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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> 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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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 cos 1 $eq_no = 1
> array_tmp1[1] := cos(array_x[1]);
> array_tmp1_g[1] := sin(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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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_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] := cos(array_x[1]);
array_tmp1_g[1] := sin(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[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];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[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];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[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];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[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];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[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];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_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(1.0 + sin(x));
> end;
exact_soln_y := proc(x) return 1.0 + sin(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_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/cospostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 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 := -5.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> 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 := 10000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + sin(x));");
> omniout_str(ALWAYS,"end;");
> 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_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_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_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 := -5.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 10000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_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 ) = 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,"2013-05-26T00:11:06-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cos")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 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,"cos diffeq.mxt")
> ;
> logitem_str(html_log_file,"cos 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_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/cospostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = 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 := -5.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
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 := 10000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(1.0 + sin(x));");
omniout_str(ALWAYS, "end;");
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_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_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_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 := -5.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 10000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_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 ) = 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, "2013-05-26T00:11:06-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "cos");
logitem_str(html_log_file, "diff ( y , x , 1 ) = 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,
"cos diffeq.mxt");
logitem_str(html_log_file,
"cos 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/cospostode.ode#################
diff ( y , x , 1 ) = cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -5.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 10000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(1.0 + sin(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 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 = 2.3777450611955943732797533891922e-183
estimated_step_error = 2.3777450611955943732797533891922e-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 = 1.5956777081256160619008740747256e-175
estimated_step_error = 1.5956777081256160619008740747256e-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 = 1.0708411947565045661970327052961e-167
estimated_step_error = 1.0708411947565045661970327052961e-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 = 7.1862937679176132330702885343963e-160
estimated_step_error = 7.1862937679176132330702885343963e-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 = 4.8226403227000255913195452206655e-152
estimated_step_error = 4.8226403227000255913195452206655e-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 = 3.2364194190356168085042457522636e-144
estimated_step_error = 3.2364194190356168085042457522636e-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 = 2.1719246871187506202952151683868e-136
estimated_step_error = 2.1719246871187506202952151683868e-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 = 1.4575544954631940368195334011604e-128
estimated_step_error = 1.4575544954631940368195334011604e-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 = 9.7814894993393649740462499302859e-121
estimated_step_error = 9.7814894993393649740462499302859e-121
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 = 6.5642556903639522743698069394296e-113
estimated_step_error = 6.5642556903639522743698069394296e-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 = 4.4052097781323668889876791239504e-105
estimated_step_error = 4.4052097781323668889876791239504e-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 = 2.9563028190094691990154760627172e-97
estimated_step_error = 2.9563028190094691990154760627172e-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 = 1.9839634875269747292572023413844e-89
estimated_step_error = 1.9839634875269747292572023413844e-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 = 1.3314452100654924958989130368116e-81
estimated_step_error = 1.3314452100654924958989130368116e-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 = 8.9355779140126794287549090660785e-74
estimated_step_error = 8.9355779140126794287549090660785e-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 = 5.9971013875699900220019585193844e-66
estimated_step_error = 5.9971013875699900220019585193844e-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 = 4.0253046264506033253741859410581e-58
estimated_step_error = 4.0253046264506033253741859410581e-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 = 2.7022941542008095516033119435620e-50
estimated_step_error = 2.7022941542008095516033119435620e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (analytic) = 1.958924274663138468893154406156
y[1] (numeric) = 1.958924274663138468893154406156
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 = 0.262
Order of pole (three term test) = -23.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.99
y[1] (analytic) = 1.9617129034267934979411460144111
y[1] (numeric) = 1.9617129034267934979411460144111
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 = 0.2538
Order of pole (three term test) = -23.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.98
y[1] (analytic) = 1.9644053617015305957417100779289
y[1] (numeric) = 1.9644053617015305957417100779289
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 = 0.2456
Order of pole (three term test) = -23.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.97
y[1] (analytic) = 1.9670013802437659963349767140779
y[1] (numeric) = 1.9670013802437659963349767140779
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 = 0.2373
Order of pole (three term test) = -23.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.96
y[1] (analytic) = 1.9695006994538088177549330230967
y[1] (numeric) = 1.9695006994538088177549330230967
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 = 0.2288
Order of pole (three term test) = -23.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.95
y[1] (analytic) = 1.9719030694018208147852650633774
y[1] (numeric) = 1.9719030694018208147852650633773
absolute error = 1e-31
relative error = 5.0712431838921535406739777612629e-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 = 0.2203
Order of pole (three term test) = -23.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.94
y[1] (analytic) = 1.9742082498528091545097085268232
y[1] (numeric) = 1.9742082498528091545097085268231
absolute error = 1e-31
relative error = 5.0653217565804260984277830335457e-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 = 0.2117
Order of pole (three term test) = -23.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.93
y[1] (analytic) = 1.9764160102906497154001803227491
y[1] (numeric) = 1.9764160102906497154001803227491
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 = 0.203
Order of pole (three term test) = -23.91
NO COMPLEX POLE (six term test) for Equation 1
bytes used=4000064, alloc=3079628, time=0.15
TOP MAIN SOLVE Loop
x[1] = -4.92
y[1] (analytic) = 1.9785261299411385076328016063411
y[1] (numeric) = 1.9785261299411385076328016063411
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 = 0.1942
Order of pole (three term test) = -24.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.91
y[1] (analytic) = 1.9805383977940689095089901022697
y[1] (numeric) = 1.9805383977940689095089901022697
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 = 0.1854
Order of pole (three term test) = -24.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.9
y[1] (analytic) = 1.9824526126243325122763772499183
y[1] (numeric) = 1.9824526126243325122763772499183
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 = 0.1765
Order of pole (three term test) = -24.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.89
y[1] (analytic) = 1.9842685830120414632826520572489
y[1] (numeric) = 1.9842685830120414632826520572489
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 = 0.1675
Order of pole (three term test) = -24.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.88
y[1] (analytic) = 1.9859861273616702952447848423184
y[1] (numeric) = 1.9859861273616702952447848423184
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 = 0.1584
Order of pole (three term test) = -24.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.87
y[1] (analytic) = 1.9876050739202153274666554112925
y[1] (numeric) = 1.9876050739202153274666554112925
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 = 0.1493
Order of pole (three term test) = -24.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.86
y[1] (analytic) = 1.9891252607943698230800966940429
y[1] (numeric) = 1.9891252607943698230800966940429
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 = 0.1401
Order of pole (three term test) = -24.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.85
y[1] (analytic) = 1.9905465359667131848079423162912
y[1] (numeric) = 1.9905465359667131848079423162912
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 = 0.1309
Order of pole (three term test) = -24.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.84
y[1] (analytic) = 1.9918687573109125703429927550405
y[1] (numeric) = 1.9918687573109125703429927550405
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 = 0.1216
Order of pole (three term test) = -24.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.83
y[1] (analytic) = 1.9930917926059354071940301512694
y[1] (numeric) = 1.9930917926059354071940301512694
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 = 0.1122
Order of pole (three term test) = -24.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.82
y[1] (analytic) = 1.9942155195492713857592409012983
y[1] (numeric) = 1.9942155195492713857592409012983
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 = 0.1028
Order of pole (three term test) = -24.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.81
y[1] (analytic) = 1.995239825769162608438756975404
y[1] (numeric) = 1.995239825769162608438756975404
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 = 0.0934
Order of pole (three term test) = -24.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.8
y[1] (analytic) = 1.9961646088358406717815964665036
y[1] (numeric) = 1.9961646088358406717815964665036
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 = 0.08394
Order of pole (three term test) = -24.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.79
y[1] (analytic) = 1.9969897762717695579681528787627
y[1] (numeric) = 1.9969897762717695579681528787627
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 = 0.07444
Order of pole (three term test) = -24.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.78
y[1] (analytic) = 1.9977152455608933113476206216477
y[1] (numeric) = 1.9977152455608933113476206216476
absolute error = 1e-31
relative error = 5.0057184186890089135139710878527e-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 = 0.06491
Order of pole (three term test) = -24.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.77
y[1] (analytic) = 1.9983409441568875752704093382995
y[1] (numeric) = 1.9983409441568875752704093382994
absolute error = 1e-31
relative error = 5.0041510830470733077738269445069e-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 = 0.05535
Order of pole (three term test) = -24.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.76
y[1] (analytic) = 1.9988668094904141640687400845694
y[1] (numeric) = 1.9988668094904141640687400845694
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 = 0.04578
Order of pole (three term test) = -24.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.75
y[1] (analytic) = 1.9992927889753779447342707555971
y[1] (numeric) = 1.999292788975377944734270755597
absolute error = 1e-31
relative error = 5.0017686529669936323667425758078e-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 = 0.03618
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.74
y[1] (analytic) = 1.9996188400141854026097970480728
y[1] (numeric) = 1.9996188400141854026097970480727
absolute error = 1e-31
relative error = 5.0009530816028215992927725888839e-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 = 0.02657
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.73
y[1] (analytic) = 1.9998449300020043652428419115577
y[1] (numeric) = 1.9998449300020043652428419115576
absolute error = 1e-31
relative error = 5.0003877050557001920560172246251e-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 = 0.01696
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.72
y[1] (analytic) = 1.9999710363300244584322978879616
y[1] (numeric) = 1.9999710363300244584322978879616
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 = 0.007329
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.71
y[1] (analytic) = 1.9999971463877179684252347125936
y[1] (numeric) = 1.9999971463877179684252347125935
absolute error = 1e-31
relative error = 5.0000071340408839722804225645299e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.999923257564100884179536541575
y[1] (numeric) = 1.9999232575641008841795365415749
absolute error = 1e-31
relative error = 5.0001918634517821144371667574917e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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
y[1] (analytic) = 1.9997493772479939935891934069429
y[1] (numeric) = 1.9997493772479939935891934069428
absolute error = 1e-31
relative error = 5.0006266354045598136158498211902e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9994755228272840075628419497597
y[1] (numeric) = 1.9994755228272840075628419497596
absolute error = 1e-31
relative error = 5.0013115368673640350322282749130e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9991017216871847858425318492734
y[1] (numeric) = 1.9991017216871847858425318492733
absolute error = 1e-31
relative error = 5.0022467048651658728604137742610e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9986280112074988384386870978325
y[1] (numeric) = 1.9986280112074988384386870978324
absolute error = 1e-31
relative error = 5.0034323265380240905854002022477e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for 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=8000884, alloc=4259060, time=0.31
x[1] = -4.65
y[1] (analytic) = 1.998054438758879376528836550896
y[1] (numeric) = 1.9980544387588793765288365508959
absolute error = 1e-31
relative error = 5.0048686392206839398734544271524e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9973810616980932866119089318828
y[1] (numeric) = 1.9973810616980932866119089318827
absolute error = 1e-31
relative error = 5.0065559305435693804450745180895e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9966079473622855016167293539807
y[1] (numeric) = 1.9966079473622855016167293539806
absolute error = 1e-31
relative error = 5.0084945385552424848456563611094e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9957351730622453425228268344515
y[1] (numeric) = 1.9957351730622453425228268344514
absolute error = 1e-31
relative error = 5.0106848518664195558183084028340e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9947628260746755038537793574031
y[1] (numeric) = 1.9947628260746755038537793574031
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] = -4.6
y[1] (analytic) = 1.9936910036334644561381046599088
y[1] (numeric) = 1.9936910036334644561381046599088
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] = -4.59
y[1] (analytic) = 1.9925198129199631380901776786878
y[1] (numeric) = 1.9925198129199631380901776786878
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] = -4.58
y[1] (analytic) = 1.9912493710522669108338538360973
y[1] (numeric) = 1.9912493710522669108338538360973
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] = -4.57
y[1] (analytic) = 1.9898798050735038459644441280651
y[1] (numeric) = 1.9898798050735038459644441280651
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] = -4.56
y[1] (analytic) = 1.9884112519391305186104760890381
y[1] (numeric) = 1.9884112519391305186104760890381
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] = -4.55
y[1] (analytic) = 1.9868438585032365759053476540251
y[1] (numeric) = 1.9868438585032365759053476540251
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] = -4.54
y[1] (analytic) = 1.9851777815038594504006139307825
y[1] (numeric) = 1.9851777815038594504006139307825
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] = -4.53
y[1] (analytic) = 1.983413187547310686937327855437
y[1] (numeric) = 1.9834131875473106869373278554369
absolute error = 1e-31
relative error = 5.0418138100442918050511844437544e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9815502530915154503296862467421
y[1] (numeric) = 1.981550253091515450329686246742
absolute error = 1e-31
relative error = 5.0465538203729634882570750985228e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9795891644283668798963291970477
y[1] (numeric) = 1.9795891644283668798963291970476
absolute error = 1e-31
relative error = 5.0515532109853890432691344775858e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9775301176650970553891350144986
y[1] (numeric) = 1.9775301176650970553891350144986
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] = -4.49
y[1] (analytic) = 1.9753733187046664372073936936592
y[1] (numeric) = 1.9753733187046664372073936936592
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] = -4.48
y[1] (analytic) = 1.9731189832251737419369954185327
y[1] (numeric) = 1.9731189832251737419369954185327
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] = -4.47
y[1] (analytic) = 1.9707673366582883122099217992716
y[1] (numeric) = 1.9707673366582883122099217992716
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] = -4.46
y[1] (analytic) = 1.9683186141667071376290809282464
y[1] (numeric) = 1.9683186141667071376290809282465
absolute error = 1e-31
relative error = 5.0804782965655823470218337484315e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9657730606206387810376080186917
y[1] (numeric) = 1.9657730606206387810376080186918
absolute error = 1e-31
relative error = 5.0870571991879749439782163352457e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9631309305733165617204080330778
y[1] (numeric) = 1.9631309305733165617204080330779
absolute error = 1e-31
relative error = 5.0939037454213920509827120066674e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9603924882355434441992145343005
y[1] (numeric) = 1.9603924882355434441992145343005
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] = -4.42
y[1] (analytic) = 1.9575580074492711781110727318389
y[1] (numeric) = 1.9575580074492711781110727318389
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] = -4.41
y[1] (analytic) = 1.9546277716602163312342415645362
y[1] (numeric) = 1.9546277716602163312342415645362
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] = -4.4
y[1] (analytic) = 1.9516020738895159540353923333804
y[1] (numeric) = 1.9516020738895159540353923333804
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] = -4.39
y[1] (analytic) = 1.9484812167044257101480289636141
y[1] (numeric) = 1.9484812167044257101480289636141
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] = -4.38
y[1] (analytic) = 1.9452655121880634029446639109382
y[1] (numeric) = 1.9452655121880634029446639109381
absolute error = 1e-31
relative error = 5.1406864190749221582649183925291e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for 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=12002272, alloc=4324584, time=0.47
x[1] = -4.37
y[1] (analytic) = 1.9419552819082009238248788504083
y[1] (numeric) = 1.9419552819082009238248788504082
absolute error = 1e-31
relative error = 5.1494491624821640336446295069048e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.938550856885107742998434718885
y[1] (numeric) = 1.9385508568851077429984347188849
absolute error = 1e-31
relative error = 5.1584924710554915520202661814938e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9350525775584491583875557983414
y[1] (numeric) = 1.9350525775584491583875557983414
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] = -4.34
y[1] (analytic) = 1.9314607937532426127959129109888
y[1] (numeric) = 1.9314607937532426127959129109888
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] = -4.33
y[1] (analytic) = 1.927775864644875483684219186773
y[1] (numeric) = 1.9277758646448754836842191867729
absolute error = 1e-31
relative error = 5.1873250326443662023907392704245e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.923998158723187843744309098984
y[1] (numeric) = 1.9239981587231878437443090989839
absolute error = 1e-31
relative error = 5.1975101715462369097550678849057e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.920128053755623783965712426991
y[1] (numeric) = 1.9201280537556237839657124269909
absolute error = 1e-31
relative error = 5.2079859884556990640262748958880e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9161659367494549840317093602846
y[1] (numeric) = 1.9161659367494549840317093602845
absolute error = 1e-31
relative error = 5.2187547060583892328965824080814e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.912112203913080307656346885248
y[1] (numeric) = 1.9121122039130803076563468852479
absolute error = 1e-31
relative error = 5.2298186160494660098514434769719e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9079672606164052928706325232994
y[1] (numeric) = 1.9079672606164052928706325232993
absolute error = 1e-31
relative error = 5.2411800801913701903259667064038e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9037315213503054992758598196613
y[1] (numeric) = 1.9037315213503054992758598196612
absolute error = 1e-31
relative error = 5.2528415314083044616053514487507e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8994054096851777658955598188531
y[1] (numeric) = 1.899405409685177765895559818853
absolute error = 1e-31
relative error = 5.2648054749183207926837872684510e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8949893582285835244657528284383
y[1] (numeric) = 1.8949893582285835244657528284382
absolute error = 1e-31
relative error = 5.2770744894039387604538382053203e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8904838085819884037968743245822
y[1] (numeric) = 1.8904838085819884037968743245821
absolute error = 1e-31
relative error = 5.2896512282222542712435410913893e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8858892112966024512108885972993
y[1] (numeric) = 1.8858892112966024512108885972992
absolute error = 1e-31
relative error = 5.3025384206555355847961602391149e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8812060258283253869946467312212
y[1] (numeric) = 1.8812060258283253869946467312212
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] = -4.21
y[1] (analytic) = 1.8764347204918013973064980899522
y[1] (numeric) = 1.8764347204918013973064980899522
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] = -4.2
y[1] (analytic) = 1.8715757724135880600185770979088
y[1] (numeric) = 1.8715757724135880600185770979088
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] = -4.19
y[1] (analytic) = 1.8666296674844440865631553259225
y[1] (numeric) = 1.8666296674844440865631553259225
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] = -4.18
y[1] (analytic) = 1.8615969003107406509691141628009
y[1] (numeric) = 1.8615969003107406509691141628009
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] = -4.17
y[1] (analytic) = 1.8564779741650011649151440014129
y[1] (numeric) = 1.8564779741650011649151440014129
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] = -4.16
y[1] (analytic) = 1.8512734009355744447809479026467
y[1] (numeric) = 1.8512734009355744447809479026467
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] = -4.15
y[1] (analytic) = 1.8459837010754463033378057292122
y[1] (numeric) = 1.8459837010754463033378057292122
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] = -4.14
y[1] (analytic) = 1.8406094035501946848766728281409
y[1] (numeric) = 1.8406094035501946848766728281409
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] = -4.13
y[1] (analytic) = 1.8351510457850935482169298759564
y[1] (numeric) = 1.8351510457850935482169298759564
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] = -4.12
y[1] (analytic) = 1.8296091736113707871634030609722
y[1] (numeric) = 1.8296091736113707871634030609723
absolute error = 1e-31
relative error = 5.4656481527481182925268286618788e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.823984341211625562574823983696
y[1] (numeric) = 1.8239843412116255625748239836961
absolute error = 1e-31
relative error = 5.4825032068845826645859201433046e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8182771110644105042650370243584
y[1] (numeric) = 1.8182771110644105042650370243585
absolute error = 1e-31
relative error = 5.4997117541374367510275810623965e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8124880538879843244705827123527
y[1] (numeric) = 1.8124880538879843244705827123528
bytes used=16004740, alloc=4324584, time=0.63
absolute error = 1e-31
relative error = 5.5172777434581765213206126297831e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8066177485832404675764376733801
y[1] (numeric) = 1.8066177485832404675764376733802
absolute error = 1e-31
relative error = 5.5352052241499646315526144876384e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.66
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] = -4.07
y[1] (analytic) = 1.8006667821758175031873792802757
y[1] (numeric) = 1.8006667821758175031873792802758
absolute error = 1e-31
relative error = 5.5534983479378683770878427074515e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.97
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.06
y[1] (analytic) = 1.7946357497573970514574266927463
y[1] (numeric) = 1.7946357497573970514574266927464
absolute error = 1e-31
relative error = 5.5721613711037589540856967547948e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.28
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] = -4.05
y[1] (analytic) = 1.7885252544261951108359071094194
y[1] (numeric) = 1.7885252544261951108359071094194
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 = 15.6
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] = -4.04
y[1] (analytic) = 1.7823359072266527390477822306665
y[1] (numeric) = 1.7823359072266527390477822306665
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 = 15.92
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] = -4.03
y[1] (analytic) = 1.7760683270883321181898793012325
y[1] (numeric) = 1.7760683270883321181898793012325
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.25
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] = -4.02
y[1] (analytic) = 1.7697231407640241142855973335445
y[1] (numeric) = 1.7697231407640241142855973335445
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.59
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] = -4.01
y[1] (analytic) = 1.7633009827670735204905561792977
y[1] (numeric) = 1.7633009827670735204905561792977
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.93
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
y[1] (analytic) = 1.7568024953079282513726390945118
y[1] (numeric) = 1.7568024953079282513726390945118
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 = 17.27
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] = -3.99
y[1] (analytic) = 1.7502283282299188332941252986201
y[1] (numeric) = 1.7502283282299188332941252986201
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 = 17.63
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] = -3.98
y[1] (analytic) = 1.7435791389442746128933574013766
y[1] (numeric) = 1.7435791389442746128933574013766
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 = 17.98
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] = -3.97
y[1] (analytic) = 1.7368555923643831819909425517513
y[1] (numeric) = 1.7368555923643831819909425517513
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 = 18.35
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] = -3.96
y[1] (analytic) = 1.7300583608392995929232130587317
y[1] (numeric) = 1.7300583608392995929232130587316
absolute error = 1e-31
relative error = 5.7801518297618127299743492282330e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.72
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] = -3.95
y[1] (analytic) = 1.7231881240865120133260043354428
y[1] (numeric) = 1.7231881240865120133260043354427
absolute error = 1e-31
relative error = 5.8031969117133688831298061025066e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.94
y[1] (analytic) = 1.7162455691239705437472433545408
y[1] (numeric) = 1.7162455691239705437472433545407
absolute error = 1e-31
relative error = 5.8266719984042471862142872707526e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.93
y[1] (analytic) = 1.7092313902013859951499438928516
y[1] (numeric) = 1.7092313902013859951499438928515
absolute error = 1e-31
relative error = 5.8505829329648424803604839697301e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.11
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] = -3.92
y[1] (analytic) = 1.7021462887308054963706074378206
y[1] (numeric) = 1.7021462887308054963706074378206
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 = 18.74
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] = -3.91
y[1] (analytic) = 1.6949909732164718739144304480765
y[1] (numeric) = 1.6949909732164718739144304480764
absolute error = 1e-31
relative error = 5.8997364340080606426504169852618e-30 %
Correct digits = 32
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] = -3.9
y[1] (analytic) = 1.6877661591839738180908881253787
y[1] (numeric) = 1.6877661591839738180908881253786
absolute error = 1e-31
relative error = 5.9249914128121564662970719604804e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 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] = -3.89
y[1] (analytic) = 1.6804725691086939204140398081587
y[1] (numeric) = 1.6804725691086939204140398081586
absolute error = 1e-31
relative error = 5.9507070712281256637356430381436e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
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] = -3.88
y[1] (analytic) = 1.6731109323435617374041895193685
y[1] (numeric) = 1.6731109323435617374041895193685
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 = 17.29
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] = -3.87
y[1] (analytic) = 1.6656819850461191054243159231035
y[1] (numeric) = 1.6656819850461191054243159231035
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.95
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] = -3.86
y[1] (analytic) = 1.6581864701049049999590093452957
y[1] (numeric) = 1.6581864701049049999590093452957
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.61
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] = -3.85
y[1] (analytic) = 1.650625137065167300788642218662
y[1] (numeric) = 1.650625137065167300788642218662
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.28
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] = -3.84
y[1] (analytic) = 1.6429987420539088918203488788627
y[1] (numeric) = 1.6429987420539088918203488788627
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 = 15.95
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] = -3.83
y[1] (analytic) = 1.6353080477042755909033702386223
y[1] (numeric) = 1.6353080477042755909033702386222
absolute error = 1e-31
relative error = 6.1150558232979302685714448612639e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.63
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] = -3.82
y[1] (analytic) = 1.6275538230792934707727719568899
y[1] (numeric) = 1.6275538230792934707727719568898
absolute error = 1e-31
relative error = 6.1441900465572534531909953642409e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.31
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
bytes used=20005520, alloc=4324584, time=0.79
x[1] = -3.81
y[1] (analytic) = 1.6197368435949631973258897105178
y[1] (numeric) = 1.6197368435949631973258897105177
absolute error = 1e-31
relative error = 6.1738423988709572043621127898811e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 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] = -3.8
y[1] (analytic) = 1.6118578909427190757335860861189
y[1] (numeric) = 1.6118578909427190757335860861188
absolute error = 1e-31
relative error = 6.2040208731747134212984858482352e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.7
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] = -3.79
y[1] (analytic) = 1.6039177530112605584170907202327
y[1] (numeric) = 1.6039177530112605584170907202326
absolute error = 1e-31
relative error = 6.2347336583971294302549049626843e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.4
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] = -3.78
y[1] (analytic) = 1.5959172238077640316744858109002
y[1] (numeric) = 1.5959172238077640316744858109001
absolute error = 1e-31
relative error = 6.2659891445626433634644199183822e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.77
y[1] (analytic) = 1.5878571033784827597125177264744
