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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> 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 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y2[1]) < min_size) then # if number 1
> min_size := omniabs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (omniabs(array_y1[1]) < min_size) then # if number 1
> min_size := omniabs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y2[1]) < min_size then
min_size := omniabs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if omniabs(array_y1[1]) < min_size then
min_size := omniabs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if 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 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 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,"");
> value3 := omniabs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> value3 := omniabs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last;
max_value3 := 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, "");
value3 := omniabs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
value3 := omniabs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, 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 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr <> 0.0) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 3;
> 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 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, 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_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if relerr <> 0. then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> 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 1;
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_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 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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 1
> 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 1;
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, 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 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #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_y2_higher[1,m]) < glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (omniabs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif
> ((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> 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) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif
> ((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> 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) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if ( not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found ) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4;
> fi;# end if 3;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if ( not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if ( not found ) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4;
> fi;# end if 3;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if (array_pole[1] > array_poles[2,1]) then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3;
> #BOTTOM WHICH RADIUS EQ = 2
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 3
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 3;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 3
> display_pole();
> fi;# end if 3
> 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, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y2_higher[1, m]) < glob_small_float
or omniabs(array_y2_higher[1, m - 1]) < glob_small_float or
omniabs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float
or omniabs(array_y1_higher[1, m - 1]) < glob_small_float or
omniabs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y2_higher[1, m]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) 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 glob_small_float < omniabs(rcs) 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_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= omniabs(array_y1_higher[1, m]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) 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 glob_small_float < omniabs(rcs) 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_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
if reached_interval() then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
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_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 3
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y2[iii]);
> fi;# end if 4;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y1[iii]);
> fi;# end if 4;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 3;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, 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_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1 order_d = 1
> array_tmp1[1] := array_y1_higher[2,1];
> #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_y2_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_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h;
> array_y2_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre sin 1 $eq_no = 2
> array_tmp4[1] := sin(array_x[1]);
> array_tmp4_g[1] := cos(array_x[1]);
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[2,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h;
> array_y1_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2 order_d = 1
> array_tmp1[2] := array_y1_higher[2,2];
> #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_y2_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_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h;
> array_y2_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 2
> array_tmp4[2] := array_tmp4_g[1] * array_x[2] / 1;
> array_tmp4_g[2] := -array_tmp4[1] * array_x[2] / 1;
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[2,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h;
> array_y1_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3 order_d = 1
> array_tmp1[3] := array_y1_higher[2,3];
> #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_y2_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_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 2
> array_tmp4[3] := array_tmp4_g[2] * array_x[2] / 2;
> array_tmp4_g[3] := -array_tmp4[2] * array_x[2] / 2;
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[2,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4 order_d = 1
> array_tmp1[4] := array_y1_higher[2,4];
> #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_y2_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_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 2
> array_tmp4[4] := array_tmp4_g[3] * array_x[2] / 3;
> array_tmp4_g[4] := -array_tmp4[3] * array_x[2] / 3;
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[2,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y1_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5 order_d = 1
> array_tmp1[5] := array_y1_higher[2,5];
> #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_y2_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_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 2
> array_tmp4[5] := array_tmp4_g[4] * array_x[2] / 4;
> array_tmp4_g[5] := -array_tmp4[4] * array_x[2] / 4;
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[2,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y1_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 diff $eq_no = 1
> array_tmp1[kkk] := array_y1_higher[2,kkk];
> #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 + 1 <= glob_max_terms) then # if number 1
> if ( not array_y2_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_y2[kkk + order_d] := temporary;
> array_y2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 2;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 1) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary / glob_h;
> fi;# end if 4;
> array_y2_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1;
> #emit sin LINEAR $eq_no = 2
> array_tmp4[kkk] := array_tmp4_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp4_g[kkk] := -array_tmp4[kkk - 1] * array_x[2] / (kkk - 1);
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 2;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 1) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary / glob_h;
> fi;# end if 4;
> array_y1_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last;
array_tmp1[1] := array_y1_higher[2, 1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y2_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp4[1] := sin(array_x[1]);
array_tmp4_g[1] := cos(array_x[1]);
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_y1_higher[2, 2];
array_tmp2[2] := array_tmp1[2];
if not array_y2_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp4[2] := array_tmp4_g[1]*array_x[2];
array_tmp4_g[2] := -array_tmp4[1]*array_x[2];
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_y1_higher[2, 3];
array_tmp2[3] := array_tmp1[3];
if not array_y2_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp4[3] := 1/2*array_tmp4_g[2]*array_x[2];
array_tmp4_g[3] := -1/2*array_tmp4[2]*array_x[2];
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_y1_higher[2, 4];
array_tmp2[4] := array_tmp1[4];
if not array_y2_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp4[4] := 1/3*array_tmp4_g[3]*array_x[2];
array_tmp4_g[4] := -1/3*array_tmp4[3]*array_x[2];
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_y1_higher[2, 5];
array_tmp2[5] := array_tmp1[5];
if not array_y2_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp4[5] := 1/4*array_tmp4_g[4]*array_x[2];
array_tmp4_g[5] := -1/4*array_tmp4[4]*array_x[2];
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_y1_higher[2, kkk];
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_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_y2[kkk + order_d] := temporary;
array_y2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 2;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 1 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary/glob_h
end if;
array_y2_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
array_tmp4[kkk] := array_tmp4_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp4_g[kkk] := -array_tmp4[kkk - 1]*array_x[2]/(kkk - 1);
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := array_tmp4[kkk]*expt(glob_h, order_d)/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 2;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 1 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary/glob_h
end if;
array_y1_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #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\n", 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 \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", 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\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", 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, " | \n")
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 Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
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 := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
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 <> 0.0) 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 rel_error <> 0. 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");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> 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")
else fprintf(file, "No Pole")
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, "\n") 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 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> 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 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> 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 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> 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 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> 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 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(2.0 - cos(x));
> end;
exact_soln_y1 := proc(x) return 2.0 - cos(x) end proc
> exact_soln_y2 := proc(x)
> return(2.0 - cos(x));
> end;
exact_soln_y2 := proc(x) return 2.0 - cos(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_log10normmin,
> 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_hmax,
> glob_hmin,
> glob_hmin_init,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_log10_abserr,
> glob_log10_relerr,
> 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_log10abserr,
> glob_log10relerr,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_log10normmin := 0.1;
> 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_hmax := 1.0;
> glob_hmin := 0.00000000001;
> glob_hmin_init := 0.001;
> 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_log10_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> 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 := 0.1e-50;
> glob_smallish_float := 0.1e-100;
> 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_log10abserr := 0.0;
> glob_log10relerr := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest5postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = sin ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_max_iter := 20;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(2.0 - cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(2.0 - cos(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 := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #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_y2_init:= Array(0..(max_terms + 1),[]);
> array_y1_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..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y2:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4_g:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_pole := 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 2
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> glob_h := 0.00001 ;
> glob_max_iter := 20;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=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);
> glob_abserr := expt(10.0 , (glob_log10_abserr));
> glob_relerr := expt(10.0 , (glob_log10_relerr));
> 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_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := false;
> array_y2_set_initial[1,3] := false;
> array_y2_set_initial[1,4] := false;
> array_y2_set_initial[1,5] := false;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 3
> glob_h := glob_display_interval;
> fi;# end if 3;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> 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_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> if (glob_subiter_method = 1 ) then # if number 3
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 4
> subiter := 1;
> while (subiter <= 2) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> fi;# end if 4;
> 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,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 4
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 4;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 4
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 4;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 4
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 4;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 4
> 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_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_log10normmin := -glob_large_float ;
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 5
> tmp := omniabs(array_y2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 6
> glob_log10normmin := log10norm;
> fi;# end if 6
> fi;# end if 5;
> display_alot(current_iter)
> ;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 5
> tmp := omniabs(array_y1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 6
> glob_log10normmin := log10norm;
> fi;# end if 6
> fi;# end if 5;
> display_alot(current_iter)
> ;
> 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 2
> #left paren 0001C
> if (reached_interval()) then # if number 5
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 5;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 5
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 6
> subiter := 1;
> while (subiter <= 2) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> fi;# end if 6;
> 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_y2
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y2_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 3
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y1
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2;#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 ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = sin ( 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,"2012-12-15T00:14:26-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest5")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;")
> ;
> 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_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 7
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 7;
> 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," 151 | ")
> ;
> logitem_str(html_log_file,"mtest5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest5 maple results")
> ;
> logitem_str(html_log_file,"Languages compared")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = sin ( x ) ;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 7
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 7;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 7;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> 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, log10norm, max_terms, opt_iter,
tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_log10normmin, 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_hmax, glob_hmin,
glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles,
glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic,
glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1,
array_const_0D0, array_y2_init, array_y1_init, array_norms, array_fact_1,
array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole,
array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_poles, array_real_pole, array_complex_pole, 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;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_log10normmin := 0.1;
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_hmax := 1.0;
glob_hmin := 0.1*10^(-10);
glob_hmin_init := 0.001;
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_log10_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
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 := 0.1*10^(-50);
glob_smallish_float := 0.1*10^(-100);
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_log10abserr := 0.;
glob_log10relerr := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest5postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = sin ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_max_iter := 20;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(2.0 - cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(2.0 - cos(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 := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y2_init := Array(0 .. max_terms + 1, []);
array_y1_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 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y2 := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4_g := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_complex_pole := 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_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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 <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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_real_pole[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_pole[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_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[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_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_g[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_h := 0.00001;
glob_max_iter := 20;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 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);
glob_abserr := expt(10.0, glob_log10_abserr);
glob_relerr := expt(10.0, glob_log10_relerr);
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_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := false;
array_y2_set_initial[1, 3] := false;
array_y2_set_initial[1, 4] := false;
array_y2_set_initial[1, 5] := false;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. 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_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < 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_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_log10normmin := -glob_large_float;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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 := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
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 ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
omniout_str(INFO, "diff ( y1 , x , 1 ) = sin ( 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, "2012-12-15T00:14:26-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest5");
logitem_str(html_log_file,
"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
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_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
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, " 151 | ");
logitem_str(html_log_file,
"mtest5 diffeq.mxt");
logitem_str(html_log_file, "mtest5 maple results");
logitem_str(html_log_file, "Languages compared");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = sin ( x ) ;")
;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest5postode.ode#################
diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;
diff ( y1 , x , 1 ) = sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_h := 0.00001 ;
glob_max_iter := 20;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(2.0 - cos(x));
end;
exact_soln_y2 := proc(x)
return(2.0 - cos(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
memory used=3.8MB, alloc=3.1MB, time=0.41
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 4.9
estimated_steps = 4900
step_error = 2.0408163265306122448979591836735e-14
est_needed_step_err = 2.0408163265306122448979591836735e-14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.0840891168028036962949267592986e-99
max_value3 = 1.0840891168028036962949267592986e-99
value3 = 1.0840891168028036962949267592986e-99
best_h = 0.001
START of Soultion
x[1] = 0.1
y2[1] (analytic) = 1.0049958347219742339044380121961
y2[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
y1[1] (analytic) = 1.0049958347219742339044380121961
y1[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
x[1] = 0.1
y2[1] (analytic) = 1.0049958347219742339044380121961
y2[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
y1[1] (analytic) = 1.0049958347219742339044380121961
y1[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.101
y2[1] (analytic) = 1.005096165624023340621597000171
y2[1] (numeric) = 1.0050959168785386879913953446422
absolute error = 2.487454846526302016555288e-07
relative error = 2.4748426385468722246457892790858e-05 %
Correct digits = 6
h = 0.001
y1[1] (analytic) = 1.005096165624023340621597000171
y1[1] (numeric) = 1.0050961656240233406699643058562
absolute error = 4.83673056852e-20
relative error = 4.8122067658243135951359049184283e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.90
NO POLE
NO POLE
x[1] = 0.102
y2[1] (analytic) = 1.0051974914298239146653143235401
y2[1] (numeric) = 1.0051969939639926090970839890418
absolute error = 4.974658313055682303344983e-07
relative error = 4.9489362592614262175472539598470e-05 %
Correct digits = 6
h = 0.001
y1[1] (analytic) = 1.0051974914298239146653143235401
y1[1] (numeric) = 1.0051974914298239147620440482383
absolute error = 9.67297246982e-20
relative error = 9.6229572320767191925391374928029e-18 %
Correct digits = 19
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.4MB, time=1.40
NO POLE
NO POLE
x[1] = 0.103
y2[1] (analytic) = 1.0052998120380501586788328071734
y2[1] (numeric) = 1.00529906587725892019067301343
absolute error = 7.461607912384881597937434e-07
relative error = 7.4222712697597351170754364123005e-05 %
Correct digits = 6
h = 0.001
y1[1] (analytic) = 1.0052998120380501586788328071734
y1[1] (numeric) = 1.0052998120380501588239200158499
absolute error = 1.450872086765e-19
relative error = 1.4432232746802554115959902071276e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.104
y2[1] (analytic) = 1.0054031273463814729626255055154
y2[1] (numeric) = 1.0054021325162657165118438128773
absolute error = 9.948301157564507816926381e-07
relative error = 9.8948380873069626185062653545595e-05 %
Correct digits = 6
h = 0.001
y1[1] (analytic) = 1.0054031273463814729626255055154
y1[1] (numeric) = 1.0054031273463814731560652147781
absolute error = 1.934397092627e-19
relative error = 1.9240014676824866665069432933987e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=1.90
NO POLE
NO POLE
x[1] = 0.105
y2[1] (analytic) = 1.0055074372515025577949868753959
y2[1] (numeric) = 1.0055061937779463676426863638163
absolute error = 1.2434735561901523005115796e-06
relative error = 0.00012366627138921185968692360093448 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0055074372515025577949868753959
y1[1] (numeric) = 1.0055074372515025580367740535003
absolute error = 2.417871781044e-19
relative error = 2.4046284407931532749010893617440e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=2.41
NO POLE
NO POLE
x[1] = 0.106
y2[1] (analytic) = 1.0056127416491035167473238881278
y2[1] (numeric) = 1.0056112495582396205743210530664
absolute error = 1.4920908638961730028350614e-06
relative error = 0.00014837628861476977800318379483821 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0056127416491035167473238881278
y1[1] (numeric) = 1.0056127416491035170374534549817
absolute error = 2.901295668539e-19
relative error = 2.8851023345042024765847792310386e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.107
y2[1] (analytic) = 1.0057190404338799609940437656082
y2[1] (numeric) = 1.0057172997520897037681430149424
absolute error = 1.7406817902572259007506658e-06
relative error = 0.00017307833701808744513849995139014 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0057190404338799609940437656082
y1[1] (numeric) = 1.0057190404338799613325105927772
absolute error = 3.384668271690e-19
relative error = 3.3654212912483104042901073827821e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=2.92
NO POLE
NO POLE
x[1] = 0.108
y2[1] (analytic) = 1.0058263334995331146169340305467
y2[1] (numeric) = 1.005824344253446432211584915212
absolute error = 1.9892460866824053491153347e-06
relative error = 0.00019777232116813818925278903740075 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0058263334995331146169340305467
y1[1] (numeric) = 1.005826333499533115003732941259
absolute error = 3.867989107123e-19
relative error = 3.8455834554114857509889324706029e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=3.43
NO POLE
NO POLE
x[1] = 0.109
y2[1] (analytic) = 1.0059346207387699209039295664461
y2[1] (numeric) = 1.0059323829552653134682931261482
absolute error = 2.2377835046074356364402979e-06
relative error = 0.00022245814573555304907841866258608 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0059346207387699209039295664461
y1[1] (numeric) = 1.005934620738769921339055335598
absolute error = 4.351257691519e-19
relative error = 4.3255869733595474165389586317185e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.11
y2[1] (analytic) = 1.0060439020433031496421603885802
y2[1] (numeric) = 1.0060414157495076547226112425088
absolute error = 2.4862937954949195491460714e-06
relative error = 0.00024713571549364671766050163935921 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0060439020433031496421603885802
y1[1] (numeric) = 1.006043902043303150125607742741
absolute error = 4.834473541608e-19
relative error = 4.8054299934516274677430909566628e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=3.94
NO POLE
NO POLE
x[1] = 0.111
y2[1] (analytic) = 1.006154177303851505405172832928
y2[1] (numeric) = 1.0061514425271406708182638939685
absolute error = 2.7347767108345869089389595e-06
relative error = 0.00027180493531944096090606219549875 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.006154177303851505405172832928
y1[1] (numeric) = 1.0061541773038515059369364503455
absolute error = 5.317636174175e-19
relative error = 5.2851106660655558436180354567542e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=4.45
NO POLE
NO POLE
x[1] = 0.112
y2[1] (analytic) = 1.0062654464101397368342158758533
y2[1] (numeric) = 1.0062624631781375932911328153294
absolute error = 2.9832320021435430830605239e-06
relative error = 0.00029646571019468548853106019605915 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0062654464101397368342158758533
y1[1] (numeric) = 1.006265446410139737414290386459
absolute error = 5.800745106057e-19
relative error = 5.7646271436142480245422983030641e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.113
y2[1] (analytic) = 1.0063777092508987469134833032516
y2[1] (numeric) = 1.0063744775914777803960161417421
absolute error = 3.2316594209665174671615095e-06
relative error = 0.00032111794520687625509828646820487 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0063777092508987469134833032516
y1[1] (numeric) = 1.006377709250898747541863288666
absolute error = 6.283799854144e-19
relative error = 6.2439775805660197202163014286936e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=4.96
NO POLE
NO POLE
x[1] = 0.114
y2[1] (analytic) = 1.0064909657138657042392014539315
y2[1] (numeric) = 1.0064874856551468281272609021877
absolute error = 3.4800587188761119405517438e-06
relative error = 0.00034576154555027116894397091799198 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0064909657138657042392014539315
y1[1] (numeric) = 1.0064909657138657049158814474699
absolute error = 6.766799935384e-19
relative error = 6.7231601334688250843944272665536e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=5.47
NO POLE
NO POLE
x[1] = 0.115
y2[1] (analytic) = 1.0066052156857841552824512681535
y2[1] (numeric) = 1.0066014872561366822331576905975
absolute error = 3.7284296474730492935775560e-06
relative error = 0.0003703964165269031868965693026335 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0066052156857841552824512681535
y1[1] (numeric) = 1.006605215685784156007425754831
absolute error = 7.249744866775e-19
relative error = 7.2021729609615264110954250682799e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=5.97
NO POLE
NO POLE
x[1] = 0.116
y2[1] (analytic) = 1.006720459052404137645612378511
y2[1] (numeric) = 1.0067164822804457512239855002248
absolute error = 3.9767719583864216268782862e-06
relative error = 0.00039502246354759077279760714077843 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.006720459052404137645612378511
y1[1] (numeric) = 1.0067204590524041384188757950483
absolute error = 7.732634165373e-19
relative error = 7.6810142238010115510705293688028e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.117
y2[1] (analytic) = 1.006836695698482294312315986721
y2[1] (numeric) = 1.0068324706130790203735937132336
absolute error = 4.2250854032739387222734874e-06
relative error = 0.00041963959213294569794165509893348 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.006836695698482294312315986721
y1[1] (numeric) = 1.0068366956984822951338627215497
absolute error = 8.215467348287e-19
relative error = 8.1596820848763428675952957453976e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=6.46
NO POLE
NO POLE
x[1] = 0.118
y2[1] (analytic) = 1.00695392550778198889079227638
y2[1] (numeric) = 1.0069494521380481667144072439316
absolute error = 4.4733697338221763850324484e-06
relative error = 0.00044424770791437816166048127403506 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.00695392550778198889079227638
y1[1] (numeric) = 1.0069539255077819897606166696485
absolute error = 8.698243932685e-19
relative error = 8.6381747092337819386911163163761e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.5MB, time=6.96
NO POLE
NO POLE
x[1] = 0.119
y2[1] (analytic) = 1.0070721483630734218504971183478
y2[1] (numeric) = 1.0070674267383716750257398406521
absolute error = 4.7216247017468247572776957e-06
relative error = 0.00046884671663509921038516667384399 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0070721483630734218504971183478
y1[1] (numeric) = 1.007072148363073422768593461927
absolute error = 9.180963435792e-19
relative error = 9.1164902640938141450305670993177e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.12
y2[1] (analytic) = 1.0071913641461337477519018321424
y2[1] (numeric) = 1.007186394296074954815299557981
absolute error = 4.9698500587929366022741614e-06
relative error = 0.00049343652415112043362947370369853 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0071913641461337477519018321424
y1[1] (numeric) = 1.007191364146133748718264369631
absolute error = 9.663625374886e-19
relative error = 9.5946269188661363562533573747258e-17 %
Correct digits = 18
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.5MB, time=7.46
NO POLE
NO POLE
x[1] = 0.121
y2[1] (analytic) = 1.0073115727377471934693287735644
y2[1] (numeric) = 1.0073063546921904582937694178332
absolute error = 5.2180455567351755593557312e-06
relative error = 0.00051801703643225091544801688435515 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0073115727377471934693287735644
y1[1] (numeric) = 1.0073115727377471944839517002951
absolute error = 1.0146229267307e-18
relative error = 1.0072582845177500130002470317079e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.5MB, time=7.97
NO POLE
NO POLE
x[1] = 0.122
y2[1] (analytic) = 1.007432774017705177406714525728
y2[1] (numeric) = 1.0074273078067577993423452848074
absolute error = 5.4662109473780643692409206e-06
