2e-30
relative error = 3.6276526311990572966326958783378e-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 = 0.3388
Order of pole (three term test) = -21.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.83
y[1] (analytic) = 3.3132377143329537450471194526374
y[1] (numeric) = 3.3132377143329537450471194526386
absolute error = 1.2e-30
relative error = 3.6218349042957008018267327233493e-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 = 0.3319
Order of pole (three term test) = -21.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.84
y[1] (analytic) = 3.3184198861239334900425915702971
y[1] (numeric) = 3.3184198861239334900425915702983
absolute error = 1.2e-30
relative error = 3.6161789079731407827383303893232e-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 = 0.3248
Order of pole (three term test) = -21.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.85
y[1] (analytic) = 3.3234702170249804178547489890459
y[1] (numeric) = 3.3234702170249804178547489890471
absolute error = 1.2e-30
relative error = 3.6106837782171717323618101869000e-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 = 0.3177
Order of pole (three term test) = -22.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.86
y[1] (analytic) = 3.3283882020072130188463443701828
y[1] (numeric) = 3.328388202007213018846344370184
absolute error = 1.2e-30
relative error = 3.6053486768049764142405654902254e-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 = 0.3104
Order of pole (three term test) = -22.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.87
y[1] (analytic) = 3.3331733492762313769147607213119
y[1] (numeric) = 3.333173349276231376914760721313
absolute error = 1.1e-30
relative error = 3.3001583918185806613417606113852e-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 = 0.3029
Order of pole (three term test) = -22.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.88
y[1] (analytic) = 3.3378251803212961996563211544049
y[1] (numeric) = 3.337825180321296199656321154406
absolute error = 1.1e-30
relative error = 3.2955590558943381808864463874907e-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 = 0.2954
Order of pole (three term test) = -22.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.89
y[1] (analytic) = 3.3423432299631794935379090372785
y[1] (numeric) = 3.3423432299631794935379090372796
absolute error = 1.1e-30
relative error = 3.2911042472801873568216377204012e-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 = 0.2877
Order of pole (three term test) = -22.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.9
y[1] (analytic) = 3.3467270464006820990482568061945
y[1] (numeric) = 3.3467270464006820990482568061956
absolute error = 1.1e-30
relative error = 3.2867932901281011028031553202566e-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 = 0.2799
Order of pole (three term test) = -22.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.91
y[1] (analytic) = 3.3509761912558134341141527941132
y[1] (numeric) = 3.3509761912558134341141527941143
absolute error = 1.1e-30
relative error = 3.2826255312418781342341742688477e-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 = 0.272
Order of pole (three term test) = -22.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.92
y[1] (analytic) = 3.3550902396176289278448741145988
y[1] (numeric) = 3.3550902396176289278448741146
absolute error = 1.2e-30
relative error = 3.5766549162527471615954105949122e-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 = 0.264
Order of pole (three term test) = -23.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.93
y[1] (analytic) = 3.3590687800847207608980022311041
y[1] (numeric) = 3.3590687800847207608980022311053
absolute error = 1.2e-30
relative error = 3.5724186629180430097151388632078e-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 = 0.2559
Order of pole (three term test) = -23.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.94
y[1] (analytic) = 3.3629114148063576634279934623528
y[1] (numeric) = 3.362911414806357663427993462354
absolute error = 1.2e-30
relative error = 3.5683366344905582484926210144125e-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 = 0.2477
Order of pole (three term test) = -23.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.95
y[1] (analytic) = 3.36661775952226965667199261745
y[1] (numeric) = 3.3666177595222696566719926174512
absolute error = 1.2e-30
relative error = 3.5644082153546371003765336453467e-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 = 0.2394
Order of pole (three term test) = -23.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.96
y[1] (analytic) = 3.3701874436010737597318850201653
y[1] (numeric) = 3.3701874436010737597318850201664
absolute error = 1.1e-30
relative error = 3.2639134125567826150360407531990e-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 = 0.231
Order of pole (three term test) = -23.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.97
y[1] (analytic) = 3.3736201100773368190139300327654
y[1] (numeric) = 3.3736201100773368190139300327666
absolute error = 1.2e-30
relative error = 3.5570098613518497706968754211786e-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 = 0.2225
Order of pole (three term test) = -23.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.98
y[1] (analytic) = 3.3769154156872717540739177042946
y[1] (numeric) = 3.3769154156872717540739177042958
absolute error = 1.2e-30
relative error = 3.5535388136329002917547960179373e-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 = 0.2139
Order of pole (three term test) = -23.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 9.99
y[1] (analytic) = 3.3800730309030636502730108000159
y[1] (numeric) = 3.380073030903063650273010800017
absolute error = 1.1e-30
relative error = 3.2543675534315597192490388781434e-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 = 0.2052
Order of pole (three term test) = -23.89
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sin ( x ) - cos ( x );
Iterations = 1000
Total Elapsed Time = 15 Seconds
Elapsed Time(since restart) = 15 Seconds
Time to Timeout = 2 Minutes 44 Seconds
Percent Done = 100.1 %
> quit
bytes used=167751752, alloc=4586680, time=15.60