y[1] (numeric) = 1.5878571033784827597125177264743
absolute error = 1e-31
relative error = 6.2977959280611618217141008793348e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.76
y[1] (analytic) = 1.579738197728742926023165037754
y[1] (numeric) = 1.5797381977287429260231650377538
absolute error = 2e-31
relative error = 1.2660325634180938433649142428847e-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] = -3.75
y[1] (analytic) = 1.5715613187423437724341555733503
y[1] (numeric) = 1.5715613187423437724341555733501
absolute error = 2e-31
relative error = 1.2726197674555378951830234547707e-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] = -3.74
y[1] (analytic) = 1.5633272841003698957523611196795
y[1] (numeric) = 1.5633272841003698957523611196793
absolute error = 2e-31
relative error = 1.2793226474972687288153697350808e-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] = -3.73
y[1] (analytic) = 1.5550369171994238207027492321657
y[1] (numeric) = 1.5550369171994238207027492321656
absolute error = 1e-31
relative error = 6.4307154958158219377964995256535e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.72
y[1] (analytic) = 1.5466910470692870258374589670562
y[1] (numeric) = 1.5466910470692870258374589670561
absolute error = 1e-31
relative error = 6.4654153258003766031183124324093e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.71
y[1] (analytic) = 1.5382905082900176562437940432504
y[1] (numeric) = 1.5382905082900176562437940432502
absolute error = 2e-31
relative error = 1.3001445365630086360305503787793e-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] = -3.7
y[1] (analytic) = 1.5298361409084932132107776257012
y[1] (numeric) = 1.529836140908493213210777625701
absolute error = 2e-31
relative error = 1.3073295541392426332892267738334e-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] = -3.69
y[1] (analytic) = 1.5213287903544065665157545481247
y[1] (numeric) = 1.5213287903544065665157545481245
absolute error = 2e-31
relative error = 1.3146402097169822685539611821911e-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] = -3.68
y[1] (analytic) = 1.512769307355723689659809225044
y[1] (numeric) = 1.5127693073557236896598092250439
absolute error = 1e-31
relative error = 6.6103932380011769549181948782446e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.67
y[1] (analytic) = 1.5041585478536115722080240589139
y[1] (numeric) = 1.5041585478536115722080240589138
absolute error = 1e-31
relative error = 6.6482353301583103575680661201057e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.66
y[1] (analytic) = 1.4954973729168448163724511464104
y[1] (numeric) = 1.4954973729168448163724511464102
absolute error = 2e-31
relative error = 1.3373477187052252983949685349721e-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] = -3.65
y[1] (analytic) = 1.4867866486556994771068113882953
y[1] (numeric) = 1.4867866486556994771068113882952
absolute error = 1e-31
relative error = 6.7259145816527546094462981301637e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.64
y[1] (analytic) = 1.4780272461353427562571566388729
y[1] (numeric) = 1.4780272461353427562571566388728
absolute error = 1e-31
relative error = 6.7657751412549409418440470343120e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.63
y[1] (analytic) = 1.4692200412887272117269048145319
y[1] (numeric) = 1.4692200412887272117269048145318
absolute error = 1e-31
relative error = 6.8063324205872485904358889197117e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.62
y[1] (analytic) = 1.4603659148289981921627435407948
y[1] (numeric) = 1.4603659148289981921627435407947
absolute error = 1e-31
relative error = 6.8475988781010078474062724623123e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.61
y[1] (analytic) = 1.4514657521614232563449401863925
y[1] (numeric) = 1.4514657521614232563449401863924
absolute error = 1e-31
relative error = 6.8895872914043516367782635919596e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.6
y[1] (analytic) = 1.4425204432948523842667273474927
y[1] (numeric) = 1.4425204432948523842667273474926
absolute error = 1e-31
relative error = 6.9323107665351759884966837015420e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.59
y[1] (analytic) = 1.433530882752717833807872932044
y[1] (numeric) = 1.4335308827527178338078729320439
absolute error = 1e-31
relative error = 6.9757827475593957390188679164873e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.58
y[1] (analytic) = 1.4244979694835825429426009483438
y[1] (numeric) = 1.4244979694835825429426009483436
absolute error = 2e-31
relative error = 1.4040034053014844719404699420603e-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] = -3.57
y[1] (analytic) = 1.4154226067712460225670994560663
y[1] (numeric) = 1.4154226067712460225670994560661
absolute error = 2e-31
relative error = 1.4130055507324750818147839640320e-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] = -3.56
y[1] (analytic) = 1.4063057021444167292824214226859
y[1] (numeric) = 1.4063057021444167292824214226857
absolute error = 2e-31
relative error = 1.4221658896428306266803128618371e-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] = -3.55
y[1] (analytic) = 1.397148167285959950820227423437
y[1] (numeric) = 1.3971481672859599508202274234367
absolute error = 3e-31
relative error = 2.1472311027882398527650304938284e-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] = -3.54
y[1] (analytic) = 1.3879509179417302792472011004845
y[1] (numeric) = 1.3879509179417302792472011004843
absolute error = 2e-31
relative error = 1.4409731454811899211550297775891e-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
bytes used=24006808, alloc=4324584, time=0.95
TOP MAIN SOLVE Loop
x[1] = -3.53
y[1] (analytic) = 1.3787148738289977886248442540066
y[1] (numeric) = 1.3787148738289977886248442540064
absolute error = 2e-31
relative error = 1.4506262592537028785338636874779e-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] = -3.52
y[1] (analytic) = 1.369440958544477074430574321433
y[1] (numeric) = 1.3694409585444770744305743214327
absolute error = 3e-31
relative error = 2.1906749475264545969147536512242e-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] = -3.51
y[1] (analytic) = 1.3601300994719683517595399234174
y[1] (numeric) = 1.3601300994719683517595399234171
absolute error = 3e-31
relative error = 2.2056713553833300808943419143317e-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] = -3.5
y[1] (analytic) = 1.3507832276896198481203688000436
y[1] (numeric) = 1.3507832276896198481203688000434
absolute error = 2e-31
relative error = 1.4806224707281869118240261821323e-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] = -3.49
y[1] (analytic) = 1.3414012778768207645082874807375
y[1] (numeric) = 1.3414012778768207645082874807373
absolute error = 2e-31
relative error = 1.4909781532082732584417893476356e-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] = -3.48
y[1] (analytic) = 1.3319851882207341153819164354428
y[1] (numeric) = 1.3319851882207341153819164354425
absolute error = 3e-31
relative error = 2.2522772974731049059890151985644e-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] = -3.47
y[1] (analytic) = 1.3225359003224787941818539871573
y[1] (numeric) = 1.322535900322478794181853987157
absolute error = 3e-31
relative error = 2.2683694251842229485094556082917e-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] = -3.46
y[1] (analytic) = 1.3130543591029702461063157759749
y[1] (numeric) = 1.3130543591029702461063157759747
absolute error = 2e-31
relative error = 1.5231661858739232919904908511474e-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] = -3.45
y[1] (analytic) = 1.3035415127084291639980863662199
y[1] (numeric) = 1.3035415127084291639980863662197
absolute error = 2e-31
relative error = 1.5342817858132545894240957970724e-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] = -3.44
y[1] (analytic) = 1.2939983124155676563944518105603
y[1] (numeric) = 1.2939983124155676563944518105601
absolute error = 2e-31
relative error = 1.5455970698033645100857626675555e-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] = -3.43
y[1] (analytic) = 1.2844257125364623690442969145914
y[1] (numeric) = 1.2844257125364623690442969145912
absolute error = 2e-31
relative error = 1.5571161340661995326373142205480e-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] = -3.42
y[1] (analytic) = 1.2748246703231240725009433576662
y[1] (numeric) = 1.274824670323124072500943357666
absolute error = 2e-31
relative error = 1.5688431880542984785198200974896e-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] = -3.41
y[1] (analytic) = 1.2651961458717732587524443075741
y[1] (numeric) = 1.2651961458717732587524443075739
absolute error = 2e-31
relative error = 1.5807825581241523921376495051245e-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] = -3.4
y[1] (analytic) = 1.2555411020268313192499024293637
y[1] (numeric) = 1.2555411020268313192499024293635
absolute error = 2e-31
relative error = 1.5929386913509896017938883917418e-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] = -3.39
y[1] (analytic) = 1.2458605042846369051360013715579
y[1] (numeric) = 1.2458605042846369051360013715577
absolute error = 2e-31
relative error = 1.6053161594912136139100283917243e-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] = -3.38
y[1] (analytic) = 1.2361553206968970979574917775896
y[1] (numeric) = 1.2361553206968970979574917775894
absolute error = 2e-31
relative error = 1.6179196630990323142062128426569e-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] = -3.37
y[1] (analytic) = 1.2264265217738830456641034843086
y[1] (numeric) = 1.2264265217738830456641034843083
absolute error = 3e-31
relative error = 2.4461310537062176349204124927867e-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] = -3.36
y[1] (analytic) = 1.2166750803873797442496139819055
y[1] (numeric) = 1.2166750803873797442496139819053
absolute error = 2e-31
relative error = 1.6438242487577010149044294936431e-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] = -3.35
y[1] (analytic) = 1.2069019716733996699760341160255
y[1] (numeric) = 1.2069019716733996699760341160253
absolute error = 2e-31
relative error = 1.6571354152541072934102333134436e-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] = -3.34
y[1] (analytic) = 1.1971081729346699907366169105927
y[1] (numeric) = 1.1971081729346699907366169105925
absolute error = 2e-31
relative error = 1.6706927955366539593483144592423e-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] = -3.33
y[1] (analytic) = 1.187294663542903107755292824136
y[1] (numeric) = 1.1872946635429031077552928241357
absolute error = 3e-31
relative error = 2.5267527026929945066036971064197e-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] = -3.32
y[1] (analytic) = 1.1774624248408603004869205523084
y[1] (numeric) = 1.1774624248408603004869205523082
absolute error = 2e-31
relative error = 1.6985680033656357243486038114125e-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] = -3.31
y[1] (analytic) = 1.167612440044218268272249994317
y[1] (numeric) = 1.1676124400442182682722499943168
absolute error = 2e-31
relative error = 1.7128971321376626092544621975425e-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] = -3.3
y[1] (analytic) = 1.1577456941432483820116542776025
y[1] (numeric) = 1.1577456941432483820116542776023
absolute error = 2e-31
relative error = 1.7274950881851771531481017532625e-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] = -3.29
y[1] (analytic) = 1.1478631738043184778505297837426
y[1] (numeric) = 1.1478631738043184778505297837425
absolute error = 1e-31
relative error = 8.7118397281249011118826148732561e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.28
y[1] (analytic) = 1.1379658672712270426149140705852
y[1] (numeric) = 1.1379658672712270426149140705851
absolute error = 1e-31
relative error = 8.7876097935866846031082477587381e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.27
y[1] (analytic) = 1.1280547642663796574965568907536
y[1] (numeric) = 1.1280547642663796574965568907535
absolute error = 1e-31
relative error = 8.8648178410942758624083430641294e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for 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=28008288, alloc=4390108, time=1.11
x[1] = -3.26
y[1] (analytic) = 1.1181308558918175822607231103361
y[1] (numeric) = 1.118130855891817582260723110336
absolute error = 1e-31
relative error = 8.9434970399989830285402269016876e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.25
y[1] (analytic) = 1.1081951345301083770358308425608
y[1] (numeric) = 1.1081951345301083770358308425607
absolute error = 1e-31
relative error = 9.0236815596922399169309039439051e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.24
y[1] (analytic) = 1.0982485937451084725401549594376
y[1] (numeric) = 1.0982485937451084725401549594375
absolute error = 1e-31
relative error = 9.1054066055293224421158072617601e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.23
y[1] (analytic) = 1.0882922281826076124058757285297
y[1] (numeric) = 1.0882922281826076124058757285296
absolute error = 1e-31
relative error = 9.1887084562751025064803856867190e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.22
y[1] (analytic) = 1.078327033470865103073444147916
y[1] (numeric) = 1.0783270334708651030734441479159
absolute error = 1e-31
relative error = 9.2736245031458595014763091746466e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.21
y[1] (analytic) = 1.0683540061210478175483883606769
y[1] (numeric) = 1.0683540061210478175483883606767
absolute error = 2e-31
relative error = 1.8720386581050493164624032052564e-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] = -3.2
y[1] (analytic) = 1.0583741434275799091372174146191
y[1] (numeric) = 1.0583741434275799091372174146189
absolute error = 2e-31
relative error = 1.8896909116873673771178760922463e-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] = -3.19
y[1] (analytic) = 1.0483884433684142001080071484512
y[1] (numeric) = 1.048388443368414200108007148451
absolute error = 2e-31
relative error = 1.9076898573720541930297837234879e-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] = -3.18
y[1] (analytic) = 1.0383979045052352180536952467261
y[1] (numeric) = 1.038397904505235218053695246726
absolute error = 1e-31
relative error = 9.6302197419829093075232787051802e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.17
y[1] (analytic) = 1.0284035258836038595712852748967
y[1] (numeric) = 1.0284035258836038595712852748966
absolute error = 1e-31
relative error = 9.7238095244840826215855691609518e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.16
y[1] (analytic) = 1.0184063069330536667073792711874
y[1] (numeric) = 1.0184063069330536667073792711872
absolute error = 2e-31
relative error = 1.9638527239909097882265143425024e-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] = -3.15
y[1] (analytic) = 1.0084072473671487064591415165711
y[1] (numeric) = 1.0084072473671487064591415165709
absolute error = 2e-31
relative error = 1.9833256903119266638062868103450e-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] = -3.14
y[1] (analytic) = 0.99840734708351304745945856367556
y[1] (numeric) = 0.99840734708351304745945856367539
absolute error = 1.7e-31
relative error = 1.7027118289603305034756063611381e-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 = 0.001536
Order of pole (three term test) = -0.8929
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.13
y[1] (analytic) = 0.98840760606384183081531851688169
y[1] (numeric) = 0.98840760606384183081531851688153
absolute error = 1.6e-31
relative error = 1.6187653658106866646129561982977e-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 = 0.01118
Order of pole (three term test) = -0.8961
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.12
y[1] (analytic) = 0.97840902427390393390900189579811
y[1] (numeric) = 0.97840902427390393390900189579794
absolute error = 1.7e-31
relative error = 1.7375146363368863469138015822298e-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 = 0.02082
Order of pole (three term test) = -0.9041
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.11
y[1] (analytic) = 0.96841260156354622681237312729664
y[1] (numeric) = 0.96841260156354622681237312729647
absolute error = 1.7e-31
relative error = 1.7554501018008983123224637425672e-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 = 0.03044
Order of pole (three term test) = -0.917
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.1
y[1] (analytic) = 0.95841933756670942080530172840333
y[1] (numeric) = 0.95841933756670942080530172840316
absolute error = 1.7e-31
relative error = 1.7737538605137690132571626221782e-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 = 0.04006
Order of pole (three term test) = -0.9347
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.09
y[1] (analytic) = 0.94843023160146550733004148942538
y[1] (numeric) = 0.94843023160146550733004148942522
absolute error = 1.6e-31
relative error = 1.6869981013767673028661671689421e-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 = 0.04966
Order of pole (three term test) = -0.9572
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.08
y[1] (analytic) = 0.9384462825700867835543703628643
y[1] (numeric) = 0.93844628257008678355437036286413
absolute error = 1.7e-31
relative error = 1.8115048581622331175874130900427e-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 = 0.05924
Order of pole (three term test) = -0.9845
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.07
y[1] (analytic) = 0.9284684888591564575576592096811
y[1] (numeric) = 0.92846848885915645755765920968093
absolute error = 1.7e-31
relative error = 1.8309722089640896924655676031862e-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 = 0.0688
Order of pole (three term test) = -1.017
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.06
y[1] (analytic) = 0.91849784823973082199610991116428
y[1] (numeric) = 0.91849784823973082199610991116411
absolute error = 1.7e-31
relative error = 1.8508481029737749182882748114373e-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 = 0.07833
Order of pole (three term test) = -1.053
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.05
y[1] (analytic) = 0.90853535776756297994659841130358
y[1] (numeric) = 0.90853535776756297994659841130342
absolute error = 1.6e-31
relative error = 1.7610762050378443336114495956612e-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 = 0.08783
Order of pole (three term test) = -1.095
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.04
y[1] (analytic) = 0.89858201368339810047339168739121
y[1] (numeric) = 0.89858201368339810047339168739105
absolute error = 1.6e-31
relative error = 1.7805831583935264591357357824551e-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 = 0.09729
Order of pole (three term test) = -1.142
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.03
y[1] (analytic) = 0.88863881131335017430909496708274
y[1] (numeric) = 0.88863881131335017430909496708258
absolute error = 1.6e-31
relative error = 1.8005065496017492295164055529252e-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 = 0.1067
Order of pole (three term test) = -1.193
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.02
y[1] (analytic) = 0.87870674496937023189124200366089
y[1] (numeric) = 0.87870674496937023189124200366073
absolute error = 1.6e-31
relative error = 1.8208577653011784393554488851644e-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 = 0.1161
Order of pole (three term test) = -1.249
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.01
y[1] (analytic) = 0.86878680784981597684978187531515
y[1] (numeric) = 0.86878680784981597684978187531499
absolute error = 1.6e-31
relative error = 1.8416485903600255800951303781468e-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 = 0.1254
Order of pole (three term test) = -1.309
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3
y[1] (analytic) = 0.85887999194013277789925519719189
y[1] (numeric) = 0.85887999194013277789925519719173
absolute error = 1.6e-31
relative error = 1.8628912246351712925858474042321e-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 = 0.1347
Order of pole (three term test) = -1.374
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.99
y[1] (analytic) = 0.84898728791365595095370496438948
y[1] (numeric) = 0.84898728791365595095370496438932
absolute error = 1.6e-31
relative error = 1.8845983005610371967032402358408e-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 = 0.1439
Order of pole (three term test) = -1.444
NO COMPLEX POLE (six term test) for Equation 1
bytes used=32012896, alloc=4390108, time=1.28
TOP MAIN SOLVE Loop
x[1] = -2.98
y[1] (analytic) = 0.83910968503254425115344604545867
y[1] (numeric) = 0.83910968503254425115344604545851
absolute error = 1.6e-31
relative error = 1.9067829016154725688271962436417e-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 = 0.1531
Order of pole (three term test) = -1.519
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.97
y[1] (analytic) = 0.82924817104885448137193550133203
y[1] (numeric) = 0.82924817104885448137193550133187
absolute error = 1.6e-31
relative error = 1.9294585817129734756590526685540e-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 = 0.1622
Order of pole (three term test) = -1.598
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.96
y[1] (analytic) = 0.81940373210576710965945549119865
y[1] (numeric) = 0.81940373210576710965945549119849
absolute error = 1.6e-31
relative error = 1.9526393855788235242991458318901e-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 = 0.1713
Order of pole (three term test) = -1.681
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.95
y[1] (analytic) = 0.80957735263897277297955268594262
y[1] (numeric) = 0.80957735263897277297955268594246
absolute error = 1.6e-31
relative error = 1.9763398701612549961909183693828e-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 = 0.1803
Order of pole (three term test) = -1.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.94
y[1] (analytic) = 0.79977001527822952850568290557688
y[1] (numeric) = 0.79977001527822952850568290557672
absolute error = 1.6e-31
relative error = 2.0005751271424959907192153342259e-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 = 0.1892
Order of pole (three term test) = -1.862
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.93
y[1] (analytic) = 0.78998270074910069667089596574089
y[1] (numeric) = 0.78998270074910069667089596574073
absolute error = 1.6e-31
relative error = 2.0253608066136142079514067832388e-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 = 0.198
Order of pole (three term test) = -1.959
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.92
y[1] (analytic) = 0.78021638777488312210437090693542
y[1] (numeric) = 0.78021638777488312210437090693526
absolute error = 1.6e-31
relative error = 2.0507131419824139094891928362249e-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 = 0.2067
Order of pole (three term test) = -2.061
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.91
y[1] (analytic) = 0.77047205297873565954698177617301
y[1] (numeric) = 0.77047205297873565954698177617285
absolute error = 1.6e-31
relative error = 2.0766489761883142188819664407505e-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 = 0.2154
Order of pole (three term test) = -2.167
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.9
y[1] (analytic) = 0.76075067078601767181574308126042
y[1] (numeric) = 0.76075067078601767181574308126027
absolute error = 1.5e-31
relative error = 1.9717366774717137315698648699419e-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 = 0.224
Order of pole (three term test) = -2.277
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.89
y[1] (analytic) = 0.75105321332684730588595415941951
y[1] (numeric) = 0.75105321332684730588595415941936
absolute error = 1.5e-31
relative error = 1.9971953696271878862323051399578e-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 = 0.2325
Order of pole (three term test) = -2.391
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.88
y[1] (analytic) = 0.74138065033888929118223307988232
y[1] (numeric) = 0.74138065033888929118223307988217
absolute error = 1.5e-31
relative error = 2.0232521570590512587715015246525e-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 = 0.2409
Order of pole (three term test) = -2.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.87
y[1] (analytic) = 0.73173394907038198121760107901286
y[1] (numeric) = 0.73173394907038198121760107901271
absolute error = 1.5e-31
relative error = 2.0499253887367773198567892989582e-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 = 0.2492
Order of pole (three term test) = -2.633
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.86
y[1] (analytic) = 0.72211407418341333579564309024676
y[1] (numeric) = 0.72211407418341333579564309024661
absolute error = 1.5e-31
relative error = 2.0772341291038284889493917742525e-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 = 0.2574
Order of pole (three term test) = -2.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.85
y[1] (analytic) = 0.71252198765745551609692107330828
y[1] (numeric) = 0.71252198765745551609692107330812
absolute error = 1.6e-31
relative error = 2.2455447378687757258580691471514e-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 = 0.2655
Order of pole (three term test) = -2.891
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.84
y[1] (analytic) = 0.70295864869316773910974393190269
y[1] (numeric) = 0.70295864869316773910974393190253
absolute error = 1.6e-31
relative error = 2.2760940532910052926458070140581e-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 = 0.2735
Order of pole (three term test) = -3.026
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.83
y[1] (analytic) = 0.6934250136164770110396869221319
y[1] (numeric) = 0.69342501361647701103968692213174
absolute error = 1.6e-31
relative error = 2.3073871991657572873666429996971e-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 = 0.2814
Order of pole (three term test) = -3.165
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.82
y[1] (analytic) = 0.68392203578294633154458714397543
y[1] (numeric) = 0.68392203578294633154458714397527
absolute error = 1.6e-31
relative error = 2.3394479433146759410116757235377e-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 = 0.2891
Order of pole (three term test) = -3.308
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.81
y[1] (analytic) = 0.67445066548243993189489871879367
y[1] (numeric) = 0.67445066548243993189489871879351
absolute error = 1.6e-31
relative error = 2.3723010175332946831137580414313e-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 = 0.2968
Order of pole (three term test) = -3.455
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.8
y[1] (analytic) = 0.66501184984409508045614624728758
y[1] (numeric) = 0.66501184984409508045614624728742
absolute error = 1.6e-31
relative error = 2.4059721648194733624384762992604e-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 = 0.3043
Order of pole (three term test) = -3.606
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.79
y[1] (analytic) = 0.65560653274160995823373840443771
y[1] (numeric) = 0.65560653274160995823373840443755
absolute error = 1.6e-31
relative error = 2.4404881893246750870459537229113e-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 = 0.3117
Order of pole (three term test) = -3.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.78
y[1] (analytic) = 0.64623565469885707561366068277266
y[1] (numeric) = 0.6462356546988570756136606827725
absolute error = 1.6e-31
relative error = 2.4758770092089592967043725912697e-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 = 0.319
Order of pole (three term test) = -3.918
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.77
y[1] (analytic) = 0.63690015279583166887871799082754
y[1] (numeric) = 0.63690015279583166887871799082738
absolute error = 1.6e-31
relative error = 2.5121677125941985593731297905834e-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 = 0.3262
Order of pole (three term test) = -4.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.76
y[1] (analytic) = 0.62760096057494448158229940755025
y[1] (numeric) = 0.62760096057494448158229940755009
absolute error = 1.6e-31
relative error = 2.5493906168248084474868903856425e-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 = 0.3332
Order of pole (three term test) = -4.245
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.75
y[1] (analytic) = 0.61833900794766830142343862762222
y[1] (numeric) = 0.61833900794766830142343862762206
absolute error = 1.6e-31
relative error = 2.5875773312613205165007324292832e-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 = 0.3401
Order of pole (three term test) = -4.414
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.74
y[1] (analytic) = 0.60911522110154758789168829835973
y[1] (numeric) = 0.60911522110154758789168829835957
absolute error = 1.6e-31
relative error = 2.6267608238495468074499070536993e-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 = 0.3469
Order of pole (three term test) = -4.586
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.73
y[1] (analytic) = 0.59993052240758048964155204210555
y[1] (numeric) = 0.59993052240758048964155204210539
absolute error = 1.6e-31
relative error = 2.6669754917270117209003837536437e-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 = 0.3535
Order of pole (three term test) = -4.762
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.72
y[1] (analytic) = 0.59078583032798251331755532599258
y[1] (numeric) = 0.59078583032798251331755532599242
absolute error = 1.6e-31
relative error = 2.7082572361489086239211678415204e-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 = 0.36
Order of pole (three term test) = -4.941
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.71
y[1] (analytic) = 0.58168205932434106738620931889141
y[1] (numeric) = 0.58168205932434106738620931889125
bytes used=36013568, alloc=4390108, time=1.44
absolute error = 1.6e-31
relative error = 2.7506435420382345634221038920160e-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 = 0.3663
Order of pole (three term test) = -5.123
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.7
y[1] (analytic) = 0.57262011976617006544394691414212
y[1] (numeric) = 0.57262011976617006544394691414196
absolute error = 1.6e-31
relative error = 2.7941735624891444981973221017357e-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 = 0.3725
Order of pole (three term test) = -5.308
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.69
y[1] (analytic) = 0.56360091783987373346449588123901
y[1] (numeric) = 0.56360091783987373346449588123885
absolute error = 1.6e-31
relative error = 2.8388882085791431765401128937389e-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 = 0.3785
Order of pole (three term test) = -5.496
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.68
y[1] (analytic) = 0.55462535545812872452910116807055
y[1] (numeric) = 0.55462535545812872452910116807039
absolute error = 1.6e-31
relative error = 2.8848302448747161936593607014022e-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 = 0.3844
Order of pole (three term test) = -5.687
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.67
y[1] (analytic) = 0.5456943301696936027526086788087
y[1] (numeric) = 0.54569433016969360275260867880855
absolute error = 1.5e-31
relative error = 2.7487916166062191765157670328756e-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 = 0.3902
Order of pole (three term test) = -5.881
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.66
y[1] (analytic) = 0.53680873506965471538185940620365
y[1] (numeric) = 0.5368087350696547153818594062035
absolute error = 1.5e-31
relative error = 2.7942913406678533872437569976247e-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 = 0.3957
Order of pole (three term test) = -6.078
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.65
y[1] (analytic) = 0.52796945871011742840438922160261
y[1] (numeric) = 0.52796945871011742840438922160246
absolute error = 1.5e-31
relative error = 2.8410734281195944544876897736441e-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 = 0.4011
Order of pole (three term test) = -6.278
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.64
y[1] (analytic) = 0.51917738501135165646944973046714
y[1] (numeric) = 0.51917738501135165646944973046699
absolute error = 1.5e-31
relative error = 2.8891859378027472320615395406634e-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 = 0.4064
Order of pole (three term test) = -6.481
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.63
y[1] (analytic) = 0.51043339317340057249431294638837
y[1] (numeric) = 0.51043339317340057249431294638822
absolute error = 1.5e-31
relative error = 2.9386792088080164904406152835225e-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 = 0.4115
Order of pole (three term test) = -6.686
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.62
y[1] (analytic) = 0.50173835758816133601123999000237
y[1] (numeric) = 0.50173835758816133601123999000221
absolute error = 1.6e-31
relative error = 3.1889130575767493806178561924717e-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 = 0.4164
Order of pole (three term test) = -6.893
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.61
y[1] (analytic) = 0.4930931477519466321090133004445
y[1] (numeric) = 0.49309314775194663210901330044435
absolute error = 1.5e-31
relative error = 3.0420215872774279555011199252902e-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 = 0.4212
Order of pole (three term test) = -7.103
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.6
y[1] (analytic) = 0.48449862817853576474227306479063
y[1] (numeric) = 0.48449862817853576474227306479048
absolute error = 1.5e-31
relative error = 3.0959839982194049252252131685056e-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 = 0.4258
Order of pole (three term test) = -7.315
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.59
y[1] (analytic) = 0.47595565831272399922686975112409
y[1] (numeric) = 0.47595565831272399922686975112393
absolute error = 1.6e-31
relative error = 3.3616576923826146897203992312226e-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 = 0.4302
Order of pole (three term test) = -7.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.58
y[1] (analytic) = 0.46746509244437879891494123552835
y[1] (numeric) = 0.4674650924443787989149412355282
absolute error = 1.5e-31
relative error = 3.2087957459165297426449108210741e-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 = 0.4345
Order of pole (three term test) = -7.747
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.57
y[1] (analytic) = 0.45902777962301155035442745125416
y[1] (numeric) = 0.45902777962301155035442745125401
absolute error = 1.5e-31
relative error = 3.2677760836869477476461733274741e-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 = 0.4386