relative error = 0.00054258815956309142003379453065003 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.007432774017705177406714525728
y1[1] (numeric) = 1.007432774017705178469591988773
absolute error = 1.0628774630450e-18
relative error = 1.0550356216883613190328908353595e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.123
y2[1] (analytic) = 1.0075549678648064297061814777427
y2[1] (numeric) = 1.007549253518823873473111988292
absolute error = 5.7143459825562330694894507e-06
relative error = 0.0005671497997440257902313912453586 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0075549678648064297061814777427
y1[1] (numeric) = 1.0075549678648064308173075759196
absolute error = 1.1111260981769e-18
relative error = 1.1027945210091909631631075294724e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.5MB, time=8.47
NO POLE
NO POLE
x[1] = 0.124
y2[1] (analytic) = 1.007678154156857113449297582485
y2[1] (numeric) = 1.007672191706442978782137730955
absolute error = 5.9624504141346671598515300e-06
relative error = 0.00059170186329220953785464929288523 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.007678154156857113449297582485
y1[1] (numeric) = 1.007678154156857114608666366363
absolute error = 1.1593687838780e-18
relative error = 1.1505348003183270680482602094481e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.5MB, time=8.96
NO POLE
NO POLE
x[1] = 0.125
y2[1] (analytic) = 1.0078023327706709468509030922118
y2[1] (numeric) = 1.0077961222466769378951658305345
absolute error = 6.2105239940089557372616773e-06
relative error = 0.00061624425664255560481082363148166 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0078023327706709468509030922118
y1[1] (numeric) = 1.0078023327706709480585085641172
absolute error = 1.2076054719054e-18
relative error = 1.1982562776823766070710820311518e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.126
y2[1] (analytic) = 1.0079275035820693264453820781963
y2[1] (numeric) = 1.0079210450155952209057818492475
absolute error = 6.4585664741055396002289488e-06
relative error = 0.00064077688634871727414717432705123 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0079275035820693264453820781963
y1[1] (numeric) = 1.0079275035820693277012181922189
absolute error = 1.2558361140226e-18
relative error = 1.2459587713992219707818996616763e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.5MB, time=9.46
NO POLE
NO POLE
x[1] = 0.127
y2[1] (analytic) = 1.0080536664658814512652555481279
y2[1] (numeric) = 1.0080469598882750693059331726606
absolute error = 6.7065776063819593223754673e-06
relative error = 0.0006652996590840682102506051255071 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0080536664658814512652555481279
y1[1] (numeric) = 1.0080536664658814525693162101268
absolute error = 1.3040606619989e-18
relative error = 1.2936420999992833129922877011455e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.5MB, time=9.96
NO POLE
NO POLE
x[1] = 0.128
y2[1] (analytic) = 1.0081808212959444480119719826911
y2[1] (numeric) = 1.0081738667388016209086771075129
absolute error = 6.9545571428271032948751782e-06
relative error = 0.00068981248164267960754631975608026 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0081808212959444480119719826911
y1[1] (numeric) = 1.0081808212959444493642510503008
absolute error = 1.3522790676097e-18
relative error = 1.3413060822476684585473909402488e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.129
y2[1] (analytic) = 1.0083089679451034972187701205446
y2[1] (numeric) = 1.0083017654402680357630325757541
absolute error = 7.2025048354614557375447905e-06
relative error = 0.00071431526094029442715753260075991 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0083089679451034972187701205446
y1[1] (numeric) = 1.0083089679451034986192614031812
absolute error = 1.4004912826366e-18
relative error = 1.3889505371461186161198882003857e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.5MB, time=10.45
NO POLE
NO POLE
x[1] = 0.13
y2[1] (analytic) = 1.0084381062852119604054878288482
y2[1] (numeric) = 1.0084306558647756230608094899558
absolute error = 7.4504204363373446783388924e-06
relative error = 0.00073880790401529870110502985548359 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0084381062852119604054878288482
y1[1] (numeric) = 1.0084381062852119618541850877156
absolute error = 1.4486972588674e-18
relative error = 1.4365752839348491924192235518974e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.5MB, time=10.95
NO POLE
NO POLE
x[1] = 0.131
y2[1] (analytic) = 1.0085682361871315082251899045384
y2[1] (numeric) = 1.0085605378834339690352889032778
absolute error = 7.6983036975391899010012606e-06
relative error = 0.00076329031802968988374282424796756 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0085682361871315082251899045384
y1[1] (numeric) = 1.0085682361871315097220868526346
absolute error = 1.4968969480962e-18
relative error = 1.4841801420944840578262892420310e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.132
y2[1] (analytic) = 1.008699357520732249602486659737
y2[1] (numeric) = 1.0086914113663610658516260353194
absolute error = 7.9461543711837508606244176e-06
relative error = 0.0007877624102700422302442744879136 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.008699357520732249602486659737
y1[1] (numeric) = 1.0086993575207322511475769618601
absolute error = 1.5450903021231e-18
relative error = 1.5317649313475874471457328895013e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.5MB, time=11.45
NO POLE
NO POLE
x[1] = 0.133
y2[1] (analytic) = 1.0088314701548928618634141529829
y2[1] (numeric) = 1.0088232761826834414888472834641
absolute error = 8.1939722094203745668695188e-06
relative error = 0.0008122240881484691820718415163214 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0088314701548928618634141529829
y1[1] (numeric) = 1.008831470154892863456691425738
absolute error = 1.5932772727551e-18
relative error = 1.5793294716613798123378675326255e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.5MB, time=11.95
NO POLE
NO POLE
x[1] = 0.134
y2[1] (analytic) = 1.0089645739575007218567459364203
y2[1] (numeric) = 1.0089561322005362906133113377309
absolute error = 8.4417569644312434345986894e-06
relative error = 0.00083667525920358273948312202309177 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0089645739575007218567459364203
y1[1] (numeric) = 1.0089645739575007234982037482252
absolute error = 1.6414578118049e-18
relative error = 1.6268735832483658171712822631178e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.135
y2[1] (analytic) = 1.0090986687954520380666051976395
y2[1] (numeric) = 1.0090899792870636064435035256819
absolute error = 8.6895083884316231016719576e-06
relative error = 0.00086111583110144980124592627122883 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0090986687954520380666051976395
y1[1] (numeric) = 1.0090986687954520397562370687317
absolute error = 1.6896318710922e-18
relative error = 1.6743970865694348780525365324007e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.5MB, time=12.46
NO POLE
NO POLE
x[1] = 0.136
y2[1] (analytic) = 1.009233754534651983716245183572
y2[1] (numeric) = 1.0092248173084183136060315226038
absolute error = 8.9372262336701102136609682e-06
relative error = 0.00088554571163654545185594710906099 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.009233754534651983716245183572
y1[1] (numeric) = 1.0092337545346519854540445860148
absolute error = 1.7377994024428e-18
relative error = 1.7218998023347749176858209999829e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.5MB, time=12.96
NO POLE
NO POLE
x[1] = 0.137
y2[1] (analytic) = 1.0093698310400148308628648026684
y2[1] (numeric) = 1.0093606461297624019826895709775
absolute error = 9.1849102524288801752316909e-06
relative error = 0.0009099648087327031766719911522922 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0093698310400148308628648026684
y1[1] (numeric) = 1.0093698310400148326488251603576
absolute error = 1.7859603576892e-18
relative error = 1.7693815515062669794463110118429e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.5MB, time=13.46
NO POLE
NO POLE
x[1] = 0.138
y2[1] (analytic) = 1.0095068981754640854833253105562
y2[1] (numeric) = 1.0094974656152670615484573621834
absolute error = 9.4325601970239348679483728e-06
relative error = 0.00093437303044406198550580549367898 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0095068981754640854833253105562
y1[1] (numeric) = 1.0095068981754640873174399992266
absolute error = 1.8341146886704e-18
relative error = 1.8168421552990809308495612322067e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.139
y2[1] (analytic) = 1.0096449558039326235506329934705
y2[1] (numeric) = 1.0096352756281128182002987424545
absolute error = 9.6801758198053503342510160e-06
relative error = 0.00095877028495601042532622583856347 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0096449558039326235506329934705
y1[1] (numeric) = 1.0096449558039326254328953407028
absolute error = 1.8822623472323e-18
relative error = 1.8642814351838595922820219543277e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.5MB, time=13.97
NO POLE
NO POLE
x[1] = 0.14
y2[1] (analytic) = 1.0097840037873628281010517729886
y2[1] (numeric) = 1.0097740760304896705766244142903
absolute error = 9.9277568731575244273586983e-06
relative error = 0.00098315648058612746286068834444101 %
Correct digits = 5
h = 0.001
y1[1] (analytic) = 1.0097840037873628281010517729886
y1[1] (numeric) = 1.0097840037873628300314550582156
absolute error = 1.9304032852270e-18
relative error = 1.9116992128878071573709625453143e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.5MB, time=14.47
NO POLE
NO POLE
x[1] = 0.141
y2[1] (analytic) = 1.0099240419867067272917086649643
y2[1] (numeric) = 1.0099138666835972278672818138794
absolute error = 1.01753031094994244268510849e-05
relative error = 0.0010075315257851202180010790911536 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0099240419867067272917086649643
y1[1] (numeric) = 1.009924041986706729270246119478
absolute error = 1.9785374545137e-18
relative error = 1.9590953103973563867515560337493e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.142
y2[1] (analytic) = 1.0100650702619261334485540350706
y2[1] (numeric) = 1.0100546474476448486139343545536
absolute error = 1.04228142812848346196805170e-05
relative error = 0.0010318953291377585290454362217912 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0100650702619261334485540350706
y1[1] (numeric) = 1.0100650702619261354752188420288
absolute error = 2.0266648069582e-18
relative error = 2.0064695499594428989578491232858e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.5MB, time=14.97
NO POLE
NO POLE
x[1] = 0.143
y2[1] (analytic) = 1.0102070884719927831045376030009
y2[1] (numeric) = 1.0101964181818517805006912359043
absolute error = 1.06702901410026038463670966e-05
relative error = 0.0010562477993638063309321617700527 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0102070884719927831045376030009
y1[1] (numeric) = 1.0102070884719927851793228974339
absolute error = 2.0747852944330e-18
relative error = 2.0538217540833676612349685675523e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.5MB, time=15.48
NO POLE
NO POLE
x[1] = 0.144
y2[1] (analytic) = 1.0103500964748884780278601571639
y2[1] (numeric) = 1.0103391787444473011348480279447
absolute error = 1.09177304411768930121292192e-05
relative error = 0.0010805888453189498277491360150093 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0103500964748884780278601571639
y1[1] (numeric) = 1.0103500964748884801507590259818
absolute error = 2.1228988688179e-18
relative error = 2.1011517455431480905737774107984e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.145
y2[1] (analytic) = 1.010494094127605227240159951634
y2[1] (numeric) = 1.0104829289926708598175972495877
absolute error = 1.11651349343674225627020463e-05
relative error = 0.0011049183759957224409264503560354 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.010494094127605227240159951634
y1[1] (numeric) = 1.0104940941276052294111654336331
absolute error = 2.1710054819991e-18
relative error = 2.1484593473783780044156659137295e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.5MB, time=15.96
NO POLE
NO POLE
x[1] = 0.146
y2[1] (analytic) = 1.0106390812861453900244917671803
y2[1] (numeric) = 1.010627668782772220304567170741
absolute error = 1.14125033731697199245964393e-05
relative error = 0.0011292363005244265146483759496291 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0106390812861453900244917671803
y1[1] (numeric) = 1.0106390812861453922435968530504
absolute error = 2.2191050858701e-18
relative error = 2.1957443828968631257214266691320e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.5MB, time=16.46
NO POLE
NO POLE
x[1] = 0.147
y2[1] (analytic) = 1.0107850578055218199229556284092
y2[1] (numeric) = 1.0107733979700116045560460774931
absolute error = 1.16598355102153669095509161e-05
relative error = 0.0011535425281740517601476592847752 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0107850578055218199229556284092
y1[1] (numeric) = 1.0107850578055218221901532607404
absolute error = 2.2671976323312e-18
relative error = 2.2430066756758644686911304060840e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.148
y2[1] (analytic) = 1.0109320235397580097238311794022
y2[1] (numeric) = 1.0109201164086598374767482501771
absolute error = 1.19071310981722470829292251e-05
relative error = 0.0011778369683531904206732734173096 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0109320235397580097238311794022
y1[1] (numeric) = 1.0109320235397580120391142526922
absolute error = 2.3152830732900e-18
relative error = 2.2902460495643250095256831291931e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.5MB, time=16.96
NO POLE
NO POLE
x[1] = 0.149
y2[1] (analytic) = 1.0110799783418882374380727307282
y2[1] (numeric) = 1.0110678239519984926449769145591
absolute error = 1.21543898897447930958161691e-05
relative error = 0.0012021195306109491390513483103674 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0110799783418882374380727307282
y1[1] (numeric) = 1.0110799783418882398014340913892
absolute error = 2.3633613606610e-18
relative error = 2.3374623286841994257829779943102e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.5MB, time=17.46
NO POLE
NO POLE
x[1] = 0.15
y2[1] (analytic) = 1.0112289220639577132650190013457
y2[1] (numeric) = 1.0112165204523200390310384369996
absolute error = 1.24016116376742339805643461e-05
relative error = 0.0012263901246378575098881473688269 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0112289220639577132650190013457
y1[1] (numeric) = 1.0112289220639577156764514477116
absolute error = 2.4114324463659e-18
relative error = 2.3846553374324700116642796635051e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.151
y2[1] (analytic) = 1.0113788545570227275471705896988
y2[1] (numeric) = 1.0113662057609279887047610451868
absolute error = 1.26487960947388424095445120e-05
relative error = 0.001250648660266773298593642956255 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0113788545570227275471705896988
y1[1] (numeric) = 1.0113788545570227300066668720325
absolute error = 2.4594962823337e-18
relative error = 2.4318249004829581507305826754132e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.5MB, time=17.95
NO POLE
NO POLE
x[1] = 0.152
y2[1] (analytic) = 1.0115297756711507997138872192414
y2[1] (numeric) = 1.0115168797281370455319703669347
absolute error = 1.28959430137541819168523067e-05
relative error = 0.0012748950474737843095344634010764 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0115297756711507997138872192414
y1[1] (numeric) = 1.0115297756711508022214400397419
absolute error = 2.5075528205005e-18
relative error = 2.4789708427878326531668700763756e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.5MB, time=18.46
NO POLE
NO POLE
x[1] = 0.153
y2[1] (analytic) = 1.0116816852554208282138558147042
y2[1] (numeric) = 1.0116685422032732548597730905833
absolute error = 1.31430521475733540827241209e-05
relative error = 0.0012991291963791068857557302469522 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0116816852554208282138558147042
y1[1] (numeric) = 1.0116816852554208307694578275139
absolute error = 2.5556020128097e-18
relative error = 2.5260929895795071514578098122214e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.154
y2[1] (analytic) = 1.0118345831579232414361794766499
y2[1] (numeric) = 1.0118211930346741541904990617293
absolute error = 1.33901232490872456804149206e-05
relative error = 0.0013233510172479810228425701496693 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0118345831579232414361794766499
y1[1] (numeric) = 1.0118345831579232440398232878621
absolute error = 2.6036438112122e-18
relative error = 2.5731911663725307856684579723309e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.5MB, time=18.96
NO POLE
NO POLE
x[1] = 0.155
y2[1] (analytic) = 1.0119884692257601496199364332395
y2[1] (numeric) = 1.0119748320696889248441511423583
absolute error = 1.36371560712247757852908812e-05
relative error = 0.0013475604204915620796238624049056 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0119884692257601496199364332395
y1[1] (numeric) = 1.0119884692257601522716146009058
absolute error = 2.6516781676663e-18
relative error = 2.6202651989651756957298981116481e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.5MB, time=19.47
NO POLE
NO POLE
x[1] = 0.156
y2[1] (analytic) = 1.0121433433050454977520570596639
y2[1] (numeric) = 1.0121294591546785446092111699407
absolute error = 1.38841503669531428458897232e-05
relative error = 0.0013717573166678090685530639750861 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0121433433050454977520570596639
y1[1] (numeric) = 1.0121433433050455004517620938013
absolute error = 2.6997050341374e-18
relative error = 2.6673149134408204022223756791694e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.157
y2[1] (analytic) = 1.0122992052409052194533660673757
y2[1] (numeric) = 1.0122850741350159413816493656984
absolute error = 1.41311058892780717167016773e-05
relative error = 0.0013959416164823695087337304911831 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0122992052409052194533660673757
y1[1] (numeric) = 1.0122992052409052222010904299744
absolute error = 2.7477243625987e-18
relative error = 2.7143401361703146786772501791887e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.5MB, time=19.97
NO POLE
NO POLE
x[1] = 0.158
y2[1] (analytic) = 1.0124560548774773918526359770927
y2[1] (numeric) = 1.0124416768550861477919835530458
absolute error = 1.43780223912440606524240469e-05
relative error = 0.0014201132307894608246906172414841 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0124560548774773918526359770927
y1[1] (numeric) = 1.0124560548774773946483720821238
absolute error = 2.7957361050311e-18
relative error = 2.7613406938135469630723750404200e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.5MB, time=20.47
NO POLE
NO POLE
x[1] = 0.159
y2[1] (analytic) = 1.0126138920579123914484970015328
y2[1] (numeric) = 1.0125992671582864568202335591583
absolute error = 1.46248996259346282634423745e-05
relative error = 0.0014442720705927482741209903499192 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0126138920579123914484970015328
y1[1] (numeric) = 1.0126138920579123942922372149555
absolute error = 2.8437402134227e-18
relative error = 2.8083164133206101428445914766488e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.5MB, time=20.97
NO POLE
NO POLE
x[1] = 0.16
y2[1] (analytic) = 1.0127727166243730509590474759817
y2[1] (numeric) = 1.0127578448870265783986151847275
absolute error = 1.48717373464725604322912542e-05
relative error = 0.0014684180470462193879949973968718 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0127727166243730509590474759817
y1[1] (numeric) = 1.012772716624373053850784115751
absolute error = 2.8917366397693e-18
relative error = 2.8552671219339484613199650750846e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.161
y2[1] (analytic) = 1.0129325284180348171590079870976
y2[1] (numeric) = 1.0129174098827287970018171392216
absolute error = 1.51185353060201571908478760e-05
relative error = 0.0014925510714550549065086319914492 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0129325284180348171590079870976
y1[1] (numeric) = 1.0129325284180348200987333231723
absolute error = 2.9397253360747e-18
relative error = 2.9021926471902997544685282996129e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.5MB, time=21.47
NO POLE
NO POLE
x[1] = 0.162
y2[1] (analytic) = 1.0130933272790859097042613628125
y2[1] (numeric) = 1.0130779619858281302247033513874
absolute error = 1.53652932577794795580114251e-05
relative error = 0.0015166710552764961945279691876678 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0130933272790859097042613628125
y1[1] (numeric) = 1.0130933272790859126919676171625
absolute error = 2.9877062543500e-18
relative error = 2.9490928169216435361903438987142e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.5MB, time=21.98
NO POLE
NO POLE
x[1] = 0.163
y2[1] (analytic) = 1.0132551130467274809436196988004
y2[1] (numeric) = 1.0132395010357724883472820773051
absolute error = 1.56120109549925963376214953e-05
relative error = 0.0015407779101207091202989408547194 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0132551130467274809436196988004
y1[1] (numeric) = 1.0132551130467274839792990454148
absolute error = 3.0356793466144e-18
relative error = 2.9959674592576232947564062093475e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.164
y2[1] (analytic) = 1.0134178855591737767176586097624
y2[1] (numeric) = 1.0134020268710228348867822410396
absolute error = 1.58586881509418308763687228e-05
relative error = 0.0015648715477516443813329556954333 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0134178855591737767176586097624
y1[1] (numeric) = 1.0134178855591737798013031746572
absolute error = 3.0836445648948e-18
relative error = 3.0428164026267770676701105971594e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.5MB, time=22.47
NO POLE
NO POLE
x[1] = 0.165
y2[1] (analytic) = 1.0135816446536522981444579067051
y2[1] (numeric) = 1.0135655393290533481366764558256
absolute error = 1.61053245989500077814508795e-05
relative error = 0.0015889518800878942615151372665614 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0135816446536522981444579067051
y1[1] (numeric) = 1.013581644653652301276059767931
absolute error = 3.1316018612259e-18
relative error = 3.0896394757582548093508869821806e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.5MB, time=22.97
NO POLE
NO POLE
x[1] = 0.166
y2[1] (analytic) = 1.0137463901664039643920869144861
y2[1] (numeric) = 1.0137300382463515836924891867771
absolute error = 1.63519200523806995977277090e-05
relative error = 0.0016130188192035458036188498620377 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0137463901664039643920869144861
y1[1] (numeric) = 1.0137463901664039675716381021367
absolute error = 3.1795511876506e-18
relative error = 3.1364365076838246803101704773874e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.167
y2[1] (analytic) = 1.0139121219326832764376716571557
y2[1] (numeric) = 1.0138955234584186379642275293262
absolute error = 1.65984742646384734441278295e-05
relative error = 0.0016370722773290303815474972779544 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0139121219326832764376716571557
y1[1] (numeric) = 1.013912121932683279665164153375
absolute error = 3.2274924962193e-18
relative error = 3.1832073277387870974906539769479e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.5MB, time=23.48
NO POLE
NO POLE
x[1] = 0.168
y2[1] (analytic) = 1.014078839786758481812880152039
y2[1] (numeric) = 1.0140619947997693126752710909746
absolute error = 1.68449869891691376090610644e-05
relative error = 0.0016611121668519696567623053716469 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.014078839786758481812880152039
y1[1] (numeric) = 1.0140788397867584850883058910299
absolute error = 3.2754257389909e-18
relative error = 3.2299517655645588839622713621658e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.5MB, time=23.97
NO POLE
NO POLE
x[1] = 0.169
y2[1] (analytic) = 1.0142465435619117403356610670895
y2[1] (numeric) = 1.0142294521039322803475564774812
absolute error = 1.70914579794599881045896083e-05
relative error = 0.0016851384003180179034929296109545 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0142465435619117403356610670895
y1[1] (numeric) = 1.0142465435619117436590119351217
absolute error = 3.3233508680322e-18
relative error = 3.2766696511096719151843546305470e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.17
y2[1] (analytic) = 1.0144152330904392908280700097875
y2[1] (numeric) = 1.0143978952034502507728908983155
absolute error = 1.73378869890400551791114720e-05
relative error = 0.001709150890431700687466253576818 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0144152330904392908280700097875
y1[1] (numeric) = 1.0144152330904392941993378452054
absolute error = 3.3712678354179e-18
relative error = 3.3233608146313567875601322501998e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=24.47
NO POLE
NO POLE
x[1] = 0.171
y2[1] (analytic) = 1.0145849082036516188200167297711
y2[1] (numeric) = 1.0145673239298801384702284200764
absolute error = 1.75842737714803497883096947e-05
relative error = 0.001733149550057249883027657762527 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0145849082036516188200167297711
y1[1] (numeric) = 1.0145849082036516222391933230022
absolute error = 3.4191765932311e-18
relative error = 3.3700250866976122373288486174595e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.5MB, time=24.97
NO POLE
NO POLE
x[1] = 0.172
y2[1] (analytic) = 1.0147555687318736252387655314679
y2[1] (numeric) = 1.014737738113793231128741410615
absolute error = 1.78306180803941100241208529e-05
relative error = 0.001757134292219435013668331000429 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0147555687318736252387655314679
y1[1] (numeric) = 1.014755568731873628705842625031
absolute error = 3.4670770935631e-18
relative error = 3.4166622981885771506386195238858e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.173
y2[1] (analytic) = 1.0149272145044447960840202072392
y2[1] (numeric) = 1.0149091375847753590365187308034
absolute error = 1.80769196694370475014764358e-05
relative error = 0.0017811050301043909011118618398188 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0149272145044447960840202072392
y1[1] (numeric) = 1.0149272145044447995989894957526
absolute error = 3.5149692885134e-18
relative error = 3.4632722802980927071501197823198e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=25.46
NO POLE
NO POLE
x[1] = 0.174
y2[1] (analytic) = 1.0150998453497193730884238159675
y2[1] (numeric) = 1.0150815221714270654947212452652
absolute error = 1.83231782923075937025707023e-05
relative error = 0.0018050616770604416082533769533933 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0150998453497193730884238159675
y1[1] (numeric) = 1.0150998453497193766512769461573
absolute error = 3.5628531301898e-18
relative error = 3.5098548645353558862412599841521e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.5MB, time=25.97
NO POLE
NO POLE
x[1] = 0.175
y2[1] (analytic) = 1.0152734610950665253633026466005
y2[1] (numeric) = 1.0152548917013637782170242379274
absolute error = 1.85693937027471462784086731e-05
relative error = 0.0018290041465989206613848791491938 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0152734610950665253633026466005
y1[1] (numeric) = 1.0152734610950665289740312173089
absolute error = 3.6107285707084e-18
relative error = 3.5564098827264671992460207871527e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.176
y2[1] (analytic) = 1.0154480615668705220294827209227
y2[1] (numeric) = 1.0154292460012159817141753329644
absolute error = 1.88155656545403153073879583e-05
relative error = 0.0018529323523949875372811724804934 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0154480615668705220294827209227
y1[1] (numeric) = 1.0154480615668705256880782831166
absolute error = 3.6585955621939e-18
relative error = 3.6029371670162666520607629083433e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.5MB, time=26.47
NO POLE
NO POLE
x[1] = 0.177
y2[1] (analytic) = 1.0156236465905309058330062047525
y2[1] (numeric) = 1.0156045848966293906634955365913
absolute error = 1.90616939015151695106681612e-05
relative error = 0.0018768462082884404008618369369573 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0156236465905309058330062047525
y1[1] (numeric) = 1.0156236465905309095394602615317
absolute error = 3.7064540567792e-18
relative error = 3.6494365498694729370504428219258e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.5MB, time=26.97
NO POLE
NO POLE
x[1] = 0.178
y2[1] (analytic) = 1.0158002159904626677455741118622
y2[1] (numeric) = 1.0157809082122651242631500302194
absolute error = 1.93077781975434824240816428e-05
relative error = 0.0019007456282845250792861234051399 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0158002159904626677455741118622
y1[1] (numeric) = 1.015800215990462671499878118468
absolute error = 3.7543040066058e-18
relative error = 3.6959078640726033290008730721171e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.179
y2[1] (analytic) = 1.0159777695900964225495407001936
y2[1] (numeric) = 1.0159582157717998815710143607184
absolute error = 1.95538182965409785263394752e-05
relative error = 0.0019246305265547402584793727894602 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0159777695900964225495407001936
y1[1] (numeric) = 1.0159777695900964263516860640173
absolute error = 3.8021453638237e-18
relative error = 3.7423509427353937473477759723381e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=27.48
NO POLE
NO POLE
x[1] = 0.18
y2[1] (analytic) = 1.0161563072118785854072839753885
y2[1] (numeric) = 1.0161365073979261178279606889327
absolute error = 1.97998139524675793232864558e-05
relative error = 0.0019485008174376388882316135323134 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0161563072118785854072839753885
y1[1] (numeric) = 1.0161563072118785892572620559802
absolute error = 3.8499780805917e-18
relative error = 3.7887656192926052469450751301325e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=27.98
NO POLE
NO POLE
x[1] = 0.181
y2[1] (analytic) = 1.0163358286772715494147757322793
y2[1] (numeric) = 1.0163157829123522217653877731812
absolute error = 2.00457649193276493879590981e-05
relative error = 0.0019723564154396257821513514172918 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0163358286772715494147757322793
y1[1] (numeric) = 1.0163358286772715533125778413564
absolute error = 3.8978021090771e-18
relative error = 3.8351517275052325000509353419224e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=217.4MB, alloc=4.5MB, time=28.48
x[1] = 0.182
y2[1] (analytic) = 1.016516333806753864139173580784
y2[1] (numeric) = 1.0164960421358026938968173802246
absolute error = 2.02916709511702423562005594e-05
relative error = 0.0019961972352357513989002266536282 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.016516333806753864139173580784
y1[1] (numeric) = 1.0165163338067538680847909822397
absolute error = 3.9456174014557e-18
relative error = 3.8815091014620003490924327811112e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.183
y2[1] (analytic) = 1.0166978224198204151402564186277
y2[1] (numeric) = 1.0166772848880183257933788321192
absolute error = 2.05375318020893468775865085e-05
relative error = 0.0020200231916705017912771677269504 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0166978224198204151402564186277
y1[1] (numeric) = 1.0166978224198204191336803285401
absolute error = 3.9934239099124e-18
relative error = 3.9278375755814431147821424702048e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.5MB, time=28.98
NO POLE
NO POLE
x[1] = 0.184
y2[1] (analytic) = 1.0168802943349826044755238294719
y2[1] (numeric) = 1.0168595109877563803430024134876
absolute error = 2.07833472262241325214159843e-05
relative error = 0.0020438341997585847098639121499786 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0168802943349826044755238294719
y1[1] (numeric) = 1.0168802943349826085167454161124
absolute error = 4.0412215866405e-18
relative error = 3.9741369846126974335407210128112e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.6MB, time=29.49
NO POLE
NO POLE
x[1] = 0.185
y2[1] (analytic) = 1.0170637493697685321887789013652
y2[1] (numeric) = 1.017042720252790772993141380027
absolute error = 2.10291169777591956375213382e-05
relative error = 0.0020676301746857118480872821235034 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0170637493697685321887789013652
y1[1] (numeric) = 1.0170637493697685362777892852076
absolute error = 4.0890103838424e-18
relative error = 4.0204071636376649034420052084208e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.186
y2[1] (analytic) = 1.0172481873407231787820129769491
y2[1] (numeric) = 1.01722691249991225397684132555
absolute error = 2.12748408109248051716513991e-05
relative error = 0.002091411031809377215697391307179 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0172481873407231787820129769491
y1[1] (numeric) = 1.0172481873407231829188032306785
absolute error = 4.1367902537294e-18
relative error = 4.0666479480722817785129772963042e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.6MB, time=29.99
NO POLE
NO POLE
x[1] = 0.187
y2[1] (analytic) = 1.0174336080634085886704098635492
y2[1] (numeric) = 1.0174120875449285915219746815015
absolute error = 2.15205184799971484351820477e-05
relative error = 0.002115176686659631627805009344644 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0174336080634085886704098635492
y1[1] (numeric) = 1.0174336080634085928549710120707
absolute error = 4.1845611485215e-18
relative error = 4.1128591736677813815617321775032e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.6MB, time=30.49
NO POLE
NO POLE
x[1] = 0.188
y2[1] (analytic) = 1.0176200113524040546202860481617
y2[1] (numeric) = 1.0175982452026647560434571397346
absolute error = 2.17661497392985768289084271e-05