Order of pole (three term test) = -7.966
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.56
y[1] (analytic) = 0.45064456357287331968931661686272
y[1] (numeric) = 0.45064456357287331968931661686257
absolute error = 1.5e-31
relative error = 3.3285656174512718240139291306148e-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 = 0.4425
Order of pole (three term test) = -8.186
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.55
y[1] (analytic) = 0.44231628260858313065422971823376
y[1] (numeric) = 0.44231628260858313065422971823361
absolute error = 1.5e-31
relative error = 3.3912384847188362516003977120663e-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 = 0.4462
Order of pole (three term test) = -8.409
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.54
y[1] (analytic) = 0.43404376955129720126523425201797
y[1] (numeric) = 0.43404376955129720126523425201782
absolute error = 1.5e-31
relative error = 3.4558726682119172872765108683277e-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 = 0.4497
Order of pole (three term test) = -8.634
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.53
y[1] (analytic) = 0.4258278516454275222133594125978
y[1] (numeric) = 0.42582785164542752221335941259765
absolute error = 1.5e-31
relative error = 3.5225502376227832224601171153527e-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 = 0.4531
Order of pole (three term test) = -8.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.52
y[1] (analytic) = 0.41766935047591810503357241770287
y[1] (numeric) = 0.41766935047591810503357241770272
absolute error = 1.5e-31
relative error = 3.5913576092926327777883372580596e-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 = 0.4563
Order of pole (three term test) = -9.088
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.51
y[1] (analytic) = 0.40956908188608717235546284497595
y[1] (numeric) = 0.40956908188608717235546284497579
absolute error = 1.6e-31
relative error = 3.9065448803701583452123343302274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4593
Order of pole (three term test) = -9.317
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.5
y[1] (analytic) = 0.40152785589604350594814529781384
y[1] (numeric) = 0.40152785589604350594814529781368
absolute error = 1.6e-31
relative error = 3.9847795775699400403582499258986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4621
Order of pole (three term test) = -9.548
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.49
y[1] (analytic) = 0.3935464766216851108565897602082
y[1] (numeric) = 0.39354647662168511085658976020805
absolute error = 1.5e-31
relative error = 3.8114939126794543686033574327260e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4647
Order of pole (three term test) = -9.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.48
y[1] (analytic) = 0.3856257421942882956954651193344
y[1] (numeric) = 0.38562574219428829569546511933425
absolute error = 1.5e-31
relative error = 3.8897818165994243201370295855222e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.79
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4672
Order of pole (three term test) = -10.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.47
y[1] (analytic) = 0.37776644468069521012545759514423
y[1] (numeric) = 0.37776644468069521012545759514407
absolute error = 1.6e-31
relative error = 4.2354211776336838735227274375645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4695
Order of pole (three term test) = -10.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.46
y[1] (analytic) = 0.36996937000410782069180628138407
y[1] (numeric) = 0.36996937000410782069180628138391
absolute error = 1.6e-31
relative error = 4.3246823378439003758800780260452e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4715
Order of pole (three term test) = -10.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.45
y[1] (analytic) = 0.36223529786549624556146714436622
y[1] (numeric) = 0.36223529786549624556146714436606
absolute error = 1.6e-31
relative error = 4.4170184668036011421764216251944e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4734
Order of pole (three term test) = -10.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.44
y[1] (analytic) = 0.35456500166562930725993892701747
y[1] (numeric) = 0.35456500166562930725993892701731
absolute error = 1.6e-31
relative error = 4.5125717216412457217207054686752e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.06
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4751
Order of pole (three term test) = -10.96
NO COMPLEX POLE (six term test) for Equation 1
bytes used=40015204, alloc=4390108, time=1.61
TOP MAIN SOLVE Loop
x[1] = -2.43
y[1] (analytic) = 0.3469592484277351002875029528101
y[1] (numeric) = 0.34695924842773510028750295280995
absolute error = 1.5e-31
relative error = 4.3232742945960726662359069702501e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4766
Order of pole (three term test) = -11.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.42
y[1] (analytic) = 0.33941879872079930749366589343977
y[1] (numeric) = 0.33941879872079930749366589343961
absolute error = 1.6e-31
relative error = 4.7139404359159712722374863274986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4779
Order of pole (three term test) = -11.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.41
y[1] (analytic) = 0.33194440658350893531425019934528
y[1] (numeric) = 0.33194440658350893531425019934512
absolute error = 1.6e-31
relative error = 4.8200842317777687803250660944082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.06
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4791
Order of pole (three term test) = -11.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.4
y[1] (analytic) = 0.32453681944884907343422847465872
y[1] (numeric) = 0.32453681944884907343422847465856
absolute error = 1.6e-31
relative error = 4.9301031627697311085545794518507e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.48
Order of pole (three term test) = -11.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.39
y[1] (analytic) = 0.31719677806936021913749968898695
y[1] (numeric) = 0.3171967780693602191374996889868
absolute error = 1.5e-31
relative error = 4.7289257133374812408654266513353e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -12.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.38
y[1] (analytic) = 0.3099250164430636405488868929798
y[1] (numeric) = 0.30992501644306364054888689297965
absolute error = 1.5e-31
relative error = 4.8398803594983923082207305164830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -12.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.37
y[1] (analytic) = 0.30272226174006218617030357971077
y[1] (numeric) = 0.30272226174006218617030357971062
absolute error = 1.5e-31
relative error = 4.9550369747435405945141511210042e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.36
y[1] (analytic) = 0.2955892342298238805689692870673
y[1] (numeric) = 0.29558923422982388056896928706714
absolute error = 1.6e-31
relative error = 5.4129170305166879076820261880712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.86
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.35
y[1] (analytic) = 0.28852664720915557779750881798679
y[1] (numeric) = 0.28852664720915557779750881798663
absolute error = 1.6e-31
relative error = 5.5454150092422677327787883324869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.24
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.34
y[1] (analytic) = 0.28153520693087387512057131320599
y[1] (numeric) = 0.28153520693087387512057131320583
absolute error = 1.6e-31
relative error = 5.6831258066876604325319607696155e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -13.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.33
y[1] (analytic) = 0.27461561253318041989715580752458
y[1] (numeric) = 0.27461561253318041989715580752442
absolute error = 1.6e-31
relative error = 5.8263256966378052046402452693812e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -13.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.32
y[1] (analytic) = 0.26776855596974867202910132227533
y[1] (numeric) = 0.26776855596974867202910132227516
absolute error = 1.7e-31
relative error = 6.3487663584818323975315533241693e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = -13.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.31
y[1] (analytic) = 0.26099472194052911324123580790174
y[1] (numeric) = 0.26099472194052911324123580790158
absolute error = 1.6e-31
relative error = 6.1303921707833611232010732491543e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4797
Order of pole (three term test) = -14.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.3
y[1] (analytic) = 0.2542947878232798226145937883565
y[1] (numeric) = 0.25429478782327982261459378835634
absolute error = 1.6e-31
relative error = 6.2919103206783282871033214241665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4787
Order of pole (three term test) = -14.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.29
y[1] (analytic) = 0.24766942360582926525809172202635
y[1] (numeric) = 0.24766942360582926525809172202619
absolute error = 1.6e-31
relative error = 6.4602241839365335350386579513743e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4776
Order of pole (three term test) = -14.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.28
y[1] (analytic) = 0.24111929181907806778334642369908
y[1] (numeric) = 0.24111929181907806778334642369893
absolute error = 1.5e-31
relative error = 6.2209870835449906822462145539389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.16
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4762
Order of pole (three term test) = -14.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.27
y[1] (analytic) = 0.23464504747074648034925739806528
y[1] (numeric) = 0.23464504747074648034925739806513
absolute error = 1.5e-31
relative error = 6.3926343904062456539158878321769e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.82
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4746
Order of pole (three term test) = -15.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.26
y[1] (analytic) = 0.22824733797987415047493836225968
y[1] (numeric) = 0.22824733797987415047493836225953
absolute error = 1.5e-31
relative error = 6.5718181568990014829080600996483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.48
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4729
Order of pole (three term test) = -15.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.25
y[1] (analytic) = 0.22192680311207875858903332441224
y[1] (numeric) = 0.22192680311207875858903332441209
absolute error = 1.5e-31
relative error = 6.7589853004031302979176096892961e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4709
Order of pole (three term test) = -15.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.24
y[1] (analytic) = 0.2156840749155799893979113293955
y[1] (numeric) = 0.21568407491557998939791132939535
absolute error = 1.5e-31
relative error = 6.9546163785486192636639211942250e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.82
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4688
Order of pole (three term test) = -15.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.23
y[1] (analytic) = 0.20951977765799523662228987281146
y[1] (numeric) = 0.20951977765799523662228987281131
absolute error = 1.5e-31
relative error = 7.1592286740991597874459400900588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4665
Order of pole (three term test) = -15.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.22
y[1] (analytic) = 0.20343452776391336147914325039084
y[1] (numeric) = 0.20343452776391336147914325039069
absolute error = 1.5e-31
relative error = 7.3733796149921826831761486715379e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.18
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.464
Order of pole (three term test) = -16.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.21
y[1] (analytic) = 0.19742893375325274748102595744403
y[1] (numeric) = 0.19742893375325274748102595744388
absolute error = 1.5e-31
relative error = 7.5976705718053684022689254998756e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4613
Order of pole (three term test) = -16.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.2
y[1] (analytic) = 0.19150359618040981569596308958388
y[1] (numeric) = 0.19150359618040981569596308958373
absolute error = 1.5e-31
relative error = 7.8327510810130939843138614453432e-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 = 0.4584
Order of pole (three term test) = -16.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.19
y[1] (analytic) = 0.185659107574204085565672354095
y[1] (numeric) = 0.18565910757420408556567235409485
absolute error = 1.5e-31
relative error = 8.0793235494815743634958364661261e-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 = 0.4553
Order of pole (three term test) = -16.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.18
y[1] (analytic) = 0.17989605237862578672599025391606
y[1] (numeric) = 0.17989605237862578672599025391591
absolute error = 1.5e-31
relative error = 8.3381485039091461710858496707916e-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 = 0.4521
Order of pole (three term test) = -17.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.17
y[1] (analytic) = 0.17421500689439194701894357605662
y[1] (numeric) = 0.17421500689439194701894357605647
absolute error = 1.5e-31
relative error = 8.6100504585652065266554418535816e-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 = 0.4487
Order of pole (three term test) = -17.36
NO COMPLEX POLE (six term test) for Equation 1
bytes used=44017712, alloc=4390108, time=1.77
TOP MAIN SOLVE Loop
x[1] = -2.16
y[1] (analytic) = 0.16861653922131680103896187965368
y[1] (numeric) = 0.16861653922131680103896187965353
absolute error = 1.5e-31
relative error = 8.8959244859792932321952802647588e-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 = 0.4451
Order of pole (three term test) = -17.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.15
y[1] (analytic) = 0.16310120920150228212435186295621
y[1] (numeric) = 0.16310120920150228212435186295607
absolute error = 1.4e-31
relative error = 8.5836273492637292481281207723556e-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 = 0.4413
Order of pole (three term test) = -17.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.14
y[1] (analytic) = 0.15766956836335427869749336293109
y[1] (numeric) = 0.15766956836335427869749336293095
absolute error = 1.4e-31
relative error = 8.8793291852848721483350159379069e-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 = 0.4373
Order of pole (three term test) = -18.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.13
y[1] (analytic) = 0.1523221598664302532814700036841
y[1] (numeric) = 0.15232215986643025328147000368396
absolute error = 1.4e-31
relative error = 9.1910461434347156412231607493080e-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 = 0.4332
Order of pole (three term test) = -18.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.12
y[1] (analytic) = 0.14705951844712373938527266634585
y[1] (numeric) = 0.1470595184471237393852726663457
absolute error = 1.5e-31
relative error = 1.0199951800735260191086066849174e-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 = 0.4289
Order of pole (three term test) = -18.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.11
y[1] (analytic) = 0.14188217036519114776262449168932
y[1] (numeric) = 0.14188217036519114776262449168917
absolute error = 1.5e-31
relative error = 1.0572152907861102950823459771473e-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 = 0.4244
Order of pole (three term test) = -18.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.1
y[1] (analytic) = 0.13679063335112622931924068673098
y[1] (numeric) = 0.13679063335112622931924068673083
absolute error = 1.5e-31
relative error = 1.0965663095876367975867029179032e-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 = 0.4198
Order of pole (three term test) = -18.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.09
y[1] (analytic) = 0.13178541655438745717837794127249
y[1] (numeric) = 0.13178541655438745717837794127235
absolute error = 1.4e-31
relative error = 1.0623330233373918743434014589414e-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 = 0.415
Order of pole (three term test) = -19.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.08
y[1] (analytic) = 0.12686702049248350512332319497538
y[1] (numeric) = 0.12686702049248350512332319497524
absolute error = 1.4e-31
relative error = 1.1035176790353848105133969695524e-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 = 0.41
Order of pole (three term test) = -19.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.07
y[1] (analytic) = 0.12203593700092191382654887955616
y[1] (numeric) = 0.12203593700092191382654887955602
absolute error = 1.4e-31
relative error = 1.1472030570711509154866976815238e-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 = 0.4049
Order of pole (three term test) = -19.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.06
y[1] (analytic) = 0.1172926491840259499572024148001
y[1] (numeric) = 0.11729264918402594995720241479996
absolute error = 1.4e-31
relative error = 1.1935956854410153199106194611632e-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 = 0.3996
Order of pole (three term test) = -19.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.05
y[1] (analytic) = 0.11263763136662457644003339531966
y[1] (numeric) = 0.11263763136662457644003339531952
absolute error = 1.4e-31
relative error = 1.2429238639111076905228984557662e-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 = 0.3941
Order of pole (three term test) = -19.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.04
y[1] (analytic) = 0.1080713490466203648284743514158
y[1] (numeric) = 0.10807134904662036482847435141565
absolute error = 1.5e-31
relative error = 1.3879719400494597488850523711685e-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 = 0.3885
Order of pole (three term test) = -20.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.03
y[1] (analytic) = 0.10359425884844009296111116803243
y[1] (numeric) = 0.10359425884844009296111116803228
absolute error = 1.5e-31
relative error = 1.4479566885984693526339265555900e-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 = 0.3827
Order of pole (three term test) = -20.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.02
y[1] (analytic) = 0.09920680847737268280298647544629
y[1] (numeric) = 0.09920680847737268280298647544614
absolute error = 1.50e-31
relative error = 1.5119930003011068057640147675423e-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 = 0.3768
Order of pole (three term test) = -20.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.01
y[1] (analytic) = 0.09490943667479904463990028972628
y[1] (numeric) = 0.094909436674799044639900289726133
absolute error = 1.47e-31
relative error = 1.5488449320765210272602647768556e-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 = 0.3707
Order of pole (three term test) = -20.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2
y[1] (analytic) = 0.09070257317431830460398013408826
y[1] (numeric) = 0.090702573174318304603980134088108
absolute error = 1.52e-31
relative error = 1.6758069223447076683619191950769e-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 = 0.3645
Order of pole (three term test) = -20.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (analytic) = 0.08658663865877480287120672894239
y[1] (numeric) = 0.08658663865877480287120672894224
absolute error = 1.50e-31
relative error = 1.7323689003695814954591467160733e-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 = 0.3581
Order of pole (three term test) = -21.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (analytic) = 0.082562044718190159795264782598
y[1] (numeric) = 0.082562044718190159795264782597857
absolute error = 1.43e-31
relative error = 1.7320307471563150850467584793062e-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 = 0.3516
Order of pole (three term test) = -21.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (analytic) = 0.07862919380860461673604900284683
y[1] (numeric) = 0.078629193808604616736049002846682
absolute error = 1.48e-31
relative error = 1.8822525429963640078306728224144e-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 = 0.3449
Order of pole (three term test) = -21.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (analytic) = 0.07478847921183176741444371050997
y[1] (numeric) = 0.074788479211831767414443710509826
absolute error = 1.44e-31
relative error = 1.9254302469787185770855050620065e-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 = 0.3381
Order of pole (three term test) = -21.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (analytic) = 0.07104028499613070428670296490852
y[1] (numeric) = 0.07104028499613070428670296490837
absolute error = 1.50e-31
relative error = 2.1114780157226274195684391178497e-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 = 0.3312
Order of pole (three term test) = -21.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (analytic) = 0.0673849859777995126910206611343
y[1] (numeric) = 0.067384985977799512691020661134156
absolute error = 1.44e-31
relative error = 2.1369745487138911974892239568577e-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 = 0.3241
Order of pole (three term test) = -21.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (analytic) = 0.06382294768369395338487062725122
y[1] (numeric) = 0.063822947683693953384870627251072
absolute error = 1.48e-31
relative error = 2.3189151452779473934487628147521e-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 = 0.317
Order of pole (three term test) = -22.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (analytic) = 0.06035452631467508157362866031297
y[1] (numeric) = 0.060354526314675081573628660312823
absolute error = 1.47e-31
relative error = 2.4356085446446001834648399781034e-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 = 0.3096
Order of pole (three term test) = -22.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (analytic) = 0.05698006870998945763811342305179
y[1] (numeric) = 0.056980068709989457638113423051639
absolute error = 1.51e-31
relative error = 2.6500494544599845881857702480037e-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 = 0.3022
Order of pole (three term test) = -22.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (analytic) = 0.05369991231258551151029038836504
y[1] (numeric) = 0.053699912312585511510290388364896
absolute error = 1.44e-31
relative error = 2.6815686245776436251227267076692e-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 = 0.2946
Order of pole (three term test) = -22.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (analytic) = 0.05051438513536952903179832786168
y[1] (numeric) = 0.050514385135369529031798327861532
bytes used=48018500, alloc=4390108, time=1.92
absolute error = 1.48e-31
relative error = 2.9298584869119249199394481066984e-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 = 0.287
Order of pole (three term test) = -22.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (analytic) = 0.04742380572840463466854257418487
y[1] (numeric) = 0.047423805728404634668542574184729
absolute error = 1.41e-31
relative error = 2.9731903172745078794418520886886e-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 = 0.2792
Order of pole (three term test) = -22.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (analytic) = 0.04442848314705605065574950782737
y[1] (numeric) = 0.04442848314705605065574950782722
absolute error = 1.50e-31
relative error = 3.3762124964633054001757758650020e-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 = 0.2713
Order of pole (three term test) = -22.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (analytic) = 0.0415287169210858180210222340968
y[1] (numeric) = 0.041528716921085818021022234096656
absolute error = 1.44e-31
relative error = 3.4674801119821100316063805471796e-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 = 0.2633
Order of pole (three term test) = -23.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (analytic) = 0.03872479702470006998754083136387
y[1] (numeric) = 0.038724797024700069987540831363725
absolute error = 1.45e-31
relative error = 3.7443708202657273756691574834066e-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 = 0.2551
Order of pole (three term test) = -23.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (analytic) = 0.03601700384755185300510632827288
y[1] (numeric) = 0.036017003847551853005106328272732
absolute error = 1.48e-31
relative error = 4.1091702304399163050081973338986e-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 = 0.2469
Order of pole (three term test) = -23.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (analytic) = 0.03340560816670239510276107025719
y[1] (numeric) = 0.033405608166702395102761070257042
absolute error = 1.48e-31
relative error = 4.4303938207453891823573732713770e-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 = 0.2386
Order of pole (three term test) = -23.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (analytic) = 0.03089087111954362541278468150195
y[1] (numeric) = 0.030890871119543625412784681501798
absolute error = 1.52e-31
relative error = 4.9205475433755140037624600887592e-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 = 0.2302
Order of pole (three term test) = -23.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (analytic) = 0.02847304417768465259154873090962
y[1] (numeric) = 0.028473044177684652591548730909477
absolute error = 1.43e-31
relative error = 5.0222940373925397211938396249093e-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 = 0.2217
Order of pole (three term test) = -23.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (analytic) = 0.02615236912180481346762682115664
y[1] (numeric) = 0.026152369121804813467626821156495
absolute error = 1.45e-31
relative error = 5.5444307674253772034793828192594e-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 = 0.2131
Order of pole (three term test) = -23.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (analytic) = 0.02392907801747580659133956689138
y[1] (numeric) = 0.023929078017475806591339566891237
absolute error = 1.43e-31
relative error = 5.9759928859592795064546349222605e-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 = 0.2044
Order of pole (three term test) = -23.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (analytic) = 0.0218033931919553284522313526944
y[1] (numeric) = 0.021803393191955328452231352694257
absolute error = 1.43e-31
relative error = 6.5586121729328754544701879836149e-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 = 0.1956
Order of pole (three term test) = -24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (analytic) = 0.01977552721195453298151855110158
y[1] (numeric) = 0.019775527211954532981518551101428
absolute error = 1.52e-31
relative error = 7.6862678992504562353019399184256e-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 = 0.1868
Order of pole (three term test) = -24.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (analytic) = 0.01784568286238153757503190054404
y[1] (numeric) = 0.017845682862381537575031900543896
absolute error = 1.44e-31
relative error = 8.0691784736100005010096445660927e-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 = 0.1779
Order of pole (three term test) = -24.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (analytic) = 0.01601405312606310126833706303201
y[1] (numeric) = 0.016014053126063101268337063031867
absolute error = 1.43e-31
relative error = 8.9296569003674308981914643995902e-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 = 0.1689
Order of pole (three term test) = -24.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (analytic) = 0.01428082116444650287931730433445
y[1] (numeric) = 0.014280821164446502879317304334303
absolute error = 1.47e-31
relative error = 1.0293525722874454667207106236044e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1599
Order of pole (three term test) = -24.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (analytic) = 0.01264616029928354891432232377794
y[1] (numeric) = 0.012646160299283548914322323777788
absolute error = 1.52e-31
relative error = 1.2019458586857494930995926112849e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1507
Order of pole (three term test) = -24.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (analytic) = 0.01111023399529854282182934291452
y[1] (numeric) = 0.011110233995298542821829342914377
absolute error = 1.43e-31
relative error = 1.2871016043452597917185174179557e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1416
Order of pole (three term test) = -24.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (analytic) = 0.00967319584384194878224777613887
y[1] (numeric) = 0.0096731958438419487822477761387189
absolute error = 1.511e-31
relative error = 1.5620483906173753314453185203331e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1323
Order of pole (three term test) = -24.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (analytic) = 0.00833518954753138465386660135212
y[1] (numeric) = 0.0083351895475313846538666013519769
absolute error = 1.431e-31
relative error = 1.7168175862585107305627452056248e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.123
Order of pole (three term test) = -24.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (analytic) = 0.00709634890588147996285070605441
y[1] (numeric) = 0.0070963489058814799628507060542598
absolute error = 1.502e-31
relative error = 2.1165813856124476899349756061856e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1137
Order of pole (three term test) = -24.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (analytic) = 0.00595679780192403593951213080643
y[1] (numeric) = 0.0059567978019240359395121308062817
absolute error = 1.483e-31
relative error = 2.4895926457684923055129263311554e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1043
Order of pole (three term test) = -24.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (analytic) = 0.00491665018981982557370275346576
y[1] (numeric) = 0.0049166501898198255737027534656171
absolute error = 1.429e-31
relative error = 2.9064504181298421876639421083895e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09491
Order of pole (three term test) = -24.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (analytic) = 0.00397601008346327249899940938704
y[1] (numeric) = 0.0039760100834632724989994093868921
absolute error = 1.479e-31
relative error = 3.7198094797378597509256238010311e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08545
Order of pole (three term test) = -24.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (analytic) = 0.00313497154608114822829695979781
y[1] (numeric) = 0.0031349715460811482282969597976612
absolute error = 1.488e-31
relative error = 4.7464545630727181156733307404651e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07595
Order of pole (three term test) = -24.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (analytic) = 0.00239361868082632786241802563206
y[1] (numeric) = 0.0023936186808263278624180256319144
absolute error = 1.456e-31
relative error = 6.0828402270714145820978052930377e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06643
Order of pole (three term test) = -24.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (analytic) = 0.0017520256223675448883300150669
y[1] (numeric) = 0.00175202562236754488833001506675
absolute error = 1.500e-31
relative error = 8.5615186264971515310914559592536e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05688
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (analytic) = 0.0012102565294759860844811087532
y[1] (numeric) = 0.0012102565294759860844811087530563
absolute error = 1.437e-31
relative error = 1.1873515779519807668049941976282e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04731
Order of pole (three term test) = -24.98
NO COMPLEX POLE (six term test) for Equation 1
bytes used=52019580, alloc=4390108, time=2.09
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (analytic) = 0.0007683655786094678675868521557
y[1] (numeric) = 0.00076836557860946786758685215554899
absolute error = 1.5101e-31
relative error = 1.9653405124327265332096577371725e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03771
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (analytic) = 0.00042639695849483565788617445377
y[1] (numeric) = 0.0004263969584948356578861744536184
absolute error = 1.5160e-31
relative error = 3.5553724523538344133991427552887e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02811
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (analytic) = 0.00018438486570912801841565625449
y[1] (numeric) = 0.00018438486570912801841565625434113
absolute error = 1.4887e-31
relative error = 8.0738730604303688142595787360795e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01849
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (analytic) = 4.235350125994744820576774828e-05
y[1] (numeric) = 4.2353501259947448205767748135080e-05
absolute error = 1.44920e-31
relative error = 3.4216769733048467989687601607867e-25 %
Correct digits = 27
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008862
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (analytic) = 3.1706816537978947007617667e-07
y[1] (numeric) = 3.170681653797894700761765255680e-07
absolute error = 1.444320e-31
relative error = 4.5552349863631680539630099569782e-23 %
Correct digits = 25
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 5.827977003370425482997658652e-05
y[1] (numeric) = 5.8279770033704254829976586367699e-05
absolute error = 1.52301e-31
relative error = 2.6132738669339558417670424465391e-25 %
Correct digits = 27
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00021623581064303610238865236553
y[1] (numeric) = 0.00021623581064303610238865236537956
absolute error = 1.5044e-31
relative error = 6.9572195073806539467798799689876e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (analytic) = 0.00047416939452094399403646155997
y[1] (numeric) = 0.00047416939452094399403646155981819
absolute error = 1.5181e-31
relative error = 3.2015984530881521099341581118039e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00083205472852398407573493129102
y[1] (numeric) = 0.00083205472852398407573493129087576
absolute error = 1.4424e-31
relative error = 1.7335398148133024518855300139803e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00128985602441699282768760588315
y[1] (numeric) = 0.001289856024416992827687605883004
absolute error = 1.460e-31
relative error = 1.1319092769752432073831674781561e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00184752750245188075726213516329
y[1] (numeric) = 0.0018475275024518807572621351631404
absolute error = 1.496e-31
relative error = 8.0973084190337439100389474628533e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00250501339594556905827662885851
y[1] (numeric) = 0.0025050133959455690582766288583653
absolute error = 1.447e-31
relative error = 5.7764162153464251471761220685957e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.0032622479568566114467992829563
y[1] (numeric) = 0.0032622479568566114467992829561541
absolute error = 1.459e-31
relative error = 4.4723761629874437982152880983915e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00411915546235994351592486743731
y[1] (numeric) = 0.0041191554623599435159248674371665
absolute error = 1.435e-31
relative error = 3.4837238193915139491127588296031e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00507565022241910214007153726443
y[1] (numeric) = 0.0050756502224191021400715372642864
absolute error = 1.436e-31
relative error = 2.8291941664088685641073188708388e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00613163658835515771316769874997
y[1] (numeric) = 0.0061316365883551577131676987498222
absolute error = 1.478e-31
relative error = 2.4104494431501866248672770892381e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00728700896241150233464586567699
y[1] (numeric) = 0.0072870089624115023346458656768398
absolute error = 1.502e-31
relative error = 2.0612023503027785106589609797144e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00854165180831353747239553604202
y[1] (numeric) = 0.0085416518083135374723955360418692
absolute error = 1.508e-31
relative error = 1.7654664856887198580218840232467e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00989543966282220514270850451817
y[1] (numeric) = 0.0098954396628222051427085045180232
absolute error = 1.468e-31
relative error = 1.4835116478102222896361962060405e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.0113482371482802072637265266643
y[1] (numeric) = 0.011348237148280207263726526664154
absolute error = 1.46e-31
relative error = 1.2865434348287820240096818961229e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.01289989898614965857091113805776
y[1] (numeric) = 0.012899898986149658570911138057615
absolute error = 1.45e-31
relative error = 1.1240398095805506029604305808478e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.0145502700115398193405254211939
y[1] (numeric) = 0.014550270011539819340525421193756
absolute error = 1.44e-31
relative error = 9.8967235581053546137867040792142e-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] = -1.39
y[1] (analytic) = 0.01629918518872345515996177555709
y[1] (numeric) = 0.016299185188723455159961775556945
absolute error = 1.45e-31
relative error = 8.8961502259829428115837862911339e-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] = -1.38
y[1] (analytic) = 0.01814646962764027212186891479395
y[1] (numeric) = 0.018146469627640272121868914793806
absolute error = 1.44e-31
relative error = 7.9354278245208982978591121637654e-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] = -1.37
y[1] (analytic) = 0.02009193860138577711231149510807
y[1] (numeric) = 0.020091938601385777112311495107922
absolute error = 1.48e-31
relative error = 7.3661383770002250569805018629405e-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] = -1.36
y[1] (analytic) = 0.02213539756468381432150756057337
y[1] (numeric) = 0.022135397564683814321507560573224
absolute error = 1.46e-31
relative error = 6.5957703977694736353111933863721e-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] = -1.35
y[1] (analytic) = 0.02427664217334093073888646073478
y[1] (numeric) = 0.024276642173340930738886460734638
absolute error = 1.42e-31
relative error = 5.8492438528395577291983312203057e-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] = -1.34
y[1] (analytic) = 0.02651545830468062521212965191045
y[1] (numeric) = 0.026515458304680625212129651910302
absolute error = 1.48e-31
relative error = 5.5816497040850464828580209942117e-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
bytes used=56020752, alloc=4390108, time=2.25
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (analytic) = 0.0288516220789554376623169622362
y[1] (numeric) = 0.028851622078955437662316962236058
absolute error = 1.42e-31
relative error = 4.9217336762349916942451976776188e-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] = -1.32
y[1] (analytic) = 0.03128489988173473726410015402723
y[1] (numeric) = 0.031284899881734737264100154027079
absolute error = 1.51e-31
relative error = 4.8266096605972932511905509893627e-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] = -1.31
y[1] (analytic) = 0.0338150483872659708307421940625
y[1] (numeric) = 0.033815048387265970830742194062354
absolute error = 1.46e-31
relative error = 4.3176043496356639764435446922450e-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] = -1.3
y[1] (analytic) = 0.03644181458280703529865136996045
y[1] (numeric) = 0.036441814582807035298651369960298
absolute error = 1.52e-31
relative error = 4.1710326925298724792600539495778e-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] = -1.29
y[1] (analytic) = 0.03916493579392734109443870871463
y[1] (numeric) = 0.03916493579392734109443870871448
absolute error = 1.50e-31
relative error = 3.8299564893773685027495879603746e-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] = -1.28
y[1] (analytic) = 0.04198413971077503629924614083971
y[1] (numeric) = 0.041984139710775036299246140839568
absolute error = 1.42e-31
relative error = 3.3822295985632963512432238484758e-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] = -1.27
y[1] (analytic) = 0.04489914441530776490981825781711
y[1] (numeric) = 0.044899144415307764909818257816966
absolute error = 1.44e-31
relative error = 3.2071880628287678264230307668763e-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] = -1.26
y[1] (analytic) = 0.04790965840948423614318377857458
y[1] (numeric) = 0.047909658409484236143183778574429
absolute error = 1.51e-31
relative error = 3.1517653227539588011569628871181e-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] = -1.25
y[1] (analytic) = 0.05101538064441378565150915296395
y[1] (numeric) = 0.051015380644413785651509152963804
absolute error = 1.46e-31
relative error = 2.8618820080486273179860913123779e-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] = -1.24
y[1] (analytic) = 0.05421600055046101371529403691821
y[1] (numeric) = 0.054216000550461013715294036918064
absolute error = 1.46e-31
relative error = 2.6929319484588673045785367812077e-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] = -1.23
y[1] (analytic) = 0.05751119806830248997617643461076
y[1] (numeric) = 0.057511198068302489976176434610609
absolute error = 1.51e-31
relative error = 2.6255756282570682490265365565107e-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] = -1.22
y[1] (analytic) = 0.06090064368093241906475472811163
y[1] (numeric) = 0.060900643680932419064754728111481
absolute error = 1.49e-31
relative error = 2.4466079665862529367599974593720e-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] = -1.21
y[1] (analytic) = 0.06438399844661406658353511145639
y[1] (numeric) = 0.064383998446614066583535111456248
absolute error = 1.42e-31
relative error = 2.2055169518206232739456278665594e-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] = -1.2
y[1] (analytic) = 0.06796091403277365032986556450517
y[1] (numeric) = 0.067960914032773650329865564505027
absolute error = 1.43e-31
relative error = 2.1041506288605727558101536819905e-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] = -1.19
y[1] (analytic) = 0.07163103275083330739797888839733
y[1] (numeric) = 0.071631032750833307397978888397178
absolute error = 1.52e-31
relative error = 2.1219853206462632487160792080685e-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] = -1.18
y[1] (analytic) = 0.07539398759197965389246197412524
y[1] (numeric) = 0.07539398759197965389246197412509
absolute error = 1.50e-31
relative error = 1.9895485673443391142221269929429e-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] = -1.17
y[1] (analytic) = 0.07924940226386436042698699103797
y[1] (numeric) = 0.079249402263864360426986991037825
absolute error = 1.45e-31
relative error = 1.8296667969458765231992844102091e-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] = -1.16
y[1] (analytic) = 0.08319689122823307338133833312567
y[1] (numeric) = 0.08319689122823307338133833312552
absolute error = 1.50e-31
relative error = 1.8029519827670811378527513107853e-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] = -1.15
y[1] (analytic) = 0.08723605973947891905596695024632
y[1] (numeric) = 0.087236059739478919055966950246179
absolute error = 1.41e-31
relative error = 1.6163040882529688778461939136828e-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] = -1.14
y[1] (analytic) = 0.0913665038841167354057844218978
y[1] (numeric) = 0.09136650388411673540578442189765
absolute error = 1.50e-31
relative error = 1.6417395174740420723356584496726e-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] = -1.13
y[1] (analytic) = 0.0955878106211740839629184775886
y[1] (numeric) = 0.095587810621174083962918477588459
absolute error = 1.41e-31
relative error = 1.4750834764779773982682016090729e-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] = -1.12
y[1] (analytic) = 0.09989955782349500288089675266085
y[1] (numeric) = 0.099899557823495002880896752660706
absolute error = 1.44e-31
relative error = 1.4414478215651639178693554284434e-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] = -1.11
y[1] (analytic) = 0.10430131431995237075937404066063
y[1] (numeric) = 0.10430131431995237075937404066048
absolute error = 1.5e-31
relative error = 1.4381410337732021933868153174032e-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] = -1.1
y[1] (analytic) = 0.1087926399385646600481974221283
y[1] (numeric) = 0.10879263993856466004819742212815
absolute error = 1.5e-31
relative error = 1.3787697410845548720831524088974e-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] = -1.09
y[1] (analytic) = 0.11337308555051276839139937136395
y[1] (numeric) = 0.1133730855505127683913993713638
absolute error = 1.5e-31
relative error = 1.3230653401698969100149433119607e-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] = -1.08
y[1] (analytic) = 0.11804219311505252626466501237524
y[1] (numeric) = 0.11804219311505252626466501237509
absolute error = 1.5e-31
relative error = 1.2707320665738484334593839176130e-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] = -1.07
y[1] (analytic) = 0.12279949572531838969293674222318
y[1] (numeric) = 0.12279949572531838969293674222302
absolute error = 1.6e-31
relative error = 1.3029369465644453346200205639303e-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] = -1.06
y[1] (analytic) = 0.12764451765501373771705407800258
bytes used=60021920, alloc=4455632, time=2.42
y[1] (numeric) = 0.12764451765501373771705407800242
absolute error = 1.6e-31
relative error = 1.2534811752153256239298080857658e-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] = -1.05
y[1] (analytic) = 0.13257677440598310561859051499973
y[1] (numeric) = 0.13257677440598310561859051499957
absolute error = 1.6e-31
relative error = 1.2068478865690316691630471445231e-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] = -1.04
y[1] (analytic) = 0.13759577275666159671920830788383
y[1] (numeric) = 0.13759577275666159671920830788367
absolute error = 1.6e-31
relative error = 1.1628264211500183556900609768471e-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] = -1.03
y[1] (analytic) = 0.14270101081139662785372561470558
y[1] (numeric) = 0.14270101081139662785372561470542
absolute error = 1.6e-31
relative error = 1.1212254145239860572209127765663e-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] = -1.02
y[1] (analytic) = 0.14789197805063707638345001454462
y[1] (numeric) = 0.14789197805063707638345001454446
absolute error = 1.6e-31
relative error = 1.0818707147538268098624849633859e-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] = -1.01
y[1] (analytic) = 0.15316815538198480987690121521799
y[1] (numeric) = 0.15316815538198480987690121521783
absolute error = 1.6e-31
relative error = 1.0446035574495057978005667805704e-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] = -1
y[1] (analytic) = 0.1585290151921034933474976783697
y[1] (numeric) = 0.15852901519210349334749767836954
absolute error = 1.6e-31
relative error = 1.0092789626309984044021634783719e-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] = -0.99
y[1] (analytic) = 0.16397402139947948321074058845289
y[1] (numeric) = 0.16397402139947948321074058845273
absolute error = 1.6e-31
relative error = 9.7576432311922248015650545411471e-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] = -0.98
y[1] (analytic) = 0.16950262950802953191546671228085
y[1] (numeric) = 0.1695026295080295319154667122807
absolute error = 1.5e-31
relative error = 8.8494202382208076469033714257426e-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] = -0.97
y[1] (analytic) = 0.17511428666154994252337996214366
y[1] (numeric) = 0.1751142866615499425233799621435
absolute error = 1.6e-31
relative error = 9.1368901447337703213371033612676e-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] = -0.96
y[1] (analytic) = 0.18080843169900172836677785356957
y[1] (numeric) = 0.18080843169900172836677785356942
absolute error = 1.5e-31
relative error = 8.2960732854378368828470107658811e-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] = -0.95
y[1] (analytic) = 0.18658449521062624931457789789744
y[1] (numeric) = 0.18658449521062624931457789789729
absolute error = 1.5e-31
relative error = 8.0392531989687688219269569151098e-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] = -0.94
y[1] (analytic) = 0.19244189959488571312978020136585
y[1] (numeric) = 0.1924418995948857131297802013657
absolute error = 1.5e-31
relative error = 7.7945603486438647566239528720038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.61
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] = -0.93
y[1] (analytic) = 0.19838005911622284791568078408935
y[1] (numeric) = 0.1983800591162228479156807840892
absolute error = 1.5e-31
relative error = 7.5612438401442894374455857105777e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.92
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] = -0.92
y[1] (analytic) = 0.20439837996363396973172389751838
y[1] (numeric) = 0.20439837996363396973172389751823
absolute error = 1.5e-31
relative error = 7.3386100235573105532625041208828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.23
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] = -0.91
y[1] (analytic) = 0.21049626031004958812104248212845
y[1] (numeric) = 0.2104962603100495881210424821283
absolute error = 1.5e-31
relative error = 7.1260173353701451048350115901447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.55
Order of pole (ratio test) Not computed
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) = 0.21667309037251661153861768428645
y[1] (numeric) = 0.2166730903725166115386176842863
absolute error = 1.5e-31
relative error = 6.9228716746556542930208821075149e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.87
Order of pole (ratio test) Not computed
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) = 0.22292825247317613450966628702682
y[1] (numeric) = 0.22292825247317613450966628702667
absolute error = 1.5e-31
relative error = 6.7286222511455234154315812754510e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.2
Order of pole (ratio test) Not computed
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) = 0.22926112110103070879035486924401
y[1] (numeric) = 0.22926112110103070879035486924386
absolute error = 1.5e-31
relative error = 6.5427578509440357175757902592561e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.53
Order of pole (ratio test) Not computed
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) = 0.23567106297449492185519717627715
y[1] (numeric) = 0.235671062974494921855197176277
absolute error = 1.5e-31
relative error = 6.3648034725516335874622918340302e-29 %
Correct digits = 31
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] = -0.86
y[1] (analytic) = 0.24215743710472302770541127047135
y[1] (numeric) = 0.24215743710472302770541127047121
absolute error = 1.4e-31
relative error = 5.7813628056963544040318961672977e-29 %
Correct digits = 31
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] = -0.85
y[1] (analytic) = 0.24871959485970729728792847576453
y[1] (numeric) = 0.24871959485970729728792847576439
absolute error = 1.4e-31
relative error = 5.6288287249329253488217665993461e-29 %
Correct digits = 31
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] = -0.84
y[1] (analytic) = 0.25535688002914067874342732937035
y[1] (numeric) = 0.25535688002914067874342732937021
absolute error = 1.4e-31
relative error = 5.4825231254401117169748415269425e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.93
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] = -0.83
y[1] (analytic) = 0.26206862889003728127141977386192
y[1] (numeric) = 0.26206862889003728127141977386177
absolute error = 1.5e-31
relative error = 5.7236915625997825378302251014268e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.29
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] = -0.82
y[1] (analytic) = 0.26885417027310412061868663531228
y[1] (numeric) = 0.26885417027310412061868663531213
absolute error = 1.5e-31
relative error = 5.5792327806419686096586315589310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.66
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] = -0.81
y[1] (analytic) = 0.27571282562985748907182314748546
y[1] (numeric) = 0.27571282562985748907182314748531
absolute error = 1.5e-31
relative error = 5.4404433184176181576751165311260e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.04
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] = -0.8
y[1] (analytic) = 0.28264390910047723837282538941861
y[1] (numeric) = 0.28264390910047723837282538941847
absolute error = 1.4e-31
relative error = 4.9532289744206489573491959500534e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (analytic) = 0.2896467275823921901859711250308
y[1] (numeric) = 0.28964672758239219018597112503066
absolute error = 1.4e-31
relative error = 4.8334742521879846550475285728800e-29 %
Correct digits = 31
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] = -0.78
y[1] (analytic) = 0.29672058079958981563210267488208
y[1] (numeric) = 0.29672058079958981563210267488193
absolute error = 1.5e-31
relative error = 5.0552610673579322849096761088239e-29 %
Correct digits = 31
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
bytes used=64022896, alloc=4455632, time=2.57
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = 0.30386476137264325298011626554779
y[1] (numeric) = 0.30386476137264325298011626554765
absolute error = 1.4e-31
relative error = 4.6073127850554410824888682423686e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (analytic) = 0.31107855488944866085224436123027
y[1] (numeric) = 0.31107855488944866085224436123013
absolute error = 1.4e-31
relative error = 4.5004709517746509093635915999796e-29 %
Correct digits = 31
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] = -0.75
y[1] (analytic) = 0.31836123997666583326675804722011
y[1] (numeric) = 0.31836123997666583326675804721996
absolute error = 1.5e-31
relative error = 4.7116288405898341549099213834300e-29 %
Correct digits = 31
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] = -0.74
y[1] (analytic) = 0.32571208837185493251611884239183
y[1] (numeric) = 0.32571208837185493251611884239168
absolute error = 1.5e-31
relative error = 4.6052942262538890674499263323624e-29 %
Correct digits = 31
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] = -0.73
y[1] (analytic) = 0.33313036499630212626740586923847
y[1] (numeric) = 0.33313036499630212626740586923832
absolute error = 1.5e-31
relative error = 4.5027417420103705359084732112501e-29 %
Correct digits = 31
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] = -0.72
y[1] (analytic) = 0.34061532802852684638199616735183
y[1] (numeric) = 0.34061532802852684638199616735168
absolute error = 1.5e-31
relative error = 4.4037947695482853405565408106191e-29 %
Correct digits = 31
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] = -0.71
y[1] (analytic) = 0.34816622897846331878987202714716
y[1] (numeric) = 0.34816622897846331878987202714701
absolute error = 1.5e-31
relative error = 4.3082868904347015267843961651665e-29 %
Correct digits = 31
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] = -0.7
y[1] (analytic) = 0.35578231276230894632738564860128
y[1] (numeric) = 0.35578231276230894632738564860113
absolute error = 1.5e-31
relative error = 4.2160611873983742018702687886282e-29 %
Correct digits = 31
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] = -0.69
y[1] (analytic) = 0.36346281777803205976257079299128
y[1] (numeric) = 0.36346281777803205976257079299113
absolute error = 1.5e-31
relative error = 4.1269696008246294445379235978419e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.68
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (analytic) = 0.37120697598153148629582181257975
y[1] (numeric) = 0.37120697598153148629582181257961
absolute error = 1.4e-31
relative error = 3.7714808464958741661647937426150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (analytic) = 0.37901401296344031964255608587341
y[1] (numeric) = 0.37901401296344031964255608587326
absolute error = 1.5e-31
relative error = 3.9576373133852704151813473320903e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.05
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] = -0.66
y[1] (analytic) = 0.3868831480265662113848545206037
y[1] (numeric) = 0.38688314802656621138485452060355
absolute error = 1.5e-31
relative error = 3.8771396677556994237903519760114e-29 %
Correct digits = 31
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
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (analytic) = 0.39481359426396043962747832139406
y[1] (numeric) = 0.39481359426396043962747832139391
absolute error = 1.5e-31
relative error = 3.7992612761888470417701412779370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (analytic) = 0.40280455863760794811645376079207
y[1] (numeric) = 0.40280455863760794811645376079192
absolute error = 1.5e-31
relative error = 3.7238903280374943744536905447973e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.15
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] = -0.63
y[1] (analytic) = 0.41085524205773048688188790920538
y[1] (numeric) = 0.41085524205773048688188790920523
absolute error = 1.5e-31
relative error = 3.6509209240884665589470578012941e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (analytic) = 0.41896483946269492415703677241779
y[1] (numeric) = 0.41896483946269492415703677241763
absolute error = 1.6e-31
relative error = 3.8189362192109815585064266691057e-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] = -0.61
y[1] (analytic) = 0.42713253989951873880902396783728
y[1] (numeric) = 0.42713253989951873880902396783712
absolute error = 1.6e-31
relative error = 3.7459098770053757757468772266227e-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] = -0.6
y[1] (analytic) = 0.43535752660496464279905455434134
y[1] (numeric) = 0.43535752660496464279905455434118
absolute error = 1.6e-31
relative error = 3.6751403208237407352789461822315e-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] = -0.59
y[1] (analytic) = 0.44363897708721622427745662112423
y[1] (numeric) = 0.44363897708721622427745662112407
absolute error = 1.6e-31
relative error = 3.6065361310339770617832571011665e-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] = -0.58
y[1] (analytic) = 0.45197606320812644381730394042354
y[1] (numeric) = 0.45197606320812644381730394042338
absolute error = 1.6e-31
relative error = 3.5400104789691710021735279796372e-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] = -0.57
y[1] (analytic) = 0.46036795126603075900553650692117
y[1] (numeric) = 0.46036795126603075900553650692102
absolute error = 1.5e-31
relative error = 3.2582632997691052158462286558419e-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] = -0.56
y[1] (analytic) = 0.46881380207911659614813055888797
y[1] (numeric) = 0.46881380207911659614813055888781
absolute error = 1.6e-31
relative error = 3.4128688039990457386906329830255e-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] = -0.55
y[1] (analytic) = 0.47731277106934083221162189224271
y[1] (numeric) = 0.47731277106934083221162189224255
absolute error = 1.6e-31
relative error = 3.3520997068975609216778934749271e-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] = -0.54
y[1] (analytic) = 0.48586400834688689532271931704176
y[1] (numeric) = 0.4858640083468868953227193170416
absolute error = 1.6e-31
relative error = 3.2931025400376351481194378935279e-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] = -0.53
y[1] (analytic) = 0.49446665879515303818633897753392
y[1] (numeric) = 0.49446665879515303818633897753376
absolute error = 1.6e-31
relative error = 3.2358096780451395036420189845115e-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] = -0.52
y[1] (analytic) = 0.50311986215626328566554105745225
y[1] (numeric) = 0.50311986215626328566554105745209
absolute error = 1.6e-31
relative error = 3.1801566989280543754287748480271e-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] = -0.51
y[1] (analytic) = 0.51182275311709250549986976232543
y[1] (numeric) = 0.51182275311709250549986976232527
absolute error = 1.6e-31
relative error = 3.1260822037623622456716194712282e-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] = -0.5
y[1] (analytic) = 0.52057446139579699972671206478443
y[1] (numeric) = 0.52057446139579699972671206478427
absolute error = 1.6e-31
relative error = 3.0735276481100884783914309912681e-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] = -0.49
y[1] (analytic) = 0.52937411182884196381864166281204
y[1] (numeric) = 0.52937411182884196381864166281188
absolute error = 1.6e-31
relative error = 3.0224371843051411115230020151642e-29 %
bytes used=68023568, alloc=4455632, time=2.73
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] = -0.48
y[1] (analytic) = 0.53822082445851711086335705741136
y[1] (numeric) = 0.5382208244585171108633570574112
absolute error = 1.6e-31
relative error = 2.9727575138135863235734969270828e-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] = -0.47
y[1] (analytic) = 0.54711371462093170929672519960359
y[1] (numeric) = 0.54711371462093170929672519960343
absolute error = 1.6e-31
relative error = 2.9244377489395629915047054353119e-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] = -0.46
y[1] (analytic) = 0.5560518930344802347584863560711
y[1] (numeric) = 0.55605189303448023475848635607094
absolute error = 1.6e-31
relative error = 2.8774292832068203440395188300703e-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] = -0.45
y[1] (analytic) = 0.5650344658887697895791557537681
y[1] (numeric) = 0.56503446588876978957915575376794
absolute error = 1.6e-31
relative error = 2.8316856697994224531030272383593e-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] = -0.44
y[1] (analytic) = 0.57406053493400039723027924922008
y[1] (numeric) = 0.57406053493400039723027924921992
absolute error = 1.6e-31
relative error = 2.7871625074940077849965132144271e-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] = -0.43
y[1] (analytic) = 0.58312919757078923378308132737543
y[1] (numeric) = 0.58312919757078923378308132737527
absolute error = 1.6e-31
relative error = 2.7438173335605738954899607736725e-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] = -0.42
y[1] (analytic) = 0.59223954694042981402721284191366
y[1] (numeric) = 0.59223954694042981402721284191349
absolute error = 1.7e-31
relative error = 2.8704601183463248918724422987667e-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] = -0.41
y[1] (analytic) = 0.60139067201557710640620235994886
y[1] (numeric) = 0.60139067201557710640620235994869
absolute error = 1.7e-31
relative error = 2.8267814568895856177479107884933e-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] = -0.4
y[1] (analytic) = 0.61058165769134950833368824320429
y[1] (numeric) = 0.61058165769134950833368824320413
absolute error = 1.6e-31
relative error = 2.6204521210966409927179760733331e-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] = -0.39
y[1] (analytic) = 0.61981158487683857176881790215284
y[1] (numeric) = 0.61981158487683857176881790215267
absolute error = 1.7e-31
relative error = 2.7427689986430365724465855821898e-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] = -0.38
y[1] (analytic) = 0.6290795305870173281545145336508
y[1] (numeric) = 0.62907953058701732815451453365063
absolute error = 1.7e-31
relative error = 2.7023610169189057163238917048124e-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] = -0.37
y[1] (analytic) = 0.63838456803503802196270753087285
y[1] (numeric) = 0.63838456803503802196270753087268
absolute error = 1.7e-31
relative error = 2.6629716398575203985767477246961e-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] = -0.36
y[1] (analytic) = 0.64772576672491002315008656407927
y[1] (numeric) = 0.6477257667249100231500865640791
absolute error = 1.7e-31
relative error = 2.6245675057759315824854873606464e-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] = -0.35
y[1] (analytic) = 0.65710219254454865081036509308237
y[1] (numeric) = 0.6571021925445486508103650930822
absolute error = 1.7e-31
relative error = 2.5871166148707492637356086730564e-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] = -0.34
y[1] (analytic) = 0.66651290785918560321822851296921
y[1] (numeric) = 0.66651290785918560321822851296904
absolute error = 1.7e-31
relative error = 2.5505882631145675391918202521756e-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] = -0.33
y[1] (analytic) = 0.67595697160513165329980430382978
y[1] (numeric) = 0.67595697160513165329980430382961
absolute error = 1.7e-31
relative error = 2.5149529798667056653847141902583e-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] = -0.32
y[1] (analytic) = 0.68543343938388223333824245658285
y[1] (numeric) = 0.68543343938388223333824245658268
absolute error = 1.7e-31
relative error = 2.4801824689616609363125066288226e-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] = -0.31
y[1] (analytic) = 0.69494136355655649843435667604104
y[1] (numeric) = 0.69494136355655649843435667604087
absolute error = 1.7e-31
relative error = 2.4462495530554912651743047235381e-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] = -0.3
y[1] (analytic) = 0.70447979333866042489467925431497
y[1] (numeric) = 0.7044797933386604248946792543148
absolute error = 1.7e-31
relative error = 2.4131281210258489347587106971978e-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] = -0.29
y[1] (analytic) = 0.71404777489516446731605979449563
y[1] (numeric) = 0.71404777489516446731605979449546
absolute error = 1.7e-31
relative error = 2.3807930782356848749610286964941e-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] = -0.28
y[1] (analytic) = 0.72364435143588626668033044154215
y[1] (numeric) = 0.72364435143588626668033044154198
absolute error = 1.7e-31
relative error = 2.3492202994838373775246154233185e-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] = -0.27
y[1] (analytic) = 0.73326856331116887126771347897946
y[1] (numeric) = 0.73326856331116887126771347897929
absolute error = 1.7e-31
relative error = 2.3183865844779033072304251577359e-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] = -0.26
y[1] (analytic) = 0.74291944810784490264661153563478
y[1] (numeric) = 0.74291944810784490264661153563461
absolute error = 1.7e-31
relative error = 2.2882696156760480795331358736711e-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] = -0.25
y[1] (analytic) = 0.75259604074547707040315129515061
y[1] (numeric) = 0.75259604074547707040315129515044
absolute error = 1.7e-31
relative error = 2.2588479183548197667085682195498e-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] = -0.24
y[1] (analytic) = 0.76229737357286541163920791551018
y[1] (numeric) = 0.76229737357286541163920791551001
absolute error = 1.7e-31
relative error = 2.2301008227696625870008356771109e-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] = -0.23
y[1] (analytic) = 0.77202247646481160459538278763993
y[1] (numeric) = 0.77202247646481160459538278763975
absolute error = 1.8e-31
relative error = 2.3315383358298417272339656621895e-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] = -0.22
y[1] (analytic) = 0.78177037691913068004820899454299
y[1] (numeric) = 0.78177037691913068004820899454281
absolute error = 1.8e-31
relative error = 2.3024663675459256872754459594368e-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] = -0.21
y[1] (analytic) = 0.79154010015390042939128757377236
y[1] (numeric) = 0.79154010015390042939128757377218
absolute error = 1.8e-31
relative error = 2.2740477704793769408106092393844e-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] = -0.2
y[1] (analytic) = 0.80133066920493878454058737288161
y[1] (numeric) = 0.80133066920493878454058737288143
absolute error = 1.8e-31
relative error = 2.2462637075727017332122316645349e-29 %
Correct digits = 31
h = 0.01
bytes used=72024548, alloc=4455632, time=2.89
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (analytic) = 0.81114110502349942200714884701869
y[1] (numeric) = 0.81114110502349942200714884701851
absolute error = 1.8e-31
relative error = 2.2190960226924420580169768980973e-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] = -0.18
y[1] (analytic) = 0.82097042657417582165819726030079
y[1] (numeric) = 0.82097042657417582165819726030061
absolute error = 1.8e-31
relative error = 2.1925272113774094548192896558279e-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] = -0.17
y[1] (analytic) = 0.83081765093300398984237562332915
y[1] (numeric) = 0.83081765093300398984237562332897
absolute error = 1.8e-31
relative error = 2.1665403930436590618116952981388e-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] = -0.16
y[1] (analytic) = 0.84068179338575403668853684031401
y[1] (numeric) = 0.84068179338575403668853684031383
absolute error = 1.8e-31
relative error = 2.1411192845638975232901285440012e-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] = -0.15
y[1] (analytic) = 0.85056186752640077850227456131236
y[1] (numeric) = 0.85056186752640077850227456131218
absolute error = 1.8e-31
relative error = 2.1162481751442135991032714325003e-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] = -0.14
y[1] (analytic) = 0.86045688535576351828201164829463
y[1] (numeric) = 0.86045688535576351828201164829445
absolute error = 1.8e-31
relative error = 2.0919119024258537505420297867259e-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] = -0.13
y[1] (analytic) = 0.87036585738030514045879418929169
y[1] (numeric) = 0.87036585738030514045879418929151
absolute error = 1.8e-31
relative error = 2.0680958297442641123580530376522e-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] = -0.12
y[1] (analytic) = 0.88028779271108064003264938572903
y[1] (numeric) = 0.88028779271108064003264938572885