relative error = 0.0021389270549398532967656146768125 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0176200113524040546202860481617
y1[1] (numeric) = 1.0176200113524040588526090686097
absolute error = 4.2323230204480e-18
relative error = 4.1590406765127353635208875328300e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.189
y2[1] (analytic) = 1.0178073970213063031697824794125
y2[1] (numeric) = 1.0177853852869631053182618063426
absolute error = 2.20117343431978515206730699e-05
relative error = 0.0021626620525275145143422176607654 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0178073970213063031697824794125
y1[1] (numeric) = 1.0178073970213063074498583011593
absolute error = 4.2800758217468e-18
relative error = 4.2051922930338095176148428908066e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.6MB, time=30.99
NO POLE
NO POLE
x[1] = 0.19
y2[1] (analytic) = 1.0179957648827296810321224958101
y2[1] (numeric) = 1.0179735076106835706430459115496
absolute error = 2.22572720461103890765842605e-05
relative error = 0.0021863815954749444117238245131896 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0179957648827296810321224958101
y1[1] (numeric) = 1.0179957648827296853599420004753
absolute error = 4.3278195046652e-18
relative error = 4.2513138599979862709885854757964e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.6MB, time=31.49
NO POLE
NO POLE
x[1] = 0.191
y2[1] (analytic) = 1.0181851147483063424812494970519
y2[1] (numeric) = 1.0181626119857038439742039180484
absolute error = 2.25027626024985070455790035e-05
relative error = 0.0022100856000100877851214330491286 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0181851147483063424812494970519
y1[1] (numeric) = 1.0181851147483063468568035185115
absolute error = 4.3755540214596e-18
relative error = 4.2974052145136983624840197490505e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.192
y2[1] (analytic) = 1.0183754464286864377196569727608
y2[1] (numeric) = 1.0183526982229195660501598877471
absolute error = 2.27482057668716694970850137e-05
relative error = 0.0022337739825372599748086936392533 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0183754464286864377196569727608
y1[1] (numeric) = 1.0183754464286864421429362971562
absolute error = 4.4232793243954e-18
relative error = 4.3434661940321516254670190896853e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.6MB, time=32.01
NO POLE
NO POLE
x[1] = 0.193
y2[1] (analytic) = 1.0185667597335383022282225208382
y2[1] (numeric) = 1.0185437661322445154957109846493
absolute error = 2.29936012937867325115361889e-05
relative error = 0.002257446659637897785619826266259 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0185667597335383022282225208382
y1[1] (numeric) = 1.0185667597335383066992178865856
absolute error = 4.4709953657474e-18
relative error = 4.3894966363491311321460127117617e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.6MB, time=32.50
NO POLE
NO POLE
x[1] = 0.194
y2[1] (analytic) = 1.0187590544715486470978565056148
y2[1] (numeric) = 1.0187358155226107989082330095389
absolute error = 2.32389489378481896234960759e-05
relative error = 0.0022811035480713064370630494125854 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0187590544715486470978565056148
y1[1] (numeric) = 1.0187590544715486516165586034142
absolute error = 4.5187020977994e-18
relative error = 4.4354963796060139682344786737381e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.195
y2[1] (analytic) = 1.0189523304504227503427750241667
y2[1] (numeric) = 1.0189288462019690419255578802802
absolute error = 2.34842484537084172171438865e-05
relative error = 0.0023047445647754025313536402979537 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0189523304504227503427750241667
y1[1] (numeric) = 1.0189523304504227549091744970114
absolute error = 4.5663994728447e-18
relative error = 4.4814652622916580317285164102868e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.6MB, time=33.00
NO POLE
NO POLE
x[1] = 0.196
y2[1] (analytic) = 1.0191465874768846491952058675394
y2[1] (numeric) = 1.0191228579772885812753319898723
absolute error = 2.37294995960679198738776671e-05
relative error = 0.0023283696268674530278168011863641 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0191465874768846491952058675394
y1[1] (numeric) = 1.0191465874768846538092933107255
absolute error = 4.6140874431861e-18
relative error = 4.5274031232437919647437379615056e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.6MB, time=33.50
NO POLE
NO POLE
x[1] = 0.197
y2[1] (analytic) = 1.019341825356677333381335182191
y2[1] (numeric) = 1.0193178506545576578056633929145
absolute error = 2.39747021196755756717892765e-05
relative error = 0.0023519786516448102122567456432652 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.019341825356677333381335182191
y1[1] (numeric) = 1.0193418253566773380431011433264
absolute error = 4.6617659611354e-18
relative error = 4.5733098016499068457441038487099e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.198
y2[1] (analytic) = 1.0195380438945629393783015557216
y2[1] (numeric) = 1.0195138240387836104968647898521
absolute error = 2.42198557793288814367658695e-05
relative error = 0.0023755715565856426500348327268811 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0195380438945629393783015557216
y1[1] (numeric) = 1.0195380438945629440877365347359
absolute error = 4.7094349790143e-18
relative error = 4.6191851370495138711252819424346e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.6MB, time=34.01
NO POLE
NO POLE
x[1] = 0.199
y2[1] (analytic) = 1.0197352428943229456520432699139
y2[1] (numeric) = 1.0197107779339930714540982972759
absolute error = 2.44649603298741979449726380e-05
relative error = 0.002399148259349662111746160205213 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0197352428943229456520432699139
y1[1] (numeric) = 1.0197352428943229504091377190676
absolute error = 4.7570944491537e-18
relative error = 4.6650289693348242156686829236581e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.6MB, time=34.51
NO POLE
NO POLE
x[1] = 0.2
y2[1] (analytic) = 1.0199334221587583688758034832518
y2[1] (numeric) = 1.0199087121432321618807270116466
absolute error = 2.47100155262069950764716052e-05
relative error = 0.0024227086777788464605307701075615 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0199334221587583688758034832518
y1[1] (numeric) = 1.0199334221587583736805478071459
absolute error = 4.8047443238941e-18
relative error = 4.7108411387525004007355888001232e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.201
y2[1] (analytic) = 1.020132581489689961129097124429
y2[1] (numeric) = 1.0201076264685666890321773931092
absolute error = 2.49550211232720969197313198e-05
relative error = 0.0024462527298981584902025151786662 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.020132581489689961129097124429
y1[1] (numeric) = 1.0201325814896899659814816800147
absolute error = 4.8523845555857e-18
relative error = 4.7566214859051053183265605072761e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.6MB, time=35.00
NO POLE
NO POLE
x[1] = 0.202
y2[1] (analytic) = 1.0203327206879584080769422978976
y2[1] (numeric) = 1.0203075207110823441501155155508
absolute error = 2.51999768760639268267823468e-05
relative error = 0.0024697803339162607035256744357818 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0203327206879584080769422978976
y1[1] (numeric) = 1.0203327206879584129769573944857
absolute error = 4.9000150965881e-18
relative error = 4.8023698517521512804096771715860e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.6MB, time=35.51
NO POLE
NO POLE
x[1] = 0.203
y2[1] (analytic) = 1.0205338395534245281291580222406
y2[1] (numeric) = 1.0205083946708849013767392487427
absolute error = 2.54448825396267524187734979e-05
relative error = 0.0024932914082262260201165820925216 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0205338395534245281291580222406
y1[1] (numeric) = 1.0205338395534245330767939215116
absolute error = 4.9476358992710e-18
relative error = 4.8480860776121214439886604420036e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=274.6MB, alloc=4.6MB, time=36.01
x[1] = 0.204
y2[1] (analytic) = 1.020735937884969472579529142089
y2[1] (numeric) = 1.0207102481471004176489874582911
absolute error = 2.56897378690549305416837979e-05
relative error = 0.002516785871406244403594839853052 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.020735937884969472579529142089
y1[1] (numeric) = 1.0207359378849694775747760581024
absolute error = 4.9952469160134e-18
relative error = 4.8937700051630130267524506243702e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.205
y2[1] (analytic) = 1.0209390154804949267246382744327
y2[1] (numeric) = 1.0209130809378754335724663292034
absolute error = 2.59345426194931521719452293e-05
relative error = 0.0025402636422203253977561088112659 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0209390154804949267246382744327
y1[1] (numeric) = 1.0209390154804949317674863736371
absolute error = 5.0428480992044e-18
relative error = 4.9394214764444407481221822483032e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.6MB, time=36.52
NO POLE
NO POLE
x[1] = 0.206
y2[1] (analytic) = 1.0211430721369233119621636705127
y2[1] (numeric) = 1.021116892840377175274891939161
absolute error = 2.61792965461366872717313517e-05
relative error = 0.0025637246396189965616860177579863 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0211430721369233119621636705127
y1[1] (numeric) = 1.0211430721369233170526030717555
absolute error = 5.0904394012428e-18
relative error = 4.9850403338585562741036903044187e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.6MB, time=37.02
NO POLE
NO POLE
x[1] = 0.207
y2[1] (analytic) = 1.0213481076501979888684408950116
y2[1] (numeric) = 1.0213216836507937572388472280725
absolute error = 2.64239994042316295936669391e-05
relative error = 0.002587168782739997793882370258375 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0213481076501979888684408950116
y1[1] (numeric) = 1.021348107650197994006461669549
absolute error = 5.1380207745374e-18
relative error = 5.0306264201716455708435084262467e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.208
y2[1] (analytic) = 1.0215541218152834612550852449989
y2[1] (numeric) = 1.0215274531643343861136505311679
absolute error = 2.66686509490751414347138310e-05
relative error = 0.0026105959909089715356005770863812 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0215541218152834612550852449989
y1[1] (numeric) = 1.0215541218152834664406774165056
absolute error = 5.1855921715067e-18
relative error = 5.0761795785151306176129698739295e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.6MB, time=37.53
NO POLE
NO POLE
x[1] = 0.209
y2[1] (analytic) = 1.0217611144261655812044708520248
y2[1] (numeric) = 1.0217342011752295655061318637809
absolute error = 2.69132509360156983389882439e-05
relative error = 0.0026340061836401488437850749666075 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0217611144261655812044708520248
y1[1] (numeric) = 1.021761114426165586437624396604
absolute error = 5.2331535445792e-18
relative error = 5.1216996523871507316784553025777e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.6MB, time=38.03
NO POLE
NO POLE
x[1] = 0.21
y2[1] (analytic) = 1.0219690852758517550838614319006
y2[1] (numeric) = 1.0219419274767313017501121670618
absolute error = 2.71577991204533337492648388e-05
relative error = 0.0026573992806370313240974094264817 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0219690852758517550838614319006
y1[1] (numeric) = 1.0219690852758517603645662780945
absolute error = 5.2807048461939e-18
relative error = 5.1671864856543312551246525645520e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.211
y2[1] (analytic) = 1.0221780341563711505379866680538
y2[1] (numeric) = 1.0221506318611133106543797451574
absolute error = 2.74022952578398836069228964e-05
relative error = 0.0026807752017930689146996520893397 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0221780341563711505379866680538
y1[1] (numeric) = 1.0221780341563711558662326968529
absolute error = 5.3282460287991e-18
relative error = 5.2126399225518805249246049871162e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.6MB, time=38.55
NO POLE
NO POLE
x[1] = 0.212
y2[1] (analytic) = 1.022387960858774904459857235895
y2[1] (numeric) = 1.0223603141196712252289571458999
absolute error = 2.76467391036792309000899951e-05
relative error = 0.0027041338671923335115998813438518 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.022387960858774904459857235895
y1[1] (numeric) = 1.0223879608587749098356342807488
absolute error = 5.3757770448538e-18
relative error = 5.2580598076862233305349646800067e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.6MB, time=39.07
NO POLE
NO POLE
x[1] = 0.213
y2[1] (analytic) = 1.0225988651731363319396104974034
y2[1] (numeric) = 1.0225709740427228043894507587541
absolute error = 2.78911304135275501597386493e-05
relative error = 0.0027274751971101884265145754650358 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0225988651731363319396104974034
y1[1] (numeric) = 1.0225988651731363373629083442305
absolute error = 5.4232978468271e-18
relative error = 5.3034459860356688498162312543940e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.214
y2[1] (analytic) = 1.0228107468885511361911779170994
y2[1] (numeric) = 1.0227826114196081426392744256915
absolute error = 2.81354689429935519034914079e-05
relative error = 0.0027507991120139536683509374915599 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0228107468885511361911779170994
y1[1] (numeric) = 1.0228107468885511416619863042975
absolute error = 5.4708083871981e-18
relative error = 5.3487983029515601028452110133594e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.6MB, time=39.57
NO POLE
NO POLE
x[1] = 0.215
y2[1] (analytic) = 1.0230236057931376194565642727558
y2[1] (numeric) = 1.022995226038689880729537382785
absolute error = 2.83797544477387270268899708e-05
relative error = 0.0027741055325635670395603873451908 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0230236057931376194565642727558
y1[1] (numeric) = 1.0230236057931376249748728912119
absolute error = 5.5183086184561e-18
relative error = 5.3941166041597087073133979304512e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.6MB, time=40.07
NO POLE
NO POLE
x[1] = 0.216
y2[1] (analytic) = 1.0232374416740368948875277565849
y2[1] (numeric) = 1.0232088176873534172963858726537
absolute error = 2.86239866834775911418839312e-05
relative error = 0.0027973943796122410387627089261608 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0232374416740368948875277565849
y1[1] (numeric) = 1.023237441674036900453326249686
absolute error = 5.5657984931011e-18
relative error = 5.4394007357621144924640912279224e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.217
y2[1] (analytic) = 1.0234522543174130994044490852411
y2[1] (numeric) = 1.0234233861520071214755867904337
absolute error = 2.88681654059779288622948074e-05
relative error = 0.0028206655742071155611886220054315 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0234522543174130994044490852411
y1[1] (numeric) = 1.0234522543174131050177270488842
absolute error = 5.6132779636431e-18
relative error = 5.4846505442375038939562249491229e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.6MB, time=40.57
NO POLE
NO POLE
x[1] = 0.218
y2[1] (analytic) = 1.023668043508453607532176759785
y2[1] (numeric) = 1.0236389312180825464941407487092
absolute error = 2.91122903710610380360110758e-05
relative error = 0.0028439190375899063886368517527217 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.023668043508453607532176759785
y1[1] (numeric) = 1.0236680435084536131929237423876
absolute error = 5.6607469826026e-18
relative error = 5.5298658764430333456775276721205e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.6MB, time=41.07
NO POLE
NO POLE
x[1] = 0.219
y2[1] (analytic) = 1.0238848090313692462126346397834
y2[1] (numeric) = 1.0238554526700346442387109698088
absolute error = 2.93563613346019739236699746e-05
relative error = 0.0028671546911975494607900868772448 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0238848090313692462126346397834
y1[1] (numeric) = 1.0238848090313692519208401422942
absolute error = 5.7082055025108e-18
relative error = 5.5750465796156909201659312681854e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.22
y2[1] (analytic) = 1.0241025506693945105939770189553
y2[1] (numeric) = 1.0240729502913419808006534370552
absolute error = 2.96003780525297933235819001e-05
relative error = 0.0028903724566628409198825416085022 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0241025506693945105939770189553
y1[1] (numeric) = 1.0241025506693945163496304948643
absolute error = 5.7556534759090e-18
relative error = 5.6201925013729083977962387339646e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.6MB, time=41.58
NO POLE
NO POLE
x[1] = 0.221
y2[1] (analytic) = 1.0243212682047877807960754132258
y2[1] (numeric) = 1.0242914238645069529974327599573
absolute error = 2.98443402808277986426532685e-05
relative error = 0.0029135722558150729208601599966855 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0243212682047877807960754132258
y1[1] (numeric) = 1.0243212682047877865991662685751
absolute error = 5.8030908553493e-18
relative error = 5.6653034897144350524264611823284e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.6MB, time=42.08
NO POLE
NO POLE
x[1] = 0.222
y2[1] (analytic) = 1.0245409614188315396521202957203
y2[1] (numeric) = 1.0245108731710560058702072319458
absolute error = 3.00882477755337819130637745e-05
relative error = 0.0029367540106806651993228166434636 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0245409614188315396521202957203
y1[1] (numeric) = 1.0245409614188315455026378891146
absolute error = 5.8505175933943e-18
relative error = 5.7103793930232263371872566371674e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.223
y2[1] (analytic) = 1.024761630091832591426120037115
y2[1] (numeric) = 1.0247312979915398511573655830859
absolute error = 3.03321002927402687544540291e-05
relative error = 0.0029599176434837923896861670867306 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.024761630091832591426120037115
y1[1] (numeric) = 1.0247616300918325973240536797322
absolute error = 5.8979336426172e-18
relative error = 5.7554200600667150868423890062203e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.6MB, time=42.58
NO POLE
NO POLE
x[1] = 0.224
y2[1] (analytic) = 1.0249832740031222815060783338625
y2[1] (numeric) = 1.0249526981055336867437969542485
absolute error = 3.05758975885947622813796140e-05
relative error = 0.0029830630766470070861490773111209 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0249832740031222815060783338625
y1[1] (numeric) = 1.0249832740031222874514172894646
absolute error = 5.9453389556021e-18
relative error = 5.8004253399982695124774643603679e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.6MB, time=43.08
NO POLE
NO POLE
x[1] = 0.225
y2[1] (analytic) = 1.0252058929310567170726304311345
y2[1] (numeric) = 1.0251750732916374170856746434883
absolute error = 3.08196394192999869557876462e-05
relative error = 0.0030061902327918586392008075567884 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0252058929310567170726304311345
y1[1] (numeric) = 1.0252058929310567230653639160782
absolute error = 5.9927334849437e-18
relative error = 5.8453950823580573458382045117070e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=331.8MB, alloc=4.6MB, time=43.56
x[1] = 0.226
y2[1] (analytic) = 1.0254294866530169887429174718627
y2[1] (numeric) = 1.0253984233274758746105331998629
absolute error = 3.10633255411141323842719998e-05
relative error = 0.0030292990347395076805503329650103 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0254294866530169887429174718627
y1[1] (numeric) = 1.02542948665301699478303465511
absolute error = 6.0401171832473e-18
relative error = 5.8903291370741946893880734578914e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.227
y2[1] (analytic) = 1.0256540549454093931894773280223
y2[1] (numeric) = 1.0256227479896990420924174646351
absolute error = 3.13069557103510970598633872e-05
relative error = 0.0030523894055113363695083457054657 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0256540549454093931894773280223
y1[1] (numeric) = 1.0256540549454093992769673311516
absolute error = 6.0874900031293e-18
relative error = 5.9352273544643741137830565320757e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.6MB, time=44.06
NO POLE
NO POLE
x[1] = 0.228
y2[1] (analytic) = 1.0258795975836656567339292952864
y2[1] (numeric) = 1.0258480470539822760018811847272
absolute error = 3.15505296833807320481105592e-05
relative error = 0.0030754612683295543540005927541991 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0258795975836656567339292952864
y1[1] (numeric) = 1.0258795975836656628687811925033
absolute error = 6.1348518972169e-18
relative error = 5.9800895852367040348742682803984e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.6MB, time=44.54
NO POLE
NO POLE
x[1] = 0.229
y2[1] (analytic) = 1.0261061143422431599152290573844
y2[1] (numeric) = 1.0260743202950265308306118484476
absolute error = 3.17940472166290846172089368e-05
relative error = 0.0030985145466178004395392525106303 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0261061143422431599152290573844
y1[1] (numeric) = 1.0261061143422431660974318755325
absolute error = 6.1822028181481e-18
relative error = 6.0249156804908325683029746494696e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.23
y2[1] (analytic) = 1.0263336049946251630322693519284
y2[1] (numeric) = 1.0263015674865585843904574188835
absolute error = 3.20375080665786418119330449e-05
relative error = 0.0031215491640017399596270354427929 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0263336049946251630322693519284
y1[1] (numeric) = 1.0263336049946251692618120705006
absolute error = 6.2295427185722e-18
relative error = 6.0697054917195502698755849174400e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.6MB, time=45.03
NO POLE
NO POLE
x[1] = 0.231
y2[1] (analytic) = 1.0265620693133210326606007951267
y2[1] (numeric) = 1.0265297884013312640866296659515
absolute error = 3.22809119897685739711291752e-05
relative error = 0.0031445650443096578412166012233835 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0265620693133210326606007951267
y1[1] (numeric) = 1.0265620693133210389374723462759
absolute error = 6.2768715511492e-18
relative error = 6.1144588708093123908684523728069e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.6MB, time=45.52
NO POLE
NO POLE
x[1] = 0.232
y2[1] (analytic) = 1.0267915070698664691430463486806
y2[1] (numeric) = 1.0267589828111236741648578239225
absolute error = 3.25242587427949781885247581e-05
relative error = 0.0031675621115730473589957096919946 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0267915070698664691430463486806
y1[1] (numeric) = 1.0267915070698664754672356172308
absolute error = 6.3241892685502e-18
relative error = 6.1591756700417275102202689194223e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.233
y2[1] (analytic) = 1.0270219180348237350539819382704
y2[1] (numeric) = 1.0269891504867414239322653272846
absolute error = 3.27675480823111217166109858e-05
relative error = 0.0031905402900271945724162596347153 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0270219180348237350539819382704
y1[1] (numeric) = 1.027021918034823741425477761728
absolute error = 6.3714958234576e-18
relative error = 6.2038557420948425867228324324672e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.6MB, time=46.02
NO POLE
NO POLE
x[1] = 0.234
y2[1] (analytic) = 1.027253301977781884637054759369
y2[1] (numeric) = 1.0272202911980168569517414040882
absolute error = 3.30107797650276853133552808e-05
relative error = 0.0032134995041117584395330086295008 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.027253301977781884637054759369
y1[1] (numeric) = 1.0272533019777818910558459279337
absolute error = 6.4187911685647e-18
relative error = 6.2484989400438353327338683890067e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.6MB, time=46.50
NO POLE
NO POLE
x[1] = 0.235
y2[1] (analytic) = 1.0274856586673569942161098326828
y2[1] (numeric) = 1.027452404713809281209578332419
absolute error = 3.32539535477130065315002638e-05
relative error = 0.0032364396784713466018653036607589 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0274856586673569942161098326828
y1[1] (numeric) = 1.027485658667357000682185089259
absolute error = 6.4660752565762e-18
relative error = 6.2931051173625746945373840437436e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.236
y2[1] (analytic) = 1.0277189878711923935790943983139
y2[1] (numeric) = 1.0276854908020052002561441923825
absolute error = 3.34970691871933229502059314e-05
relative error = 0.00325936073795608683464257761755 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0277189878711923935790943983139
y1[1] (numeric) = 1.0277189878711924000924424385221
absolute error = 6.5133480402082e-18
relative error = 6.3376741279246858039891339137334e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.6MB, time=46.99
NO POLE
NO POLE
x[1] = 0.237
y2[1] (analytic) = 1.0279532893559588983347087647578
y2[1] (numeric) = 1.0279195492295185453193599729446
absolute error = 3.37401264403530153487918132e-05
relative error = 0.0032822626076221941569416746372656 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0279532893559588983347087647578
y1[1] (numeric) = 1.0279532893559589048953182369455
absolute error = 6.5606094721877e-18
relative error = 6.3822058260041201592285711498021e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.6MB, time=47.49
NO POLE
NO POLE
x[1] = 0.238
y2[1] (analytic) = 1.0281885628873550432415712561047
y2[1] (numeric) = 1.0281545797622909083907489201728
absolute error = 3.39831250641348508223359319e-05
relative error = 0.0033051452127325335963712496662113 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0281885628873550432415712561047
y1[1] (numeric) = 1.0281885628873550498494307613581
absolute error = 6.6078595052534e-18
relative error = 6.4267000662769824556637884243703e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.239
y2[1] (analytic) = 1.0284248082301073165096639283
y2[1] (numeric) = 1.0283905821652917762838250408457
absolute error = 3.42260648155402258388874543e-05
relative error = 0.0033280084787571786031055390208048 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0284248082301073165096639283
y1[1] (numeric) = 1.0284248082301073231647620204551
absolute error = 6.6550980921551e-18
relative error = 6.4711567038219866592035774401001e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.6MB, time=47.99
NO POLE
NO POLE
x[1] = 0.24
y2[1] (analytic) = 1.0286620251479703950738247530366
y2[1] (numeric) = 1.028627556202518765664586703064
absolute error = 3.44689454516294092380499726e-05
relative error = 0.0033508523313739651082167098609431 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0286620251479703950738247530366
y1[1] (numeric) = 1.0286620251479704017761499386911
absolute error = 6.7023251856545e-18
relative error = 6.5155755941222654789889399675776e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.6MB, time=48.49
NO POLE
NO POLE
x[1] = 0.241
y2[1] (analytic) = 1.0289002134037273808390509958078
y2[1] (numeric) = 1.0288655016369978590538803033873
absolute error = 3.47117667295217851706924205e-05
relative error = 0.0033736766964690412214017628888036 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0289002134037273808390509958078
y1[1] (numeric) = 1.0289002134037273875885917343321
absolute error = 6.7495407385243e-18
relative error = 6.5599565930655181099314186780786e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.242
y2[1] (analytic) = 1.0291393727591900378973775428355
y2[1] (numeric) = 1.0291044182307836418013979981536
absolute error = 3.49545284063960959795446819e-05
relative error = 0.0033964815001374125633465748097616 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0291393727591900378973775428355
y1[1] (numeric) = 1.0291393727591900446941222463844
absolute error = 6.7967447035489e-18
relative error = 6.6042995569457054734825130624137e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.6MB, time=48.98
NO POLE
NO POLE
x[1] = 0.243
y2[1] (analytic) = 1.0293795029751990307160929600163
y2[1] (numeric) = 1.0293443057449595400310725250032
absolute error = 3.51972302394906850204350131e-05
relative error = 0.0034192666686834832281161202868573 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0293795029751990307160929600163
y1[1] (numeric) = 1.0293795029751990375600299935408
absolute error = 6.8439370335245e-18
relative error = 6.6486043424641532152970258106991e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.6MB, time=49.47
NO POLE
NO POLE
x[1] = 0.244
y2[1] (analytic) = 1.0296206038116241632970550956892
y2[1] (numeric) = 1.0295851639396380595576311692323
absolute error = 3.54398719861037394239264569e-05
relative error = 0.0034420321286215923711061988672548 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0296206038116241632970550956892
y1[1] (numeric) = 1.0296206038116241701881727769479
absolute error = 6.8911176812587e-18
relative error = 6.6928708067301605185850649924486e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.245
y2[1] (analytic) = 1.0298626750273646193068670679285
y2[1] (numeric) = 1.0298269925739610257740699584416
absolute error = 3.56824534035935327971094869e-05
relative error = 0.0034647778066765464182381045458032 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0298626750273646193068670679285
y1[1] (numeric) = 1.0298626750273646262451536674994
absolute error = 6.9382865995709e-18
relative error = 6.7370988072623778271277933637098e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.6MB, time=49.95
NO POLE
NO POLE
x[1] = 0.246
y2[1] (analytic) = 1.0301057163803492031776735062069
y2[1] (numeric) = 1.0300697914060998245098081980267
absolute error = 3.59249742493786678653081802e-05
relative error = 0.0034875036297841468922236071639222 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0301057163803492031776735062069
y1[1] (numeric) = 1.0301057163803492101631172474991
absolute error = 6.9854437412922e-18
relative error = 6.7812882019896901881234324412615e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.6MB, time=50.44
NO POLE
NO POLE
x[1] = 0.247
y2[1] (analytic) = 1.0303497276275365821783359466519
y2[1] (numeric) = 1.0303135601932556438592824893747
absolute error = 3.61674342809383190534572772e-05
relative error = 0.003510209525091713851873358951518 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0303497276275365821783359466519
y1[1] (numeric) = 1.0303497276275365892109250059172
absolute error = 7.0325890592653e-18
relative error = 6.8254388492520922778612117369992e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=389.1MB, alloc=4.6MB, time=50.93
x[1] = 0.248
y2[1] (analytic) = 1.0305947085249155294557453097401
y2[1] (numeric) = 1.0305582986916597169807384021941
absolute error = 3.64098332558124750069075460e-05
relative error = 0.0035328954199586049405673891856154 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0305947085249155294557453097401
y1[1] (numeric) = 1.0305947085249155365354678160852
absolute error = 7.0797225063451e-18
relative error = 6.8695506078022343246715499072357e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.249
y2[1] (analytic) = 1.0308406588275051680460284191387
y2[1] (numeric) = 1.0308040066565735658649770022059
absolute error = 3.66521709316021810514169328e-05
relative error = 0.0035555612419567300401516990575235 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0308406588275051680460284191387
y1[1] (numeric) = 1.0308406588275051751728724545367
absolute error = 7.1268440353980e-18
relative error = 6.9136233368056976259367308055659e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.6MB, time=51.43
NO POLE
NO POLE
x[1] = 0.25
y2[1] (analytic) = 1.0310875782893552158554045505058
y2[1] (numeric) = 1.0310506838422892460738124654701
absolute error = 3.68944470659697815920850357e-05
relative error = 0.0035782069188710615266701094168535 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0310875782893552158554045505058
y1[1] (numeric) = 1.0310875782893552230293581498084
absolute error = 7.1739535993026e-18
relative error = 6.9576568958426203511644038180466e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.6MB, time=51.93
NO POLE
NO POLE
x[1] = 0.251
y2[1] (analytic) = 1.0313354666635462316104470294153
y2[1] (numeric) = 1.0312983300021295924479960409103
absolute error = 3.71366614166391624509885050e-05
relative error = 0.0036008323787001401244854411049856 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0313354666635462316104470294153
y1[1] (numeric) = 1.0313354666635462388314981803645
absolute error = 7.2210511509492e-18
relative error = 7.0016511449081503493502713035720e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.252
y2[1] (analytic) = 1.0315843237021898617775039281638
y2[1] (numeric) = 1.0315469448884484657843606531324
absolute error = 3.73788137413959931432750314e-05
relative error = 0.0036234375496565763554888127772462 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0315843237021898617775039281638
y1[1] (numeric) = 1.0315843237021898690456405714042
absolute error = 7.2681366432404e-18
relative error = 7.0456059444139564883182156200058e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.6MB, time=52.42
NO POLE
NO POLE
x[1] = 0.253
y2[1] (analytic) = 1.0318341491564290884510309420608
y2[1] (numeric) = 1.0317965282526310004819394684143
absolute error = 3.76209037980879690914736465e-05
relative error = 0.0036460223601675475802403189845826 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0318341491564290884510309420608
y1[1] (numeric) = 1.0318341491564290957662409711514
absolute error = 7.3152100290906e-18
relative error = 7.0895211551886645962708269736503e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.6MB, time=52.93
NO POLE
NO POLE
x[1] = 0.254
y2[1] (analytic) = 1.0320849427764384782105885568886
y2[1] (numeric) = 1.0320470798450938531568107777681
absolute error = 3.78629313446250537777791205e-05