absolute error = 1.8e-31
relative error = 2.0447858244818103613980206358942e-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] = -0.11
y[1] (analytic) = 0.89022169916282519133505050991655
y[1] (numeric) = 0.89022169916282519133505050991636
absolute error = 1.9e-31
relative error = 2.1342998062019629850527875685954e-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] = -0.1
y[1] (analytic) = 0.90016658335317184769318580158938
y[1] (numeric) = 0.90016658335317184769318580158919
absolute error = 1.9e-31
relative error = 2.1107204323475235749159832101243e-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] = -0.09
y[1] (analytic) = 0.91012145080198895030874601739286
y[1] (numeric) = 0.91012145080198895030874601739268
absolute error = 1.8e-31
relative error = 1.9777580216506927951776751398085e-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] = -0.08
y[1] (analytic) = 0.9200853060308273126931236526855
y[1] (numeric) = 0.92008530603082731269312365268532
absolute error = 1.8e-31
relative error = 1.9563403395333554915168198043397e-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] = -0.07
y[1] (analytic) = 0.93005715266246723602345269319211
y[1] (numeric) = 0.93005715266246723602345269319193
absolute error = 1.8e-31
relative error = 1.9353649341302889538878530045664e-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] = -0.06
y[1] (analytic) = 0.94003599352055540080090886214302
y[1] (numeric) = 0.94003599352055540080090886214283
absolute error = 1.9e-31
relative error = 2.0211992020478452459420952680309e-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] = -0.05
y[1] (analytic) = 0.95002083072932167120513499915451
y[1] (numeric) = 0.95002083072932167120513499915432
absolute error = 1.9e-31
relative error = 1.9999561467945799048246075694872e-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] = -0.04
y[1] (analytic) = 0.96001066581336584054745318828408
y[1] (numeric) = 0.9600106658133658405474531882839
absolute error = 1.8e-31
relative error = 1.8749791685647117186467905904025e-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] = -0.03
y[1] (analytic) = 0.97000449979750433923147365807374
y[1] (numeric) = 0.97000449979750433923147365807355
absolute error = 1.9e-31
relative error = 1.9587538000046795092340390925636e-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] = -0.02
y[1] (analytic) = 0.98000133330666692063350970530702
y[1] (numeric) = 0.98000133330666692063350970530684
absolute error = 1.8e-31
relative error = 1.8367321949721623427010785678790e-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] = -0.01
y[1] (analytic) = 0.9900001666658333353174575617309
y[1] (numeric) = 0.99000016666583333531745756173071
absolute error = 1.9e-31
relative error = 1.9191915960973063700044830402096e-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
y[1] (analytic) = 1
y[1] (numeric) = 0.99999999999999999999999999999981
absolute error = 1.9e-31
relative error = 1.9000000000000000000000000000000e-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] = 0.01
y[1] (analytic) = 1.0099998333341666646825424382691
y[1] (numeric) = 1.0099998333341666646825424382689
absolute error = 2e-31
relative error = 1.9801983465657500986123806865695e-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 = 0.009642
Order of pole (three term test) = -0.8953
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = 1.019998666693333079366490294693
y[1] (numeric) = 1.0199986666933330793664902946928
absolute error = 2e-31
relative error = 1.9607868767943286670247322610197e-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 = 0.01928
Order of pole (three term test) = -0.9025
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 1.0299955002024956607685263419263
y[1] (numeric) = 1.0299955002024956607685263419261
absolute error = 2e-31
relative error = 1.9417560558340330850208568304264e-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 = 0.02891
Order of pole (three term test) = -0.9146
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 1.0399893341866341594525468117159
y[1] (numeric) = 1.0399893341866341594525468117158
absolute error = 1e-31
relative error = 9.6154832278360869901409491156178e-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 = 0.03853
Order of pole (three term test) = -0.9315
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = 1.0499791692706783287948650008455
y[1] (numeric) = 1.0499791692706783287948650008454
absolute error = 1e-31
relative error = 9.5239984684134814593878718895478e-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 = 0.04813
Order of pole (three term test) = -0.9532
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = 1.059964006479444599199091137857
y[1] (numeric) = 1.0599640064794445991990911378569
absolute error = 1e-31
relative error = 9.4342826160804408979170185153014e-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 = 0.05772
Order of pole (three term test) = -0.9798
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = 1.0699428473375327639765473068079
y[1] (numeric) = 1.0699428473375327639765473068078
absolute error = 1e-31
relative error = 9.3462936126767897201305870160174e-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 = 0.06728
Order of pole (three term test) = -1.011
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 1.0799146939691726873068763473145
y[1] (numeric) = 1.0799146939691726873068763473144
absolute error = 1e-31
relative error = 9.2599906787502797218066607825604e-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 = 0.07681
Order of pole (three term test) = -1.047
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 1.0898785491980110496912539826071
y[1] (numeric) = 1.089878549198011049691253982607
absolute error = 1e-31
relative error = 9.1753342676195588013178870947670e-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 = 0.08632
Order of pole (three term test) = -1.088
NO COMPLEX POLE (six term test) for Equation 1
bytes used=76027804, alloc=4455632, time=3.04
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 1.0998334166468281523068141984106
y[1] (numeric) = 1.0998334166468281523068141984105
absolute error = 1e-31
relative error = 9.0922860213576684349079136797722e-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 = 0.09579
Order of pole (three term test) = -1.134
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 1.1097783008371748086649494900834
y[1] (numeric) = 1.1097783008371748086649494900833
absolute error = 1e-31
relative error = 9.0108087286049636460847024873501e-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 = 0.1052
Order of pole (three term test) = -1.184
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 1.119712207288919359967350614271
y[1] (numeric) = 1.1197122072889193599673506142708
absolute error = 2e-31
relative error = 1.7861732568250369765302667137980e-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 = 0.1146
Order of pole (three term test) = -1.239
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 1.1296341426196948595412058107083
y[1] (numeric) = 1.1296341426196948595412058107081
absolute error = 2e-31
relative error = 1.7704847300045926851243791841683e-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 = 0.1239
Order of pole (three term test) = -1.299
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 1.1395431146442364817179883517054
y[1] (numeric) = 1.1395431146442364817179883517052
absolute error = 2e-31
relative error = 1.7550893637090657749553200652311e-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 = 0.1332
Order of pole (three term test) = -1.364
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 1.1494381324735992214977254386876
y[1] (numeric) = 1.1494381324735992214977254386875
absolute error = 1e-31
relative error = 8.6999027763938257948745204743370e-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 = 0.1425
Order of pole (three term test) = -1.433
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 1.159318206614245963311463159686
y[1] (numeric) = 1.1593182066142459633114631596858
absolute error = 2e-31
relative error = 1.7251518940955305009267624609262e-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 = 0.1517
Order of pole (three term test) = -1.507
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 1.1691823490669960101576243766708
y[1] (numeric) = 1.1691823490669960101576243766707
absolute error = 1e-31
relative error = 8.5529857750418229057076547011110e-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 = 0.1608
Order of pole (three term test) = -1.585
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 1.1790295734258241783418027396992
y[1] (numeric) = 1.1790295734258241783418027396991
absolute error = 1e-31
relative error = 8.4815514601077358374588506352999e-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 = 0.1698
Order of pole (three term test) = -1.668
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 1.1888588949765005779928511529813
y[1] (numeric) = 1.1888588949765005779928511529812
absolute error = 1e-31
relative error = 8.4114271611667284337748517832377e-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 = 0.1788
Order of pole (three term test) = -1.755
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 1.1986693307950612154594126271184
y[1] (numeric) = 1.1986693307950612154594126271183
absolute error = 1e-31
relative error = 8.3425843500702022187891560514118e-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 = 0.1877
Order of pole (three term test) = -1.847
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 1.2084598998460995706087124262276
y[1] (numeric) = 1.2084598998460995706087124262276
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 = 0.1966
Order of pole (three term test) = -1.943
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 1.218229623080869319951791005457
y[1] (numeric) = 1.218229623080869319951791005457
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 = 0.2054
Order of pole (three term test) = -2.044
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 1.2279775235351883954046172123601
y[1] (numeric) = 1.2279775235351883954046172123601
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 = 0.214
Order of pole (three term test) = -2.149
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 1.2377026264271345883607920844898
y[1] (numeric) = 1.2377026264271345883607920844898
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 = 0.2226
Order of pole (three term test) = -2.259
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 1.2474039592545229295968487048494
y[1] (numeric) = 1.2474039592545229295968487048494
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 = 0.2311
Order of pole (three term test) = -2.373
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 1.2570805518921550973533884643652
y[1] (numeric) = 1.2570805518921550973533884643652
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 = 0.2395
Order of pole (three term test) = -2.491
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 1.2667314366888311287322865210205
y[1] (numeric) = 1.2667314366888311287322865210205
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 = 0.2479
Order of pole (three term test) = -2.613
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 1.2763556485641137333196695584578
y[1] (numeric) = 1.2763556485641137333196695584578
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 = 0.2561
Order of pole (three term test) = -2.739
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 1.2859522251048355326839402055044
y[1] (numeric) = 1.2859522251048355326839402055043
absolute error = 1e-31
relative error = 7.7763386576703993762228663985883e-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 = 0.2642
Order of pole (three term test) = -2.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 1.295520206661339575105320745685
y[1] (numeric) = 1.295520206661339575105320745685
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 = 0.2722
Order of pole (three term test) = -3.004
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 1.305058636443443501565643323959
y[1] (numeric) = 1.3050586364434435015656433239589
absolute error = 1e-31
relative error = 7.6624909569213548956184351464992e-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 = 0.2801
Order of pole (three term test) = -3.143
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 1.3145665606161177666617575434172
y[1] (numeric) = 1.3145665606161177666617575434171
absolute error = 1e-31
relative error = 7.6070701169464929556001576561235e-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 = 0.2879
Order of pole (three term test) = -3.285
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 1.3240430283948683467001956961702
y[1] (numeric) = 1.3240430283948683467001956961702
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 = 0.2956
Order of pole (three term test) = -3.431
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 1.3334870921408143967817714870308
y[1] (numeric) = 1.3334870921408143967817714870308
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 = 0.3031
Order of pole (three term test) = -3.581
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 1.3428978074554513491896349069176
y[1] (numeric) = 1.3428978074554513491896349069176
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 = 0.3106
Order of pole (three term test) = -3.735
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 1.3522742332750899768499134359207
y[1] (numeric) = 1.3522742332750899768499134359207
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 = 0.3179
Order of pole (three term test) = -3.893
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 1.3616154319649619780372924691272
y[1] (numeric) = 1.3616154319649619780372924691271
absolute error = 1e-31
relative error = 7.3442175854080117807128590095045e-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 = 0.325
Order of pole (three term test) = -4.054
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 1.3709204694129826718454854663492
y[1] (numeric) = 1.3709204694129826718454854663491
absolute error = 1e-31
relative error = 7.2943691651798890258868008186844e-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 = 0.3321
Order of pole (three term test) = -4.219
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=80029484, alloc=4521156, time=3.21
x[1] = 0.39
y[1] (analytic) = 1.3801884151231614282311820978472
y[1] (numeric) = 1.3801884151231614282311820978471
absolute error = 1e-31
relative error = 7.2453875792803605858750550935429e-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 = 0.339
Order of pole (three term test) = -4.387
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 1.3894183423086504916663117567957
y[1] (numeric) = 1.3894183423086504916663117567956
absolute error = 1e-31
relative error = 7.1972563593654957565209332448654e-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 = 0.3458
Order of pole (three term test) = -4.559
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 1.3986093279844228935937976400511
y[1] (numeric) = 1.398609327984422893593797640051
absolute error = 1e-31
relative error = 7.1499594632414575740331010403020e-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 = 0.3524
Order of pole (three term test) = -4.734
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 1.4077604530595701859727871580863
y[1] (numeric) = 1.4077604530595701859727871580862
absolute error = 1e-31
relative error = 7.1034812622178727307631452987902e-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 = 0.3589
Order of pole (three term test) = -4.912
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 1.4168708024292107662169186726246
y[1] (numeric) = 1.4168708024292107662169186726244
absolute error = 2e-31
relative error = 1.4115613057810352777553867719432e-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 = 0.3653
Order of pole (three term test) = -5.093
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 1.4259394650659996027697207507799
y[1] (numeric) = 1.4259394650659996027697207507798
absolute error = 1e-31
relative error = 7.0129204254383618154964292748691e-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 = 0.3715
Order of pole (three term test) = -5.278
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 1.4349655341112302104208442462319
y[1] (numeric) = 1.4349655341112302104208442462318
absolute error = 1e-31
relative error = 6.9688084921103463695038126770442e-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 = 0.3776
Order of pole (three term test) = -5.466
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 1.4439481069655197652415136439289
y[1] (numeric) = 1.4439481069655197652415136439288
absolute error = 1e-31
relative error = 6.9254566363989086005517729136524e-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 = 0.3835
Order of pole (three term test) = -5.657
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 1.4528862853790682907032748003964
y[1] (numeric) = 1.4528862853790682907032748003963
absolute error = 1e-31
relative error = 6.8828511223718581594824423813170e-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 = 0.3892
Order of pole (three term test) = -5.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 1.4617791755414828891366429425886
y[1] (numeric) = 1.4617791755414828891366429425885
absolute error = 1e-31
relative error = 6.8409785604557727842596851575514e-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 = 0.3949
Order of pole (three term test) = -6.047
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 1.470625888171158036181358337188
y[1] (numeric) = 1.4706258881711580361813583371878
absolute error = 2e-31
relative error = 1.3599651795108553335897032276593e-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 = 0.4003
Order of pole (three term test) = -6.246
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 1.4794255386042030002732879352156
y[1] (numeric) = 1.4794255386042030002732879352154
absolute error = 2e-31
relative error = 1.3518760815004887495457772563323e-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 = 0.4056
Order of pole (three term test) = -6.448
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 1.4881772468829074945001302376746
y[1] (numeric) = 1.4881772468829074945001302376744
absolute error = 2e-31
relative error = 1.3439259363688979012428704319126e-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 = 0.4107
Order of pole (three term test) = -6.653
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 1.4968801378437367143344589425478
y[1] (numeric) = 1.4968801378437367143344589425476
absolute error = 2e-31
relative error = 1.3361123241844934559451623257491e-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 = 0.4157
Order of pole (three term test) = -6.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 1.5055333412048469618136610224661
y[1] (numeric) = 1.5055333412048469618136610224659
absolute error = 2e-31
relative error = 1.3284328850528422535436688681207e-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 = 0.4205
Order of pole (three term test) = -7.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 1.5141359916531131046772806829582
y[1] (numeric) = 1.5141359916531131046772806829581
absolute error = 1e-31
relative error = 6.6044265872592697963164134977544e-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 = 0.4251
Order of pole (three term test) = -7.281
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 1.5226872289306591677883781077573
y[1] (numeric) = 1.5226872289306591677883781077571
absolute error = 2e-31
relative error = 1.3134673766224100386001291625475e-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 = 0.4295
Order of pole (three term test) = -7.496
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 1.531186197920883403851869441112
y[1] (numeric) = 1.5311861979208834038518694411118
absolute error = 2e-31
relative error = 1.3061768730123704185584278128488e-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 = 0.4338
Order of pole (three term test) = -7.712
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 1.5396320487339692409944634930788
y[1] (numeric) = 1.5396320487339692409944634930786
absolute error = 2e-31
relative error = 1.2990116707719800529642780620819e-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 = 0.4379
Order of pole (three term test) = -7.931
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 1.5480239367918735561826960595765
y[1] (numeric) = 1.5480239367918735561826960595762
absolute error = 3e-31
relative error = 1.9379545294481706612613473985737e-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 = 0.4418
Order of pole (three term test) = -8.151
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 1.5563610229127837757225433788758
y[1] (numeric) = 1.5563610229127837757225433788755
absolute error = 3e-31
relative error = 1.9275733302453152399987334892936e-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 = 0.4456
Order of pole (three term test) = -8.373
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 1.5646424733950353572009454456587
y[1] (numeric) = 1.5646424733950353572009454456584
absolute error = 3e-31
relative error = 1.9173709336232307994808196421009e-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 = 0.4492
Order of pole (three term test) = -8.598
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 1.5728674601004812611909760321627
y[1] (numeric) = 1.5728674601004812611909760321625
absolute error = 2e-31
relative error = 1.2715629579317711552779454373119e-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 = 0.4526
Order of pole (three term test) = -8.824
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 1.5810351605373050758429632275822
y[1] (numeric) = 1.581035160537305075842963227582
absolute error = 2e-31
relative error = 1.2649940051430053586700397545788e-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 = 0.4558
Order of pole (three term test) = -9.051
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 1.5891447579422695131181120907946
y[1] (numeric) = 1.5891447579422695131181120907944
absolute error = 2e-31
relative error = 1.2585385881332379195706824475417e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.85
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4588
Order of pole (three term test) = -9.281
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 1.5971954413623920518835462392079
y[1] (numeric) = 1.5971954413623920518835462392077
absolute error = 2e-31
relative error = 1.2521949087796166065122300387062e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4617
Order of pole (three term test) = -9.511
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 1.6051864057360395603725216786059
y[1] (numeric) = 1.6051864057360395603725216786057
absolute error = 2e-31
relative error = 1.2459612122636456400116671165425e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4643
Order of pole (three term test) = -9.743
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 1.6131168519734337886151454793963
y[1] (numeric) = 1.6131168519734337886151454793961
absolute error = 2e-31
relative error = 1.2398357859526829489548511754486e-29 %
Correct digits = 31
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 = 0.4668
Order of pole (three term test) = -9.977
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 1.6209859870365596803574439141266
y[1] (numeric) = 1.6209859870365596803574439141264
absolute error = 2e-31
relative error = 1.2338169583170443819415541659175e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.05
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4691
Order of pole (three term test) = -10.21
NO COMPLEX POLE (six term test) for Equation 1
bytes used=84032096, alloc=4521156, time=3.37
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 1.6287930240184685137041781874202
y[1] (numeric) = 1.6287930240184685137041781874201
absolute error = 1e-31
relative error = 6.1395154894073344668541915317869e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4712
Order of pole (three term test) = -10.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 1.6365371822219679402374292070087
y[1] (numeric) = 1.6365371822219679402374292070086
absolute error = 1e-31
relative error = 6.1104630610486631158265560320066e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4731
Order of pole (three term test) = -10.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 1.6442176872376910536726143513987
y[1] (numeric) = 1.6442176872376910536726143513986
absolute error = 1e-31
relative error = 6.0819197346065175188260274521277e-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
Radius of convergence (three term test) for eq 1 = 0.4749
Order of pole (three term test) = -10.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 1.6518337710215366812101279728528
y[1] (numeric) = 1.6518337710215366812101279728527
absolute error = 1e-31
relative error = 6.0538779236943083185531773730902e-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
Radius of convergence (three term test) for eq 1 = 0.4764
Order of pole (three term test) = -11.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 1.6593846719714731536180038326482
y[1] (numeric) = 1.659384671971473153618003832648
absolute error = 2e-31
relative error = 1.2052660445656945536150895065502e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4777
Order of pole (three term test) = -11.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 1.6668696350036978737325941307615
y[1] (numeric) = 1.6668696350036978737325941307614
absolute error = 1e-31
relative error = 5.9992694029595274613422544528161e-30 %
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
Radius of convergence (three term test) for eq 1 = 0.4789
Order of pole (three term test) = -11.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 1.6742879116281450674838811576082
y[1] (numeric) = 1.674287911628145067483881157608
absolute error = 2e-31
relative error = 1.1945376814284703077492832633462e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -11.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 1.6816387600233341667332419527799
y[1] (numeric) = 1.6816387600233341667332419527797
absolute error = 2e-31
relative error = 1.1893160692681990159058726194793e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -12.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 1.6889214451105513391477556387697
y[1] (numeric) = 1.6889214451105513391477556387695
absolute error = 2e-31
relative error = 1.1841876990726981171496781810990e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -12.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 1.6961352386273567470198837344522
y[1] (numeric) = 1.696135238627356747019883734452
absolute error = 2e-31
relative error = 1.1791512577844641788356820844134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 1.7032794192004101843678973251179
y[1] (numeric) = 1.7032794192004101843678973251177
absolute error = 2e-31
relative error = 1.1742054635632729773279155190613e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 1.7103532724176078098140288749692
y[1] (numeric) = 1.710353272417607809814028874969
absolute error = 2e-31
relative error = 1.1693490650460606702297887705380e-29 %
Correct digits = 31
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
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 1.7173560908995227616271746105814
y[1] (numeric) = 1.7173560908995227616271746105812
absolute error = 2e-31
relative error = 1.1645808406295243207824381777694e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 1.7242871743701425109281768525145
y[1] (numeric) = 1.7242871743701425109281768525144
absolute error = 1e-31
relative error = 5.7994979888734933269737662144258e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.04
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -13.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 1.7311458297268958793813133646877
y[1] (numeric) = 1.7311458297268958793813133646876
absolute error = 1e-31
relative error = 5.7765208616639718042472695734813e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -13.81
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 1.7379313711099627187285802261381
y[1] (numeric) = 1.737931371109962718728580226138
absolute error = 1e-31
relative error = 5.7539671394580506308555960959128e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.29
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -14.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 1.7446431199708593212565726706296
y[1] (numeric) = 1.7446431199708593212565726706296
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 = 17.93
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4789
Order of pole (three term test) = -14.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 1.7512804051402927027120715242355
y[1] (numeric) = 1.7512804051402927027120715242354
absolute error = 1e-31
relative error = 5.7101078563138000370993153595601e-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
Radius of convergence (three term test) for eq 1 = 0.4778
Order of pole (three term test) = -14.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 1.7578425628952769722945887295286
y[1] (numeric) = 1.7578425628952769722945887295286
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 = 17.22
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4764
Order of pole (three term test) = -14.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 1.7643289370255050781448028237228
y[1] (numeric) = 1.7643289370255050781448028237228
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4749
Order of pole (three term test) = -15.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 1.770738878898969291209645130756
y[1] (numeric) = 1.7707388788989692912096451307559
absolute error = 1e-31
relative error = 5.6473600479241280545894125024680e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4732
Order of pole (three term test) = -15.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 1.7770717475268238654903337129732
y[1] (numeric) = 1.7770717475268238654903337129731
absolute error = 1e-31
relative error = 5.6272348113784054238570141075072e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4712
Order of pole (three term test) = -15.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 1.7833269096274833884613823157136
y[1] (numeric) = 1.7833269096274833884613823157135
absolute error = 1e-31
relative error = 5.6074968341552619311245879096031e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4691
Order of pole (three term test) = -15.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 1.7895037396899504118789575178716
y[1] (numeric) = 1.7895037396899504118789575178715
absolute error = 1e-31
relative error = 5.5881414373197124198260167760830e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4668
Order of pole (three term test) = -15.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 1.7956016200363660302682761024816
y[1] (numeric) = 1.7956016200363660302682761024816
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 = 15.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4644
Order of pole (three term test) = -16.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 1.8016199408837771520843192159106
y[1] (numeric) = 1.8016199408837771520843192159106
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 = 14.92
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4617
Order of pole (three term test) = -16.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 1.8075581004051142868702197986342
y[1] (numeric) = 1.8075581004051142868702197986341
absolute error = 1e-31
relative error = 5.5323256263567825837214471555805e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4589
Order of pole (three term test) = -16.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 1.8134155047893737506854221021026
y[1] (numeric) = 1.8134155047893737506854221021025
absolute error = 1e-31
relative error = 5.5144559940009386778827118227612e-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 = 0.4558
Order of pole (three term test) = -16.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=88033672, alloc=4521156, time=3.54
x[1] = 0.96
y[1] (analytic) = 1.8191915683009982716332221464304
y[1] (numeric) = 1.8191915683009982716332221464304
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 = 0.4526
Order of pole (three term test) = -17.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 1.8248857133384500574766200378563
y[1] (numeric) = 1.8248857133384500574766200378563
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 = 0.4492
Order of pole (three term test) = -17.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 1.8304973704919704680845332877192
y[1] (numeric) = 1.8304973704919704680845332877191
absolute error = 1e-31
relative error = 5.4629961021535732938417309594081e-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 = 0.4457
Order of pole (three term test) = -17.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 1.8360259786005205167892594115471
y[1] (numeric) = 1.8360259786005205167892594115471
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 = 0.4419
Order of pole (three term test) = -17.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 1.8414709848078965066525023216303
y[1] (numeric) = 1.8414709848078965066525023216303
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 = 0.438
Order of pole (three term test) = -18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 1.846831844618015190123098784782
y[1] (numeric) = 1.846831844618015190123098784782
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 = 0.4339
Order of pole (three term test) = -18.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 1.8521080219493629236165499854554
y[1] (numeric) = 1.8521080219493629236165499854554
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 = 0.4296
Order of pole (three term test) = -18.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 1.8572989891886033721462743852944
y[1] (numeric) = 1.8572989891886033721462743852944
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 = 0.4252
Order of pole (three term test) = -18.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 1.8624042272433384032807916921162
y[1] (numeric) = 1.8624042272433384032807916921161
absolute error = 1e-31
relative error = 5.3694036201805817188446247790652e-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 = 0.4205
Order of pole (three term test) = -18.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 1.8674232255940168943814094850003
y[1] (numeric) = 1.8674232255940168943814094850002
absolute error = 1e-31
relative error = 5.3549724898698611141401121522493e-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 = 0.4158
Order of pole (three term test) = -19.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 1.8723554823449862622829459219974
y[1] (numeric) = 1.8723554823449862622829459219973
absolute error = 1e-31
relative error = 5.3408661412285568070262524031186e-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 = 0.4108
Order of pole (three term test) = -19.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 1.8772005042746816103070632577768
y[1] (numeric) = 1.8772005042746816103070632577767
absolute error = 1e-31
relative error = 5.3270814583889269437213141478418e-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 = 0.4057
Order of pole (three term test) = -19.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 1.8819578068849474737353349876248
y[1] (numeric) = 1.8819578068849474737353349876246
absolute error = 2e-31
relative error = 1.0627230816138424591468231301519e-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 = 0.4004
Order of pole (three term test) = -19.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 1.886626914449487231608600628636
y[1] (numeric) = 1.8866269144494872316086006286359
absolute error = 1e-31
relative error = 5.3004650381116680305033592422926e-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 = 0.395
Order of pole (three term test) = -19.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 1.8912073600614353399518025778717
y[1] (numeric) = 1.8912073600614353399518025778716
absolute error = 1e-31
relative error = 5.2876274760664810486298889444334e-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 = 0.3894
Order of pole (three term test) = -20.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 1.8956986856800476292406259593394
y[1] (numeric) = 1.8956986856800476292406259593393
absolute error = 1e-31
relative error = 5.2750999278203755255959132055767e-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 = 0.3836
Order of pole (three term test) = -20.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 1.9001004421765049971191032473392
y[1] (numeric) = 1.9001004421765049971191032473391
absolute error = 1e-31
relative error = 5.2628796762687535009278191791115e-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 = 0.3777
Order of pole (three term test) = -20.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 1.9044121893788259160370815224114
y[1] (numeric) = 1.9044121893788259160370815224113
absolute error = 1e-31
relative error = 5.2509640800302600469780576938800e-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 = 0.3717
Order of pole (three term test) = -20.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 1.9086334961158832645942155781022
y[1] (numeric) = 1.9086334961158832645942155781021
absolute error = 1e-31
relative error = 5.2393505722027037878934821367571e-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 = 0.3655
Order of pole (three term test) = -20.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 1.9127639402605210809440330497537
y[1] (numeric) = 1.9127639402605210809440330497536
absolute error = 1e-31
relative error = 5.2280366591593033891786913326237e-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 = 0.3591
Order of pole (three term test) = -21.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 1.9168031087717669266186616668743
y[1] (numeric) = 1.9168031087717669266186616668743
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 = 0.3526
Order of pole (three term test) = -21.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 1.920750597736135639573013008962
y[1] (numeric) = 1.920750597736135639573013008962
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 = 0.346
Order of pole (three term test) = -21.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 1.9246060124080203461075380258748
y[1] (numeric) = 1.9246060124080203461075380258747
absolute error = 1e-31
relative error = 5.1958686274123412040520623721069e-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 = 0.3392
Order of pole (three term test) = -21.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 1.9283689672491666926020211116027
y[1] (numeric) = 1.9283689672491666926020211116026
absolute error = 1e-31
relative error = 5.1857295827909311668193449338272e-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 = 0.3323
Order of pole (three term test) = -21.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 1.9320390859672263496701344354948
y[1] (numeric) = 1.9320390859672263496701344354948
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 = 0.3253
Order of pole (three term test) = -21.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 1.9356160015533859334164648885436
y[1] (numeric) = 1.9356160015533859334164648885436
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 = 0.3181
Order of pole (three term test) = -22.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 1.9390993563190675809352452718884
y[1] (numeric) = 1.9390993563190675809352452718884
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 = 0.3108
Order of pole (three term test) = -22.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 1.9424888019316975100238235653892
y[1] (numeric) = 1.9424888019316975100238235653893
absolute error = 1e-31
relative error = 5.1480348252486984463185370933518e-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 = 0.3034
Order of pole (three term test) = -22.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 1.9457839994495389862847059630818
y[1] (numeric) = 1.9457839994495389862847059630818
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 = 0.2959
Order of pole (three term test) = -22.49
bytes used=92035032, alloc=4521156, time=3.70
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 1.948984619355586214348490847036
y[1] (numeric) = 1.9489846193555862143484908470361
absolute error = 1e-31
relative error = 5.1308768169275793224616963221774e-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 = 0.2882
Order of pole (three term test) = -22.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 1.9520903415905157638568162214254
y[1] (numeric) = 1.9520903415905157638568162214255
absolute error = 1e-31
relative error = 5.1227137325274828493281968055245e-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 = 0.2804
Order of pole (three term test) = -22.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 1.9551008555846922350901817421829
y[1] (numeric) = 1.955100855584692235090181742183
absolute error = 1e-31
relative error = 5.1148256477077757504971036809715e-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 = 0.2725
Order of pole (three term test) = -22.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 1.9580158602892249637007538591603
y[1] (numeric) = 1.9580158602892249637007538591604
absolute error = 1e-31
relative error = 5.1072109285789273967217335580500e-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 = 0.2645
Order of pole (three term test) = -23.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 1.9608350642060726589055612912854
y[1] (numeric) = 1.9608350642060726589055612912855
absolute error = 1e-31
relative error = 5.0998680014164907043302000758074e-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 = 0.2564
Order of pole (three term test) = -23.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 1.9635581854171929647013486300396
y[1] (numeric) = 1.9635581854171929647013486300397
absolute error = 1e-31
relative error = 5.0927953519621938824785291886094e-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 = 0.2482
Order of pole (three term test) = -23.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 1.9661849516127340291692578059375
y[1] (numeric) = 1.9661849516127340291692578059376
absolute error = 1e-31
relative error = 5.0859915247533800906999030424176e-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 = 0.2399
Order of pole (three term test) = -23.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 1.9687151001182652627358998459728
y[1] (numeric) = 1.9687151001182652627358998459729
absolute error = 1e-31
relative error = 5.0794551224802801103037495575985e-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 = 0.2315
Order of pole (three term test) = -23.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 1.9711483779210445623376830377638
y[1] (numeric) = 1.9711483779210445623376830377639
absolute error = 1e-31
relative error = 5.0731848053706262018646746885778e-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 = 0.223
Order of pole (three term test) = -23.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 1.9734845416953193747878703480896
y[1] (numeric) = 1.9734845416953193747878703480897
absolute error = 1e-31
relative error = 5.0671792906011378093288912483107e-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 = 0.2145
Order of pole (three term test) = -23.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 1.9757233578266590692611135392652
y[1] (numeric) = 1.9757233578266590692611135392654
absolute error = 2e-31
relative error = 1.0122874703470863415713470931436e-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 = 0.2058
Order of pole (three term test) = -23.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 1.9778646024353161856784924394266
y[1] (numeric) = 1.9778646024353161856784924394268
absolute error = 2e-31
relative error = 1.0111915636375861210377309014810e-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 = 0.197
Order of pole (three term test) = -23.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 1.9799080613986142228876885048919
y[1] (numeric) = 1.9799080613986142228876885048921
absolute error = 2e-31
relative error = 1.0101479149426730243932814239125e-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 = 0.1882
Order of pole (three term test) = -24.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 1.981853530372359727878131085206
y[1] (numeric) = 1.9818535303723597278781310852062
absolute error = 2e-31
relative error = 1.0091563121842969042260942984493e-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 = 0.1793
Order of pole (three term test) = -24.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 1.9837008148112765448400382244429
y[1] (numeric) = 1.9837008148112765448400382244431
absolute error = 2e-31
relative error = 1.0082165541633223111072689310665e-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 = 0.1703
Order of pole (three term test) = -24.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 1.9854497299884601806594745788061
y[1] (numeric) = 1.9854497299884601806594745788063
absolute error = 2e-31
relative error = 1.0073284504723392761674314487082e-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) = -24.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 1.9871001010138503414290888619422
y[1] (numeric) = 1.9871001010138503414290888619424
absolute error = 2e-31
relative error = 1.0064918214133087322649379412998e-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) = -24.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 1.9886517628517197927362734733357
y[1] (numeric) = 1.9886517628517197927362734733359
absolute error = 2e-31
relative error = 1.0057064979199811606020492374513e-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) = -24.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 1.9901045603371777948572914954818
y[1] (numeric) = 1.990104560337177794857291495482
absolute error = 2e-31
relative error = 1.0049723214850307406707637042120e-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) = -24.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 1.991458348191686462527604463958
y[1] (numeric) = 1.9914583481916864625276044639582
absolute error = 2e-31
relative error = 1.0042891440918509065468827275543e-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) = -24.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 1.992712991037588497665354134323
y[1] (numeric) = 1.9927129910375884976653541343232
absolute error = 2e-31
relative error = 1.0036568281509607760961452352316e-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) = -24.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 1.99386836341164484228683230125
y[1] (numeric) = 1.9938683634116448422868323012502
absolute error = 2e-31
relative error = 1.0030752464409754258069740119821e-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) = -24.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 1.9949243497775808978599284627356
y[1] (numeric) = 1.9949243497775808978599284627357
absolute error = 1e-31
relative error = 5.0127214102704821841242620645313e-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 = 0.09641
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 1.9958808445376400564840751325627
y[1] (numeric) = 1.9958808445376400564840751325628
absolute error = 1e-31
relative error = 5.0103191417304127067601727394102e-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 = 0.08695
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 1.9967377520431433885532007170437
y[1] (numeric) = 1.9967377520431433885532007170438
absolute error = 1e-31
relative error = 5.0081689444533177841620622655524e-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 = 0.07747
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 1.9974949866040544309417233711415
y[1] (numeric) = 1.9974949866040544309417233711416
absolute error = 1e-31
relative error = 5.0062703871918205606571889060541e-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 = 0.06795
Order of pole (three term test) = -24.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 1.9981524724975481192427378648367
y[1] (numeric) = 1.9981524724975481192427378648368
absolute error = 1e-31
relative error = 5.0046230893985347452258781746880e-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 = 0.0584
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=96036392, alloc=4521156, time=3.86
x[1] = 1.52
y[1] (analytic) = 1.9987101439755830071723123941168
y[1] (numeric) = 1.9987101439755830071723123941169
absolute error = 1e-31
relative error = 5.0032267210638441383542159379082e-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 = 0.04883
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 1.999167945271476015924265068709
y[1] (numeric) = 1.999167945271476015924265068709
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 = 0.03924
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 1.99952583060547905600596353844
y[1] (numeric) = 1.9995258306054790560059635384401
absolute error = 1e-31
relative error = 5.0011857045987181874359925072167e-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 = 0.02964
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 1.9997837641893569638976113476345
y[1] (numeric) = 1.9997837641893569638976113476345
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 = 0.02002
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 1.9999417202299662957451700234135
y[1] (numeric) = 1.9999417202299662957451700234135
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 = 0.0104
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 1.9999996829318346202105299238233
y[1] (numeric) = 1.9999996829318346202105299238233
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 = 0.0007668
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 1.9999576464987400525517942322517
y[1] (numeric) = 1.9999576464987400525517942322517
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] = 1.59
y[1] (analytic) = 1.9998156151342908719815843437455
y[1] (numeric) = 1.9998156151342908719815843437455
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] = 1.6
y[1] (analytic) = 1.9995736030415051643421138255462
y[1] (numeric) = 1.9995736030415051643421138255462
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] = 1.61
y[1] (analytic) = 1.9992316344213905321324131478443
y[1] (numeric) = 1.9992316344213905321324131478443
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] = 1.62
y[1] (analytic) = 1.9987897434705240139155188912468
y[1] (numeric) = 1.9987897434705240139155188912468
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] = 1.63
y[1] (analytic) = 1.9982479743776324551116699849331
y[1] (numeric) = 1.9982479743776324551116699849331
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] = 1.64
y[1] (analytic) = 1.9976063813191736721375819743679
y[1] (numeric) = 1.9976063813191736721375819743679
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] = 1.65
y[1] (analytic) = 1.9968650284539188517717030402022
y[1] (numeric) = 1.9968650284539188517717030402022
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] = 1.66
y[1] (analytic) = 1.996023989916536727501000590613
y[1] (numeric) = 1.996023989916536727501000590613
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] = 1.67
y[1] (analytic) = 1.9950833498101801744262972465342
y[1] (numeric) = 1.9950833498101801744262972465343
absolute error = 1e-31
relative error = 5.0123219167517177023992799637250e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9940432021980759640604878691936
y[1] (numeric) = 1.9940432021980759640604878691936
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] = 1.69
y[1] (analytic) = 1.9929036510941185200371492939456
y[1] (numeric) = 1.9929036510941185200371492939456
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] = 1.7
y[1] (analytic) = 1.9916648104524686153461333986479
y[1] (numeric) = 1.9916648104524686153461333986479
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] = 1.71
y[1] (analytic) = 1.9903268041561580512177522238611
y[1] (numeric) = 1.9903268041561580512177522238612
absolute error = 1e-31
relative error = 5.0243005214612057356568071563363e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9888897660047014571781706570855
y[1] (numeric) = 1.9888897660047014571781706570855
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] = 1.73
y[1] (analytic) = 1.9873538397007164510856776762221
y[1] (numeric) = 1.9873538397007164510856776762221
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] = 1.74
y[1] (analytic) = 1.9857191788355534971206826956656
y[1] (numeric) = 1.9857191788355534971206826956656
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) = 1.983985946873936898731662936968
y[1] (numeric) = 1.983985946873936898731662936968
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] = 1.76
y[1] (analytic) = 1.982154317137618462424968099456
y[1] (numeric) = 1.982154317137618462424968099456
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] = 1.77
y[1] (analytic) = 1.9802244727880454670184814488984
y[1] (numeric) = 1.9802244727880454670184814488985
absolute error = 1e-31
relative error = 5.0499325391734799011994076432569e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 1.9781966068080446715477686473056
y[1] (numeric) = 1.9781966068080446715477686473057
absolute error = 1e-31
relative error = 5.0551092674937315569886011239238e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9760709219825241934086604331086
y[1] (numeric) = 1.9760709219825241934086604331087
absolute error = 1e-31
relative error = 5.0605471133431501111877332917962e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9738476308781951865323731788434
y[1] (numeric) = 1.9738476308781951865323731788434
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=100037052, alloc=4521156, time=4.02
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 1.9715269558223153474084512690904
y[1] (numeric) = 1.9715269558223153474084512690904
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] = 1.82
y[1] (analytic) = 1.969109128880456374587215318498
y[1] (numeric) = 1.9691091288804563745872153184981
absolute error = 1e-31
relative error = 5.0784386976487858095515012631170e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9665943918332976048972389297428
y[1] (numeric) = 1.9665943918332976048972389297429
absolute error = 1e-31
relative error = 5.0849326335553134481580791756847e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9639829961524481469948936717271
y[1] (numeric) = 1.9639829961524481469948936717272
absolute error = 1e-31
relative error = 5.0916937771816537247673939979239e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9612752029752999300124591686361
y[1] (numeric) = 1.9612752029752999300124591686362
absolute error = 1e-31
relative error = 5.0987235166333456303367967199455e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9584712830789141819789777659032
y[1] (numeric) = 1.9584712830789141819789777659033
absolute error = 1e-31
relative error = 5.1060232980689879986702279614650e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9555715168529439493442504921726
y[1] (numeric) = 1.9555715168529439493442504921727
absolute error = 1e-31
relative error = 5.1135946263385799919092474160174e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9525761942715953653314574258151
y[1] (numeric) = 1.9525761942715953653314574258152
absolute error = 1e-31
relative error = 5.1214390656496147396653627917283e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9494856148646304709682016721383
y[1] (numeric) = 1.9494856148646304709682016721384
absolute error = 1e-31
relative error = 5.1295582402614373141324107594334e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.946300087687414488489709611635
y[1] (numeric) = 1.946300087687414488489709611635
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] = 1.91
y[1] (analytic) = 1.9430199312900105423618865769482
y[1] (numeric) = 1.9430199312900105423618865769483
absolute error = 1e-31
relative error = 5.1466275970523864581213008447325e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.939645473685324918426371339687
y[1] (numeric) = 1.9396454736853249184263713396871
absolute error = 1e-31
relative error = 5.1555813346652507782178678239525e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9361770523163060466151293727488
y[1] (numeric) = 1.9361770523163060466151293727489
absolute error = 1e-31
relative error = 5.1648169200418439720928143642985e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9326150140222004873089793388657
y[1] (numeric) = 1.9326150140222004873089793388658
absolute error = 1e-31
relative error = 5.1743362891442005597916062389953e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9289597150038692957132970350915
y[1] (numeric) = 1.9289597150038692957132970350916
absolute error = 1e-31
relative error = 5.1841414427775859610102511549344e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.92521152078816823258555628949
y[1] (numeric) = 1.9252115207881682325855562894901
absolute error = 1e-31
relative error = 5.1942344474990828103291395378429e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9213708061913953832639509971532
y[1] (numeric) = 1.9213708061913953832639509971532
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] = 1.98
y[1] (analytic) = 1.917437955281809840204735217402
y[1] (numeric) = 1.917437955281809840204735217402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.9134133613412251971287932710576
y[1] (numeric) = 1.9134133613412251971287932710576
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
y[1] (analytic) = 1.9092974268256816953960198659117
y[1] (numeric) = 1.9092974268256816953960198659117
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) = 1.9050905633252009553600997102737
y[1] (numeric) = 1.9050905633252009553600997102737
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] = 2.02
y[1] (analytic) = 1.9007931915226273171970135245537
y[1] (numeric) = 1.9007931915226273171970135245537
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] = 2.03
y[1] (analytic) = 1.8964057411515599070388888319676
y[1] (numeric) = 1.8964057411515599070388888319676
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] = 2.04
y[1] (analytic) = 1.8919286509533796351715256485842
y[1] (numeric) = 1.8919286509533796351715256485842
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8873623686333754235599666046803
y[1] (numeric) = 1.8873623686333754235599666046803
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) = 1.8827073508159740500427975851999
y[1] (numeric) = 1.8827073508159740500427975851999
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) = 1.8779640629990780861734511204438
y[1] (numeric) = 1.8779640629990780861734511204438
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) = 1.8731329795075164948766768050246
y[1] (numeric) = 1.8731329795075164948766768050246
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
bytes used=104038124, alloc=4521156, time=4.19
x[1] = 2.09
y[1] (analytic) = 1.8682145834456125428216220587275
y[1] (numeric) = 1.8682145834456125428216220587275
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) = 1.863209366648873770680759313269
y[1] (numeric) = 1.863209366648873770680759313269
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] = 2.11
y[1] (analytic) = 1.8581178296348088522373755083107
y[1] (numeric) = 1.8581178296348088522373755083107
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) = 1.8529404815528762606147273336542
y[1] (numeric) = 1.8529404815528762606147273336542
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] = 2.13
y[1] (analytic) = 1.8476778401335697467185299963159
y[1] (numeric) = 1.8476778401335697467185299963159
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) = 1.8423304316366457213025066370689
y[1] (numeric) = 1.8423304316366457213025066370689
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) = 1.8368987907984977178756481370438
y[1] (numeric) = 1.8368987907984977178756481370438
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) = 1.8313834607786831989610381203463
y[1] (numeric) = 1.8313834607786831989610381203463
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] = 2.17
y[1] (analytic) = 1.8257849931056080529810564239434
y[1] (numeric) = 1.8257849931056080529810564239434
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) = 1.8201039476213742132740097460839
y[1] (numeric) = 1.820103947621374213274009746084
absolute error = 1e-31
relative error = 5.4941916988140298536327700705833e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.814340892425795914434327645905
y[1] (numeric) = 1.8143408924257959144343276459051
absolute error = 1e-31
relative error = 5.5116433971952635456861645933305e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 1.8084964038195901843040369104161
y[1] (numeric) = 1.8084964038195901843040369104162
absolute error = 1e-31
relative error = 5.5294552861038301567256314290129e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.56
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 1.802571066246747252518974042556
y[1] (numeric) = 1.802571066246747252518974042556
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 = 14.87
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] = 2.22
y[1] (analytic) = 1.7965654722360866385208567496092
y[1] (numeric) = 1.7965654722360866385208567496092
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 = 15.18
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] = 2.23
y[1] (analytic) = 1.7904802223420047633777101271885
y[1] (numeric) = 1.7904802223420047633777101271886
absolute error = 1e-31
relative error = 5.5850938062413689785812703547248e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.5
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] = 2.24
y[1] (analytic) = 1.7843159250844200106020886706045
y[1] (numeric) = 1.7843159250844200106020886706046
absolute error = 1e-31
relative error = 5.6043886956436133623004795320691e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.82
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 1.7780731968879212414109666755878
y[1] (numeric) = 1.7780731968879212414109666755879
absolute error = 1e-31
relative error = 5.6240654307722171190821043758260e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.15
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] = 2.26
y[1] (analytic) = 1.7717526620201258495250616377403
y[1] (numeric) = 1.7717526620201258495250616377405
absolute error = 2e-31
relative error = 1.1288257344677162523309845369758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.48
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] = 2.27
y[1] (analytic) = 1.7653549525292535196507426019347
y[1] (numeric) = 1.7653549525292535196507426019349
absolute error = 2e-31
relative error = 1.1329166393050681408669489206921e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.82
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 1.7588807081809219322166535763009
y[1] (numeric) = 1.7588807081809219322166535763011
absolute error = 2e-31
relative error = 1.1370867795056150350099992146104e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.16
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] = 2.29
y[1] (analytic) = 1.7523305763941707347419082779736
y[1] (numeric) = 1.7523305763941707347419082779738
absolute error = 2e-31
relative error = 1.1413371580352532145903746172057e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 1.7457052121767201773854062116435
y[1] (numeric) = 1.7457052121767201773854062116436
absolute error = 1e-31
relative error = 5.7283440126360154499912976992372e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.87
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] = 2.31
y[1] (analytic) = 1.7390052780594708867587641920983
y[1] (numeric) = 1.7390052780594708867587641920984
absolute error = 1e-31
relative error = 5.7504138291971404760439061093416e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.23
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] = 2.32
y[1] (analytic) = 1.7322314440302513279708986777247
y[1] (numeric) = 1.7322314440302513279708986777248
absolute error = 1e-31
relative error = 5.7729006331473579286921492026410e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.6
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] = 2.33
y[1] (analytic) = 1.7253843874668195801028441924754
y[1] (numeric) = 1.7253843874668195801028441924755
absolute error = 1e-31
relative error = 5.7958099497363786177046107865010e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.98
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] = 2.34
y[1] (analytic) = 1.718464793069126124879428686794
y[1] (numeric) = 1.7184647930691261248794286867941
absolute error = 1e-31
relative error = 5.8191474392328414070824568526825e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 1.7114733527908444222024911820132
y[1] (numeric) = 1.7114733527908444222024911820133
absolute error = 1e-31
relative error = 5.8429189000771308407099791936325e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.24
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] = 2.36
y[1] (analytic) = 1.7044107657701761194310307129327
y[1] (numeric) = 1.7044107657701761194310307129328
absolute error = 1e-31
relative error = 5.8671302721332415280843951046881e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.86
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=108039920, alloc=4521156, time=4.34
x[1] = 2.37
y[1] (analytic) = 1.6972777382599378138296964202892
y[1] (numeric) = 1.6972777382599378138296964202893
absolute error = 1e-31
relative error = 5.8917876400429766323243923406339e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.48
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] = 2.38
y[1] (analytic) = 1.6900749835569363594511131070202
y[1] (numeric) = 1.6900749835569363594511131070203
absolute error = 1e-31
relative error = 5.9168972366858972633842040931045e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.12
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] = 2.39
y[1] (analytic) = 1.682803221930639780862500311013
y[1] (numeric) = 1.6828032219306397808625003110132
absolute error = 2e-31
relative error = 1.1884930893497149134414363654770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 1.6754631805511509265657715253413
y[1] (numeric) = 1.6754631805511509265657715253414
absolute error = 1e-31
relative error = 5.9684988104068370815749986399565e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.4
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] = 2.41
y[1] (analytic) = 1.6680555934164910646857498006547
y[1] (numeric) = 1.6680555934164910646857498006548
absolute error = 1e-31
relative error = 5.9950040271248527805796052913975e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.06
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] = 2.42
y[1] (analytic) = 1.6605812012792006925063341065602
y[1] (numeric) = 1.6605812012792006925063341065603
absolute error = 1e-31
relative error = 6.0219879595750384454833072308559e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.72
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] = 2.43
y[1] (analytic) = 1.6530407515722648997124970471899
y[1] (numeric) = 1.65304075157226489971249704719
absolute error = 1e-31
relative error = 6.0494576376829488891749456671227e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.38
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] = 2.44
y[1] (analytic) = 1.6454349983343706927400610729825
y[1] (numeric) = 1.6454349983343706927400610729826
absolute error = 1e-31
relative error = 6.0774202628014654497184761948944e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.06
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] = 2.45
y[1] (analytic) = 1.6377647021345037544385328556338
y[1] (numeric) = 1.6377647021345037544385328556338
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 = 15.73
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] = 2.46
y[1] (analytic) = 1.6300306299958921793081937186159
y[1] (numeric) = 1.6300306299958921793081937186159
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 = 15.41
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] = 2.47
y[1] (analytic) = 1.6222335553193047898745424048558
y[1] (numeric) = 1.6222335553193047898745424048557
absolute error = 1e-31
relative error = 6.1643404966011176812438993960883e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 1.6143742578057117043045348806656
y[1] (numeric) = 1.6143742578057117043045348806655
absolute error = 1e-31
relative error = 6.1943505055588478063216065453407e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 1.6064535233783148891434102397918
y[1] (numeric) = 1.6064535233783148891434102397917
absolute error = 1e-31
relative error = 6.2248921954308108540006066531960e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 1.5984721441039564940518547021862
y[1] (numeric) = 1.5984721441039564940518547021861
absolute error = 1e-31
relative error = 6.2559738916223809323680023061471e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 1.590430918113912827644537155024
y[1] (numeric) = 1.590430918113912827644537155024
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 1.5823306495240818949664275822971
y[1] (numeric) = 1.5823306495240818949664275822971
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] = 2.53
y[1] (analytic) = 1.5741721483545724777866405874022
y[1] (numeric) = 1.5741721483545724777866405874022
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 1.565956230448702798734765747982
y[1] (numeric) = 1.565956230448702798734765747982
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] = 2.55
y[1] (analytic) = 1.5576837173914168693457702817662
y[1] (numeric) = 1.5576837173914168693457702817662
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] = 2.56
y[1] (analytic) = 1.5493554364271266803106833831373
y[1] (numeric) = 1.5493554364271266803106833831372
absolute error = 1e-31
relative error = 6.4542969062414659438401251231488e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 1.5409722203769884496455725487458