relative error = 0.0036685867388752906280285945454724 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0320849427764384782105885568886
y1[1] (numeric) = 1.032084942776438485572859818315
absolute error = 7.3622712614264e-18
relative error = 7.1333966384791576288172557333442e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.255
y2[1] (analytic) = 1.0323367043114244319462546505563
y2[1] (numeric) = 1.0322985994152854522254205822501
absolute error = 3.81048961389797208340683062e-05
relative error = 0.0036911306146375900129807739249816 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0323367043114244319462546505563
y1[1] (numeric) = 1.0323367043114244393555749437431
absolute error = 7.4093202931868e-18
relative error = 7.1772322559516730325844487865970e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.6MB, time=53.43
NO POLE
NO POLE
x[1] = 0.256
y2[1] (analytic) = 1.0325894335096254356522027035565
y2[1] (numeric) = 1.0325510867116862484561332972184
absolute error = 3.83467979391871960694063381e-05
relative error = 0.0037136539165282617334981091268239 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0325894335096254356522027035565
y1[1] (numeric) = 1.0325894335096254431085597808791
absolute error = 7.4563570773226e-18
relative error = 7.2210278696921165627030563284795e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=411.9MB, alloc=4.6MB, time=53.95
NO POLE
NO POLE
x[1] = 0.257
y2[1] (analytic) = 1.032843130118312312188194824666
y2[1] (numeric) = 1.0328045414818089664887600240063
absolute error = 3.85886365033456994348006597e-05
relative error = 0.0037361565738376326524360108847754 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.032843130118312312188194824666
y1[1] (numeric) = 1.0328431301183123196915763914629
absolute error = 7.5033815667969e-18
relative error = 7.2647833422074334611076482992214e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.258
y2[1] (analytic) = 1.0330977938837884740087378304194
y2[1] (numeric) = 1.0330589634721988573218128695059
absolute error = 3.88304115896166869249609135e-05
relative error = 0.0037586385160730154555905185269948 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0330977938837884740087378304194
y1[1] (numeric) = 1.0330977938837884815591315450048
absolute error = 7.5503937145854e-18
relative error = 7.3084985364267768125957898423520e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.6MB, time=54.45
NO POLE
NO POLE
x[1] = 0.259
y2[1] (analytic) = 1.0333534245513901768596496492213
y2[1] (numeric) = 1.0333143524284339517672328264276
absolute error = 3.90721229562250924168227937e-05
relative error = 0.0037810996729591791861961780369323 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0333534245513901768596496492213
y1[1] (numeric) = 1.0333534245513901844570431228972
absolute error = 7.5973934736759e-18
relative error = 7.3521733157018927680568043206394e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=419.6MB, alloc=4.6MB, time=54.96
NO POLE
NO POLE
x[1] = 0.26
y2[1] (analytic) = 1.0336100218654867744417823535499
y2[1] (numeric) = 1.0335707080951253148723377595288
absolute error = 3.93137703614595694445940211e-05
relative error = 0.0038035399744388153532830081837768 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0336100218654867744417823535499
y1[1] (numeric) = 1.0336100218654867820861631506185
absolute error = 7.6443807970686e-18
relative error = 7.3958075438082719444891854208751e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.261
y2[1] (analytic) = 1.0338675855694809740416471565521
y2[1] (numeric) = 1.0338280302159173013087360758858
absolute error = 3.95553535636727329110806663e-05
relative error = 0.0038259593506729996118826560632366 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0338675855694809740416471565521
y1[1] (numeric) = 1.0338675855694809817330027943283
absolute error = 7.6913556377762e-18
relative error = 7.4394010849460984153579099157882e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=423.4MB, alloc=4.6MB, time=55.46
NO POLE
NO POLE
x[1] = 0.262
y2[1] (analytic) = 1.0341261154058090931286857424248
y2[1] (numeric) = 1.0340863185334878117279506903155
absolute error = 3.97968723212814007350521093e-05
relative error = 0.0038483577320416490132159785306829 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0341261154058090931286857424248
y1[1] (numeric) = 1.0341261154058091008670036912488
absolute error = 7.7383179488240e-18
relative error = 7.4829538037411900220505873257500e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=427.2MB, alloc=4.6MB, time=55.97
NO POLE
NO POLE
x[1] = 0.263
y2[1] (analytic) = 1.0343856111159413169189313333344
y2[1] (numeric) = 1.034345572789548550083496930345
absolute error = 4.00383263927668354344029894e-05
relative error = 0.0038707350491439748231361293615681 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0343856111159413169189313333344
y1[1] (numeric) = 1.0343856111159413247041990165839
absolute error = 7.7852676832495e-18
relative error = 7.5264655652454466235034025606692e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.264
y2[1] (analytic) = 1.0346460724403819569048019292326
y2[1] (numeric) = 1.0346057927248452819191570586721
absolute error = 4.02797155366749856448705605e-05
relative error = 0.0038930912327989309072427764885426 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0346460724403819569048019292326
y1[1] (numeric) = 1.0346460724403819647370067233356
absolute error = 7.8322047941030e-18
relative error = 7.5699362349382569029975711117256e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=431.0MB, alloc=4.6MB, time=56.47
NO POLE
NO POLE
x[1] = 0.265
y2[1] (analytic) = 1.0349074991186697103507671907983
y2[1] (numeric) = 1.0348669780791580936231931248646
absolute error = 4.05210395116167275740659337e-05
relative error = 0.0039154262140456576812243141281277 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0349074991186697103507671907983
y1[1] (numeric) = 1.0349074991186697182298964252458
absolute error = 7.8791292344475e-18
relative error = 7.6133656787272193687244398030589e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=434.8MB, alloc=4.6MB, time=56.97
NO POLE
NO POLE
x[1] = 0.266
y2[1] (analytic) = 1.0351698908893779207546294698607
y2[1] (numeric) = 1.0351291285913016526482388921059
absolute error = 4.07622980762681063905777548e-05
relative error = 0.0039377399241439216251258642124883 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0351698908893779207546294698607
y1[1] (numeric) = 1.0351698908893779286806704272191
absolute error = 7.9260409573584e-18
relative error = 7.6567537629486617492115560989847e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.267
y2[1] (analytic) = 1.0354332474901148392741585260421
y2[1] (numeric) = 1.0353922439991254686966106191176
absolute error = 4.10034909893705775479069245e-05
relative error = 0.0039600322945745503603814737365339 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0354332474901148392741585260421
y1[1] (numeric) = 1.0354332474901148472470984419663
absolute error = 7.9729399159242e-18
relative error = 7.7001003543691180629276129381290e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=438.6MB, alloc=4.6MB, time=57.47
NO POLE
NO POLE
x[1] = 0.268
y2[1] (analytic) = 1.0356975686575238871188185030108
y2[1] (numeric) = 1.0356563240395141558707755119699
absolute error = 4.12446180097312480429910409e-05
relative error = 0.0039823032570398632885892049859498 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0356975686575238871188185030108
y1[1] (numeric) = 1.0356975686575238951386445662566
absolute error = 8.0198260632458e-18
relative error = 7.7434053201854443616257745563918e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.6MB, time=57.97
NO POLE
NO POLE
x[1] = 0.269
y2[1] (analytic) = 1.0359628541272839189063247726353
y2[1] (numeric) = 1.0359213684483876957887156953328
absolute error = 4.14856788962231176090773025e-05
relative error = 0.0040045527434640977911477756866381 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0359628541272839189063247726353
y1[1] (numeric) = 1.0359628541272839269730241250723
absolute error = 8.0666993524370e-18
relative error = 7.7866685280260853006687983751577e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.27
y2[1] (analytic) = 1.0362291036341094869837672905078
y2[1] (numeric) = 1.0361873769607017016639245878267
absolute error = 4.17266734077853198427026811e-05
relative error = 0.0040267806859938309890130323983545 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0362291036341094869837672905078
y1[1] (numeric) = 1.0362291036341094950973270271325
absolute error = 8.1135597366247e-18
relative error = 7.8298898459520419073232128732926e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=446.3MB, alloc=4.6MB, time=58.47
NO POLE
NO POLE
x[1] = 0.271
y2[1] (analytic) = 1.0364963169117511067130361417346
y2[1] (numeric) = 1.0364543493104476833497716014973
absolute error = 4.19676013034233632645402373e-05
relative error = 0.004048987016998397061971825018996 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0364963169117511067130361417346
y1[1] (numeric) = 1.036496316911751114873443310683
absolute error = 8.1604071689484e-18
relative error = 7.8730691424571551454857601187483e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=450.1MB, alloc=4.6MB, time=58.97
NO POLE
NO POLE
x[1] = 0.272
y2[1] (analytic) = 1.0367644936929955227202839915894
y2[1] (numeric) = 1.0367222852306533133479701210729
absolute error = 4.22084623422093723138705165e-05
relative error = 0.0040711716690703001269697880930132 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0367644936929955227202839915894
y1[1] (numeric) = 1.03676449369299553092752559415
absolute error = 8.2072416025606e-18
relative error = 7.9162062864692497590642738803804e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.6MB, time=59.48
NO POLE
NO POLE
x[1] = 0.273
y2[1] (analytic) = 1.0370336337096659761091591915901
y2[1] (numeric) = 1.0369911844533826937808827545577
absolute error = 4.24492562832823282764370324e-05
relative error = 0.0040933345750256226751681200354102 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0370336337096659761091591915901
y1[1] (numeric) = 1.0370336337096659843632221822172
absolute error = 8.2540629906271e-18
relative error = 7.9593011473511725362896493911713e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.274
y2[1] (analytic) = 1.0373037366926224726375423277883
y2[1] (numeric) = 1.0372610467097366243273968828785
absolute error = 4.26899828858483101454449098e-05
relative error = 0.004115475667904429567542677756158 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0373037366926224726375423277883
y1[1] (numeric) = 1.0373037366926224809384136141146
absolute error = 8.3008712863263e-18
relative error = 8.0023535949008575306816809956050e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=457.7MB, alloc=4.6MB, time=59.98
NO POLE
NO POLE
x[1] = 0.275
y2[1] (analytic) = 1.0375748023717620518575180345561
y2[1] (numeric) = 1.0375318717298528711221025727313
absolute error = 4.29306419091807354154618248e-05
relative error = 0.0041375948809711675889765662554492 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0375748023717620518575180345561
y1[1] (numeric) = 1.0375748023717620602051844774061
absolute error = 8.3476664428500e-18
relative error = 8.0453634993528294623533182633784e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.6MB, time=60.48
NO POLE
NO POLE
x[1] = 0.276
y2[1] (analytic) = 1.0378468304760190572183129339225
y2[1] (numeric) = 1.0378036592429064366175039534727
absolute error = 4.31712331126206008089804498e-05
relative error = 0.004159692147715060560934894940233 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0378468304760190572183129339225
y1[1] (numeric) = 1.0378468304760190656127613473255
absolute error = 8.3944484134030e-18
relative error = 8.0883307313785411193858725124318e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.277
y2[1] (analytic) = 1.0381198207333654071319295975428
y2[1] (numeric) = 1.0380764089771098304089941958664
absolute error = 4.34117562555767229354016764e-05
relative error = 0.0041817674018505000129474883299189 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0381198207333654071319295975428
y1[1] (numeric) = 1.0381198207333654155731467487462
absolute error = 8.4412171512034e-18
relative error = 8.1312551620873771079355622905113e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=465.4MB, alloc=4.6MB, time=60.98
NO POLE
NO POLE
x[1] = 0.278
y2[1] (analytic) = 1.0383937728708108670012054656899
y2[1] (numeric) = 1.0383501206597133410223232677335
absolute error = 4.36522110975259788821979564e-05
relative error = 0.0042038205773174314132620732776619 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0383937728708108670012054656899
y1[1] (numeric) = 1.0383937728708108754891780751723
absolute error = 8.4879726094824e-18
relative error = 8.1741366630271670827037396241867e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.6MB, time=61.48
NO POLE
NO POLE
x[1] = 0.279
y2[1] (analytic) = 1.0386686866144033222100246952314
y2[1] (numeric) = 1.0386247940170053086632866790607
absolute error = 4.38925973980135467380161707e-05
relative error = 0.0042258516082817359591668123021074 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0386686866144033222100246952314
y1[1] (numeric) = 1.038668686614403330744739436716
absolute error = 8.5347147414846e-18
relative error = 8.2169751061851721177649518657992e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.28
y2[1] (analytic) = 1.0389445616892290520754099464035
y2[1] (numeric) = 1.0389004287743123989293624669003
absolute error = 4.41329149166531460474795032e-05
relative error = 0.0042478604291356079276170070457823 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0389445616892290520754099464035
y1[1] (numeric) = 1.0389445616892290606568534468713
absolute error = 8.5814435004678e-18
relative error = 8.2597703639885808128963164830972e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=473.0MB, alloc=4.6MB, time=61.98
NO POLE
NO POLE
x[1] = 0.281
y2[1] (analytic) = 1.0392213978194130047612201563121
y2[1] (numeric) = 1.0391770246559998774830227084486
absolute error = 4.43731634131272781974478635e-05
relative error = 0.0042698469744979275869363518627186 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0392213978194130047612201563121
y1[1] (numeric) = 1.0392213978194130133893789960154
absolute error = 8.6281588397033e-18
relative error = 8.3025223093054782891801192882212e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=476.8MB, alloc=4.6MB, time=62.49
NO POLE
NO POLE
x[1] = 0.282
y2[1] (analytic) = 1.0394991947281190731531793854871
y2[1] (numeric) = 1.0394545813854718856864448890133
absolute error = 4.46133426471874667344964738e-05
relative error = 0.0042918111792146296704982701095002 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0394991947281190731531793854871
y1[1] (numeric) = 1.0394991947281190818280400979629
absolute error = 8.6748607124758e-18
relative error = 8.3452308154454213779876469785000e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.283
y2[1] (analytic) = 1.0397779521375503716949608624835
y2[1] (numeric) = 1.0397330986851717171973474901821
absolute error = 4.48534523786544976133723014e-05
relative error = 0.004313752978359067413427608393535 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0397779521375503716949608624835
y1[1] (numeric) = 1.0397779521375503804165099345669
absolute error = 8.7215490720834e-18
relative error = 8.3878957561601015954237056384795e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.6MB, time=62.99
NO POLE
NO POLE
x[1] = 0.284
y2[1] (analytic) = 1.0400576697689495141850493904688
y2[1] (numeric) = 1.0400125762765820955256732023791
absolute error = 4.50934923674186593761880897e-05
relative error = 0.0043356723072323721534972924657847 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0400576697689495141850493904688
y1[1] (numeric) = 1.0400576697689495229532732623064
absolute error = 8.7682238718376e-18
relative error = 8.4305170056439995772784876554804e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=484.4MB, alloc=4.6MB, time=63.50
NO POLE
NO POLE
x[1] = 0.285
y2[1] (analytic) = 1.040338347342598892534104318956
y2[1] (numeric) = 1.0402930138802254525508422051503
absolute error = 4.53334623734399832621138057e-05
relative error = 0.0043575691013638084975284561078079 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.040338347342598892534104318956
y1[1] (numeric) = 1.0403383473425989013489893840199
absolute error = 8.8148850650639e-18
relative error = 8.4730944385356077132287255391897e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.286
y2[1] (analytic) = 1.0406199845778209564825443233454
y2[1] (numeric) = 1.0405744112156642079992969979463
absolute error = 4.55733621567484832473253991e-05
relative error = 0.0043794432965111250547360376889441 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0406199845778209564825443233454
y1[1] (numeric) = 1.0406199845778209653440769284462
absolute error = 8.8615326051008e-18
relative error = 8.5156279299171057669077293327371e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.6MB, time=64.00
NO POLE
NO POLE
x[1] = 0.287
y2[1] (analytic) = 1.0409025811929784942780742747098
y2[1] (numeric) = 1.0408567680015010498820593038828
absolute error = 4.58131914774443960149708270e-05
relative error = 0.0044012948286609007385948898627225 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0409025811929784942780742747098
y1[1] (numeric) = 1.0409025811929785031862407200108
absolute error = 8.9081664453010e-18
relative error = 8.5581173553161430761367624458006e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=492.1MB, alloc=4.6MB, time=64.50
NO POLE
NO POLE
x[1] = 0.288
y2[1] (analytic) = 1.0411861369054749143128735223236
y2[1] (numeric) = 1.0411400839553792158920186089432
absolute error = 4.60529500956984208549133804e-05
relative error = 0.0044231236340288866389340648750667 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0411861369054749143128735223236
y1[1] (numeric) = 1.0411861369054749232676600613541
absolute error = 8.9547865390305e-18
relative error = 8.6005625907055934186376328086465e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.289
y2[1] (analytic) = 1.0414706514317545277201639517677
y2[1] (numeric) = 1.04142435879398277576067093936
absolute error = 4.62926377717519594930124077e-05
relative error = 0.0044449296490603434660991114966524 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0414706514317545277201639517677
y1[1] (numeric) = 1.0414706514317545367215567914371
absolute error = 9.0013928396694e-18
relative error = 8.6429635125049350723910341036624e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.6MB, time=65.01
NO POLE
NO POLE
x[1] = 0.29
y2[1] (analytic) = 1.0417561244873028319298752220681
y2[1] (numeric) = 1.0417095922330369145740255204585
absolute error = 4.65322542659173558497016096e-05
relative error = 0.0044667128104303745691539486813206 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0417561244873028319298752220681
y1[1] (numeric) = 1.0417561244873028409778605226794
absolute error = 9.0479853006113e-18
relative error = 8.6853199975802772136734315972494e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=499.7MB, alloc=4.6MB, time=65.52
NO POLE
NO POLE
x[1] = 0.291
y2[1] (analytic) = 1.0420425557866467951831236262249
y2[1] (numeric) = 1.0419957839873082170473960010805
absolute error = 4.67717993385781357276251444e-05
relative error = 0.0044884730550442545302251572332204 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0420425557866467951831236262249
y1[1] (numeric) = 1.0420425557866468042776875014885
absolute error = 9.0945638752636e-18
relative error = 8.7276319232452424345003918134240e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.292
y2[1] (analytic) = 1.0423299450433551420052200606774
y2[1] (numeric) = 1.0422829337706049527587919688204
absolute error = 4.70112727501892464280918570e-05
relative error = 0.0045102103200377533372223513037087 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0423299450433551420052200606774
y1[1] (numeric) = 1.0423299450433551511463485777253
absolute error = 9.1411285170479e-18
relative error = 8.7698991672619362156307402243813e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=503.5MB, alloc=4.6MB, time=66.02
NO POLE
NO POLE
x[1] = 0.293
y2[1] (analytic) = 1.0426182919700386396369216307212
y2[1] (numeric) = 1.0425710412957773623406255227053
absolute error = 4.72506742612772962961080159e-05
relative error = 0.0045319245427774561372986501620864 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0426182919700386396369216307212
y1[1] (numeric) = 1.0426182919700386488246008101208
absolute error = 9.1876791793996e-18
relative error = 8.8121216078411399586837461320638e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.6MB, time=66.52
NO POLE
NO POLE
x[1] = 0.294
y2[1] (analytic) = 1.0429075962783503854236404606493
y2[1] (numeric) = 1.0428601062747179446294467116371
absolute error = 4.74900036324407941937490122e-05
relative error = 0.0045536156608610785735451626064783 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0429075962783503854236404606493
y1[1] (numeric) = 1.0429075962783503946578562764172
absolute error = 9.2342158157679e-18
relative error = 8.8542991236428796960050164162785e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=511.1MB, alloc=4.6MB, time=67.02
x[1] = 0.295
y2[1] (analytic) = 1.043197857678986095162322319432
y2[1] (numeric) = 1.0431501284183617447734206888849
absolute error = 4.77292606243503889016305471e-05
relative error = 0.0045752836121177777075428170634166 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.043197857678986095162322319432
y1[1] (numeric) = 1.0431978576789861044430606990482
absolute error = 9.2807383796162e-18
relative error = 8.8964315937773697432570435271558e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.296
y2[1] (analytic) = 1.0434890758816843924057067150814
y2[1] (numeric) = 1.0434411074366866432972584751743
absolute error = 4.79684449977491084482399071e-05
relative error = 0.0045969283346084585305238147302685 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0434890758816843924057067150814
y1[1] (numeric) = 1.0434890758816844017329535395035
absolute error = 9.3272468244221e-18
relative error = 8.9385188978055638930205130562036e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=514.9MB, alloc=4.6MB, time=67.53
NO POLE
NO POLE
x[1] = 0.297
y2[1] (analytic) = 1.0437812505952270987236791534653
y2[1] (numeric) = 1.0437330430387136461243122654673
absolute error = 4.82075565134525993668879980e-05
relative error = 0.0046185497666260760660234461068776 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0437812505952270987236791534653
y1[1] (numeric) = 1.0437812505952271080974202571422
absolute error = 9.3737411036769e-18
relative error = 8.9805609157392190952014872580163e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=518.8MB, alloc=4.6MB, time=68.04
NO POLE
NO POLE
x[1] = 0.298
y2[1] (analytic) = 1.0440743815274395249214253002402
y2[1] (numeric) = 1.0440259349325071755555452573616
absolute error = 4.84465949323493658800428786e-05
relative error = 0.004640147846695933067030988022671 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0440743815274395249214253002402
y1[1] (numeric) = 1.0440743815274395343416464711268
absolute error = 9.4202211708866e-18
relative error = 9.0225575280423881445981896628675e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.299
y2[1] (analytic) = 1.0443684683851907632140958277764
y2[1] (numeric) = 1.044319782825175362205085022163
absolute error = 4.86855600154010090108056134e-05
relative error = 0.0046617225135759733107758850696617 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0443684683851907632140958277764
y1[1] (numeric) = 1.0443684683851907726807828073473
absolute error = 9.4666869795709e-18
relative error = 9.0645086156309872505499206809331e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.6MB, time=68.54
NO POLE
NO POLE
x[1] = 0.3
y2[1] (analytic) = 1.044663510874393980357689772432
y2[1] (numeric) = 1.0446145864228703378920684831031
absolute error = 4.89244515236424656212893289e-05
relative error = 0.0046832737062570704944124094188207 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.044663510874393980357689772432
y1[1] (numeric) = 1.044663510874393989870828255696
absolute error = 9.5131384832640e-18
relative error = 9.1064140598740798014486730668192e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=526.4MB, alloc=4.6MB, time=69.05
NO POLE
NO POLE
x[1] = 0.301
y2[1] (analytic) = 1.0449595087000067117358632713184
y2[1] (numeric) = 1.044910345430788529488485608881
absolute error = 4.91632692181822473776624374e-05
relative error = 0.0047048013639633127349924842687054 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0449595087000067117358632713184
y1[1] (numeric) = 1.0449595087000067212954389068331
absolute error = 9.5595756355147e-18
relative error = 9.1482737425944804929100644732950e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.302
y2[1] (analytic) = 1.0452564615660311564023695917739
y2[1] (numeric) = 1.0452070595531709537227279747094
absolute error = 4.94020128602026796416170645e-05
relative error = 0.0047263054261522826772423420296295 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0452564615660311564023695917739
y1[1] (numeric) = 1.0452564615660311660083679816594
absolute error = 9.6059983898855e-18
relative error = 9.1900875460683941362978973613728e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=530.2MB, alloc=4.6MB, time=69.55
NO POLE
NO POLE
x[1] = 0.303
y2[1] (analytic) = 1.0455543691755144730788354111266
y2[1] (numeric) = 1.045504728493303512938547387342
absolute error = 4.96406822109601402880237846e-05
relative error = 0.0047477858325153332127841644920633 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0455543691755144730788354111266
y1[1] (numeric) = 1.0455543691755144827312421110804
absolute error = 9.6524066999538e-18
relative error = 9.2318553530270559963328221718186e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.6MB, time=70.06
NO POLE
NO POLE
x[1] = 0.304
y2[1] (analytic) = 1.0458532312305490771075773489994
y2[1] (numeric) = 1.0458033519535172918091288151479
absolute error = 4.98792770317852984485338515e-05
relative error = 0.0047692425229778588145688159579895 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0458532312305490771075773489994
y1[1] (numeric) = 1.0458532312305490868063778683107
absolute error = 9.6988005193113e-18
relative error = 9.2735770466566406490427515139756e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.305
y2[1] (analytic) = 1.0461530474322729383591617993617
y2[1] (numeric) = 1.0461029296351888550059809091843
absolute error = 5.01177970840833531808901774e-05
relative error = 0.0047906754376995624904102241654071 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0461530474322729383591617993617
y1[1] (numeric) = 1.0461530474322729481043416009258
absolute error = 9.7451798015641e-18
relative error = 9.3152525105988325106755471487195e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=537.8MB, alloc=4.6MB, time=70.56
NO POLE
NO POLE
x[1] = 0.306
y2[1] (analytic) = 1.0464538174808698800944101547946
y2[1] (numeric) = 1.0464034612387405458223464464025
absolute error = 5.03562421293342720637083921e-05
relative error = 0.0048120845170747183596358861551425 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0464538174808698800944101547946
y1[1] (numeric) = 1.0464538174808698898859546551276
absolute error = 9.7915445003330e-18
relative error = 9.3568816289515789047272069755270e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=541.6MB, alloc=4.6MB, time=71.07
NO POLE
NO POLE
x[1] = 0.307
y2[1] (analytic) = 1.0467555410755698787805505609892
y2[1] (numeric) = 1.0467049464636407857508340716011
absolute error = 5.05946119290930297164893881e-05
relative error = 0.0048334697017324298569913710252354 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0467555410755698787805505609892
y1[1] (numeric) = 1.0467555410755698886184451302426
absolute error = 9.8378945692534e-18
relative error = 9.3984642862694520889699153352035e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.308
y2[1] (analytic) = 1.0470582179146493648612163853508
y2[1] (numeric) = 1.0470073850084043750149717605203
absolute error = 5.08329062449898462446248305e-05
relative error = 0.0048548309325368835680595548401332 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0470582179146493648612163853508
y1[1] (numeric) = 1.0470582179146493747454463473258
absolute error = 9.8842299619750e-18
relative error = 9.4400003675638120315884117660562e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=545.5MB, alloc=4.6MB, time=71.58
NO POLE
NO POLE
x[1] = 0.309
y2[1] (analytic) = 1.0473618476954315244799906297348
y2[1] (numeric) = 1.0473107765705927940543814725478
absolute error = 5.10711248387304256091571870e-05
relative error = 0.0048761681505875987005776509050778 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0473618476954315244799906297348
y1[1] (numeric) = 1.0473618476954315344105412618975
absolute error = 9.9305506321627e-18
relative error = 9.4814897583041070265768015465396e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=549.3MB, alloc=4.6MB, time=72.08
NO POLE
NO POLE
x[1] = 0.31
y2[1] (analytic) = 1.0476664301142866021571945637978
y2[1] (numeric) = 1.0476151208468145059632735078878
absolute error = 5.13092674720961939210559100e-05
relative error = 0.0048974812972196721961568866732926 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0476664301142866021571945637978
y1[1] (numeric) = 1.0476664301142866121340510972933
absolute error = 9.9768565334955e-18
relative error = 9.5229323444172554233542684111222e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.311
y2[1] (analytic) = 1.0479719648666322044196179021966
y2[1] (numeric) = 1.0479204175327252598819581307235
absolute error = 5.15473339069445376597714731e-05
relative error = 0.004918770314004019487030921904077 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0479719648666322044196179021966
y1[1] (numeric) = 1.0479719648666322144427655218643
absolute error = 1.00231476196677e-17
relative error = 9.5643280122892155261106725625522e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=553.1MB, alloc=4.6MB, time=72.58
NO POLE
NO POLE
x[1] = 0.312
y2[1] (analytic) = 1.0482784516469336043828868959338
y2[1] (numeric) = 1.0482266663230283953410710668868
absolute error = 5.17853239052090418158290470e-05
relative error = 0.0049400351427476109025797989954044 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0482784516469336043828868959338
y1[1] (numeric) = 1.048278451646933614452310740322
absolute error = 1.00694238443882e-17
relative error = 9.6056766487647326283521034214739e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=556.9MB, alloc=4.6MB, time=73.08
NO POLE
NO POLE
x[1] = 0.313
y2[1] (analytic) = 1.0485858901487040472861657555049
y2[1] (numeric) = 1.0485338669114751475582085318349
absolute error = 5.20232372288997279572236700e-05
relative error = 0.0049612757254937037304963592119308 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0485858901487040472861657555049
y1[1] (numeric) = 1.0485858901487040574018509168857
absolute error = 1.01156851613808e-17
relative error = 9.6469781411480325243839734954240e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.314
y2[1] (analytic) = 1.0488942800645050569788858711721
y2[1] (numeric) = 1.0488420189908649536866664923248
absolute error = 5.22610736401032922193788473e-05
relative error = 0.0049824920045220699375816458156162 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0488942800645050569788858711721
y1[1] (numeric) = 1.0488942800645050671408173955563
absolute error = 1.01619315243842e-17
relative error = 9.6882323772032201553085210549772e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=560.7MB, alloc=4.6MB, time=73.58
NO POLE
NO POLE
x[1] = 0.315
y2[1] (analytic) = 1.0492036210859467433591963436608
y2[1] (numeric) = 1.049151122253045760015977913071
absolute error = 5.24988329009833432184305898e-05
relative error = 0.0050036839223492195552748418134653 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0492036210859467433591963436608
y1[1] (numeric) = 1.0492036210859467535673592308128
absolute error = 1.02081628871520e-17
relative error = 9.7294392451546699171826424593026e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=564.5MB, alloc=4.6MB, time=74.09
NO POLE
NO POLE
x[1] = 0.316
y2[1] (analytic) = 1.0495139129036881107638283868539
y2[1] (numeric) = 1.0494611763889143301239407878759
absolute error = 5.27365147737806398875989780e-05
relative error = 0.005024851421728619735141752311523 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0495139129036881107638283868539
y1[1] (numeric) = 1.0495139129036881210182075903067
absolute error = 1.02543792034528e-17
relative error = 9.7705986336875029243931523593460e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=568.3MB, alloc=4.6MB, time=74.59
x[1] = 0.317
y2[1] (analytic) = 1.0498251552074373673090652126448
y2[1] (numeric) = 1.0497721810884165539798288032292
absolute error = 5.29741190208133292364094156e-05
relative error = 0.005045994445650909479663735958045 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0498251552074373673090652126448
y1[1] (numeric) = 1.0498251552074373776096456397152
absolute error = 1.03005804270704e-17
relative error = 9.8117104319481510415872865004417e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.318
y2[1] (analytic) = 1.0501373476859522351825080570062
y2[1] (numeric) = 1.050084136040547757998475531193
absolute error = 5.32116454044771840325258132e-05
relative error = 0.0050671129373441100537863121324583 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0501373476859522351825080570062
y1[1] (numeric) = 1.0501373476859522455292745688096
absolute error = 1.03467665118034e-17
relative error = 9.8527745295443409163028034668620e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=572.2MB, alloc=4.6MB, time=75.10
NO POLE
NO POLE
x[1] = 0.319
y2[1] (analytic) = 1.0504504900270402618853280555329
y2[1] (numeric) = 1.0503970409333530160449220975128
absolute error = 5.34490936872458404059580201e-05
relative error = 0.0050882068402738310828034170729953 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0504504900270402618853280555329
y1[1] (numeric) = 1.0504504900270402722782654669988
absolute error = 1.03929374114659e-17
relative error = 9.8937908165461175664565964236966e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=576.0MB, alloc=4.6MB, time=75.61
NO POLE
NO POLE
x[1] = 0.32
y2[1] (analytic) = 1.0507645819175591324246927262339
y2[1] (numeric) = 1.0507108954539274613893173203332
absolute error = 5.36864636316710353754059007e-05
relative error = 0.0051092760981434723422694492030646 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0507645819175591324246927262339
y1[1] (numeric) = 1.0507645819175591428637858061209
absolute error = 1.04390930798870e-17
relative error = 9.9347591834857164668292119585503e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.321
y2[1] (analytic) = 1.0510796230434169824560548671731
y2[1] (numeric) = 1.0510256992884165996117583646447
absolute error = 5.39237550003828442965025284e-05
relative error = 0.005130320654894421245746827532256 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0510796230434169824560548671731
y1[1] (numeric) = 1.051079623043416992941288338084
absolute error = 1.04852334709109e-17
relative error = 9.9756795213579990573501717864591e-16 %
Correct digits = 17
h = 0.001
TOP MAIN SOLVE Loop
memory used=579.8MB, alloc=4.6MB, time=76.11
NO POLE
NO POLE
x[1] = 0.322
y2[1] (analytic) = 1.0513956130895727123749907266948
y2[1] (numeric) = 1.051341452122016622456759007646
absolute error = 5.41609675560899182317190488e-05
relative error = 0.0051513404547062460363117839627372 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0513956130895727123749907266948
y1[1] (numeric) = 1.0513956130895727229063492650921
absolute error = 1.05313585383973e-17
relative error = 1.0016551721621165156649754055282e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=583.6MB, alloc=4.6MB, time=76.60
NO POLE
NO POLE
x[1] = 0.323
y2[1] (analytic) = 1.051712551740036302358273354424
y2[1] (numeric) = 1.0516581536389747226370316605805
absolute error = 5.43981010615797212416938435e-05
relative error = 0.0051723354419968846878555168455612 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.051712551740036302358273354424
y1[1] (numeric) = 1.0517125517400363129357415906451
absolute error = 1.05774682362211e-17
relative error = 1.0057375676196790859786257079329e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.324
y2[1] (analytic) = 1.0520304386778691283538660919921
y2[1] (numeric) = 1.0519758035225894095862683432908
absolute error = 5.46351552797187675977487013e-05
relative error = 0.0051933055614228295223316452169636 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0520304386778691283538660919921
y1[1] (numeric) = 1.0520304386778691389774286102647
absolute error = 1.06235625182726e-17
relative error = 1.0098151277470333986245087450570e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=587.4MB, alloc=4.6MB, time=77.11
NO POLE
NO POLE
x[1] = 0.325
y2[1] (analytic) = 1.0523492735851842790195202135225
y2[1] (numeric) = 1.0522944014552108261606048587367
absolute error = 5.48721299734528589153547858e-05
relative error = 0.0052142507578793075492141183192894 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0523492735851842790195202135225
y1[1] (numeric) = 1.0523492735851842896891615519801
absolute error = 1.06696413384576e-17
relative error = 1.0138878418291535934500991536070e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=591.2MB, alloc=4.6MB, time=77.62
NO POLE
NO POLE
x[1] = 0.326
y2[1] (analytic) = 1.0526690561431468736096597773046
y2[1] (numeric) = 1.0526139471182410662884514660389
absolute error = 5.51090249058073212083112657e-05
relative error = 0.005235170976500456533542348719393 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0526690561431468736096597773046
y1[1] (numeric) = 1.0526690561431468843253644280017
absolute error = 1.07157046506971e-17
relative error = 1.0179556991974435165564045098445e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.327
y2[1] (analytic) = 1.0529897860319743808102358017967
y2[1] (numeric) = 1.0529344401921344935683724022439
absolute error = 5.53458398398872418633995528e-05
relative error = 0.0052560661626594967990423467765144 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0529897860319743808102358017967
y1[1] (numeric) = 1.0529897860319743915719882107247
absolute error = 1.07617524089280e-17
relative error = 1.0220186892298322685110901005369e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=595.1MB, alloc=4.6MB, time=78.12
NO POLE
NO POLE
x[1] = 0.328
y2[1] (analytic) = 1.0533114629309369385212309311322
y2[1] (numeric) = 1.0532558803563980608146956549579
absolute error = 5.55825745388777065352761743e-05
relative error = 0.0052769362619688987729240361705575 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0533114629309369385212309311322
y1[1] (numeric) = 1.0533114629309369493290154982346
absolute error = 1.08077845671024e-17
relative error = 1.0260768013507358983461709373915e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=598.9MB, alloc=4.6MB, time=78.62
NO POLE
NO POLE
x[1] = 0.329
y2[1] (analytic) = 1.0536340865183576745864948076487
y2[1] (numeric) = 1.0535782672895916305505334402655
absolute error = 5.58192287660440359613673832e-05
relative error = 0.0052977812202805462790657206828261 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0536340865183576745864948076487
y1[1] (numeric) = 1.053634086518357685440295886837
absolute error = 1.08538010791883e-17
relative error = 1.0301300250311512755132380335682e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.33
y2[1] (analytic) = 1.0539576564716130284705894216338
y2[1] (numeric) = 1.0539016006693282964478928929406
absolute error = 5.60558022847320226965286932e-05
relative error = 0.0053186009836858955864068491009558 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0539576564716130284705894216338
y1[1] (numeric) = 1.0539576564716130393703913208029
absolute error = 1.08998018991691e-17
relative error = 1.0341783497886351674051174758197e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=602.7MB, alloc=4.6MB, time=79.12
NO POLE
NO POLE
x[1] = 0.331
y2[1] (analytic) = 1.0542821724671330738823227614669
y2[1] (numeric) = 1.0542258801722747057145555288642
absolute error = 5.62922948583681677672326027e-05
relative error = 0.0053393954985161302194797838615937 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0542821724671330738823227614669
y1[1] (numeric) = 1.0542821724671330848281097425109
absolute error = 1.09457869810440e-17
relative error = 1.0382217651873679558497681692060e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=606.5MB, alloc=4.6MB, time=79.63
NO POLE
NO POLE
x[1] = 0.332
y2[1] (analytic) = 1.0546076341804018423446481406519
y2[1] (numeric) = 1.0545511054741513824274030927981
absolute error = 5.65287062504599172450478538e-05
relative error = 0.0053601647113423115381202174046023 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0546076341804018423446481406519
y1[1] (numeric) = 1.0546076341804018533364044194798
absolute error = 1.09917562788279e-17
relative error = 1.0422602608381690595103171581856e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.333
y2[1] (analytic) = 1.0549340412859576477106056318672
y2[1] (numeric) = 1.0548772762497330518118664582142
absolute error = 5.67650362245958987391736530e-05
relative error = 0.0053809085689755250935041947423475 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0549340412859576477106056318672
y1[1] (numeric) = 1.0549340412859576587483153784186
absolute error = 1.10377097465514e-17
relative error = 1.0462938263985210413633340637503e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=610.3MB, alloc=4.6MB, time=80.16
NO POLE
NO POLE
x[1] = 0.334
y2[1] (analytic) = 1.0552613934573934116249810921192
y2[1] (numeric) = 1.0552043921728489654671732997583
absolute error = 5.70012845444461578077923609e-05
relative error = 0.0054016270184670227677673884180601 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0552613934573934116249810921192
y1[1] (numeric) = 1.0552613934573934227086284303804
absolute error = 1.10836473382612e-17
relative error = 1.0503224515726308112637267742166e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=614.1MB, alloc=4.6MB, time=80.67
NO POLE
NO POLE
x[1] = 0.335
y2[1] (analytic) = 1.0555896903673569899313573173679
y2[1] (numeric) = 1.0555324529163832275370693131278
absolute error = 5.72374509737623942880042401e-05
relative error = 0.0054223200071083607045693299724373 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0555896903673569899313573173679
y1[1] (numeric) = 1.0555896903673570010609263253877
absolute error = 1.11295690080198e-17
relative error = 1.0543461261114236354145521781274e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.336
y2[1] (analytic) = 1.0559189316875515000242309195995
y2[1] (numeric) = 1.0558614581522751218256868116686
absolute error = 5.74735352763781985441079309e-05
relative error = 0.0054429874824315330380717270332814 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0559189316875515000242309195995
y1[1] (numeric) = 1.0559189316875515111997056295048
absolute error = 1.11754747099053e-17
relative error = 1.0583648398125458618318674888293e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=617.9MB, alloc=4.6MB, time=81.18
NO POLE
NO POLE
x[1] = 0.337
y2[1] (analytic) = 1.056249117088735649145867574257
y2[1] (numeric) = 1.056191407551519439858233583851
absolute error = 5.77095372162092876339904060e-05
relative error = 0.0054636293922091014279057845356828 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.056249117088735649145867574257
y1[1] (numeric) = 1.0562491170887356603672319722691
absolute error = 1.12213643980121e-17
relative error = 1.0623785825204520827461018761631e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=621.8MB, alloc=4.6MB, time=81.69
NO POLE
NO POLE
x[1] = 0.338
y2[1] (analytic) = 1.0565802462407240636275673412012
y2[1] (numeric) = 1.056522300784166809886173950962
absolute error = 5.79454565572537413933902392e-05
relative error = 0.0054842456844543204078085996043138 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0565802462407240636275673412012
y1[1] (numeric) = 1.0565802462407240748948053676517
absolute error = 1.12672380264505e-17
relative error = 1.0663873441263872589199315801683e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=625.6MB, alloc=4.6MB, time=82.21
x[1] = 0.339
y2[1] (analytic) = 1.0569123188123876190750108179637
y2[1] (numeric) = 1.0568541375193240268365730198609
absolute error = 5.81812930635922384377981028e-05
relative error = 0.0055048363074212585557132088773374 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0569123188123876190750108179637
y1[1] (numeric) = 1.0569123188123876303881063673106
absolute error = 1.13130955493469e-17
relative error = 1.0703911145684248813501955845449e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.34
y2[1] (analytic) = 1.0572453344716537714973559399734
y2[1] (numeric) = 1.0571869174251543832052741814813
absolute error = 5.84170464993882920817584921e-05
relative error = 0.0055254012096049154931807325291745 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0572453344716537714973559399734
y1[1] (numeric) = 1.0572453344716537828562928608172
absolute error = 1.13589369208438e-17
relative error = 1.0743898838314853789955565809047e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=629.4MB, alloc=4.6MB, time=82.72
NO POLE
NO POLE
x[1] = 0.341
y2[1] (analytic) = 1.0575792928855068893797542986879
y2[1] (numeric) = 1.0575206401688780008935789619298
absolute error = 5.86527166288884861753367581e-05
relative error = 0.0055459403397413347221662777708619 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0575792928855068893797542986879
y1[1] (numeric) = 1.0575792928855069007845163937877
absolute error = 1.14047620950998e-17
relative error = 1.0783836419473537267985652615594e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=633.2MB, alloc=4.6MB, time=83.23
NO POLE
NO POLE
x[1] = 0.342
y2[1] (analytic) = 1.0579141937199885866989549051396
y2[1] (numeric) = 1.0578553054167721639880973895288
absolute error = 5.88883032164227108575156108e-05
relative error = 0.0055664536468077123072128334716146 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0579141937199885866989549051396
y1[1] (numeric) = 1.0579141937199885981495259314294
absolute error = 1.14505710262898e-17
relative error = 1.0823723789947151607650370623604e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.343
y2[1] (analytic) = 1.0582500366401980568816623833228
y2[1] (numeric) = 1.0581909128341716524834360979812
absolute error = 5.91238060264043982262853416e-05
relative error = 0.0055869410800225014112693047261578 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0582500366401980568816623833228
y1[1] (numeric) = 1.0582500366401980683780260519275
absolute error = 1.14963636686047e-17
relative error = 1.0863560850991428128219396619414e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=637.0MB, alloc=4.6MB, time=83.74
NO POLE
NO POLE
x[1] = 0.344
y2[1] (analytic) = 1.0585868213102924077053156350886
y2[1] (numeric) = 1.0585274620854690769473904429961
absolute error = 5.93592248233307579251920925e-05
relative error = 0.0056074025888455126934300980184388 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0585868213102924077053156350886
y1[1] (numeric) = 1.0585868213102924192474556113407
absolute error = 1.15421399762521e-17
relative error = 1.0903347504331790704234682953939e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=640.8MB, alloc=4.6MB, time=84.25
NO POLE
NO POLE
x[1] = 0.345
y2[1] (analytic) = 1.0589245473934869971409520758003
y2[1] (numeric) = 1.0588649528341152141283059672122
absolute error = 5.95945593717830126461085881e-05
relative error = 0.0056278381229780105769942731012378 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0589245473934869971409520758003
y1[1] (numeric) = 1.0589245473934870087288519792557
absolute error = 1.15878999034554e-17
relative error = 1.0943083652162649199828471116145e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.346
y2[1] (analytic) = 1.0592632145520557701378215979091
y2[1] (numeric) = 1.0592033847426193435042736060845
absolute error = 5.98298094364266335479918246e-05
relative error = 0.0056482476323628053963422225417559 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0592632145520557701378215979091
y1[1] (numeric) = 1.059263214552055781771465002364
absolute error = 1.16336434044549e-17
relative error = 1.0982769197148574719240839207269e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=644.6MB, alloc=4.6MB, time=84.76
NO POLE
NO POLE
x[1] = 0.347
y2[1] (analytic) = 1.0596028224473315963494134778678
y2[1] (numeric) = 1.0595427574725495847738220855675
absolute error = 6.00649747820115755913923003e-05
relative error = 0.0056686310671843414312271237565899 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0596028224473315963494134778678
y1[1] (numeric) = 1.0596028224473316080287839113749
absolute error = 1.16793704335071e-17
relative error = 1.1022404042423766217653909210331e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=648.5MB, alloc=4.6MB, time=85.27
NO POLE
NO POLE
x[1] = 0.348
y2[1] (analytic) = 1.0599433707397066088005585003816
y2[1] (numeric) = 1.0598830706845332362877700209308
absolute error = 6.03000551733725127884794508e-05
relative error = 0.0056889883778687808371770266682846 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0599433707397066088005585003816
y1[1] (numeric) = 1.0599433707397066205256394452664
absolute error = 1.17250809448848e-17
relative error = 1.1061988091592265256752465511480e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.349
y2[1] (analytic) = 1.0602848590886325434952676329222
y2[1] (numeric) = 1.060224324038257114421899284883
absolute error = 6.05350503754290733683480392e-05
relative error = 0.0057093195150840834808013924307487 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0602848590886325434952676329222
y1[1] (numeric) = 1.0602848590886325552660425257999
absolute error = 1.17707748928777e-17
relative error = 1.1101521248728634287758344265355e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=652.3MB, alloc=4.6MB, time=85.78
NO POLE
NO POLE
x[1] = 0.35
y2[1] (analytic) = 1.0606272871526210799649676426963
y2[1] (numeric) = 1.0605665171924678938901102723587
absolute error = 6.07699601531860748573703376e-05
relative error = 0.0057296244297400826888931818241732 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0606272871526210799649676426963
y1[1] (numeric) = 1.0606272871526210917814198744881
absolute error = 1.18164522317918e-17
relative error = 1.1141003418377494587685287924152e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=656.1MB, alloc=4.6MB, time=86.29
NO POLE
NO POLE
x[1] = 0.351
y2[1] (analytic) = 1.0609706545892441827567931078597
y2[1] (numeric) = 1.060909649804972448997718748842
absolute error = 6.10047842717337590743590177e-05
relative error = 0.0057499030729885569203142033706334 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0609706545892441827567931078597
y1[1] (numeric) = 1.0609706545892441946189060238094
absolute error = 1.18621129159497e-17
relative error = 1.1180434505553905741589944652429e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.352
y2[1] (analytic) = 1.0613149610551344438615933347137
y2[1] (numeric) = 1.0612537215326381958345530289579
absolute error = 6.12395224962480270403057558e-05
relative error = 0.0057701553962232973697473697878526 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0613149610551344438615933347137
y1[1] (numeric) = 1.0613149610551344557693502344044
absolute error = 1.19077568996907e-17
relative error = 1.1219814415743548320673952805200e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=659.9MB, alloc=4.6MB, time=86.80
NO POLE
NO POLE
x[1] = 0.353
y2[1] (analytic) = 1.0616602062059854260813117529063
y2[1] (numeric) = 1.0615987320313934354075092922629
absolute error = 6.14741745919906738024606434e-05
relative error = 0.0057903813510801715124947742396529 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0616602062059854260813117529063
y1[1] (numeric) = 1.0616602062059854380346958902772
absolute error = 1.19533841373709e-17
relative error = 1.1259143054902898583848196330111e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=663.7MB, alloc=4.6MB, time=87.31
NO POLE
NO POLE
x[1] = 0.354
y2[1] (analytic) = 1.0620063896965520073353944212866
y2[1] (numeric) = 1.0619446809562276977122219037083
absolute error = 6.17087403243096231725175783e-05
relative error = 0.0058105808894371825995950828268273 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0620063896965520073353944212866
y1[1] (numeric) = 1.0620063896965520193343890046497
absolute error = 1.19989945833631e-17
relative error = 1.1298420329459206897291237541898e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.355
y2[1] (analytic) = 1.062353511180650725905883338033
y2[1] (numeric) = 1.062291567961192086743504667134
absolute error = 6.19432194586391623786708990e-05
relative error = 0.0058307539634145251126276454686147 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.062353511180650725905883338033
y1[1] (numeric) = 1.0623535111806507379504715300897
absolute error = 1.20445881920567e-17
relative error = 1.1337646146310468581493654082917e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=667.5MB, alloc=4.6MB, time=87.82
NO POLE
NO POLE
x[1] = 0.356
y2[1] (analytic) = 1.0627015703111601266208493099901
y2[1] (numeric) = 1.0626393926993996264442180013814
absolute error = 6.21776117605001766313086087e-05
relative error = 0.0058509005253746361876639509647499 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0627015703111601266208493099901
y1[1] (numeric) = 1.0627015703111601387110142278483
absolute error = 1.20901649178582e-17
relative error = 1.1376820412825951804891389891459e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=671.3MB, alloc=4.6MB, time=88.34
NO POLE
NO POLE
x[1] = 0.357
y2[1] (analytic) = 1.0630505667400211079758181978111
y2[1] (numeric) = 1.0629881548230256075922160901856
absolute error = 6.24119169955003836021076255e-05
relative error = 0.0058710205279222430179195927271507 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0630505667400211079758181978111
y1[1] (numeric) = 1.063050566740021120111542913002
absolute error = 1.21357247151909e-17
relative error = 1.1415943036845964282459563417120e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.358
y2[1] (analytic) = 1.0634005001182372701928434155077
y2[1] (numeric) = 1.06333785398330793562502711893
absolute error = 6.26461349293345678162965777e-05
relative error = 0.00589111392390440624475176615435 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0634005001182372701928434155077
y1[1] (numeric) = 1.0634005001182372823741109540026
absolute error = 1.21812675384949e-17
relative error = 1.1455013926681894942957172366581e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=675.2MB, alloc=4.6MB, time=88.85
NO POLE
NO POLE
x[1] = 0.359
y2[1] (analytic) = 1.0637513700958752642168766253644
y2[1] (numeric) = 1.063688489830547479401918773611
absolute error = 6.28802653277848149578517534e-05
relative error = 0.0059111806664105593467384865651392 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0637513700958752642168766253644
y1[1] (numeric) = 1.0637513700958752764436699675919
absolute error = 1.22267933422275e-17
relative error = 1.1494032991116623943863119948464e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=679.0MB, alloc=4.6MB, time=89.36
NO POLE
NO POLE
x[1] = 0.36
y2[1] (analytic) = 1.0641031763220651416490876318753
y2[1] (numeric) = 1.0640400620141084209030002399772
absolute error = 6.31143079567207460873918981e-05
relative error = 0.0059312207087725440366661949272441 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0641031763220651416490876318753
y1[1] (numeric) = 1.0641031763220651539213897127382
absolute error = 1.22723020808629e-17
relative error = 1.1533000139404266449124682925632e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.361
y2[1] (analytic) = 1.064455918445000705616783541413
y2[1] (numeric) = 1.0643925701824186058650110037695
absolute error = 6.33482625820997517725376435e-05
relative error = 0.0059512340045646416763422065927605 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.064455918445000705616783541413
y1[1] (numeric) = 1.0644559184450007179345772503054
absolute error = 1.23177937088924e-17
relative error = 1.1571915281270379046825911996510e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=682.8MB, alloc=4.6MB, time=89.87
NO POLE
NO POLE
x[1] = 0.362
y2[1] (analytic) = 1.0648095961119398625795763177395
y2[1] (numeric) = 1.0647460139829698953534458163033
absolute error = 6.35821289699672261305014362e-05
relative error = 0.0059712205076036007192375533499399 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0648095961119398625795763177395
y1[1] (numeric) = 1.0648095961119398749428444985637
absolute error = 1.23632681808242e-17
relative error = 1.1610778326911782517072256014928e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=686.6MB, alloc=4.6MB, time=90.38
NO POLE
NO POLE
x[1] = 0.363
y2[1] (analytic) = 1.0651642089692049750714469272204
y2[1] (numeric) = 1.0651003930623185182706642532962
absolute error = 6.38159068864568007826739242e-05
relative error = 0.0059911801719486601910541704049976 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0651642089692049750714469272204
y1[1] (numeric) = 1.0651642089692049874801723784043
absolute error = 1.24087254511839e-17
relative error = 1.1649589186997034547769879116388e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=690.4MB, alloc=4.6MB, time=90.89
NO POLE
NO POLE
x[1] = 0.364
y2[1] (analytic) = 1.0655197566621832153783533317088
y2[1] (numeric) = 1.065455707066085424799632358862
absolute error = 6.40495960977905787209728468e-05
relative error = 0.006011112951901569218398085336661 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0655197566621832153783533317088
y1[1] (numeric) = 1.0655197566621832278325188062231
absolute error = 1.24541654745143e-17
relative error = 1.1688347772666236973493954397388e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.365
y2[1] (analytic) = 1.0658762388353269201510286515192
y2[1] (numeric) = 1.0658119556389566407829429309581
absolute error = 6.42831963702793680857205611e-05
relative error = 0.006031018802006602615827274207705 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0658762388353269201510286515192
y1[1] (numeric) = 1.0658762388353269326506168568945
absolute error = 1.24995882053753e-17
relative error = 1.1727053995530929645762807241632e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=694.2MB, alloc=4.6MB, time=91.40
NO POLE
NO POLE
x[1] = 0.366
y2[1] (analytic) = 1.0662336551321539459526148857234
y2[1] (numeric) = 1.066169138424683623036760069296
absolute error = 6.45167074703229158548164274e-05
relative error = 0.0060508976770505725416291595250457 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0662336551321539459526148857234
y1[1] (numeric) = 1.0662336551321539584976084840676
absolute error = 1.25449935983442e-17
relative error = 1.1765707767674352102097642503913e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=698.1MB, alloc=4.6MB, time=91.91
NO POLE
NO POLE
x[1] = 0.367
y2[1] (analytic) = 1.0665920051952480257407766421643
y2[1] (numeric) = 1.0665272550660836155993326717993
absolute error = 6.47501291644101414439703650e-05
relative error = 0.0060707495320628362327683340321603 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0665920051952480257407766421643
y1[1] (numeric) = 1.06659200519524803833115825018
absolute error = 1.25903816080157e-17
relative error = 1.1804309001651415877801824443727e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.368
y2[1] (analytic) = 1.0669512886662591262839383951033
y2[1] (numeric) = 1.0668863052050400069137206311264
absolute error = 6.49834612191193702177639769e-05
relative error = 0.0060905743223152998295300017771887 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0669512886662591262839383951033
y1[1] (numeric) = 1.066951288666259138919690584105
absolute error = 1.26357521890017e-17
relative error = 1.1842857610488481865660256511879e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=701.9MB, alloc=4.6MB, time=92.42
NO POLE
NO POLE
x[1] = 0.369
y2[1] (analytic) = 1.0673115051859038065112878542941
y2[1] (numeric) = 1.0672462884825026879443765485605
absolute error = 6.52167034011185669113057336e-05
relative error = 0.0061103720033224183004688328196194 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0673115051859038065112878542941
y1[1] (numeric) = 1.0673115051859038191923931502257
absolute error = 1.26811052959316e-17
relative error = 1.1881353507683599041139706400355e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=705.7MB, alloc=4.6MB, time=92.93
NO POLE
NO POLE
x[1] = 0.37
y2[1] (analytic) = 1.0676726543939655767961870955091
y2[1] (numeric) = 1.0676072045384884112272248487155
absolute error = 6.54498554771655689622467936e-05
relative error = 0.0061301425308411914783564281660583 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0676726543939655767961870955091
y1[1] (numeric) = 1.0676726543939655895226279789615
absolute error = 1.27264408834524e-17
relative error = 1.1919796607206547836101680647735e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.371
y2[1] (analytic) = 1.0680347359292952591726321691378
y2[1] (numeric) = 1.0679690530120811508528792450088
absolute error = 6.56829172141083197529241290e-05
relative error = 0.0061498858608711562179033865230441 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0680347359292952591726321691378
y1[1] (numeric) = 1.0680347359292952719443910753662
absolute error = 1.27717589062284e-17
relative error = 1.1958186823498501363461933809703e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=709.5MB, alloc=4.6MB, time=93.44
NO POLE
NO POLE
x[1] = 0.372
y2[1] (analytic) = 1.0683977494298113484844009704265
y2[1] (numeric) = 1.068331833541432463382638572713
absolute error = 6.59158883788851017623977135e-05
relative error = 0.0061696019496543746861140525114551 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0683977494298113484844009704265
y1[1] (numeric) = 1.0683977494298113613014602893682
absolute error = 1.28170593189417e-17
relative error = 1.1996524071472428581197674560727e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=713.3MB, alloc=4.6MB, time=93.96
NO POLE
NO POLE
x[1] = 0.373
y2[1] (analytic) = 1.0687616945325003744665282222431
y2[1] (numeric) = 1.0686955457637618496969000736212
absolute error = 6.61487687385247696281486219e-05
relative error = 0.0061892907536754187962134063855697 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0687616945325003744665282222431
y1[1] (numeric) = 1.0687616945325003873288702985349
absolute error = 1.28623420762918e-17
relative error = 1.2034808266512647010577781884391e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.374
y2[1] (analytic) = 1.0691265708734172647587454889206
y2[1] (numeric) = 1.0690601893153571177756282839423
absolute error = 6.63815580601469831172049783e-05
relative error = 0.0062089522296613507961662263018019 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0691265708734172647587454889206
y1[1] (numeric) = 1.0691265708734172776663526219165
absolute error = 1.29076071329959e-17
relative error = 1.2073039324475023584805541348783e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=717.1MB, alloc=4.6MB, time=94.47
NO POLE
NO POLE
x[1] = 0.375
y2[1] (analytic) = 1.0694923780876857088505232077704
y2[1] (numeric) = 1.0694257638315747464105167449884
absolute error = 6.66142561109624400064627820e-05
relative error = 0.006228586334581700022888615406744 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0694923780876857088505232077704
y1[1] (numeric) = 1.0694923780876857218033776515596
absolute error = 1.29528544437892e-17
relative error = 1.2111217161687167571506375865556e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=720.9MB, alloc=4.6MB, time=94.99
NO POLE
NO POLE
x[1] = 0.376
y2[1] (analytic) = 1.0698591158094985229573507932542
y2[1] (numeric) = 1.069792268946840249848478824522
absolute error = 6.68468626582731088719687322e-05
relative error = 0.0062481930256484358333312361149502 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0698591158094985229573507932542
y1[1] (numeric) = 1.0698591158094985359554347566783
absolute error = 1.29980839634241e-17
relative error = 1.2149341694947587414849263784643e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.377
y2[1] (analytic) = 1.070226783672118015827889937563
y2[1] (numeric) = 1.0701597042946485433661030053033
absolute error = 6.70793774694724617869322597e-05
relative error = 0.0062677722603159367236921314472041 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.070226783672118015827889937563
y1[1] (numeric) = 1.0702267836721180288711855842341
absolute error = 1.30432956466711e-17
relative error = 1.2187412841526430256490702746266e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=724.8MB, alloc=4.6MB, time=95.50
NO POLE
NO POLE
x[1] = 0.378
y2[1] (analytic) = 1.0705953813078763554816353004824
y2[1] (numeric) = 1.0705280695075643097747070664121
absolute error = 6.73118003120457069282340703e-05
relative error = 0.0062873239962809556480948386110858 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0705953813078763554816353004824
y1[1] (numeric) = 1.0705953813078763685701247488011
absolute error = 1.30884894483187e-17
relative error = 1.2225430519165278378466530623536e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=728.6MB, alloc=4.6MB, time=96.01
NO POLE
NO POLE
x[1] = 0.379
y2[1] (analytic) = 1.070964908348175936876715850913
y2[1] (numeric) = 1.0708973642172223668556246523215
absolute error = 6.75441309535700210911985915e-05
relative error = 0.0063068481914825815481446104609467 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.070964908348175936876715850913
y1[1] (numeric) = 1.070964908348175950010381174086
absolute error = 1.31336653231730e-17
relative error = 1.2263394646076658451831699273161e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.38
y2[1] (analytic) = 1.0713353644234897505074691922754
y2[1] (numeric) = 1.0712675880543280357253567944668
absolute error = 6.77763691617147821123978086e-05
relative error = 0.0063263448041021971048519568386264 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0713353644234897505074691922754
y1[1] (numeric) = 1.0713353644234897636862924183336
absolute error = 1.31788232260582e-17
relative error = 1.2301305140944384390680129277128e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=732.4MB, alloc=4.6MB, time=96.52
NO POLE
NO POLE
x[1] = 0.381
y2[1] (analytic) = 1.0717067491633617519314202742562
y2[1] (numeric) = 1.0716387406486575101302200201887
absolute error = 6.80085147042418012002540675e-05
relative error = 0.0063458137925634327244883982516645 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0717067491633617519314202742562
y1[1] (numeric) = 1.0717067491633617651553833860725
absolute error = 1.32239631118163e-17
relative error = 1.2339161922923145546884861805319e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=736.2MB, alloc=4.6MB, time=97.03
NO POLE
NO POLE
x[1] = 0.382
y2[1] (analytic) = 1.0720790621964072322252949639468
y2[1] (numeric) = 1.0720108216290582266701217544341
absolute error = 6.82405673490055551732095127e-05
relative error = 0.0063652551155321167700142884483782 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0720790621964072322252949639468
y1[1] (numeric) = 1.0720790621964072454943798992542
absolute error = 1.32690849353074e-17
relative error = 1.2376964911638647951092492008920e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.383
y2[1] (analytic) = 1.072452303150313189369698020393
y2[1] (numeric) = 1.0723838306234492359510927904694
absolute error = 6.84725268639534186052299236e-05
relative error = 0.0063846687319162220497928098083529 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.072452303150313189369698020393
y1[1] (numeric) = 1.0724523031503132026838866718028
absolute error = 1.33141886514098e-17
relative error = 1.2414714027187561309624703895872e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=740.0MB, alloc=4.6MB, time=97.54
NO POLE
NO POLE
x[1] = 0.384