y[1] (numeric) = 1.5409722203769884496455725487458
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] = 2.58
y[1] (analytic) = 1.5325349075556212010850587644716
y[1] (numeric) = 1.5325349075556212010850587644716
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] = 2.59
y[1] (analytic) = 1.5240443416872760007731302488759
y[1] (numeric) = 1.5240443416872760007731302488759
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] = 2.6
y[1] (analytic) = 1.5155013718214642352577269352094
y[1] (numeric) = 1.5155013718214642352577269352094
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] = 2.61
y[1] (analytic) = 1.5069068522480533678909866995555
y[1] (numeric) = 1.5069068522480533678909866995555
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 1.4982616424118386639887600099976
y[1] (numeric) = 1.4982616424118386639887600099976
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] = 2.63
y[1] (analytic) = 1.4895666068265994275056870536116
y[1] (numeric) = 1.4895666068265994275056870536116
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] = 2.64
y[1] (analytic) = 1.4808226149886483435305502695329
y[1] (numeric) = 1.4808226149886483435305502695328
absolute error = 1e-31
relative error = 6.7530032961285223035000128588586e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for 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=112041232, alloc=4521156, time=4.51
x[1] = 2.65
y[1] (analytic) = 1.4720305412898825715956107783974
y[1] (numeric) = 1.4720305412898825715956107783973
absolute error = 1e-31
relative error = 6.7933373116276463929622807634632e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 1.4631912649303452846181405937964
y[1] (numeric) = 1.4631912649303452846181405937963
absolute error = 1e-31
relative error = 6.8343765027028414840271986631591e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 1.4543056698303063972473913211913
y[1] (numeric) = 1.4543056698303063972473913211912
absolute error = 1e-31
relative error = 6.8761335443097295179643921677375e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 1.4453746445418712754708988319294
y[1] (numeric) = 1.4453746445418712754708988319294
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] = 2.69
y[1] (analytic) = 1.436399082160126266535504118761
y[1] (numeric) = 1.4363990821601262665355041187609
absolute error = 1e-31
relative error = 6.9618535156410134689666493987095e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 1.4273798802338299345560530858579
y[1] (numeric) = 1.4273798802338299345560530858578
absolute error = 1e-31
relative error = 7.0058434607904267797675710847523e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 1.4183179406756589326137906811086
y[1] (numeric) = 1.4183179406756589326137906811085
absolute error = 1e-31
relative error = 7.0506053073235437914383616903355e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 1.4092141696720174866824446740074
y[1] (numeric) = 1.4092141696720174866824446740073
absolute error = 1e-31
relative error = 7.0961534557429366788879393526631e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 1.4000694775924195103584479578944
y[1] (numeric) = 1.4000694775924195103584479578943
absolute error = 1e-31
relative error = 7.1425026829355283900967676110507e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 1.3908847788984524121083117016403
y[1] (numeric) = 1.3908847788984524121083117016401
absolute error = 2e-31
relative error = 1.4379336306950977797316343373181e-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] = 2.75
y[1] (analytic) = 1.3816609920523316985765613723778
y[1] (numeric) = 1.3816609920523316985765613723776
absolute error = 2e-31
relative error = 1.4475330862668287119521462972938e-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] = 2.76
y[1] (analytic) = 1.3723990394250555184177005924498
y[1] (numeric) = 1.3723990394250555184177005924496
absolute error = 2e-31
relative error = 1.4573020984027122311852859218502e-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] = 2.77
y[1] (analytic) = 1.3630998472041683311212820091725
y[1] (numeric) = 1.3630998472041683311212820091723
absolute error = 2e-31
relative error = 1.4672439470242529137252962894959e-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] = 2.78
y[1] (analytic) = 1.3537643453011429243863393172273
y[1] (numeric) = 1.3537643453011429243863393172272
absolute error = 1e-31
relative error = 7.3868099974043225636108880988959e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 1.3443934672583900417662615955623
y[1] (numeric) = 1.3443934672583900417662615955621
absolute error = 2e-31
relative error = 1.4876597132523878476707375692431e-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] = 2.8
y[1] (analytic) = 1.3349881501559049195438537527124
y[1] (numeric) = 1.3349881501559049195438537527122
absolute error = 2e-31
relative error = 1.4981406387513121402988476048624e-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] = 2.81
y[1] (analytic) = 1.3255493345175600681051012812063
y[1] (numeric) = 1.3255493345175600681051012812061
absolute error = 2e-31
relative error = 1.5088084222288938287329434848217e-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] = 2.82
y[1] (analytic) = 1.3160779642170536684554128560246
y[1] (numeric) = 1.3160779642170536684554128560243
absolute error = 3e-31
relative error = 2.2795002131843506168479856380455e-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] = 2.83
y[1] (analytic) = 1.3065749863835229889603130778681
y[1] (numeric) = 1.3065749863835229889603130778678
absolute error = 3e-31
relative error = 2.2960794682773765725803158632272e-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] = 2.84
y[1] (analytic) = 1.2970413513068322608902560680973
y[1] (numeric) = 1.297041351306832260890256068097
absolute error = 3e-31
relative error = 2.3129563270880716746085794943971e-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] = 2.85
y[1] (analytic) = 1.2874780123425444839030789266917
y[1] (numeric) = 1.2874780123425444839030789266914
absolute error = 3e-31
relative error = 2.3301368809720879836539577894521e-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] = 2.86
y[1] (analytic) = 1.2778859258165866642043569097532
y[1] (numeric) = 1.2778859258165866642043569097529
absolute error = 3e-31
relative error = 2.3476273894189411165786211289924e-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] = 2.87
y[1] (analytic) = 1.2682660509296180187823989209871
y[1] (numeric) = 1.2682660509296180187823989209868
absolute error = 3e-31
relative error = 2.3654342854963670011957727083442e-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] = 2.88
y[1] (analytic) = 1.2586193496611107088177669201177
y[1] (numeric) = 1.2586193496611107088177669201173
absolute error = 4e-31
relative error = 3.1780855753385796650456475741914e-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] = 2.89
y[1] (analytic) = 1.2489467866731526941140458405805
y[1] (numeric) = 1.2489467866731526941140458405801
absolute error = 4e-31
relative error = 3.2026984997934850976340977751985e-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] = 2.9
y[1] (analytic) = 1.2392493292139823281842569187396
y[1] (numeric) = 1.2392493292139823281842569187392
absolute error = 4e-31
relative error = 3.2277604721699359494621608101687e-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] = 2.91
y[1] (analytic) = 1.229527947021264340453018223827
y[1] (numeric) = 1.2295279470212643404530182238266
absolute error = 4e-31
relative error = 3.2532810740013387622925457247450e-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] = 2.92
y[1] (analytic) = 1.2197836122251168778956290930646
y[1] (numeric) = 1.2197836122251168778956290930642
absolute error = 4e-31
relative error = 3.2792701589942175252235791894286e-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=116041944, alloc=4521156, time=4.67
x[1] = 2.93
y[1] (analytic) = 1.2100172992508993033291040342591
y[1] (numeric) = 1.2100172992508993033291040342587
absolute error = 4e-31
relative error = 3.3057378621581117357198114099627e-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] = 2.94
y[1] (analytic) = 1.2002299847217704714943170944231
y[1] (numeric) = 1.2002299847217704714943170944227
absolute error = 4e-31
relative error = 3.3326946092979455514922821192404e-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] = 2.95
y[1] (analytic) = 1.1904226473610272270204473140574
y[1] (numeric) = 1.190422647361027227020447314057
absolute error = 4e-31
relative error = 3.3601511268853523048700450715492e-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] = 2.96
y[1] (analytic) = 1.1805962678942328903405445088014
y[1] (numeric) = 1.180596267894232890340544508801
absolute error = 4e-31
relative error = 3.3881184523262879701788275698032e-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] = 2.97
y[1] (analytic) = 1.170751828951145518628064498668
y[1] (numeric) = 1.1707518289511455186280644986676
absolute error = 4e-31
relative error = 3.4166079446431653699229679897348e-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] = 2.98
y[1] (analytic) = 1.1608903149674557488465539545413
y[1] (numeric) = 1.160890314967455748846553954541
absolute error = 3e-31
relative error = 2.5842234716930183173243269372778e-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] = 2.99
y[1] (analytic) = 1.1510127120863440490462950356105
y[1] (numeric) = 1.1510127120863440490462950356102
absolute error = 3e-31
relative error = 2.6064004059191944315529243141445e-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] = 3
y[1] (analytic) = 1.1411200080598672221007448028081
y[1] (numeric) = 1.1411200080598672221007448028078
absolute error = 3e-31
relative error = 2.6289960554636154528328783203420e-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] = 3.01
y[1] (analytic) = 1.1312131921501840231502181246848
y[1] (numeric) = 1.1312131921501840231502181246845
absolute error = 3e-31
relative error = 2.6520199912959545544553436322264e-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] = 3.02
y[1] (analytic) = 1.1212932550306297681087579963391
y[1] (numeric) = 1.1212932550306297681087579963388
absolute error = 3e-31
relative error = 2.6754820708504579425038196999236e-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] = 3.03
y[1] (analytic) = 1.1113611886866498256909050329173
y[1] (numeric) = 1.1113611886866498256909050329169
absolute error = 4e-31
relative error = 3.5991899309773420495461350994889e-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] = 3.04
y[1] (analytic) = 1.1014179863166018995266083126088
y[1] (numeric) = 1.1014179863166018995266083126084
absolute error = 4e-31
relative error = 3.6316821131430139406694916077635e-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] = 3.05
y[1] (analytic) = 1.0914646422324370200534015886964
y[1] (numeric) = 1.091464642232437020053401588696
absolute error = 4e-31
relative error = 3.6648003473741156043474375626958e-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] = 3.06
y[1] (analytic) = 1.0815021517602691780038900888357
y[1] (numeric) = 1.0815021517602691780038900888353
absolute error = 4e-31
relative error = 3.6985594466821354012012967012881e-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] = 3.07
y[1] (analytic) = 1.0715315111408435424423407903189
y[1] (numeric) = 1.0715315111408435424423407903185
absolute error = 4e-31
relative error = 3.7329746800831456110202306009587e-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] = 3.08
y[1] (analytic) = 1.0615537174299132164456296371357
y[1] (numeric) = 1.0615537174299132164456296371353
absolute error = 4e-31
relative error = 3.7680617893593230538051602323753e-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] = 3.09
y[1] (analytic) = 1.0515697683985344926699585105746
y[1] (numeric) = 1.0515697683985344926699585105742
absolute error = 4e-31
relative error = 3.8038370065466162663557389723232e-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] = 3.1
y[1] (analytic) = 1.0415806624332905791946982715967
y[1] (numeric) = 1.0415806624332905791946982715963
absolute error = 4e-31
relative error = 3.8403170721846857708863738592162e-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] = 3.11
y[1] (analytic) = 1.0315873984364537731876268727034
y[1] (numeric) = 1.031587398436453773187626872703
absolute error = 4e-31
relative error = 3.8775192543672795921686194180398e-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] = 3.12
y[1] (analytic) = 1.0215909757260960660909981042019
y[1] (numeric) = 1.0215909757260960660909981042015
absolute error = 4e-31
relative error = 3.9154613686333700268877518867403e-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] = 3.13
y[1] (analytic) = 1.0115923939361581691846814831183
y[1] (numeric) = 1.0115923939361581691846814831179
absolute error = 4e-31
relative error = 3.9541617987416786850333532636119e-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] = 3.14
y[1] (analytic) = 1.0015926529164869525405414363244
y[1] (numeric) = 1.001592652916486952540541436324
absolute error = 4e-31
relative error = 3.9936395183736646345327266444476e-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] = 3.15
y[1] (analytic) = 0.99159275263285129354085848342893
y[1] (numeric) = 0.99159275263285129354085848342849
absolute error = 4.4e-31
relative error = 4.4373055251939210004885439927396e-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 = 0.008107
Order of pole (three term test) = -0.8946
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 0.98159369306694633329262072881263
y[1] (numeric) = 0.98159369306694633329262072881219
absolute error = 4.4e-31
relative error = 4.4825063884145317479488930755361e-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 = 0.01775
Order of pole (three term test) = -0.901
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 0.97159647411639614042871472510327
y[1] (numeric) = 0.97159647411639614042871472510283
absolute error = 4.4e-31
relative error = 4.5286290319255368759710430872690e-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 = 0.02738
Order of pole (three term test) = -0.9124
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 0.96160209549476478194630475327388
y[1] (numeric) = 0.96160209549476478194630475327344
absolute error = 4.4e-31
relative error = 4.5756971834967832310669968290697e-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 = 0.037
Order of pole (three term test) = -0.9285
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 0.95161155663158579989199285154883
y[1] (numeric) = 0.95161155663158579989199285154839
absolute error = 4.4e-31
relative error = 4.6237353564459177357974584759506e-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 = 0.04661
Order of pole (three term test) = -0.9495
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 0.9416258565724200908627825853809
y[1] (numeric) = 0.94162585657242009086278258538046
absolute error = 4.4e-31
relative error = 4.6727688808549594592273188529471e-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 = 0.05619
Order of pole (three term test) = -0.9752
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=120042860, alloc=4521156, time=4.83
x[1] = 3.21
y[1] (analytic) = 0.93164599387895218245161163932314
y[1] (numeric) = 0.93164599387895218245161163932269
absolute error = 4.5e-31
relative error = 4.8301608438888220331470922256761e-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 = 0.06576
Order of pole (three term test) = -1.006
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 0.92167296652913489692655585208396
y[1] (numeric) = 0.92167296652913489692655585208351
absolute error = 4.5e-31
relative error = 4.8824259400232186624363588292243e-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 = 0.0753
Order of pole (three term test) = -1.041
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = 0.91170777181739238759412427147028
y[1] (numeric) = 0.91170777181739238759412427146983
absolute error = 4.5e-31
relative error = 4.9357920806463336885743435540541e-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 = 0.08481
Order of pole (three term test) = -1.081
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 0.90175140625489152745984504056236
y[1] (numeric) = 0.90175140625489152745984504056192
absolute error = 4.4e-31
relative error = 4.8793935551194293603994503288698e-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 = 0.09428
Order of pole (three term test) = -1.126
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 0.89180486546989162296416915743917
y[1] (numeric) = 0.89180486546989162296416915743873
absolute error = 4.4e-31
relative error = 4.9338147506984521545413936187389e-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 = 0.1037
Order of pole (three term test) = -1.176
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 0.88186914410818241773927688966392
y[1] (numeric) = 0.88186914410818241773927688966348
absolute error = 4.4e-31
relative error = 4.9894023726724635103575052408843e-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 = 0.1131
Order of pole (three term test) = -1.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 0.87194523573362034250344310924638
y[1] (numeric) = 0.87194523573362034250344310924594
absolute error = 4.4e-31
relative error = 5.0461884756994095874845530100089e-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 = 0.1225
Order of pole (three term test) = -1.289
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 0.86203413272877295738508592941475
y[1] (numeric) = 0.86203413272877295738508592941431
absolute error = 4.4e-31
relative error = 5.1042062407340879198931845679909e-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 = 0.1318
Order of pole (three term test) = -1.353
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 0.85213682619568152214947021625736
y[1] (numeric) = 0.85213682619568152214947021625692
absolute error = 4.4e-31
relative error = 5.1634900226569957120511496645365e-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 = 0.141
Order of pole (three term test) = -1.421
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 0.84225430585675161798834572239752
y[1] (numeric) = 0.84225430585675161798834572239708
absolute error = 4.4e-31
relative error = 5.2240754002726824273379813880667e-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 = 0.1502
Order of pole (three term test) = -1.494
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 0.83238755995578173172775000568302
y[1] (numeric) = 0.83238755995578173172775000568259
absolute error = 4.3e-31
relative error = 5.1658628827038519302295407078665e-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 = 0.1593
Order of pole (three term test) = -1.572
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 0.82253757515913969951307944769159
y[1] (numeric) = 0.82253757515913969951307944769116
absolute error = 4.3e-31
relative error = 5.2277247020211343679749267165640e-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 = 0.1684
Order of pole (three term test) = -1.654
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 0.81270533645709689224470717586405
y[1] (numeric) = 0.81270533645709689224470717586362
absolute error = 4.3e-31
relative error = 5.2909705487420520704096066478282e-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 = 0.1774
Order of pole (three term test) = -1.741
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 0.80289182706533000926338308940728
y[1] (numeric) = 0.80289182706533000926338308940685
absolute error = 4.3e-31
relative error = 5.3556405172500478764952038449259e-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 = 0.1863
Order of pole (three term test) = -1.832
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 0.79309802832660033002396588397449
y[1] (numeric) = 0.79309802832660033002396588397406
absolute error = 4.3e-31
relative error = 5.4217761820348973426413875756893e-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 = 0.1952
Order of pole (three term test) = -1.928
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 0.78332491961262025575038601809447
y[1] (numeric) = 0.78332491961262025575038601809404
absolute error = 4.3e-31
relative error = 5.4894206635561784153719234086793e-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 = 0.204
Order of pole (three term test) = -2.028
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 0.77357347822611695433589651569143
y[1] (numeric) = 0.773573478226116954335896515691
absolute error = 4.3e-31
relative error = 5.5586186975545483602973234604070e-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 = 0.2127
Order of pole (three term test) = -2.132
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 0.76384467930310290204250822241037
y[1] (numeric) = 0.76384467930310290204250822240994
absolute error = 4.3e-31
relative error = 5.6294167080186042102323499937925e-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 = 0.2213
Order of pole (three term test) = -2.241
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 0.75413949571536309486399862844206
y[1] (numeric) = 0.75413949571536309486399862844163
absolute error = 4.3e-31
relative error = 5.7018628840292971538251515258835e-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 = 0.2298
Order of pole (three term test) = -2.354
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 0.74445889797316868075009757063626
y[1] (numeric) = 0.74445889797316868075009757063583
absolute error = 4.3e-31
relative error = 5.7760072607191510723297311684589e-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 = 0.2382
Order of pole (three term test) = -2.472
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 0.73480385412822674124755569242589
y[1] (numeric) = 0.73480385412822674124755569242546
absolute error = 4.3e-31
relative error = 5.8519018045999928866669396922807e-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 = 0.2465
Order of pole (three term test) = -2.593
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = 0.7251753296768759274990566423338
y[1] (numeric) = 0.72517532967687592749905664233337
absolute error = 4.3e-31
relative error = 5.9296005035306381189283757785919e-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 = 0.2548
Order of pole (three term test) = -2.719
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 0.71557428746353763095570308540863
y[1] (numeric) = 0.7155742874635376309557030854082
absolute error = 4.3e-31
relative error = 6.0091594616150991729638389297957e-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 = 0.2629
Order of pole (three term test) = -2.849
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 0.70600168758443234360554818943968
y[1] (numeric) = 0.70600168758443234360554818943925
absolute error = 4.3e-31
relative error = 6.0906369993425167897985337895305e-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 = 0.2709
Order of pole (three term test) = -2.982
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 0.69645848729157083600191363378011
y[1] (numeric) = 0.69645848729157083600191363377967
absolute error = 4.4e-31
relative error = 6.3176773351000165754524667063483e-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 = 0.2789
Order of pole (three term test) = -3.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 0.68694564089702975389368422402507
y[1] (numeric) = 0.68694564089702975389368422402464
absolute error = 4.3e-31
relative error = 6.2595928178319306243002720367419e-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 = 0.2867
Order of pole (three term test) = -3.262
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 0.67746409967752120581814601284274
y[1] (numeric) = 0.6774640996775212058181460128423
absolute error = 4.4e-31
relative error = 6.4948091007249508973879407364774e-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 = 0.2944
Order of pole (three term test) = -3.408
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 0.66801481177926588461808356455725
y[1] (numeric) = 0.66801481177926588461808356455681
absolute error = 4.4e-31
relative error = 6.5866802987205395215721285304450e-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 = 0.3019
Order of pole (three term test) = -3.557
NO COMPLEX POLE (six term test) for Equation 1
bytes used=124045780, alloc=4521156, time=5.00
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 0.6585987221231792354917125192625
y[1] (numeric) = 0.65859872212317923549171251926206
absolute error = 4.4e-31
relative error = 6.6808511043194187500047573359962e-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 = 0.3094
Order of pole (three term test) = -3.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 0.64921677231038015187963119995636
y[1] (numeric) = 0.64921677231038015187963119995593
absolute error = 4.3e-31
relative error = 6.6233655435264059947082791232531e-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 = 0.3167
Order of pole (three term test) = -3.867
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 0.63986990052803164824046007658263
y[1] (numeric) = 0.63986990052803164824046007658219
absolute error = 4.4e-31
relative error = 6.8763978370744495344013584060473e-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 = 0.3239
Order of pole (three term test) = -4.028
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 0.63055904145552292556942567856704
y[1] (numeric) = 0.6305590414555229255694256785666
absolute error = 4.4e-31
relative error = 6.9779349921673562015181040686339e-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 = 0.331
Order of pole (three term test) = -4.192
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 0.62128512617100221137515574599336
y[1] (numeric) = 0.62128512617100221137515574599293
absolute error = 4.3e-31
relative error = 6.9211378461625526233408024711103e-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 = 0.3379
Order of pole (three term test) = -4.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 0.61204908205826972075279889951549
y[1] (numeric) = 0.61204908205826972075279889951506
absolute error = 4.3e-31
relative error = 7.0255803432291095165365949225973e-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 = 0.3447
Order of pole (three term test) = -4.531
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 0.60285183271404004917977257656305
y[1] (numeric) = 0.60285183271404004917977257656262
absolute error = 4.3e-31
relative error = 7.1327642492872455344072199426038e-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 = 0.3514
Order of pole (three term test) = -4.705
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 0.59369429785558327071757857731409
y[1] (numeric) = 0.59369429785558327071757857731365
absolute error = 4.4e-31
relative error = 7.4112215931545031993395191574636e-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 = 0.3579
Order of pole (three term test) = -4.883
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 0.58457739322875397743290054393371
y[1] (numeric) = 0.58457739322875397743290054393328
absolute error = 4.3e-31
relative error = 7.3557411726959221458960176428654e-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 = 0.3643
Order of pole (three term test) = -5.064
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 0.57550203051641745705739905165624
y[1] (numeric) = 0.5755020305164174570573990516558
absolute error = 4.4e-31
relative error = 7.6454986545429405816086674018052e-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 = 0.3705
Order of pole (three term test) = -5.249
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 0.56646911724728216619212706795597
y[1] (numeric) = 0.56646911724728216619212706795554
absolute error = 4.3e-31
relative error = 7.5908816016229713618133726096388e-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 = 0.3766
Order of pole (three term test) = -5.436
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 0.55747955670514761573327265250731
y[1] (numeric) = 0.55747955670514761573327265250687
absolute error = 4.4e-31
relative error = 7.8926661024220685791359430762306e-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 = 0.3826
Order of pole (three term test) = -5.626
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 0.54853424783857674365505981360747
y[1] (numeric) = 0.54853424783857674365505981360704
absolute error = 4.3e-31
relative error = 7.8390729784759194961172454212873e-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 = 0.3883
Order of pole (three term test) = -5.819
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 0.53963408517100180783725645920515
y[1] (numeric) = 0.53963408517100180783725645920472
absolute error = 4.3e-31
relative error = 7.9683624851780732299961663853924e-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 = 0.394
Order of pole (three term test) = -6.015
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 0.53077995871127278827309518546809
y[1] (numeric) = 0.53077995871127278827309518546766
absolute error = 4.3e-31
relative error = 8.1012855316548633724097039107679e-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 = 0.3994
Order of pole (three term test) = -6.214
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 0.52197275386465724374284336112709
y[1] (numeric) = 0.52197275386465724374284336112666
absolute error = 4.3e-31
relative error = 8.2379778794257729248967092785617e-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 = 0.4048
Order of pole (three term test) = -6.416
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 0.51321335134430052289318861170468
y[1] (numeric) = 0.51321335134430052289318861170425
absolute error = 4.3e-31
relative error = 8.3785817121410973102422518445146e-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 = 0.4099
Order of pole (three term test) = -6.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 0.50450262708315518362754885358965
y[1] (numeric) = 0.50450262708315518362754885358922
absolute error = 4.3e-31
relative error = 8.5232460034172387242753993235820e-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 = 0.4149
Order of pole (three term test) = -6.827
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 0.49584145214638842779197594108609
y[1] (numeric) = 0.49584145214638842779197594108566
absolute error = 4.3e-31
relative error = 8.6721269094914254488490465863527e-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 = 0.4197
Order of pole (three term test) = -7.036
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 0.48723069264427631034019077495596
y[1] (numeric) = 0.48723069264427631034019077495553
absolute error = 4.3e-31
relative error = 8.8253881886283376017507432420393e-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 = 0.4244
Order of pole (three term test) = -7.248
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 0.47867120964559343348424545187534
y[1] (numeric) = 0.47867120964559343348424545187491
absolute error = 4.3e-31
relative error = 8.9832016493820584130726359155342e-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 = 0.4288
Order of pole (three term test) = -7.461
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 0.47016385909150678678922237429879
y[1] (numeric) = 0.47016385909150678678922237429836
absolute error = 4.3e-31
relative error = 9.1457476300046746502332209215844e-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 = 0.4331
Order of pole (three term test) = -7.677
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 0.46170949170998234375620595674963
y[1] (numeric) = 0.4617094917099823437562059567492
absolute error = 4.3e-31
relative error = 9.3132155114995923340004872130135e-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 = 0.4373
Order of pole (three term test) = -7.896
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 0.45330895293071297416254103294378
y[1] (numeric) = 0.45330895293071297416254103294335
absolute error = 4.3e-31
relative error = 9.4858042670453128362100695368189e-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 = 0.4412
Order of pole (three term test) = -8.116
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 0.44496308280057617929725076783427
y[1] (numeric) = 0.44496308280057617929725076783384
absolute error = 4.3e-31
relative error = 9.6637230507663858778977863050108e-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 = 0.445
Order of pole (three term test) = -8.338
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 0.43667271589963010424763888032052
y[1] (numeric) = 0.43667271589963010424763888032009
absolute error = 4.3e-31
relative error = 9.8471918291051681308634541286438e-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 = 0.4486
Order of pole (three term test) = -8.562
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 0.42843868125765622756584442664971
y[1] (numeric) = 0.42843868125765622756584442664928
absolute error = 4.3e-31
relative error = 1.0036442058353849243274485225434e-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 = 0.452
Order of pole (three term test) = -8.788
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 0.42026180227125707397683496224605
y[1] (numeric) = 0.42026180227125707397683496224562
absolute error = 4.3e-31
bytes used=128047336, alloc=4521156, time=5.16
relative error = 1.0231717412244318775839571629412e-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 = 0.4553
Order of pole (three term test) = -9.015
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 0.41214289662151724028748227352559
y[1] (numeric) = 0.41214289662151724028748227352516
absolute error = 4.3e-31
relative error = 1.0433274563867625140148984651194e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.81
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4584
Order of pole (three term test) = -9.244
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 0.40408277619223596832551418909979
y[1] (numeric) = 0.40408277619223596832551418909936
absolute error = 4.3e-31
relative error = 1.0641384026609298579262141669442e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4612
Order of pole (three term test) = -9.474
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 0.39608224698873944158290927976732
y[1] (numeric) = 0.39608224698873944158290927976688
absolute error = 4.4e-31
relative error = 1.1108803874577825587254071853189e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4639
Order of pole (three term test) = -9.706
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 0.38814210905728092426641391388112
y[1] (numeric) = 0.38814210905728092426641391388068
absolute error = 4.4e-31
relative error = 1.1336054237162555160334667849512e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4664
Order of pole (three term test) = -9.939
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 0.38026315640503680267411028948219
y[1] (numeric) = 0.38026315640503680267411028948176
absolute error = 4.3e-31
relative error = 1.1307958521808146555106616401153e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4688
Order of pole (three term test) = -10.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 0.37244617692070652922722804311009
y[1] (numeric) = 0.37244617692070652922722804310965
absolute error = 4.4e-31