y2[1] (analytic) = 1.0728264716518387005620840879077
y2[1] (numeric) = 1.0727577672588215746662056771049
absolute error = 6.87043930171258958784108028e-05
relative error = 0.006404054600865808575377774729179 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0728264716518387005620840879077
y1[1] (numeric) = 1.0728264716518387139213583029275
absolute error = 1.33592742150198e-17
relative error = 1.2452409190137179020663470694332e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=743.8MB, alloc=4.6MB, time=98.05
NO POLE
NO POLE
x[1] = 0.385
y2[1] (analytic) = 1.0732015673268152954576493952072
y2[1] (numeric) = 1.0731326311612386386045069415431
absolute error = 6.89361655766568531424536641e-05
relative error = 0.0064234126817729626002356774287121 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0732015673268152954576493952072
y1[1] (numeric) = 1.073201567326815308861990976259
absolute error = 1.34043415810518e-17
relative error = 1.2490050321525350991115151428126e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=747.6MB, alloc=4.6MB, time=98.56
NO POLE
NO POLE
x[1] = 0.386
y2[1] (analytic) = 1.0735775898001473303377709195101
y2[1] (numeric) = 1.0735084219558365565875901389494
absolute error = 6.91678443107737501807805607e-05
relative error = 0.0064427429342717319513345327941526 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0735775898001473303377709195101
y1[1] (numeric) = 1.0735775898001473437871616239484
absolute error = 1.34493907044383e-17
relative error = 1.2527637342860316008953640702249e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.387
y2[1] (analytic) = 1.0739545386958123632056188471909
y2[1] (numeric) = 1.0738851392668245653334357922039
absolute error = 6.93994289877978721830549870e-05
relative error = 0.0064620453182380576656034116877439 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0739545386958123632056188471909
y1[1] (numeric) = 1.0739545386958123767000403873212
absolute error = 1.34944215401303e-17
relative error = 1.2565170176120899491624993668657e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=751.5MB, alloc=4.6MB, time=99.08
NO POLE
NO POLE
x[1] = 0.388
y2[1] (analytic) = 1.0743324136368615298085672354074
y2[1] (numeric) = 1.0742627827174853852471433580247
absolute error = 6.96309193761445614238773827e-05
relative error = 0.0064813197937897019433372351937558 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0743324136368615298085672354074
y1[1] (numeric) = 1.0743324136368615433480012785045
absolute error = 1.35394340430971e-17
relative error = 1.2602648743756144906903635884152e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=755.3MB, alloc=4.6MB, time=99.58
NO POLE
NO POLE
x[1] = 0.389
y2[1] (analytic) = 1.0747112142454199205870268523226
y2[1] (numeric) = 1.0746413519301755971381794287629
absolute error = 6.98623152443234488474235597e-05
relative error = 0.0065005663212861724306913226728968 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0747112142454199205870268523226
y1[1] (numeric) = 1.0747112142454199341714550206486
absolute error = 1.35844281683260e-17
relative error = 1.2640072968684845504748906865949e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.39
y2[1] (analytic) = 1.0750909401426869585493232471189
y2[1] (numeric) = 1.0750208465263260198637654526524
absolute error = 7.00936163609386855577944665e-05
relative error = 0.0065197848613286428434794003322675 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0750909401426869585493232471189
y1[1] (numeric) = 1.0750909401426869721787271179418
absolute error = 1.36294038708229e-17
relative error = 1.2677442774295906770782220935733e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=759.1MB, alloc=4.6MB, time=100.08
NO POLE
NO POLE
x[1] = 0.391
y2[1] (analytic) = 1.0754715909489367780722421749589
y2[1] (numeric) = 1.0754012661264420888980273291574
absolute error = 7.03248224946891742148458015e-05
relative error = 0.006538975374759869944557267977704 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0754715909489367780722421749589
y1[1] (numeric) = 1.075471590948936791746603280571
absolute error = 1.36743611056121e-17
relative error = 1.2714758084447956853398574793367e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=762.9MB, alloc=4.6MB, time=100.59
NO POLE
NO POLE
x[1] = 0.392
y2[1] (analytic) = 1.0758531662835186046268635763786
y2[1] (numeric) = 1.0757826103501042358265283103007
absolute error = 7.05559334143688003352660779e-05
relative error = 0.0065581378226641068871420906471095 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0758531662835186046268635763786
y1[1] (numeric) = 1.0758531662835186183461634041151
absolute error = 1.37192998277365e-17
relative error = 1.2752018823469322222540616849300e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.393
y2[1] (analytic) = 1.0762356657648571354293043853106
y2[1] (numeric) = 1.0761648788159682687658057134707
absolute error = 7.07869488888666634986718399e-05
relative error = 0.0065772721663670129364843296960336 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0762356657648571354293043853106
y1[1] (numeric) = 1.076235665764857149193524377568
absolute error = 1.37642199922574e-17
relative error = 1.2789224916157624330602901832712e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=766.7MB, alloc=4.6MB, time=101.13
NO POLE
NO POLE
x[1] = 0.394
y2[1] (analytic) = 1.0766190890104529210159895150267
y2[1] (numeric) = 1.0765480711417657537075310262026
absolute error = 7.10178686871673084584888241e-05
relative error = 0.0065963783674355595823756536069246 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0766190890104529210159895150267
y1[1] (numeric) = 1.076619089010452934825111069281
absolute error = 1.38091215542543e-17
relative error = 1.2826376287779369757898172884894e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=770.5MB, alloc=4.6MB, time=101.65
NO POLE
NO POLE
x[1] = 0.395
y2[1] (analytic) = 1.0770034356368827477430694467592
y2[1] (numeric) = 1.076932186944304396786912058805
absolute error = 7.12486925783509561573879542e-05
relative error = 0.0066154563876779330550417724030485 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0770034356368827477430694467592
y1[1] (numeric) = 1.0770034356368827615970739155851
absolute error = 1.38540044688259e-17
relative error = 1.2863472864070648072549809823937e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.396
y2[1] (analytic) = 1.0773887052598000212096019216175
y2[1] (numeric) = 1.0773172258394684274749548764622
absolute error = 7.14794203315937346470451553e-05
relative error = 0.006634506189143433257034021302073 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0773887052598000212096019216175
y1[1] (numeric) = 1.0773887052598000351084706127069
absolute error = 1.38988686910894e-17
relative error = 1.2900514571236242949825657808143e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=774.3MB, alloc=4.6MB, time=102.18
NO POLE
NO POLE
x[1] = 0.397
y2[1] (analytic) = 1.0777748974939351506041143126486
y2[1] (numeric) = 1.0777031874422189826942023185815
absolute error = 7.17100517161679099119940671e-05
relative error = 0.0066535277341223691237976781942936 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0777748974939351506041143126486
y1[1] (numeric) = 1.077774897493935164547828488829
absolute error = 1.39437141761804e-17
relative error = 1.2937501335949294548457974594908e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=778.2MB, alloc=4.6MB, time=102.69
NO POLE
NO POLE
x[1] = 0.398
y2[1] (analytic) = 1.0781620119530959339741623305114
y2[1] (numeric) = 1.0780900713665944918575649896794
absolute error = 7.19405865014421165973408320e-05
relative error = 0.0066725209851459504256584364523759 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0781620119530959339741623305114
y1[1] (numeric) = 1.0781620119530959479627032097648
absolute error = 1.39885408792534e-17
relative error = 1.2974433085351511778253174120837e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.399
y2[1] (analytic) = 1.0785500482501679444184997932385
y2[1] (numeric) = 1.0784778772257110628298596830082
absolute error = 7.21710244568815886401102303e-05
relative error = 0.0066914859049861760240311690737146 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0785500482501679444184997932385
y1[1] (numeric) = 1.0785500482501679584518485487204
absolute error = 1.40333487554819e-17
relative error = 1.3011309747053005913349473990041e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=782.0MB, alloc=4.6MB, time=103.20
NO POLE
NO POLE
x[1] = 0.4
y2[1] (analytic) = 1.0789390059971149172014732679482
y2[1] (numeric) = 1.0788666046317628688116692754157
absolute error = 7.24013653520483898039925325e-05
relative error = 0.0067104224566557185947171124508543 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0789390059971149172014732679482
y1[1] (numeric) = 1.078939005997114931279611028006
absolute error = 1.40781377600578e-17
relative error = 1.3048131249131468455798685177044e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=785.8MB, alloc=4.6MB, time=103.71
NO POLE
NO POLE
x[1] = 0.401
y2[1] (analytic) = 1.0793288848049791377892544701431
y2[1] (numeric) = 1.079256253196022536145137209611
absolute error = 7.26316089566016441172605321e-05
relative error = 0.0067293306034078058312168676782239 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0793288848049791377892544701431
y1[1] (numeric) = 1.0793288848049791519121623183353
absolute error = 1.41229078481922e-17
relative error = 1.3084897520132640567953959259510e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.402
y2[1] (analytic) = 1.0797196842838818308075223843972
y2[1] (numeric) = 1.0796468225288415330413087580748
absolute error = 7.28617550402977662136263224e-05
relative error = 0.0067482103087360981410471653805059 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0797196842838818308075223843972
y1[1] (numeric) = 1.0797196842838818449751813595121
absolute error = 1.41676589751149e-17
relative error = 1.3121608489069570170940222340468e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=789.6MB, alloc=4.6MB, time=104.23
NO POLE
NO POLE
x[1] = 0.403
y2[1] (analytic) = 1.0801114040430235499202061487794
y2[1] (numeric) = 1.0800383122396505592286303413038
absolute error = 7.30918033729906915758074756e-05
relative error = 0.0067670615363745628481091656338167 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0801114040430235499202061487794
y1[1] (numeric) = 1.0801114040430235641325972448544
absolute error = 1.42123910960750e-17
relative error = 1.3158264085422881775496514377642e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=793.4MB, alloc=4.6MB, time=104.75
NO POLE
NO POLE
x[1] = 0.404
y2[1] (analytic) = 1.0805040436906845686288988243055
y2[1] (numeric) = 1.0804307219369599365222172519238
absolute error = 7.33217537246321066815723817e-05
relative error = 0.0067858842502973449142151687436982 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0805040436906845686288988243055
y1[1] (numeric) = 1.0805040436906845828860029906458
absolute error = 1.42571041663403e-17
relative error = 1.3194864239139927850203107138550e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.405
y2[1] (analytic) = 1.0808976028342252719925512500355
y2[1] (numeric) = 1.0808240512283600003134992154358
absolute error = 7.35516058652716790520345997e-05
relative error = 0.006804678414718634192938994886425 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0808976028342252719925512500355
y1[1] (numeric) = 1.0808976028342252862943493912331
absolute error = 1.43017981411976e-17
relative error = 1.3231408880634767406679659822148e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=797.2MB, alloc=4.6MB, time=105.25
NO POLE
NO POLE
x[1] = 0.406
y2[1] (analytic) = 1.0812920810800865492670542641556
y2[1] (numeric) = 1.0812182997205214919798522979818
absolute error = 7.37813595650572872019661738e-05
relative error = 0.0068234439940925292290129520633356 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0812920810800865492670542641556
y1[1] (numeric) = 1.0812920810800865636135272401087
absolute error = 1.43464729759531e-17
relative error = 1.3267897940788229852850291622359e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=801.1MB, alloc=4.6MB, time=105.77
NO POLE
NO POLE
x[1] = 0.407
y2[1] (analytic) = 1.0816874780337901874643166514964
y2[1] (numeric) = 1.0816134670191959522138247515317
absolute error = 7.40110145942352504918999647e-05
relative error = 0.0068421809531128976165512520413434 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0816874780337901874643166514964
y1[1] (numeric) = 1.0816874780337902018554452774283
absolute error = 1.43911286259319e-17
relative error = 1.3304331350947139419103186612504e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=804.9MB, alloc=4.6MB, time=106.28
x[1] = 0.408
y2[1] (analytic) = 1.0820837932999392658304452584406
y2[1] (numeric) = 1.0820095527292161152715634672977
absolute error = 7.42405707231505588817911429e-05
relative error = 0.0068608892567132329294359535218061 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0820837932999392658304452584406
y1[1] (numeric) = 1.0820837932999392802662103049189
absolute error = 1.44357650464783e-17
relative error = 1.3340709042924273355240716954568e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.409
y2[1] (analytic) = 1.0824810264822185512426327970737
y2[1] (numeric) = 1.0824065564544963041400467889834
absolute error = 7.44700277222471025860080903e-05
relative error = 0.0068795688700665082372570113913433 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0824810264822185512426327970737
y1[1] (numeric) = 1.0824810264822185657230149900296
absolute error = 1.44803821929559e-17
relative error = 1.3377030948998128227557737597424e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=808.7MB, alloc=4.6MB, time=106.79
NO POLE
NO POLE
x[1] = 0.41
y2[1] (analytic) = 1.082879177183394894524357941723
y2[1] (numeric) = 1.0828044777980328266227285186664
absolute error = 7.46993853620679016294230566e-05
relative error = 0.0068982197585850262202527908357637 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.082879177183394894524357941723
y1[1] (numeric) = 1.0828791771833949090493379624707
absolute error = 1.45249800207477e-17
relative error = 1.3413297001912679507651422441930e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=812.5MB, alloc=4.6MB, time=107.29
NO POLE
NO POLE
x[1] = 0.411
y2[1] (analytic) = 1.0832782450053176276785014027179
y2[1] (numeric) = 1.0832033163619043723431970297048
absolute error = 7.49286434132553353043730131e-05
relative error = 0.0069168418879202658967514653697199 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0832782450053176276785014027179
y1[1] (numeric) = 1.0832782450053176422480598879736
absolute error = 1.45695584852557e-17
relative error = 1.3449507134876672916658986081226e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.412
y2[1] (analytic) = 1.0836782295489189620379807442877
y2[1] (numeric) = 1.0836030717472724106664524830407
absolute error = 7.51578016465513715282612470e-05
relative error = 0.0069354352239627259766670597554583 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0836782295489189620379807442877
y1[1] (numeric) = 1.0836782295489189766520982861892
absolute error = 1.46141175419015e-17
relative error = 1.3485661281563832917905925417716e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=816.3MB, alloc=4.6MB, time=107.79
NO POLE
NO POLE
x[1] = 0.413
y2[1] (analytic) = 1.084079130414214387333505795996
y2[1] (numeric) = 1.0840037435543815895374042256569
absolute error = 7.53868598327977961015703391e-05
relative error = 0.0069539997328417648546565224408231 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.084079130414214387333505795996
y1[1] (numeric) = 1.0840791304142144019921629421221
absolute error = 1.46586571461261e-17
relative error = 1.3521759376112325605191334586715e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=820.1MB, alloc=4.6MB, time=108.28
NO POLE
NO POLE
x[1] = 0.414
y2[1] (analytic) = 1.0844809472003030716780555899898
y2[1] (numeric) = 1.0844053313825601352361895327226
absolute error = 7.56158177429364418660572672e-05
relative error = 0.006972535380925437256596118164949 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0844809472003030716780555899898
y1[1] (numeric) = 1.0844809472003030863812328433796
absolute error = 1.47031772533898e-17
relative error = 1.3557801353124307811161852256329e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.415
y2[1] (analytic) = 1.0848836795053682624676768396186
y2[1] (numeric) = 1.084807834830220253049913938143
absolute error = 7.58446751480094177629014756e-05
relative error = 0.006991042134820327553086620313119 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0848836795053682624676768396186
y1[1] (numeric) = 1.0848836795053682772153546587912
absolute error = 1.47476778191726e-17
relative error = 1.3593787147665930928645329651337e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=823.9MB, alloc=4.6MB, time=108.80
NO POLE
NO POLE
x[1] = 0.416
y2[1] (analytic) = 1.0852873269266776881982030586595
y2[1] (numeric) = 1.085211253494858528860412481805
absolute error = 7.60734318191593377905768545e-05
relative error = 0.0070095199613713797537472557330397 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0852873269266776881982030586595
y1[1] (numeric) = 1.0852873269266777029903618576334
absolute error = 1.47921587989739e-17
relative error = 1.3629716695266692575412798327607e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=827.8MB, alloc=4.6MB, time=109.31
NO POLE
NO POLE
x[1] = 0.417
y2[1] (analytic) = 1.0856918890605839611974925044623
y2[1] (numeric) = 1.0856155869730563316476302857924
absolute error = 7.63020875276295498622186699e-05
relative error = 0.0070279688276617241961081116679986 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0856918890605839611974925044623
y1[1] (numeric) = 1.085691889060583976034112652775
absolute error = 1.48366201483127e-17
relative error = 1.3665589931919243093676423643848e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.418
y2[1] (analytic) = 1.0860973655025249812727822128099
y2[1] (numeric) = 1.0860208348604802169082199562224
absolute error = 7.65306420447643645622565875e-05
relative error = 0.0070463887010125009429597571399096 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0860973655025249812727822128099
y1[1] (numeric) = 1.0860973655025249961538440355376
absolute error = 1.48810618227277e-17
relative error = 1.3701406794079093274841554077120e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=831.6MB, alloc=4.6MB, time=109.82
NO POLE
NO POLE
x[1] = 0.419
y2[1] (analytic) = 1.0865037558470243402727544771743
y2[1] (numeric) = 1.0864269967518823309889523921405
absolute error = 7.67590951420092838020850338e-05
relative error = 0.0070647795489826799020671594570659 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0865037558470243402727544771743
y1[1] (numeric) = 1.0865037558470243551982382549514
absolute error = 1.49254837777771e-17
relative error = 1.3737167218664039499241843300245e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=835.4MB, alloc=4.6MB, time=110.32
NO POLE
NO POLE
x[1] = 0.42
y2[1] (analytic) = 1.0869110596876917275639112103343
y2[1] (numeric) = 1.0868340722411008163345366680964
absolute error = 7.69874465909112293745422379e-05
relative error = 0.007083141339368877682202591703524 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0869110596876917275639112103343
y1[1] (numeric) = 1.0869110596876917425337971793734
absolute error = 1.49698859690391e-17
relative error = 1.3772871143054227080155137227783e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.421
y2[1] (analytic) = 1.087319276617223336420850712016
y2[1] (numeric) = 1.0872420609210602176494437426143
absolute error = 7.72156961631187714069694017e-05
relative error = 0.0071014740402051711994991302551051 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.087319276617223336420850712016
y1[1] (numeric) = 1.0873192766172233514351190641274
absolute error = 1.50142683521114e-17
relative error = 1.3808518505091286671219188623585e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=839.2MB, alloc=4.6MB, time=110.82
NO POLE
NO POLE
x[1] = 0.422
y2[1] (analytic) = 1.0877284062274022713300404523114
y2[1] (numeric) = 1.0876509623837718889733278307688
absolute error = 7.74438436303823567126215426e-05
relative error = 0.0071197776197629080481725323833257 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0877284062274022713300404523114
y1[1] (numeric) = 1.0877284062274022863886713349231
absolute error = 1.50586308826117e-17
relative error = 1.3844109243078384875408658006387e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=843.0MB, alloc=4.6MB, time=111.32
NO POLE
NO POLE
x[1] = 0.423
y2[1] (analytic) = 1.0881384481090989562066785671374
y2[1] (numeric) = 1.0880607762203344016696383654776
absolute error = 7.76718887645545370402016598e-05
relative error = 0.0071380520465505136497047654825815 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0881384481090989562066785671374
y1[1] (numeric) = 1.088138448109098971309652083315
absolute error = 1.51029735161776e-17
relative error = 1.3879643295779716262639962301029e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.424
y2[1] (analytic) = 1.088549401852271543524235848908
y2[1] (numeric) = 1.0884715020209339533270145589345
absolute error = 7.78998313375901972212899735e-05
relative error = 0.0071562972893132951946272305739475 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.088549401852271543524235848908
y1[1] (numeric) = 1.0885494018522715586715320573741
absolute error = 1.51472962084661e-17
relative error = 1.3915120602419622006525668151422e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=846.8MB, alloc=4.6MB, time=111.82
NO POLE
NO POLE
x[1] = 0.425
y2[1] (analytic) = 1.0889612670459663243562691029099
y2[1] (numeric) = 1.088883139374844777573053662821
absolute error = 7.81276711215467832154400889e-05
relative error = 0.0071745133170332423910857857244671 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0889612670459663243562691029099
y1[1] (numeric) = 1.0889612670459663395478680180647
absolute error = 1.51915989151548e-17
relative error = 1.3950541102683264585505773573969e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=850.6MB, alloc=4.6MB, time=112.31
NO POLE
NO POLE
x[1] = 0.426
y2[1] (analytic) = 1.0893740432783181393300958276049
y2[1] (numeric) = 1.0892956878704295548000431135629
absolute error = 7.83554078885845300527140420e-05
relative error = 0.0071927000989288250344130307418164 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0893740432783181393300958276049
y1[1] (numeric) = 1.0893740432783181545659774195459
absolute error = 1.52358815919410e-17
relative error = 1.3985904736715366199366479221150e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.427
y2[1] (analytic) = 1.089787730136550790491919265217
y2[1] (numeric) = 1.0897091470951398238022458369342
absolute error = 7.85830414109666896734282828e-05
relative error = 0.0072108576044547874119759632137213 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.089787730136550790491919265217
y1[1] (numeric) = 1.0897877301365508057720634597589
absolute error = 1.52801441945419e-17
relative error = 1.4021211445119952390649989080680e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=854.5MB, alloc=4.6MB, time=112.81
NO POLE
NO POLE
x[1] = 0.428
y2[1] (analytic) = 1.0902023272069774540829919575135
y2[1] (numeric) = 1.0901235166355163943243270747568
absolute error = 7.88105714610597586648827567e-05
relative error = 0.0072289858033019395576090599781401 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0902023272069774540829919575135
y1[1] (numeric) = 1.0902023272069774694073786362085
absolute error = 1.53243866786950e-17
relative error = 1.4056461168960272686917651115958e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=858.3MB, alloc=4.6MB, time=113.31
NO POLE
NO POLE
x[1] = 0.429
y2[1] (analytic) = 1.0906178340750010942264050306518
y2[1] (numeric) = 1.0905387960771897605205101853038
absolute error = 7.90379978113337058948453480e-05
relative error = 0.0072470846653969453699840777839211 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0906178340750010942264050306518
y1[1] (numeric) = 1.0906178340750011095950140308096
absolute error = 1.53686090001578e-17
relative error = 1.4091653849758072580544663640021e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=862.1MB, alloc=4.6MB, time=113.81
x[1] = 0.43
y2[1] (analytic) = 1.0910342503251148775240895223366
y2[1] (numeric) = 1.0909549850048805153240479582853
absolute error = 7.92653202343622000415640513e-05
relative error = 0.0072651541609021076093084035003209 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0910342503251148775240895223366
y1[1] (numeric) = 1.0910342503251148929369006370444
absolute error = 1.54128111147078e-17
relative error = 1.4126789429493135146602168419750e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.431
y2[1] (analytic) = 1.09145157554090258856361515432
y2[1] (numeric) = 1.0913720830023997657265950749794
absolute error = 7.94925385028228370200793406e-05
relative error = 0.0072831942602151497867836192793138 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.09145157554090258856361515432
y1[1] (numeric) = 1.0914515755409026040206081324632
absolute error = 1.54569929781432e-17
relative error = 1.4161867850603458078946607254904e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=865.9MB, alloc=4.6MB, time=114.32
NO POLE
NO POLE
x[1] = 0.432
y2[1] (analytic) = 1.0918698093050390463343710434825
y2[1] (numeric) = 1.091790089652649548967066434171
absolute error = 7.97196523894973673046093115e-05
relative error = 0.0073012049339689949612950827738996 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0918698093050390463343710434825
y1[1] (numeric) = 1.0918698093050390618355255897644
absolute error = 1.55011545462819e-17
relative error = 1.4196889055983866389191288828277e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=869.7MB, alloc=4.6MB, time=114.83
NO POLE
NO POLE
x[1] = 0.433
y2[1] (analytic) = 1.0922889511992905215527119353457
y2[1] (numeric) = 1.0922090045376232496295651550745
absolute error = 7.99466616672719231467802712e-05
relative error = 0.0073191861530315414578417574322201 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0922889511992905215527119353457
y1[1] (numeric) = 1.0922889511992905370980077103082
absolute error = 1.55452957749625e-17
relative error = 1.4231852988986452354184225048794e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.434
y2[1] (analytic) = 1.0927090008045151548956526349088
y2[1] (numeric) = 1.0926288272384060176499631593471
absolute error = 8.01735661091372456894755617e-05
relative error = 0.0073371378885054355222532659641755 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0927090008045151548956526349088
y1[1] (numeric) = 1.0927090008045151704850692549525
absolute error = 1.55894166200437e-17
relative error = 1.4266759593419543259770934389942e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=873.5MB, alloc=4.6MB, time=115.31
NO POLE
NO POLE
x[1] = 0.435
y2[1] (analytic) = 1.0931299577006633761426924011461
y2[1] (numeric) = 1.0930495573351751872307163256473
absolute error = 8.04003654881889119760754988e-05
relative error = 0.0073550601117278409267781803871434 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0931299577006633761426924011461
y1[1] (numeric) = 1.0931299577006633917762094385507
absolute error = 1.56335170374046e-17
relative error = 1.4301608813547487917237393648459e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=877.3MB, alloc=4.6MB, time=115.82
NO POLE
NO POLE
x[1] = 0.436
y2[1] (analytic) = 1.0935518214667783242253501633781
y2[1] (numeric) = 1.093471194407200696663495301958
absolute error = 8.06270595776275618548614201e-05
relative error = 0.0073729527942702055411639084523935 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0935518214667783242253501633781
y1[1] (numeric) = 1.093551821466778339902947146323
absolute error = 1.56775969829449e-17
relative error = 1.4336400594090345312741419772374e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.437
y2[1] (analytic) = 1.0939745916809962681839905100158
y2[1] (numeric) = 1.0938937380328455090592121530787
absolute error = 8.08536481507591247783569371e-05
relative error = 0.0073908159079380248838841881296028 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0939745916809962681839905100158
y1[1] (numeric) = 1.0939745916809962839056469226003
absolute error = 1.57216564125845e-17
relative error = 1.4371134880223018613966459921258e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=881.2MB, alloc=4.6MB, time=116.32
NO POLE
NO POLE
x[1] = 0.438
y2[1] (analytic) = 1.0943982679205470290315194928856
y2[1] (numeric) = 1.0943171877895660339850221132946
absolute error = 8.10801309809950464973795910e-05
relative error = 0.0074086494247706026682051616721066 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0943982679205470290315194928856
y1[1] (numeric) = 1.0943982679205470447972147751498
absolute error = 1.57656952822642e-17
relative error = 1.4405811617575389412283514897244e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=885.0MB, alloc=4.6MB, time=116.83
NO POLE
NO POLE
x[1] = 0.439
y2[1] (analytic) = 1.0948228497617544025235283834771
y2[1] (numeric) = 1.0947415432539125500078788072568
absolute error = 8.13065078418525156495762203e-05
relative error = 0.0074264533170408083578152702125029 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0948228497617544025235283834771
y1[1] (numeric) = 1.094822849761754418333241931422
absolute error = 1.58097135479449e-17
relative error = 1.4440430752231074691565769618022e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.44
y2[1] (analytic) = 1.0952483367800365828344626110016
y2[1] (numeric) = 1.0951668040015296281442203955532
absolute error = 8.15327785069546902422154484e-05
relative error = 0.0074442275572548317467777892309361 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0952483367800365828344626110016
y1[1] (numeric) = 1.0952483367800365986881737766102
absolute error = 1.58537111656086e-17
relative error = 1.4474992230727823286816364119973e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=888.8MB, alloc=4.6MB, time=117.35
NO POLE
NO POLE
x[1] = 0.441
y2[1] (analytic) = 1.0956747285499065871393922061318
y2[1] (numeric) = 1.0955929696071565562153631953189
absolute error = 8.17589427500309240290108129e-05
relative error = 0.0074619721181519345785977181384737 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0956747285499065871393922061318
y1[1] (numeric) = 1.0956747285499066030370802973892
absolute error = 1.58976880912574e-17
relative error = 1.4509496000056079210304190766689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=892.6MB, alloc=4.6MB, time=117.85
NO POLE
NO POLE
x[1] = 0.442
y2[1] (analytic) = 1.0961020246449726811009591686834
y2[1] (numeric) = 1.0960200396446277641081784205284
absolute error = 8.19850003449169927807481550e-05
relative error = 0.0074796869727041992192269424464094 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0961020246449726811009591686834
y1[1] (numeric) = 1.0961020246449726970426034495979
absolute error = 1.59416442809145e-17
relative error = 1.4543942007659366140850289854863e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.443
y2[1] (analytic) = 1.0965302246379388052610762723304
y2[1] (numeric) = 1.0964480136868732499406267813281
absolute error = 8.22109510655553204494910023e-05
relative error = 0.0074973720941162743988631093586084 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0965302246379388052610762723304
y1[1] (numeric) = 1.0965302246379388212466559629542
absolute error = 1.59855796906238e-17
relative error = 1.4578330201433387438115996175984e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=896.4MB, alloc=4.6MB, time=118.35
NO POLE
NO POLE
x[1] = 0.444
y2[1] (analytic) = 1.0969593281006050023369509146883
y2[1] (numeric) = 1.0968768913059190071317247769101
absolute error = 8.24367946859952052261377782e-05
relative error = 0.0075150274558251180374284957382178 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0969593281006050023369509146883
y1[1] (numeric) = 1.0969593281006050183664451911381
absolute error = 1.60294942764498e-17
relative error = 1.4612660529725394935752719403939e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=900.2MB, alloc=4.6MB, time=118.84
NO POLE
NO POLE
x[1] = 0.445
y2[1] (analytic) = 1.0973893346038678454210067167782
y2[1] (numeric) = 1.0973066720728874523755156119961
absolute error = 8.26625309803930454911047821e-05
relative error = 0.0075326530314997371686453053192175 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0973893346038678454210067167782
y1[1] (numeric) = 1.0973893346038678614943947112561
absolute error = 1.60733879944779e-17
relative error = 1.4646932941333916922041743677432e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.446
y2[1] (analytic) = 1.0978202437177208670842746719854
y2[1] (numeric) = 1.097737355557997854518616762997
absolute error = 8.28881597230125656579089884e-05
relative error = 0.0075502487950409249776533097904868 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0978202437177208670842746719854
y1[1] (numeric) = 1.0978202437177208832015354727998
absolute error = 1.61172608008144e-17
relative error = 1.4681147385508206709831108264891e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=904.0MB, alloc=4.6MB, time=119.34
NO POLE
NO POLE
x[1] = 0.447
y2[1] (analytic) = 1.0982520550112549893828247411573
y2[1] (numeric) = 1.0981689413305667643409153163355
absolute error = 8.31136806882250419094248218e-05
relative error = 0.0075678147205809949671445488863692 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0982520550112549893828247411573
y1[1] (numeric) = 1.0982520550112550055439373927439
absolute error = 1.61611126515866e-17
relative error = 1.4715303811947776789574491013175e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=907.9MB, alloc=4.6MB, time=119.82
NO POLE
NO POLE
x[1] = 0.448
y2[1] (analytic) = 1.0986847680526589547668078874449
y2[1] (numeric) = 1.0986014289590084452389812982728
absolute error = 8.33390936505095278265891721e-05
relative error = 0.0075853507824835122670179287702002 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0986847680526589547668078874449
y1[1] (numeric) = 1.0986847680526589709717513903875
absolute error = 1.62049435029426e-17
relative error = 1.4749402170801654272365681531757e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.449
y2[1] (analytic) = 1.0991183824092197578916776418816
y2[1] (numeric) = 1.0990348180108353048117683128618
absolute error = 8.35643983844530799093290198e-05
relative error = 0.0076028569553430221025840081546662 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0991183824092197578916776418816
y1[1] (numeric) = 1.0991183824092197741404309529331
absolute error = 1.62487533110515e-17
relative error = 1.4783442412667995279768184407015e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=911.7MB, alloc=4.6MB, time=120.32
NO POLE
NO POLE
x[1] = 0.45
y2[1] (analytic) = 1.0995528976473230783311593885136
y2[1] (numeric) = 1.099469108052658327348169902362
absolute error = 8.37895946647509829894861516e-05
relative error = 0.0076203332139847754363770393412665 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0995528976473230783311593885136
y1[1] (numeric) = 1.099552897647323094623701420617
absolute error = 1.62925420321034e-17
relative error = 1.4817424488593511629030925038323e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=915.5MB, alloc=4.6MB, time=120.81
NO POLE
NO POLE
x[1] = 0.451
y2[1] (analytic) = 1.0999883133324537141915346561489
y2[1] (numeric) = 1.0999042986501875072159991425959
absolute error = 8.40146822662069755355135530e-05
relative error = 0.0076377795334644517986574385866945 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.0999883133324537141915346561489
y1[1] (numeric) = 1.0999883133324537305278442784588
absolute error = 1.63363096223099e-17
relative error = 1.4851348350073346715880785737327e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.452
y2[1] (analytic) = 1.1004246290291960166268068024775
y2[1] (numeric) = 1.1003403893682322831519580843031
absolute error = 8.42396609637334748487181744e-05
relative error = 0.007655195889067879321713298869351 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1004246290291960166268068024775
y1[1] (numeric) = 1.1004246290291960330068628403806
absolute error = 1.63800560379031e-17
relative error = 1.4885213949049581882858759482525e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=919.3MB, alloc=4.6MB, time=121.31
NO POLE
NO POLE
x[1] = 0.453
y2[1] (analytic) = 1.100861844301234325254313575431
y2[1] (numeric) = 1.1007773797707019734521627505595
absolute error = 8.44645305323518021508248715e-05
relative error = 0.0076725822563107519930943296066559 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.100861844301234325254313575431
y1[1] (numeric) = 1.1008618443012343416780948105677
absolute error = 1.64237812351367e-17
relative error = 1.4919021237911647252934411720041e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=923.1MB, alloc=4.6MB, time=121.80
NO POLE
NO POLE
x[1] = 0.454
y2[1] (analytic) = 1.101299958711353404470351136208
y2[1] (numeric) = 1.1012152694206062120627884997725
absolute error = 8.46892907471924075626364355e-05
relative error = 0.007689938610938344142935715472691 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.101299958711353404470351136208
y1[1] (numeric) = 1.1012999587113534209378363064936
absolute error = 1.64674851702856e-17
relative error = 1.4952770169495362891557255653864e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=926.9MB, alloc=4.6MB, time=122.30
NO POLE
NO POLE
x[1] = 0.455
y2[1] (analytic) = 1.1017389718214388806653732283767
y2[1] (numeric) = 1.1016540578800553855703996636428
absolute error = 8.49139413834950949735647339e-05
relative error = 0.0077072649289252221805528303587094 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1017389718214388806653732283767
y1[1] (numeric) = 1.1017389718214388971765410280224
absolute error = 1.65111677996457e-17
relative error = 1.4986460697082157130895593818887e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.456
y2[1] (analytic) = 1.1021788831924776803383282778904
y2[1] (numeric) = 1.1020937447102610710915264698002
absolute error = 8.51384822166092468018080902e-05
relative error = 0.0077245611864749535955105257538756 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1021788831924776803383282778904
y1[1] (numeric) = 1.1021788831924776968931573574248
absolute error = 1.65548290795344e-17
relative error = 1.5020092774398915229731552822672e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=930.8MB, alloc=4.6MB, time=122.79
NO POLE
NO POLE
x[1] = 0.457
y2[1] (analytic) = 1.1026196923845584691096963097179
y2[1] (numeric) = 1.1025343294715364750610513595728
absolute error = 8.53629130219940486449501451e-05
relative error = 0.0077418273600198132383928378357952 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1026196923845584691096963097179
y1[1] (numeric) = 1.1026196923845584857081652760085
absolute error = 1.65984689662906e-17
relative error = 1.5053666355617368306347682794120e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=934.6MB, alloc=4.6MB, time=123.28
NO POLE
NO POLE
x[1] = 0.458
y2[1] (analytic) = 1.1030613989568720916327866680871
y2[1] (numeric) = 1.1029758117232968729189659125394
absolute error = 8.55872335752187138207555477e-05
relative error = 0.0077590634262204868965204250156652 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1030613989568720916327866680871
y1[1] (numeric) = 1.1030613989568721082748740843613
absolute error = 1.66420874162742e-17
relative error = 1.5087181395353023840822763655689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.459
y2[1] (analytic) = 1.1035040024677120124028566290802
y2[1] (numeric) = 1.1034181910240600496950586911457
absolute error = 8.58114436519627077979379345e-05
relative error = 0.0077762693619657721798838607262538 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1035040024677120124028566290802
y1[1] (numeric) = 1.103504002467712029088541014947
absolute error = 1.66856843858668e-17
relative error = 1.5120637848665179596680799480453e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=938.4MB, alloc=4.6MB, time=123.78
NO POLE
NO POLE
x[1] = 0.46
y2[1] (analytic) = 1.1039475024744747574636100964996
y2[1] (numeric) = 1.1038614669314467414910934207324
absolute error = 8.60355430280159725166757672e-05
relative error = 0.0077934451443722767325810670155627 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1039475024744747574636100964996
y1[1] (numeric) = 1.1039475024744747741928699279712
absolute error = 1.67292598314716e-17
relative error = 1.5154035671056206258239905562523e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=942.2MB, alloc=4.6MB, time=124.28
NO POLE
NO POLE
x[1] = 0.461
y2[1] (analytic) = 1.104391898533660357010634674543
y2[1] (numeric) = 1.1043056390021810778600360228337
absolute error = 8.62595314792791505986517093e-05
relative error = 0.0078105907507841137850666844052758 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.104391898533660357010634674543
y1[1] (numeric) = 1.104391898533660373783448384056
absolute error = 1.67728137095130e-17
relative error = 1.5187374818470553586332703602262e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.462
y2[1] (analytic) = 1.1048371902008727888913345138855
y2[1] (numeric) = 1.1047507067920910250818881225571
absolute error = 8.64834087817638094463913284e-05
relative error = 0.0078277061587725950625400348334803 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1048371902008727888913345138855
y1[1] (numeric) = 1.1048371902008728057076804903227
absolute error = 1.68163459764372e-17
relative error = 1.5220655247294657533860167521879e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=946.0MB, alloc=4.6MB, time=124.78
NO POLE
NO POLE
x[1] = 0.463
y2[1] (analytic) = 1.1052833770308204230009154312754
y2[1] (numeric) = 1.1051966698561088303356837542467
absolute error = 8.67071747115926652316770287e-05
relative error = 0.0078447913461359210648165506608723 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1052833770308204230009154312754
y1[1] (numeric) = 1.1052833770308204398607720199873
absolute error = 1.68598565887119e-17
relative error = 1.5253876914356026781261950170453e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=949.8MB, alloc=4.6MB, time=125.28
NO POLE
NO POLE
x[1] = 0.464
y2[1] (analytic) = 1.1057304585773164665739779066934
y2[1] (numeric) = 1.1056435277482714667672050934711
absolute error = 8.69308290449998067728132223e-05
relative error = 0.0078618462908988687330451136879555 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1057304585773164665739779066934
y1[1] (numeric) = 1.1057304585773164834773234095199
absolute error = 1.69033455028265e-17
relative error = 1.5287039776922777152631433481450e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.465
y2[1] (analytic) = 1.1061784343932794103712726665209
y2[1] (numeric) = 1.1060912800217210794519721476567
absolute error = 8.71543715583309193005188642e-05
relative error = 0.0078788709713124765186506784622533 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1061784343932794103712726665209
y1[1] (numeric) = 1.106178434393279427318085341813
absolute error = 1.69468126752921e-17
relative error = 1.5320143792702979854335741949788e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=953.6MB, alloc=4.6MB, time=125.78
NO POLE
NO POLE
x[1] = 0.466
y2[1] (analytic) = 1.1066273040307334757611726659979
y2[1] (numeric) = 1.1065399262287054322530604424146
absolute error = 8.73778020280435081122235833e-05
relative error = 0.0078958653658537268698978441893747 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1066273040307334757611726659979
y1[1] (numeric) = 1.1066273040307334927514307286393
absolute error = 1.69902580626414e-17
relative error = 1.5353188919843914442648951945512e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=957.5MB, alloc=4.6MB, time=126.28
NO POLE
NO POLE
x[1] = 0.467
y2[1] (analytic) = 1.1070770670408090626954143895363
y2[1] (numeric) = 1.1069894659205783555732998457797
absolute error = 8.76011202307071221145437566e-05
relative error = 0.0079128294532252261514866930599155 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1070770670408090626954143895363
y1[1] (numeric) = 1.1070770670408090797290960109655
absolute error = 1.70336816214292e-17
relative error = 1.5386175116931859103364935781689e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.468
y2[1] (analytic) = 1.107527722973743198578660493185
y2[1] (numeric) = 1.1074398986478001950014067782016
absolute error = 8.78243259430035772537149834e-05
relative error = 0.0079297632123548820126072309067038 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.107527722973743198578660493185
y1[1] (numeric) = 1.1075277229737432156557438014169
absolute error = 1.70770833082319e-17
relative error = 1.5419102342990972071870407414816e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=961.3MB, alloc=4.6MB, time=126.78
NO POLE
NO POLE
x[1] = 0.469
y2[1] (analytic) = 1.1079792713788799880314349197206
y2[1] (numeric) = 1.1078912239599382608516011621913
absolute error = 8.80474189417271798337575293e-05
relative error = 0.0079466666223955782188931519241855 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1079792713788799880314349197206
y1[1] (numeric) = 1.1079792713788800051518979993684
absolute error = 1.71204630796478e-17
relative error = 1.5451970557482891374525360909766e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=965.1MB, alloc=4.6MB, time=127.26
NO POLE
NO POLE
x[1] = 0.47
y2[1] (analytic) = 1.1084317118046710635459807234666
y2[1] (numeric) = 1.1083434414056672785962585720452
absolute error = 8.82703990037849497221514214e-05
relative error = 0.0079635396627248469637294046261494 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1084317118046710635459807234666
y1[1] (numeric) = 1.1084317118046710807098016157637
absolute error = 1.71638208922971e-17
relative error = 1.5484779720306058470106409659644e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.471
y2[1] (analytic) = 1.1088850437986760370345899490213
y2[1] (numeric) = 1.1087965505327698401911471510311
absolute error = 8.84932659061968434427979902e-05
relative error = 0.0079803823129445386743811640115853 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1088850437986760370345899490213
y1[1] (numeric) = 1.1088850437986760542417466518433
absolute error = 1.72071567028220e-17
relative error = 1.5517529791795127316297368468225e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=968.9MB, alloc=4.6MB, time=127.74
NO POLE
NO POLE
x[1] = 0.472
y2[1] (analytic) = 1.109339266907562952269954015601
y2[1] (numeric) = 1.1092505508881368562927979708375
absolute error = 8.87160194260959771560447635e-05
relative error = 0.0079971945528804893284243168300492 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.109339266907562952269954015601
y1[1] (numeric) = 1.1093392669075629695204244834878
absolute error = 1.72504704678868e-17
relative error = 1.5550220732720368489474215413633e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=972.7MB, alloc=4.6MB, time=128.24
NO POLE
NO POLE
x[1] = 0.473
y2[1] (analytic) = 1.1097943806771087382170821666872
y2[1] (numeric) = 1.1097054420177680093675566159528
absolute error = 8.89386593407288495255507344e-05
relative error = 0.0080139763625821852959694463224752 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1097943806771087382170821666872
y1[1] (numeric) = 1.1097943806771087555108443108647
absolute error = 1.72937621441775e-17
relative error = 1.5582852504286617853479839400650e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.474
y2[1] (analytic) = 1.1102503846521996632563346530956
y2[1] (numeric) = 1.1101612234667722076918628839614
absolute error = 8.91611854274555644717691342e-05
relative error = 0.0080307277223224257231825609359042 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1102503846521996632563346530956
y1[1] (numeric) = 1.1102503846521996805933663414982
absolute error = 1.73370316884026e-17
relative error = 1.5615425068133302288467331564196e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=976.5MB, alloc=4.6MB, time=128.74
NO POLE
NO POLE
x[1] = 0.475
y2[1] (analytic) = 1.1107072783768317902971164264731
y2[1] (numeric) = 1.110617894779368040243304601514
absolute error = 8.93835974637500538118249591e-05
relative error = 0.0080474486125969824726164523090886 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1107072783768317902971164264731
y1[1] (numeric) = 1.1107072783768318076773954837657
absolute error = 1.73802790572926e-17
relative error = 1.5647938386333288583546182355579e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=980.3MB, alloc=4.6MB, time=129.25
NO POLE
NO POLE
x[1] = 0.476
y2[1] (analytic) = 1.1111650613941114327817762295659
y2[1] (numeric) = 1.1110754554988842324819906649568
absolute error = 8.96058952272002997855646091e-05
relative error = 0.0080641390141242576358765921582828 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1111650613941114327817762295659
y1[1] (numeric) = 1.111165061394111450205280437166
absolute error = 1.74235042076001e-17
relative error = 1.5680392421392268809129328302913e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=984.2MB, alloc=4.6MB, time=129.75
x[1] = 0.477
y2[1] (analytic) = 1.1116237332462556115792550793985
y2[1] (numeric) = 1.1115339051677601030217875242844
absolute error = 8.98280784955085574675551141e-05
relative error = 0.0080807989078449386341548894768169 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1116237332462556115792550793985
y1[1] (numeric) = 1.1116237332462556290459621754983
absolute error = 1.74667070960998e-17
relative error = 1.5712787136248050934828848431311e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.478
y2[1] (analytic) = 1.1120832934745925127680272497516
y2[1] (numeric) = 1.111993243327546021190962439218
absolute error = 9.00501470464915770648105336e-05
relative error = 0.008097428274921650922173430113395 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1120832934745925127680272497516
y1[1] (numeric) = 1.1120832934745925302779149293406
absolute error = 1.75098876795890e-17
relative error = 1.5745122494270294510758262236463e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=988.0MB, alloc=4.6MB, time=130.26
NO POLE
NO POLE
x[1] = 0.479
y2[1] (analytic) = 1.1125437416195619463078759700387
y2[1] (numeric) = 1.1124534695189038654817759468031
absolute error = 9.02721006580808261000232356e-05
relative error = 0.0081140270967386083110885140273523 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1125437416195619463078759700387
y1[1] (numeric) = 1.1125437416195619638609218849258
absolute error = 1.75530459148871e-17
relative error = 1.5777398459259341878681602840129e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=991.8MB, alloc=4.6MB, time=130.77
NO POLE
NO POLE
x[1] = 0.48
y2[1] (analytic) = 1.1130050772207158056000451688413
y2[1] (numeric) = 1.1129145832816074828885650909739
absolute error = 9.04939391083227114800778674e-05
relative error = 0.0081305953549012609259128921086764 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1130050772207158056000451688413
y1[1] (numeric) = 1.1130050772207158231962269276771
absolute error = 1.75961817588358e-17
relative error = 1.5809614995445674943721441283030e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.481
y2[1] (analytic) = 1.1134672998167185279353077019906
y2[1] (numeric) = 1.1133765841545431491338580760378
absolute error = 9.07156621753788014496259528e-05
relative error = 0.0081471330312359408130210893930108 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1134672998167185279353077019906
y1[1] (numeric) = 1.11346729981671854557460287029
absolute error = 1.76392951682994e-17
relative error = 1.5841772067489456856652001937331e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=995.6MB, alloc=4.6MB, time=131.28
NO POLE
NO POLE
x[1] = 0.482
y2[1] (analytic) = 1.1139304089453475558294896171662
y2[1] (numeric) = 1.113839471675710029782060118005
absolute error = 9.09372696375260474294991612e-05
relative error = 0.0081636401077895052133090851078064 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1139304089453475558294896171662
y1[1] (numeric) = 1.1139304089453475735118757173304
absolute error = 1.76823861001642e-17
relative error = 1.5873869640479260652176210152646e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=999.4MB, alloc=4.6MB, time=131.79
NO POLE
NO POLE
x[1] = 0.483
y2[1] (analytic) = 1.1143944041434937992459891195241
y2[1] (numeric) = 1.1143032453822206422402493801148
absolute error = 9.11587612731570057397394093e-05
relative error = 0.0081801165668289775165854062301813 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1143944041434937992459891195241
y1[1] (numeric) = 1.1143944041434938169714436308636
absolute error = 1.77254545113395e-17
relative error = 1.5905907679932230597014526953486e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.484
y2[1] (analytic) = 1.1148592849471620987048280158762
y2[1] (numeric) = 1.114767904810301318645620991802
absolute error = 9.13801368607800592070240742e-05
relative error = 0.008196562390841185912775882645926 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1148592849471620987048280158762
y1[1] (numeric) = 1.1148592849471621164733283746331
absolute error = 1.77685003587569e-17
relative error = 1.5937886151792712077867398100789e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1003.2MB, alloc=4.6MB, time=132.31
NO POLE
NO POLE
x[1] = 0.485
y2[1] (analytic) = 1.1153250508914716892777725284065
y2[1] (numeric) = 1.1152334494952926696391162636975
absolute error = 9.16013961790196386562647090e-05
relative error = 0.0082129775625323997555289104547817 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1153250508914716892777725284065
y1[1] (numeric) = 1.1153250508914717070892961277769
absolute error = 1.78115235993704e-17
relative error = 1.5969805022431596008012416739436e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1007.0MB, alloc=4.6MB, time=132.81
NO POLE
NO POLE
x[1] = 0.486
y2[1] (analytic) = 1.115791701510656665469059482842
y2[1] (numeric) = 1.1156998789716500490247733250722
absolute error = 9.18225390066164442861577698e-05
relative error = 0.0082293620648279636538120791665176 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.115791701510656665469059482842
y1[1] (numeric) = 1.1157917015106566833235836729989
absolute error = 1.78545241901569e-17
relative error = 1.6001664258646017199337813572501e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.487
y2[1] (analytic) = 1.1162592363380664469812629903921
y2[1] (numeric) = 1.1161671927729440193143345244133
absolute error = 9.20435651224276669284659788e-05
relative error = 0.0082457158808719293070944405021696 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1162592363380664469812629903921
y1[1] (numeric) = 1.1162592363380664648787650785079
absolute error = 1.78975020881158e-17
relative error = 1.6033463827658241074549977811287e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1010.9MB, alloc=4.6MB, time=133.32
NO POLE
NO POLE
x[1] = 0.488
y2[1] (analytic) = 1.1167276549061662453658358576272
y2[1] (numeric) = 1.1166353904318608181566450485633
absolute error = 9.22644743054272091908090639e-05
relative error = 0.008262038994026685099711534144804 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1167276549061662453658358576272
y1[1] (numeric) = 1.1167276549061662633062931078964
absolute error = 1.79404572502692e-17
relative error = 1.6065203697115084323637497324035e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1014.7MB, alloc=4.6MB, time=133.81
NO POLE
NO POLE
x[1] = 0.489
y2[1] (analytic) = 1.117196956746537531557859073795
y2[1] (numeric) = 1.1171044714802028256513763310625
absolute error = 9.24852663347059064827427325e-05
relative error = 0.0082783313878725834700125419631906 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.117196956746537531557859073795
y1[1] (numeric) = 1.1171969567465375495412487074569
absolute error = 1.79833896336619e-17
relative error = 1.6096883835087151880836698017132e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.49
y2[1] (analytic) = 1.1176671413898785042945318408633
y2[1] (numeric) = 1.1175744354488890325466069360107
absolute error = 9.27059409894717479249048526e-05
relative error = 0.0082945930462075660698906194005022 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1176671413898785042945318408633
y1[1] (numeric) = 1.1176671413898785223208310362248
absolute error = 1.80262991953615e-17
relative error = 1.6128504210068159194518689281073e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1018.5MB, alloc=4.6MB, time=134.31
NO POLE
NO POLE
x[1] = 0.491
y2[1] (analytic) = 1.1181382083660045594169337278386
y2[1] (numeric) = 1.1180452818679555093197927199057
absolute error = 9.29264980490500971410079329e-05
relative error = 0.0083108239530467867302985541070571 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1181382083660045594169337278386
y1[1] (numeric) = 1.1181382083660045774861196202971
absolute error = 1.80691858924585e-17
relative error = 1.6160064790974250122423476247198e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1022.3MB, alloc=4.6MB, time=134.81
NO POLE
NO POLE
x[1] = 0.492
y2[1] (analytic) = 1.1186101572038487600545896476376
y2[1] (numeric) = 1.1185170102665558761416571905281
absolute error = 9.31469372928839129324571095e-05
relative error = 0.0083270240926222322483524297613322 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1186101572038487600545896476376
y1[1] (numeric) = 1.1186101572038487781666393297038
absolute error = 1.81120496820662e-17
relative error = 1.6191565547143131688792862628015e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.493
y2[1] (analytic) = 1.1190829874314623076923674719854
y2[1] (numeric) = 1.1189896201729617737225320990207
absolute error = 9.33672585005339698353729647e-05
relative error = 0.0083431934493823410116259305935004 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1190829874314623076923674719854
y1[1] (numeric) = 1.1190829874314623258472579933062
absolute error = 1.81548905213208e-17
relative error = 1.6223006448333383697570160631970e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1026.1MB, alloc=4.6MB, time=135.31
NO POLE
NO POLE
x[1] = 0.494
y2[1] (analytic) = 1.1195566985760150141192372174827
y2[1] (numeric) = 1.1194631111145633350406774188615
absolute error = 9.35874614516790785597986212e-05
relative error = 0.008359332007991619475237312034233 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1195566985760150141192372174827
y1[1] (numeric) = 1.1195566985760150323169455848641
absolute error = 1.81977083673814e-17
relative error = 1.6254387464723674740595978333368e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1029.9MB, alloc=4.6MB, time=135.81
NO POLE
NO POLE
x[1] = 0.495
y2[1] (analytic) = 1.1200312901637957742584198541208
y2[1] (numeric) = 1.1199374826178696579521089834493
absolute error = 9.38075459261163063108706715e-05
relative error = 0.0083754397533302565073298878895698 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1200312901637957742584198541208
y1[1] (numeric) = 1.1200312901637957924989230315511
absolute error = 1.82405031774303e-17
relative error = 1.6285708566912242028466569085545e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.496
y2[1] (analytic) = 1.1205067617202130398784529061372
y2[1] (numeric) = 1.1204127342085092786814611725142
absolute error = 9.40275117037611969917336230e-05
relative error = 0.0083915166704937356185451478356685 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1205067617202130398784529061372
y1[1] (numeric) = 1.1205067617202130581617278148099
absolute error = 1.82832749086727e-17
relative error = 1.6316969725915831071092905945432e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1033.7MB, alloc=4.6MB, time=136.29
NO POLE
NO POLE
x[1] = 0.497
y2[1] (analytic) = 1.1209831127697952941846991341835
y2[1] (numeric) = 1.1208888654112306461934111565292
absolute error = 9.42473585646479912879776543e-05
relative error = 0.0084075627447924450910853228202536 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1209831127697952941846991341835
y1[1] (numeric) = 1.1209831127697953125107226525202
absolute error = 1.83260235183367e-17
relative error = 1.6348170913168899695712280609216e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1037.6MB, alloc=4.6MB, time=136.78
NO POLE
NO POLE
x[1] = 0.498
y2[1] (analytic) = 1.1214603428361915272908237073372
y2[1] (numeric) = 1.1213658757499025974441903277382
absolute error = 9.44670862889298466333795990e-05
relative error = 0.0084235779617512860229593640631542 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1214603428361915272908237073372
y1[1] (numeric) = 1.121460342836191545659572671011
absolute error = 1.83687489636738e-17
relative error = 1.6379312100523263977078185549673e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1041.4MB, alloc=4.6MB, time=137.27
x[1] = 0.499
y2[1] (analytic) = 1.1219384514421717125697643935207
y2[1] (numeric) = 1.1218437647475148335127076663293
absolute error = 9.46866946568790570567271914e-05
relative error = 0.0084395623071092783030028959067974 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1219384514421717125697643935207
y1[1] (numeric) = 1.1219384514421717309812155954793
absolute error = 1.84114512019586e-17
relative error = 1.6410393260247026071640763451856e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.5
y2[1] (analytic) = 1.1224174381096272838837184173962
y2[1] (numeric) = 1.1223225319261783966108089106687
absolute error = 9.49061834488872729095067275e-05
relative error = 0.0084555157668191645322587470155435 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1224174381096272838837184173962
y1[1] (numeric) = 1.1224174381096273023378486078849
absolute error = 1.84541301904887e-17
relative error = 1.6441414365023677046574630438253e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1045.2MB, alloc=4.6MB, time=137.77
NO POLE
NO POLE
x[1] = 0.501
y2[1] (analytic) = 1.1228973023595716136926687557886
y2[1] (numeric) = 1.1228021768071261479721945213767
absolute error = 9.51255524454657204742344119e-05
relative error = 0.0084714383270470119073001610488564 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1228973023595716136926687557886
y1[1] (numeric) = 1.1228973023595716321894546423739
absolute error = 1.84967858865853e-17
relative error = 1.6472375387951819480284728423307e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1049.0MB, alloc=4.6MB, time=138.27
NO POLE
NO POLE
x[1] = 0.502
y2[1] (analytic) = 1.1233780437121404920409717621522
y2[1] (numeric) = 1.1232826989107132466195185503667
absolute error = 9.53448014272454214532117855e-05
relative error = 0.0084873299741718120810737406739964 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1233780437121404920409717621522
y1[1] (numeric) = 1.1233780437121405105803900097448
absolute error = 1.85394182475926e-17
relative error = 1.6503276302543816670999628246212e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.503
y2[1] (analytic) = 1.1238596616865926064215271335312
y2[1] (numeric) = 1.1237640977564176290091896477893
absolute error = 9.55639301749774123374857419e-05
relative error = 0.0085031906947850790168335889568639 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1238596616865926064215271335312
y1[1] (numeric) = 1.1238596616865926250035543644096
absolute error = 1.85820272308784e-17
relative error = 1.6534117082725507181712786345915e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1052.8MB, alloc=4.6MB, time=138.78
NO POLE
NO POLE
x[1] = 0.504
y2[1] (analytic) = 1.1243421558013100225170503558855
y2[1] (numeric) = 1.1242463728628404895533945621197
absolute error = 9.57829384695329636557937658e-05
relative error = 0.0085190204756904448507319848580422 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1243421558013100225170503558855
y1[1] (numeric) = 1.124342155801310041141663149719
absolute error = 1.86246127938335e-17
relative error = 1.6564897702834846967690874368662e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1056.6MB, alloc=4.6MB, time=139.29
NO POLE
NO POLE
x[1] = 0.505
y2[1] (analytic) = 1.1248255255737986658179668865485
y2[1] (numeric) = 1.1247295237477067620188636114049
absolute error = 9.60018260919037991032751436e-05
relative error = 0.0085348193039032537786252658868146 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1248255255737986658179668865485
y1[1] (numeric) = 1.1248255255737986844851417804209
absolute error = 1.86671748938724e-17
relative error = 1.6595618137621704889927896471550e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.506
y2[1] (analytic) = 1.1253097705206888041164464559634
y2[1] (numeric) = 1.1252135499278656018018967269461
absolute error = 9.62205928232023145497290173e-05
relative error = 0.0085505871666501539826463950405385 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1253097705206888041164464559634
y1[1] (numeric) = 1.1253097705206888228261599443965
absolute error = 1.87097134884331e-17
relative error = 1.6626278362246853151070159187244e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1060.5MB, alloc=4.6MB, time=139.79
NO POLE
NO POLE
x[1] = 0.507
y2[1] (analytic) = 1.1257948901577355308760949947039
y2[1] (numeric) = 1.1256984509192908690791677944297
absolute error = 9.64392384446617969272002742e-05
relative error = 0.0085663240513686876130879636782944 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1257948901577355308760949947039
y1[1] (numeric) = 1.1257948901577355496283235296809
absolute error = 1.87522285349770e-17
relative error = 1.6656878352281043352723350135281e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1064.3MB, alloc=4.6MB, time=140.30
NO POLE
NO POLE
x[1] = 0.508
y2[1] (analytic) = 1.1262808839998192494768208161278
y2[1] (numeric) = 1.1261842262370816128338241417431
absolute error = 9.66577627376366429966743847e-05
relative error = 0.008582029945706878841131129782464 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1262808839998192494768208161278
y1[1] (numeric) = 1.1262808839998192682715408071166
absolute error = 1.87947199909888e-17
relative error = 1.6687418083704079150072069665237e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.509
y2[1] (analytic) = 1.126767751560946158334390809836
y2[1] (numeric) = 1.1266708753954625557563971474161
absolute error = 9.68761654836025779936624199e-05
relative error = 0.0085977048375228199979472152921741 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.126767751560946158334390809836
y1[1] (numeric) = 1.1267677515609461771715786238134
absolute error = 1.88371878139774e-17
relative error = 1.6717897532904773029388092324378e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1068.1MB, alloc=4.6MB, time=140.80
NO POLE
NO POLE
x[1] = 0.51
y2[1] (analytic) = 1.1272554923542487368941915264245
y2[1] (numeric) = 1.1271583979077845800200390688177
absolute error = 9.70944464641568741524576068e-05
relative error = 0.0086133487148842558156893905254999 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1272554923542487368941915264245
y1[1] (numeric) = 1.1272554923542487557738234878993
absolute error = 1.88796319614748e-17
relative error = 1.6748316676679123220614565936706e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1071.9MB, alloc=4.6MB, time=141.30
NO POLE
NO POLE
x[1] = 0.511
y2[1] (analytic) = 1.1277441058919862324987091598053
y2[1] (numeric) = 1.1276467932865252139296003149122
absolute error = 9.73126054610185691088448931e-05
relative error = 0.0086289615660681657858820595501084 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1277441058919862324987091598053
y1[1] (numeric) = 1.1277441058919862514207615508422
absolute error = 1.89220523910369e-17
relative error = 1.6778675492230174381064206334074e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.512
y2[1] (analytic) = 1.1282335916855451481282415596589
y2[1] (numeric) = 1.1281360610432891194440605145373
absolute error = 9.75306422560286841810451216e-05
relative error = 0.0086445433795603446507052330672607 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1282335916855451481282415596589
y1[1] (numeric) = 1.1282335916855451670926906199022
absolute error = 1.89644490602433e-17
relative error = 1.6808973957166986582524295260091e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1075.7MB, alloc=4.6MB, time=141.79