relative error = 1.1813787528652109687566786077511e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.31
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4709
Order of pole (three term test) = -10.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 0.36469195229572440909662976137772
y[1] (numeric) = 0.36469195229572440909662976137728
absolute error = 4.4e-31
relative error = 1.2064976954665815656159574446606e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4728
Order of pole (three term test) = -10.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 0.35700125794609110817965112113726
y[1] (numeric) = 0.35700125794609110817965112113682
absolute error = 4.4e-31
relative error = 1.2324886543297337555490322134309e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4746
Order of pole (three term test) = -10.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 0.349374862934832699211357781338
y[1] (numeric) = 0.34937486293483269921135778133756
absolute error = 4.4e-31
relative error = 1.2593922650985660480976494675271e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4762
Order of pole (three term test) = -11.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 0.3418135298950950000409906547043
y[1] (numeric) = 0.34181352989509500004099065470386
absolute error = 4.4e-31
relative error = 1.2872515612095259218554632187004e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4775
Order of pole (three term test) = -11.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 0.33431801495388089457568407689649
y[1] (numeric) = 0.33431801495388089457568407689605
absolute error = 4.4e-31
relative error = 1.3161121456787122727944504204334e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4787
Order of pole (three term test) = -11.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 0.32688906765643826259581048063146
y[1] (numeric) = 0.32688906765643826259581048063102
absolute error = 4.4e-31
relative error = 1.3460223774214492439735880708809e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.29
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4797
Order of pole (three term test) = -11.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 0.31952743089130607958596019184132
y[1] (numeric) = 0.31952743089130607958596019184087
absolute error = 4.5e-31
relative error = 1.4083297911066574006638833068111e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = -12.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 0.31223384081602618190911187462131
y[1] (numeric) = 0.31223384081602618190911187462087
absolute error = 4.4e-31
relative error = 1.4092002290656762813732500102040e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -12.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 0.30500902678352812608556955192351
y[1] (numeric) = 0.30500902678352812608556955192307
absolute error = 4.4e-31
relative error = 1.4425802561977224737387203700223e-28 %
Correct digits = 30
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
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -12.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 0.29785371126919450362939256217935
y[1] (numeric) = 0.29785371126919450362939256217891
absolute error = 4.4e-31
relative error = 1.4772352445269227872931577295702e-28 %
Correct digits = 30
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
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 0.29076860979861400485005610714845
y[1] (numeric) = 0.29076860979861400485005610714801
absolute error = 4.4e-31
relative error = 1.5132307449031155029210505316551e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.11
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 0.28375443087602945625275664545921
y[1] (numeric) = 0.28375443087602945625275664545877
absolute error = 4.4e-31
relative error = 1.5506365791067885028594810021876e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 0.27681187591348798667399566455718
y[1] (numeric) = 0.27681187591348798667399566455673
absolute error = 4.5e-31
relative error = 1.6256527958382771710886321939845e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -13.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 0.26994163916070040707678694126831
y[1] (numeric) = 0.26994163916070040707678694126787
absolute error = 4.4e-31
relative error = 1.6299819522769558228150096329330e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -13.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 0.26314440763561681800905744824866
y[1] (numeric) = 0.26314440763561681800905744824822
absolute error = 4.4e-31
relative error = 1.6720856960383513317295894147611e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.48
Order of pole (three term test) = -14.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 0.2564208610557253871066425986234
y[1] (numeric) = 0.25642086105572538710664259862296
absolute error = 4.4e-31
relative error = 1.7159290324057495088968714465184e-28 %
Correct digits = 30
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
Radius of convergence (three term test) for eq 1 = 0.4791
Order of pole (three term test) = -14.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 0.24977167177008116670587470137992
y[1] (numeric) = 0.24977167177008116670587470137947
absolute error = 4.5e-31
relative error = 1.8016454660808461240190550320117e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.478
Order of pole (three term test) = -14.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 0.24319750469207174862736090548817
y[1] (numeric) = 0.24319750469207174862736090548772
absolute error = 4.5e-31
relative error = 1.8503479325158965067943358182838e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.27
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4766
Order of pole (three term test) = -14.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 0.2366990172329264795094438207023
y[1] (numeric) = 0.23669901723292647950944382070185
absolute error = 4.5e-31
relative error = 1.9011485778885687333802067937695e-28 %
Correct digits = 30
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
Radius of convergence (three term test) for eq 1 = 0.4751
Order of pole (three term test) = -14.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 0.23027685923597588571440266645551
y[1] (numeric) = 0.23027685923597588571440266645506
absolute error = 4.5e-31
relative error = 1.9541694354049841223702581550044e-28 %
Correct digits = 30
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
Radius of convergence (three term test) for eq 1 = 0.4734
Order of pole (three term test) = -15.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 0.2239316729116678818101206987675
y[1] (numeric) = 0.22393167291166788181012069876705
absolute error = 4.5e-31
relative error = 2.0095415451904700469827565529955e-28 %
Correct digits = 30
h = 0.01
bytes used=132048692, alloc=4521156, time=5.33
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4716
Order of pole (three term test) = -15.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 0.21766409277334726095221776933351
y[1] (numeric) = 0.21766409277334726095221776933305
absolute error = 4.6e-31
relative error = 2.1133481142385581192467725221500e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.92
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4695
Order of pole (three term test) = -15.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 0.21147474557380488916409289058062
y[1] (numeric) = 0.21147474557380488916409289058016
absolute error = 4.6e-31
relative error = 2.1752006309399226042516461494023e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4672
Order of pole (three term test) = -15.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 0.20536425024260294854257330725366
y[1] (numeric) = 0.2053642502426029485425733072532
absolute error = 4.6e-31
relative error = 2.2399224765585451347063274626962e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4648
Order of pole (three term test) = -16.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 0.19933321782418249681262071972431
y[1] (numeric) = 0.19933321782418249681262071972385
absolute error = 4.6e-31
relative error = 2.3076936449484949105483608510652e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.97
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4621
Order of pole (three term test) = -16.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 0.19338225141675953242356232661989
y[1] (numeric) = 0.19338225141675953242356232661943
absolute error = 4.6e-31
relative error = 2.3787084731403326614605861344101e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4593
Order of pole (three term test) = -16.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 0.18751194611201567552941728764728
y[1] (numeric) = 0.18751194611201567552941728764682
absolute error = 4.6e-31
relative error = 2.4531770350525065599038713257999e-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 = 0.4563
Order of pole (three term test) = -16.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 0.18172288893558949573496297564155
y[1] (numeric) = 0.18172288893558949573496297564108
absolute error = 4.7e-31
relative error = 2.5863555370099165897999748177517e-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 = 0.4531
Order of pole (three term test) = -17.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 0.17601565878837443742517601630396
y[1] (numeric) = 0.17601565878837443742517601630349
absolute error = 4.7e-31
relative error = 2.6702169752129051743985794253083e-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 = 0.4498
Order of pole (three term test) = -17.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 0.17039082638862921283659693902778
y[1] (numeric) = 0.17039082638862921283659693902732
absolute error = 4.6e-31
relative error = 2.6996758554995625020518334796071e-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 = 0.4462
Order of pole (three term test) = -17.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 0.16484895421490645178307012404365
y[1] (numeric) = 0.16484895421490645178307012404318
absolute error = 4.7e-31
relative error = 2.8510948233695272813958883440131e-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 = 0.4425
Order of pole (three term test) = -17.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 0.15939059644980531512332717185912
y[1] (numeric) = 0.15939059644980531512332717185866
absolute error = 4.6e-31
relative error = 2.8859920863955199724294567678862e-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 = 0.4386
Order of pole (three term test) = -17.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 0.15401629892455369666219427078778
y[1] (numeric) = 0.15401629892455369666219427078732
absolute error = 4.6e-31
relative error = 2.9866968834599462687231441213041e-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 = 0.4345
Order of pole (three term test) = -18.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 0.14872659906442555521905209735327
y[1] (numeric) = 0.14872659906442555521905209735281
absolute error = 4.6e-31
relative error = 3.0929235449049479264258568712996e-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 = 0.4303
Order of pole (three term test) = -18.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 0.14352202583499883508485599858706
y[1] (numeric) = 0.1435220258349988350848559985866
absolute error = 4.6e-31
relative error = 3.2050829642611261824911018803224e-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 = 0.4259
Order of pole (three term test) = -18.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 0.13840309968925934903088583719909
y[1] (numeric) = 0.13840309968925934903088583719863
absolute error = 4.6e-31
relative error = 3.3236249840703379557772080683120e-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 = 0.4213
Order of pole (three term test) = -18.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 0.13337033251555591343684467407746
y[1] (numeric) = 0.133370332515555913436844674077
absolute error = 4.6e-31
relative error = 3.4490429117461110552822142186291e-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 = 0.4165
Order of pole (three term test) = -19.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 0.12842422758641193998142290209118
y[1] (numeric) = 0.12842422758641193998142290209072
absolute error = 4.6e-31
relative error = 3.5818786582966435702993101059113e-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 = 0.4116
Order of pole (three term test) = -19.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = 0.1235652795081986026935019100478
y[1] (numeric) = 0.12356527950819860269350191004734
absolute error = 4.6e-31
relative error = 3.7227286000634088095300552585552e-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 = 0.4065
Order of pole (three term test) = -19.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 0.11879397417167461300535326877877
y[1] (numeric) = 0.11879397417167461300535326877831
absolute error = 4.6e-31
relative error = 3.8722502821164390994932983731783e-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 = 0.4013
Order of pole (three term test) = -19.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 0.11411078870339754878911140270074
y[1] (numeric) = 0.11411078870339754878911140270028
absolute error = 4.6e-31
relative error = 4.0311701043067446863892417621110e-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 = 0.3959
Order of pole (three term test) = -19.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 0.10951619141801159620312567541779
y[1] (numeric) = 0.10951619141801159620312567541733
absolute error = 4.6e-31
relative error = 4.2002921581177816024090408223551e-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 = 0.3903
Order of pole (three term test) = -20.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 0.10501064177141647553424717156172
y[1] (numeric) = 0.10501064177141647553424717156126
absolute error = 4.6e-31
relative error = 4.3805084155309902073921637137162e-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 = 0.3846
Order of pole (three term test) = -20.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 0.10059459031482223410444018114688
y[1] (numeric) = 0.10059459031482223410444018114642
absolute error = 4.6e-31
relative error = 4.5728105115829546957464230251770e-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 = 0.3787
Order of pole (three term test) = -20.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 0.09626847864969450072414018033867
y[1] (numeric) = 0.09626847864969450072414018033821
absolute error = 4.60e-31
relative error = 4.7783034120012009583388681962239e-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 = 0.3727
Order of pole (three term test) = -20.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 0.09203273938359470712936747670058
y[1] (numeric) = 0.092032739383594707129367476700112
absolute error = 4.68e-31
relative error = 5.0851469067911209464237615091700e-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 = 0.3665
Order of pole (three term test) = -20.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 0.08788779608691969234365311475198
y[1] (numeric) = 0.087887796086919692343653114751512
absolute error = 4.68e-31
relative error = 5.3249713934930752472030142847274e-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 = 0.3601
Order of pole (three term test) = -20.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 0.08383406325054501596829063971536
y[1] (numeric) = 0.0838340632505450159682906397149
absolute error = 4.60e-31
relative error = 5.4870297605073971070111229998958e-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 = 0.3537
Order of pole (three term test) = -21.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=136051292, alloc=4521156, time=5.49
x[1] = 4.31
y[1] (analytic) = 0.07987194624437621603428757300901
y[1] (numeric) = 0.079871946244376216034287573008542
absolute error = 4.68e-31
relative error = 5.8593789434917129160533222378748e-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 = 0.3471
Order of pole (three term test) = -21.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 0.07600184127681215625569090101602
y[1] (numeric) = 0.076001841276812156255690901015554
absolute error = 4.66e-31
relative error = 6.1314303992023762985570122332177e-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 = 0.3403
Order of pole (three term test) = -21.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 0.07222413535512451631578081322702
y[1] (numeric) = 0.072224135355124516315780813226558
absolute error = 4.62e-31
relative error = 6.3967536299099457707179922794738e-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 = 0.3334
Order of pole (three term test) = -21.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 0.06853920624675738720408708901116
y[1] (numeric) = 0.068539206246757387204087089010696
absolute error = 4.64e-31
relative error = 6.7698478784462432457340233873705e-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 = 0.3264
Order of pole (three term test) = -21.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 0.06494742244155084161244420165858
y[1] (numeric) = 0.064947422441550841612444201658117
absolute error = 4.63e-31
relative error = 7.1288433411914829040270761300521e-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 = 0.3193
Order of pole (three term test) = -22.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 0.06144914311489225700156528111504
y[1] (numeric) = 0.061449143114892257001565281114575
absolute error = 4.65e-31
relative error = 7.5672332668753979320973987624604e-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 = 0.312
Order of pole (three term test) = -22.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 0.05804471809179907617512114959174
y[1] (numeric) = 0.058044718091799076175121149591272
absolute error = 4.68e-31
relative error = 8.0627491249048204334797698670447e-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 = 0.3046
Order of pole (three term test) = -22.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 0.05473448781193659705533608906184
y[1] (numeric) = 0.054734487811936597055336089061371
absolute error = 4.69e-31
relative error = 8.5686377775461639295051718576714e-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 = 0.2971
Order of pole (three term test) = -22.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 0.05151878329557428985197103638587
y[1] (numeric) = 0.051518783295574289851971036385403
absolute error = 4.67e-31
relative error = 9.0646550661090153484750643416998e-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 = 0.2894
Order of pole (three term test) = -22.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 0.04839792611048404596460766661961
y[1] (numeric) = 0.048397926110484045964607666619147
absolute error = 4.63e-31
relative error = 9.5665256181236267001530697398507e-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 = 0.2817
Order of pole (three term test) = -22.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 0.04537222833978366876575843546385
y[1] (numeric) = 0.045372228339783668765758435463381
absolute error = 4.69e-31
relative error = 1.0336719556459768872344916426392e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2738
Order of pole (three term test) = -22.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 0.04244199255072882188892726816111
y[1] (numeric) = 0.042441992550728821888927268160643
absolute error = 4.67e-31
relative error = 1.1003253427411965088163330684124e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2658
Order of pole (three term test) = -23.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 0.03960751176445655580078546569952
y[1] (numeric) = 0.039607511764456555800785465699059
absolute error = 4.61e-31
relative error = 1.1639206288482314590582740267668e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2577
Order of pole (three term test) = -23.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 0.03686906942668343827959196692216
y[1] (numeric) = 0.036869069426683438279591966921694
absolute error = 4.66e-31
relative error = 1.2639320906286272056032796330703e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2495
Order of pole (three term test) = -23.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 0.03422693937936121896239198130831
y[1] (numeric) = 0.034226939379361218962391981307842
absolute error = 4.68e-31
relative error = 1.3673439941936588492996044826319e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2413
Order of pole (three term test) = -23.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 0.03168138583329286237091907175356
y[1] (numeric) = 0.031681385833292862370919071753096
absolute error = 4.64e-31
relative error = 1.4645823968735565800287027272957e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2329
Order of pole (three term test) = -23.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 0.02923266334171168779007820072841
y[1] (numeric) = 0.029232663341711687790078200727948
absolute error = 4.62e-31
relative error = 1.5804239066400033222513968885275e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2244
Order of pole (three term test) = -23.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 0.02688101677482625806300458146732
y[1] (numeric) = 0.026881016774826258063004581466851
absolute error = 4.69e-31
relative error = 1.7447256698980699928309806231084e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2158
Order of pole (three term test) = -23.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 0.02462668129533356279260630634082
y[1] (numeric) = 0.024626681295333562792606306340353
absolute error = 4.67e-31
relative error = 1.8963172276424044708002199704352e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2072
Order of pole (three term test) = -23.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 0.02246988233490294461086498550137
y[1] (numeric) = 0.022469882334902944610864985500906
absolute error = 4.64e-31
relative error = 2.0649863363069728354422538264186e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1984
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 0.02041083557163312010367080295234
y[1] (numeric) = 0.020410835571633120103670802951872
absolute error = 4.68e-31
relative error = 2.2928997608036396182152772481993e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1896
Order of pole (three term test) = -24.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 0.01844974690848454967031375325789
y[1] (numeric) = 0.018449746908484549670313753257427
absolute error = 4.63e-31
relative error = 2.5095195196801240122514675462163e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1807
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 0.01658681245268931306267214456304
y[1] (numeric) = 0.016586812452689313062672144562577
absolute error = 4.63e-31
relative error = 2.7913741794610525638619403477732e-27 %
Correct digits = 29
h = 0.01
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) = -24.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 0.01482221849614054959938606921746
y[1] (numeric) = 0.014822218496140549599386069216994
absolute error = 4.66e-31
relative error = 3.1439288263179926384322739473977e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1627
Order of pole (three term test) = -24.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 0.01315614149676342409465234597491
y[1] (numeric) = 0.013156141496763424094652345974442
absolute error = 4.68e-31
relative error = 3.5572739934055427494281822051247e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1536
Order of pole (three term test) = -24.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 0.01158874806086948138952391096191
y[1] (numeric) = 0.011588748060869481389523910961445
absolute error = 4.65e-31
relative error = 4.0125128060218779827316058265665e-27 %
Correct digits = 29
h = 0.01
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) = -24.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 0.01012019492649615403555587193493
y[1] (numeric) = 0.010120194926496154035555871934461
absolute error = 4.69e-31
relative error = 4.6342980881928394490268596437045e-27 %
Correct digits = 29
h = 0.01
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) = -24.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 0.00875062894773308916614616390269
y[1] (numeric) = 0.0087506289477330891661461639022244
absolute error = 4.656e-31
relative error = 5.3207604022636212223616107008366e-27 %
Correct digits = 29
h = 0.01
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) = -24.62
NO COMPLEX POLE (six term test) for Equation 1
bytes used=140053080, alloc=4521156, time=5.65
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 0.00748018708003686190982232131219
y[1] (numeric) = 0.007480187080036861909822321311721
absolute error = 4.690e-31
relative error = 6.2698966614306763614622147857072e-27 %
Correct digits = 29
h = 0.01
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) = -24.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 0.00630899636653554386189534009117
y[1] (numeric) = 0.0063089963665355438618953400907059
absolute error = 4.641e-31
relative error = 7.3561621062535341040151778794298e-27 %
Correct digits = 29
h = 0.01
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) = -24.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 0.00523717392532449614622064259686
y[1] (numeric) = 0.0052371739253244961462206425963992
absolute error = 4.608e-31
relative error = 8.7986384750712428789255285556297e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09791
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 0.00426482693775465747717316554853
y[1] (numeric) = 0.0042648269377546574771731655480697
absolute error = 4.603e-31
relative error = 1.0792935017483695584811449733342e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08846
Order of pole (three term test) = -24.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 0.0033920526377144983832706460193
y[1] (numeric) = 0.0033920526377144983832706460188313
absolute error = 4.687e-31
relative error = 1.3817592179695692831583351906583e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07898
Order of pole (three term test) = -24.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 0.00261893830190671338809106811717
y[1] (numeric) = 0.0026189383019067133880910681167044
absolute error = 4.656e-31
relative error = 1.7778196594437553010420629021515e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06947
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 0.00194556124112062347116344910397
y[1] (numeric) = 0.00194556124112062347116344910351
absolute error = 4.600e-31
relative error = 2.3643563115753924163575413085437e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05992
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 0.00137198879250116156131290216748
y[1] (numeric) = 0.0013719887925011615613129021670122
absolute error = 4.678e-31
relative error = 3.4096488437576209164350805296635e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05036
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 0.00089827831281521415746815072662
y[1] (numeric) = 0.00089827831281521415746815072615302
absolute error = 4.6698e-31
relative error = 5.1986115365123256769199342919758e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04077
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 0.00052447717271599243715805024033
y[1] (numeric) = 0.00052447717271599243715805023986265
absolute error = 4.6735e-31
relative error = 8.9107786632512384503224722418066e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03117
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 0.00025062275200600641080659305708
y[1] (numeric) = 0.00025062275200600641080659305661878
absolute error = 4.6122e-31
relative error = 1.8402958083747577209959371504648e-25 %
Correct digits = 27
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02155
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 7.674243589911582046345842503e-05
y[1] (numeric) = 7.6742435899115820463458424563870e-05
absolute error = 4.66130e-31
relative error = 6.0739536677304044963069626578796e-25 %
Correct digits = 27
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01193
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 2.85361228203157476528740643e-06
y[1] (numeric) = 2.8536122820315747652874059615900e-06
absolute error = 4.684100e-31
relative error = 1.6414633583877219868690731180310e-23 %
Correct digits = 25
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0023
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 2.896366997554156770211203836e-05
y[1] (numeric) = 2.8963669975541567702112037895790e-05
absolute error = 4.64210e-31
relative error = 1.6027319755818344676772149394142e-24 %
Correct digits = 26
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00015506999799563475715808844232
y[1] (numeric) = 0.00015506999799563475715808844185403
absolute error = 4.6597e-31
relative error = 3.0049010512859948757127004258148e-25 %
Correct digits = 27
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00038115998581459739020295192723
y[1] (numeric) = 0.00038115998581459739020295192676497
absolute error = 4.6503e-31
relative error = 1.2200388742437365692909887326833e-25 %
Correct digits = 27
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00070721102462205526572924440292
y[1] (numeric) = 0.00070721102462205526572924440245605
absolute error = 4.6395e-31
relative error = 6.5602766903689348316990944381003e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00113319050958583593125991543056
y[1] (numeric) = 0.001133190509585835931259915430099
absolute error = 4.610e-31
relative error = 4.0681597321926792229926924031747e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00165905584311242472959066170051
y[1] (numeric) = 0.0016590558431124247295906617000496
absolute error = 4.604e-31
relative error = 2.7750723516110200283810515506890e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00228475443910668865237937835233
y[1] (numeric) = 0.0022847544391066886523793783518628
absolute error = 4.672e-31
relative error = 2.0448587034266559884885586017530e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00301022372823044203184712123726
y[1] (numeric) = 0.0030102237282304420318471212367973
absolute error = 4.627e-31
relative error = 1.5370950526391534353514589362971e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00383539116415932821840353349637
y[1] (numeric) = 0.0038353911641593282184035334959007
absolute error = 4.693e-31
relative error = 1.2236040078140633046010641575575e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00476017423083739156124302459597
y[1] (numeric) = 0.004760174230837391561243024595508
absolute error = 4.620e-31
relative error = 9.7055271003962124950860737923037e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00578448045072861424075909870166
y[1] (numeric) = 0.0057844804507286142407590987011953
absolute error = 4.647e-31
relative error = 8.0335650532186741331557698308175e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.0069082073940645928059698487306
y[1] (numeric) = 0.0069082073940645928059698487301343
absolute error = 4.657e-31
relative error = 6.7412567897153904276934897766115e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00813124268908742965700724495948
y[1] (numeric) = 0.0081312426890874296570072449590192
absolute error = 4.608e-31
relative error = 5.6670304604045170776967352652323e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.00945346403328681519205768370882
y[1] (numeric) = 0.0094534640332868151920576837083549
absolute error = 4.651e-31
relative error = 4.9198896654424813952961174238345e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.01087473920563017691990330595709
y[1] (numeric) = 0.010874739205630176919903305956626
bytes used=144053868, alloc=4521156, time=5.82
absolute error = 4.64e-31
relative error = 4.2667689884440939713481024497452e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.01239492607978467253334458870749
y[1] (numeric) = 0.012394926079784672533344588707027
absolute error = 4.63e-31
relative error = 3.7353994450610175885333733358617e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.01401387263832970475521515768158
y[1] (numeric) = 0.014013872638329704755215157681113
absolute error = 4.67e-31
relative error = 3.3324121893522583229026778586469e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.0157314169879585367173479427511
y[1] (numeric) = 0.015731416987958536717347942750637
absolute error = 4.63e-31
relative error = 2.9431550912063353203282039664558e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.01754738737566748772362275008167
y[1] (numeric) = 0.017547387375667487723622750081207
absolute error = 4.63e-31
relative error = 2.6385694353680835232581507268867e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.01946160220593109049100989773031
y[1] (numeric) = 0.019461602205931090491009897729846
absolute error = 4.64e-31
relative error = 2.3841819141621958196265477131650e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.02147387005886149236719839365887
y[1] (numeric) = 0.02147387005886149236719839365841
absolute error = 4.60e-31
relative error = 2.1421383231765183192811636233364e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 0.02358398970935028459981967725086
y[1] (numeric) = 0.0235839897093502845998196772504
absolute error = 4.60e-31
relative error = 1.9504757493072724942264736690619e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.02579175014719084549029147317684
y[1] (numeric) = 0.02579175014719084549029147317638
absolute error = 4.60e-31
relative error = 1.7835160366195689173659019837138e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.02809693059817918521473493662265
y[1] (numeric) = 0.028096930598179185214734936622182
absolute error = 4.68e-31
relative error = 1.6656623696480519715528931964360e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.03049930054619118224506697690327
y[1] (numeric) = 0.030499300546191182245066976902801
absolute error = 4.69e-31
relative error = 1.5377401828927179154957944824496e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.03299861975623400366502328592209
y[1] (numeric) = 0.03299861975623400366502328592163
absolute error = 4.60e-31
relative error = 1.3939976986858613453781900731598e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.03559463829846940425828992207108
y[1] (numeric) = 0.035594638298469404258289922070613
absolute error = 4.67e-31
relative error = 1.3119953518956852133191911380094e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
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) = 0.03828709657320650205885398558889
y[1] (numeric) = 0.038287096573206502058853985588428
absolute error = 4.62e-31
relative error = 1.2066728515614575633282337601911e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = cos ( x ) ;
Iterations = 1000
Total Elapsed Time = 5 Seconds
Elapsed Time(since restart) = 5 Seconds
Time to Timeout = 2 Minutes 54 Seconds
Percent Done = 100.1 %
> quit
bytes used=146021632, alloc=4521156, time=5.90