NO POLE
NO POLE
x[1] = 0.513
y2[1] (analytic) = 1.1287239492454397310143545333464
y2[1] (numeric) = 1.1286262006888085805718258578145
absolute error = 9.77485566311504425286755319e-05
relative error = 0.0086600941440549810426603358829817 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1287239492454397310143545333464
y1[1] (numeric) = 1.1287239492454397500211764600437
absolute error = 1.90068219266973e-17
relative error = 1.6839212049503778469110975599727e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1079.5MB, alloc=4.6MB, time=142.29
NO POLE
NO POLE
x[1] = 0.514
y2[1] (analytic) = 1.1292151780813124621255938238659
y2[1] (numeric) = 1.1291172117329439926384043154347
absolute error = 9.79663483684694871895084312e-05
relative error = 0.008675613848454234288092548927906 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1292151780813124621255938238659
y1[1] (numeric) = 1.1292151780813124811747647718919
absolute error = 1.90491709480260e-17
relative error = 1.6869389747659155521076058511009e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.515
y2[1] (analytic) = 1.1297072777019345465249632781811
y2[1] (numeric) = 1.1296090936846843524259694681841
absolute error = 9.81840172501940989938099970e-05
relative error = 0.0086911024818678093900329333134883 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1297072777019345465249632781811
y1[1] (numeric) = 1.1297072777019345656164593600615
absolute error = 1.90914960818804e-17
relative error = 1.6899507030455334666381816957458e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1083.3MB, alloc=4.6MB, time=142.78
NO POLE
NO POLE
x[1] = 0.516
y2[1] (analytic) = 1.1302002476152064045986788484863
y2[1] (numeric) = 1.1301018460521477491843228071889
absolute error = 9.84015630586554143560412974e-05
relative error = 0.0087065600336125302058112296338416 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1302002476152064045986788484863
y1[1] (numeric) = 1.1302002476152064237324761344216
absolute error = 1.91337972859353e-17
relative error = 1.6929563877117188309847418469004e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1087.2MB, alloc=4.6MB, time=143.28
NO POLE
NO POLE
x[1] = 0.517
y2[1] (analytic) = 1.1306940873281581641557071976931
y2[1] (numeric) = 1.1305954683425818565127634939555
absolute error = 9.86189855763076429437037376e-05
relative error = 0.0087219864932119108348773725941664 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1306940873281581641557071976931
y1[1] (numeric) = 1.1306940873281581833317817155828
absolute error = 1.91760745178897e-17
relative error = 1.6959560267271727439222059919654e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.518
y2[1] (analytic) = 1.1311887963469501533975968096429
y2[1] (numeric) = 1.1310899600623644251123736983792
absolute error = 9.88362845857282852231112637e-05
relative error = 0.0087373818503957252322564121663857 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1311887963469501533975968096429
y1[1] (numeric) = 1.1311887963469501726159245451092
absolute error = 1.92183277354663e-17
relative error = 1.6989496180946784849407779877494e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1091.0MB, alloc=4.6MB, time=143.77
NO POLE
NO POLE
x[1] = 0.519
y2[1] (analytic) = 1.1316843741768733947581086342535
y2[1] (numeric) = 1.1315853207170037764082267624758
absolute error = 9.90534598696183498818717777e-05
relative error = 0.0087527460950995750630476910450982 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1316843741768733947581086342535
y1[1] (numeric) = 1.1316843741768734140186655306653
absolute error = 1.92605568964118e-17
relative error = 1.7019371598570403136723980860422e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1094.8MB, alloc=4.6MB, time=144.27
NO POLE
NO POLE
x[1] = 0.52
y2[1] (analytic) = 1.1321808203223500996121524280115
y2[1] (numeric) = 1.1320815498111392970410245676697
absolute error = 9.92705112108025711278603418e-05
relative error = 0.0087680792174644558133647974513582 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1321808203223500996121524280115
y1[1] (numeric) = 1.1321808203223501189149143865086
absolute error = 1.93027619584971e-17
relative error = 1.7049186500970130401172238509525e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.521
memory used=1098.6MB, alloc=4.6MB, time=144.76
y2[1] (analytic) = 1.1326781342869341638535340809147
y2[1] (numeric) = 1.1325786468485419342276696140423
absolute error = 9.94874383922296258644668724e-05
relative error = 0.0087833812078363211730979951773695 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1326781342869341638535340809147
y1[1] (numeric) = 1.1326781342869341831984769604319
absolute error = 1.93449428795172e-17
relative error = 1.7078940869372047383535684242734e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.522
y2[1] (analytic) = 1.1331763155733116643410183521593
y2[1] (numeric) = 1.13307661133211469199027645101
absolute error = 9.97042411969723507419011493e-05
relative error = 0.0087986520567656457058655327672592 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1331763155733116643410183521593
y1[1] (numeric) = 1.1331763155733116837281179694503
absolute error = 1.93870996172910e-17
relative error = 1.7108634685399703376178508588212e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1102.4MB, alloc=4.6MB, time=145.25
NO POLE
NO POLE
x[1] = 0.523
y2[1] (analytic) = 1.133675363683301356212210568549
y2[1] (numeric) = 1.133575442763893128253126230461
absolute error = 9.99209194082279590843380880e-05
relative error = 0.008813891755006985821504453579833 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.133675363683301356212210568549
y1[1] (numeric) = 1.133675363683301375641442698211
absolute error = 1.94292321296620e-17
relative error = 1.7138267931073843297033003227933e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1106.2MB, alloc=4.6MB, time=145.76
NO POLE
NO POLE
x[1] = 0.524
y2[1] (analytic) = 1.134175278117855171064759971788
y2[1] (numeric) = 1.1340751406450458528070672854391
absolute error = 0.0001001374728093182576926863489
relative error = 0.0088291002935185390664352719128246 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.134175278117855171064759971788
y1[1] (numeric) = 1.1341752781178551905361003462855
absolute error = 1.94713403744975e-17
relative error = 1.7167840588810807433763489888953e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.525
y2[1] (analytic) = 1.1346760583770587160043865334936
y2[1] (numeric) = 1.134575704475875026140863770014
absolute error = 0.0001003539011836898635227634796
relative error = 0.0088442776634617017472181499610186 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1346760583770587160043865334936
y1[1] (numeric) = 1.1346760583770587355178108431829
absolute error = 1.95134243096893e-17
relative error = 1.7197352641422251895572014019762e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1110.0MB, alloc=4.6MB, time=146.26
NO POLE
NO POLE
x[1] = 0.526
y2[1] (analytic) = 1.135177703960131773559232189945
y2[1] (numeric) = 1.1350771337558168591389935290319
absolute error = 0.0001005702043149144202386609131
relative error = 0.008859423856200624902601010014556 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.135177703960131773559232189945
y1[1] (numeric) = 1.1351777039601317931147160830985
absolute error = 1.95554838931535e-17
relative error = 1.7226804072114071512452630769738e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1113.9MB, alloc=4.6MB, time=146.75
NO POLE
NO POLE
x[1] = 0.527
y2[1] (analytic) = 1.1356802143654288024600365822581
y2[1] (numeric) = 1.1355794279834421136453954999901
absolute error = 0.000100786381986688814641082268
relative error = 0.0088745388633017686393423485265139 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1356802143654288024600365822581
y1[1] (numeric) = 1.1356802143654288220575556650886
absolute error = 1.95975190828305e-17
relative error = 1.7256194864485496245208012272811e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.528
y2[1] (analytic) = 1.1361835890904394392856365218521
y2[1] (numeric) = 1.1360825866564566038926660833294
absolute error = 0.0001010024339828353929704385227
relative error = 0.0088896226765334548470733872279124 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1361835890904394392856365218521
y1[1] (numeric) = 1.1361835890904394589251663585372
absolute error = 1.96395298366851e-17
relative error = 1.7285525002528272577446541701763e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1117.7MB, alloc=4.6MB, time=147.23
NO POLE
NO POLE
x[1] = 0.529
y2[1] (analytic) = 1.1366878276317890009732875357502
y2[1] (numeric) = 1.1365866092717016987962030519904
absolute error = 0.0001012183600873021770844837598
relative error = 0.0089046752878654183074456041881893 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1366878276317890009732875357502
y1[1] (numeric) = 1.1366878276317890206548036484569
absolute error = 1.96815161127067e-17
relative error = 1.7314794470625929646157318171445e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1121.5MB, alloc=4.6MB, time=147.71
NO POLE
NO POLE
x[1] = 0.53
y2[1] (analytic) = 1.1371929294852389881933049814358
y2[1] (numeric) = 1.1370914953251548251127947061314
absolute error = 0.0001014341600841630805102753044
relative error = 0.0089196966894683562127906382807902 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1371929294852389881933049814358
y1[1] (numeric) = 1.1371929294852390079167828503446
absolute error = 1.97234778689088e-17
relative error = 1.7344003253552426379908339186937e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.531
y2[1] (analytic) = 1.1376988941456875895875213566629
y2[1] (numeric) = 1.1375972443119299714631511144599
absolute error = 0.000101649833757618124370242203
relative error = 0.0089346868737134761095000564669578 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1376988941456875895875213566629
y1[1] (numeric) = 1.1376988941456876093529364199927
absolute error = 1.97654150633298e-17
relative error = 1.7373151336471939523789479856795e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1125.3MB, alloc=4.6MB, time=148.21
NO POLE
NO POLE
x[1] = 0.532
y2[1] (analytic) = 1.138205721107170186871055565808
y2[1] (numeric) = 1.1381038557262781932178734196901
absolute error = 0.0001018653808919936531821461179
relative error = 0.0089496458331720422813125187531165 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.138205721107170186871055565808
y1[1] (numeric) = 1.1382057211071702066783832198404
absolute error = 1.98073276540324e-17
relative error = 1.7402238704937416867910068284090e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1129.1MB, alloc=4.6MB, time=148.71
NO POLE
NO POLE
x[1] = 0.533
y2[1] (analytic) = 1.1387134098628598607968890410339
y2[1] (numeric) = 1.1386113290615881182463563221976
absolute error = 0.0001020808012717425505327188363
relative error = 0.0089645735606149205876754730564615 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1387134098628598607968890410339
y1[1] (numeric) = 1.138713409862859880646104640138
absolute error = 1.98492155991041e-17
relative error = 1.7431265344890095002819534362560e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.534
y2[1] (analytic) = 1.1392219599050678979827427537335
y2[1] (numeric) = 1.1391196638103864535281179930118
absolute error = 0.0001022960946814444546247607217
relative error = 0.0089794700490121217723276654878611 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1392219599050678979827427537335
y1[1] (numeric) = 1.1392219599050679178738216103904
absolute error = 1.98910788566569e-17
relative error = 1.7460231242658310812032574427884e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1132.9MB, alloc=4.6MB, time=149.21
NO POLE
NO POLE
x[1] = 0.535
y2[1] (analytic) = 1.1397313707252442985997482894172
y2[1] (numeric) = 1.1396288594643384926260508048581
absolute error = 0.0001025112609058059736974845591
relative error = 0.0089943352915323432572274632351093 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1397313707252442985997482894172
y1[1] (numeric) = 1.1397313707252443185326656742448
absolute error = 1.99329173848276e-17
relative error = 1.7489136384956837284716170577005e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1136.7MB, alloc=4.6MB, time=149.70
NO POLE
NO POLE
x[1] = 0.536
y2[1] (analytic) = 1.1402416418139782849224052974161
y2[1] (numeric) = 1.1401389155142486240210854080412
absolute error = 0.0001027262997296609013198893749
relative error = 0.0090091692815425094369302614469774 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1402416418139782849224052974161
y1[1] (numeric) = 1.1402416418139783048971364391938
absolute error = 1.99747311417777e-17
relative error = 1.7517980758885865023919423395225e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.537
y2[1] (analytic) = 1.1407527726609988107393167654858
y2[1] (numeric) = 1.1406498314500608403077598165484
absolute error = 0.0001029412109379704315569489374
relative error = 0.0090239720126073104884960846797823 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1407527726609988107393167654858
y1[1] (numeric) = 1.1407527726609988307558368511792
absolute error = 2.00165200856934e-17
relative error = 1.7546764351930068885294969240006e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1140.6MB, alloc=4.6MB, time=150.19
NO POLE
NO POLE
x[1] = 0.538
y2[1] (analytic) = 1.1412647627551750716241927086173
y2[1] (numeric) = 1.1411616067608592482501843088458
absolute error = 0.0001031559943158233740083997715
relative error = 0.0090387434784887397119859014721473 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1412647627551750716241927086173
y1[1] (numeric) = 1.1412647627551750916824768834031
absolute error = 2.00582841747858e-17
relative error = 1.7575487151957847123286676995479e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1144.4MB, alloc=4.6MB, time=150.68
NO POLE
NO POLE
x[1] = 0.539
y2[1] (analytic) = 1.1417776115845170160666120010952
y2[1] (numeric) = 1.1416742409348685796978920874449
absolute error = 0.0001033706496484363687199136503
relative error = 0.0090534836731456294165821506248003 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1417776115845170160666120010952
y1[1] (numeric) = 1.1417776115845170361666353683859
absolute error = 2.01000233672907e-17
relative error = 1.7604149147220207026878942970858e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.54
y2[1] (analytic) = 1.1422913186361758574620312210822
y2[1] (numeric) = 1.1421877334594547033610647814317
absolute error = 0.0001035851767211541009664396505
relative error = 0.0090681925907331853673455325122974 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1422913186361758574620312210822
y1[1] (numeric) = 1.1422913186361758776037688425511
absolute error = 2.01417376214689e-17
relative error = 1.7632750326350086065978769130968e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1148.2MB, alloc=4.6MB, time=151.18
NO POLE
NO POLE
x[1] = 0.541
y2[1] (analytic) = 1.1428058833964445869605285177651
y2[1] (numeric) = 1.1427020838211251374446210167756
absolute error = 0.0001037995753194495159075009895
relative error = 0.0090828702256025198075962525557544 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1428058833964445869605285177651
y1[1] (numeric) = 1.1428058833964446071439554133714
absolute error = 2.01834268956063e-17
relative error = 1.7661290678361494671993340385451e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1152.0MB, alloc=4.6MB, time=151.68
NO POLE
NO POLE
x[1] = 0.542
y2[1] (analytic) = 1.1433213053507584871737696523608
y2[1] (numeric) = 1.1432172915055295631406554203724
absolute error = 0.0001040138452289240331142319884
relative error = 0.0090975165723001830718836191229445 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1433213053507584871737696523608
y1[1] (numeric) = 1.1433213053507585073988608003745
absolute error = 2.02250911480137e-17
relative error = 1.7689770192648393767817530228129e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.543
y2[1] (analytic) = 1.1438375839836956467396825060591
y2[1] (numeric) = 1.143733355997460338978714565424
absolute error = 0.0001042279862353077609679406351
relative error = 0.0091121316255676938044831986255241 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1438375839836956467396825060591
y1[1] (numeric) = 1.1438375839836956670064128430856
absolute error = 2.02667303370265e-17
relative error = 1.7718188858983482754916967691584e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1155.8MB, alloc=4.6MB, time=152.17
NO POLE
NO POLE
x[1] = 0.544
y2[1] (analytic) = 1.1443547187789774757443254902696
y2[1] (numeric) = 1.1442502767808530160333955079234
absolute error = 0.0001044419981244597109299823462
relative error = 0.0091267153803410677983356189454057 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1443547187789774757443254902696
y1[1] (numeric) = 1.1443547187789774960526699112755
absolute error = 2.03083444210059e-17
relative error = 1.7746546667518296432415919728731e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1159.6MB, alloc=4.6MB, time=152.67
NO POLE
NO POLE
x[1] = 0.545
y2[1] (analytic) = 1.1448727092194692220004344373497
y2[1] (numeric) = 1.1447680533387868539887517066884
absolute error = 0.0001046558806823680116827306613
relative error = 0.009141267831750345469315593235482 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1448727092194692220004344373497
y1[1] (numeric) = 1.1448727092194692423503677956873
absolute error = 2.03499333583376e-17
relative error = 1.7774843608781112889643886803373e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1163.5MB, alloc=4.6MB, time=153.16
NO POLE
NO POLE
x[1] = 0.546
y2[1] (analytic) = 1.1453915547871804881821316933069
y2[1] (numeric) = 1.1452866851534853380589902625812
absolute error = 0.0001048696336951501231414307257
relative error = 0.0091557889751191179806938109046234 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1453915547871804881821316933069
y1[1] (numeric) = 1.1453915547871805085736288007396
absolute error = 2.03914971074327e-17
relative error = 1.7803079673676782718208977101088e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.547
y2[1] (analytic) = 1.1459112549632657498152802778119
y2[1] (numeric) = 1.1458061717063166967649435562596
absolute error = 0.0001050832569490530503367215523
relative error = 0.0091702788059640520326280166973355 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1459112549632657498152802778119
y1[1] (numeric) = 1.1459112549632657702483159045394
absolute error = 2.04330356267275e-17
relative error = 1.7831254853485593678801451001017e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1167.3MB, alloc=4.6MB, time=153.65
NO POLE
NO POLE
x[1] = 0.548
y2[1] (analytic) = 1.1464318092280248741229651212096
y2[1] (numeric) = 1.146326512477794420565797508032
absolute error = 0.0001052967502304535571676131776
relative error = 0.0091847373199944133314928735037837 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1464318092280248741229651212096
y1[1] (numeric) = 1.146431809228024894597513995893
absolute error = 2.04745488746834e-17
relative error = 1.7859369139862220623335259597628e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1171.1MB, alloc=4.6MB, time=154.15
NO POLE
NO POLE
x[1] = 0.549
y2[1] (analytic) = 1.1469532170609036397255825330915
y2[1] (numeric) = 1.1468477069475777813455578281305
absolute error = 0.000105510113325858380024704961
relative error = 0.0091991645131115887538310850232972 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1469532170609036397255825330915
y1[1] (numeric) = 1.1469532170609036602416193428787
absolute error = 2.05160368097872e-17
relative error = 1.7887422524835021987586593900511e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.55
y2[1] (analytic) = 1.1474754779404942571950182023822
y2[1] (numeric) = 1.1473697545944723527537347709791
absolute error = 0.0001057233460219044412834314031
relative error = 0.0092135603814086072196807423941134 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1474754779404942571950182023822
y1[1] (numeric) = 1.1474754779404942777525175929333
absolute error = 2.05574993905511e-17
relative error = 1.7915415000805071737909870491842e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1174.9MB, alloc=4.6MB, time=154.65
NO POLE
NO POLE
x[1] = 0.551
y2[1] (analytic) = 1.1479985913445358904623931748063
y2[1] (numeric) = 1.1478926548964305313997260528161
absolute error = 0.0001059364481053590626671219902
relative error = 0.0092279249211696592900059588264314 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1479985913445358904623931748063
y1[1] (numeric) = 1.1479985913445359110613297503186
absolute error = 2.05989365755123e-17
relative error = 1.7943346560544840524884723923908e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1178.7MB, alloc=4.6MB, time=155.15
NO POLE
NO POLE
x[1] = 0.552
y2[1] (analytic) = 1.1485225567499151790788564000321
y2[1] (numeric) = 1.148416407330552058900376738331
absolute error = 0.0001061494193631201784796617011
relative error = 0.0092422581288696155029295707869836 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1485225567499151790788564000321
y1[1] (numeric) = 1.1485225567499151997192047232658
absolute error = 2.06403483232337e-17
relative error = 1.7971217197197833211120986566592e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.553
y2[1] (analytic) = 1.1490473736326667613289015877443
y2[1] (numeric) = 1.1489410113730845447801940487992
absolute error = 0.0001063622595822165487075389451
relative error = 0.0092565600011735434634380172649832 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1490473736326667613289015877443
y1[1] (numeric) = 1.1490473736326667820106361800479
absolute error = 2.06817345923036e-17
relative error = 1.7999026904277352141336893381866e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1182.5MB, alloc=4.6MB, time=155.65
NO POLE
NO POLE
x[1] = 0.554
y2[1] (analytic) = 1.1495730414679737981956852593716
y2[1] (numeric) = 1.1494664664994239902236941915438
absolute error = 0.0001065749685498079719910678278
relative error = 0.009270830534936223701199462635061 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1495730414679737981956852593716
y1[1] (numeric) = 1.1495730414679738189187806007073
absolute error = 2.07230953413357e-17
relative error = 1.8026775675665519819577272288053e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1186.3MB, alloc=4.6MB, time=156.14
NO POLE
NO POLE
x[1] = 0.555
y2[1] (analytic) = 1.150099559730168498177822030195
y2[1] (numeric) = 1.1499927721841153126793574584209
absolute error = 0.0001067875460531854984645717741
relative error = 0.0092850697272016643111068078302479 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.150099559730168498177822030195
y1[1] (numeric) = 1.1500995597301685189422525591643
absolute error = 2.07644305289693e-17
relative error = 1.8054463505612473238676065339315e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.556
y2[1] (analytic) = 1.1506269278927326429571323050854
y2[1] (numeric) = 1.1505199279008528713146669894172
absolute error = 0.0001069999918797716424653156682
relative error = 0.0092992775752026143911274416126357 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1506269278927326429571323050854
y1[1] (numeric) = 1.1506269278927326637628724189545
absolute error = 2.08057401138691e-17
relative error = 1.8082090388735207877743902284280e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1190.2MB, alloc=4.6MB, time=156.64
NO POLE
NO POLE
x[1] = 0.557
y2[1] (analytic) = 1.1511551454282981139168167201663
y2[1] (numeric) = 1.151047933122480993321705746365
absolute error = 0.0001072123058171205951109738013
relative error = 0.0093134540763600762920114222535031 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1511551454282981139168167201663
y1[1] (numeric) = 1.151155145428298134763840774892
absolute error = 2.08470240547257e-17
relative error = 1.8109656320017028073531258931724e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1194.0MB, alloc=4.6MB, time=157.14
NO POLE
NO POLE
x[1] = 0.558
y2[1] (analytic) = 1.1516842118086474195095308122717
y2[1] (numeric) = 1.1515767873209945010727853912213
absolute error = 0.0001074244876529184367454210504
relative error = 0.0093275992282828166933792533407553 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1516842118086474195095308122717
y1[1] (numeric) = 1.1516842118086474403978131225267
absolute error = 2.08882823102550e-17
relative error = 1.8137161294806038911413847629649e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.559
y2[1] (analytic) = 1.1522141265047142234748325481675
y2[1] (numeric) = 1.1521064899675392401255799133259
absolute error = 0.0001076365371749833492526348416
relative error = 0.0093417130287668765206795286478109 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1522141265047142234748325481675
y1[1] (numeric) = 1.1522141265047142444043473873663
absolute error = 2.09295148391988e-17
relative error = 1.8164605308814678893144188432047e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1197.8MB, alloc=4.6MB, time=157.65
NO POLE
NO POLE
x[1] = 0.56
y2[1] (analytic) = 1.1527448889865838739054744961337
y2[1] (numeric) = 1.1526370405324126080772360005497
absolute error = 0.000107848454171265828238495584
relative error = 0.0093557954757950797174754738132604 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1527448889865838739054744961337
y1[1] (numeric) = 1.1527448889865838948761960964583
absolute error = 2.09707216003246e-17
relative error = 1.8191988358118555067150385364753e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1201.6MB, alloc=4.6MB, time=158.15
NO POLE
NO POLE
x[1] = 0.561
y2[1] (analytic) = 1.153276498723493933162011573659
y2[1] (numeric) = 1.1531684384850640842669313002658
absolute error = 0.0001080602384298488950802733932
relative error = 0.0093698465675365408874878100956031 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.153276498723493933162011573659
y1[1] (numeric) = 1.1532764987234939541739141260846
absolute error = 2.10119025524256e-17
relative error = 1.8219310439155449980283676204898e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.562
y2[1] (analytic) = 1.1538089551838347086351944566842
y2[1] (numeric) = 1.1537006832940957603263508676298
absolute error = 0.0001082718897389483088435890544
relative error = 0.0093838663023461718207894108179212 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1538089551838347086351944566842
y1[1] (numeric) = 1.1538089551838347296882521110052
absolute error = 2.10530576543210e-17
relative error = 1.8246571548724586589596183841925e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1205.4MB, alloc=4.6MB, time=158.64
NO POLE
NO POLE
x[1] = 0.563
y2[1] (analytic) = 1.1543422578351497843556178880455
y2[1] (numeric) = 1.1542337744272628715775512507373
absolute error = 0.0001084834078869127780666373082
relative error = 0.0093978546787641869185149179677358 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1543422578351497843556178880455
y1[1] (numeric) = 1.154342257835149805449804752901
absolute error = 2.10941868648555e-17
relative error = 1.8273771683985197397790459680931e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1209.2MB, alloc=4.6MB, time=159.14
NO POLE
NO POLE
x[1] = 0.564
y2[1] (analytic) = 1.1548764061441365534500922755128
y2[1] (numeric) = 1.1547677113514743292776808148386
absolute error = 0.0001086947926622241724114606742
relative error = 0.0094118116955156075304158378053594 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1548764061441365534500922755128
y1[1] (numeric) = 1.1548764061441365745853824184127
absolute error = 2.11352901428999e-17
relative error = 1.8300910842456045280200278829025e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.565
y2[1] (analytic) = 1.1554113995766467514442061230971
y2[1] (numeric) = 1.1553024935327932537100240609341
absolute error = 0.000108906043853497734182062163
relative error = 0.0094257373515097652195586439727717 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1554113995766467514442061230971
y1[1] (numeric) = 1.1554113995766467726205735704482
absolute error = 2.11763674473511e-17
relative error = 1.8327989022014421609449874707469e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1213.0MB, alloc=4.6MB, time=159.64
NO POLE
NO POLE
x[1] = 0.566
y2[1] (analytic) = 1.1559472375976869904105459931083
y2[1] (numeric) = 1.1558381204364375081208368477516
absolute error = 0.0001091171612494822897091453567
relative error = 0.0094396316458398039684300869740313 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1559472375976869904105459931083
y1[1] (numeric) = 1.15594723759768701162796473024
absolute error = 2.12174187371317e-17
relative error = 1.8355006220894796405717382905201e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1216.9MB, alloc=4.6MB, time=160.14
NO POLE
NO POLE
x[1] = 0.567
y2[1] (analytic) = 1.1564839196714192939620398507875
y2[1] (numeric) = 1.1563745915267802335014385803137
absolute error = 0.0001093281446390604606012704738
relative error = 0.0094534945777821813406802443944858 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1564839196714192939620398507875
y1[1] (numeric) = 1.1564839196714193152204838219779
absolute error = 2.12584439711904e-17
relative error = 1.8381962437688159292468881387571e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1220.7MB, alloc=4.6MB, time=160.63
x[1] = 0.568
y2[1] (analytic) = 1.157021445261161633089888798216
y2[1] (numeric) = 1.1569119062673503842150265830484
absolute error = 0.0001095389938112488748622151676
relative error = 0.0094673261467961686126998493768709 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.157021445261161633089888798216
y1[1] (numeric) = 1.1570214452611616543893319067179
absolute error = 2.12994431085019e-17
relative error = 1.8408857671340925463342018274913e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.569
y2[1] (analytic) = 1.1575598138293884628455513596132
y2[1] (numeric) = 1.1574500641208332644676770306726
absolute error = 0.0001097497085551983778743289406
relative error = 0.0094811263525233498891941092276609 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1575598138293884628455513596132
y1[1] (numeric) = 1.1575598138293884841859674676803
absolute error = 2.13404161080671e-17
relative error = 1.8435691921154099201627909337955e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1224.5MB, alloc=4.6MB, time=161.12
NO POLE
NO POLE
x[1] = 0.57
y2[1] (analytic) = 1.158099024837731259866243636084
y2[1] (numeric) = 1.157989064549071065622995965893
absolute error = 0.000109960288660194243247670191
relative error = 0.0094948951947871202168805748911152 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.158099024837731259866243636084
y1[1] (numeric) = 1.1580990248377312812476065649972
absolute error = 2.13813629289132e-17
relative error = 1.8462465186782348742261058890847e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1228.3MB, alloc=4.6MB, time=161.60
NO POLE
NO POLE
x[1] = 0.571
y2[1] (analytic) = 1.158639077746979060743417804361
y2[1] (numeric) = 1.1585289070130634043598830893173
absolute error = 0.0001101707339156563835347150437
relative error = 0.009508632673592182710403648919013 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.158639077746979060743417804361
y1[1] (numeric) = 1.1586390777469790821657013344541
absolute error = 2.14222835300931e-17
relative error = 1.8489177468232474935644987134526e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.572
y2[1] (analytic) = 1.1591799720170790012336805911064
y2[1] (numeric) = 1.1590695909729678616728701638576
absolute error = 0.0001103810441111395608104272488
relative error = 0.0095223387891240447045230270545163 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1591799720170790012336805911064
y1[1] (numeric) = 1.1591799720170790226968584617928
absolute error = 2.14631778706864e-17
relative error = 1.8515828765863259874943045347837e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1232.1MB, alloc=4.6MB, time=162.09
NO POLE
NO POLE
x[1] = 0.573
y2[1] (analytic) = 1.1597217071071368563116125119018
y2[1] (numeric) = 1.1596111158881005227144950333318
absolute error = 0.00011059121903633359711747857
relative error = 0.0095360135417485129465977611876781 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1597217071071368563116125119018
y1[1] (numeric) = 1.1597217071071368778156584217005
absolute error = 2.15040459097987e-17
relative error = 1.8542419080383845493818297335904e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1235.9MB, alloc=4.6MB, time=162.57
NO POLE
NO POLE
x[1] = 0.574
y2[1] (analytic) = 1.1602642824754175810639478221502
y2[1] (numeric) = 1.1601534812169365174791714129342
absolute error = 0.000110801258481063584776409216
relative error = 0.0095496569320111878433517110091418 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1602642824754175810639478221502
y1[1] (numeric) = 1.1602642824754176026088354287121
absolute error = 2.15448876065619e-17
relative error = 1.8568948412852974011191879451756e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.575
y2[1] (analytic) = 1.1608076975793458524245742857562
y2[1] (numeric) = 1.1606966864171105623280137677511
absolute error = 0.0001110111622352900965605180051
relative error = 0.0095632689606369567758699227814817 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1608076975793458524245742857562
y1[1] (numeric) = 1.1608076975793458740102772058906
absolute error = 2.15857029201344e-17
relative error = 1.8595416764678139813607148913235e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1239.7MB, alloc=4.6MB, time=163.06
NO POLE
NO POLE
x[1] = 0.576
y2[1] (analytic) = 1.1613519518755066117498110266296
y2[1] (numeric) = 1.1612407309454175023540757545404
absolute error = 0.0001112209300891093957352720892
relative error = 0.0095768496285294864967389389022732 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1613519518755066117498110266296
y1[1] (numeric) = 1.1613519518755066333763028363305
absolute error = 2.16264918097009e-17
relative error = 1.8621824137614394763845688447247e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1243.6MB, alloc=4.6MB, time=163.54
NO POLE
NO POLE
x[1] = 0.577
y2[1] (analytic) = 1.1618970448196456082334218877795
y2[1] (numeric) = 1.1617856142578128545874598615838
absolute error = 0.0001114305618327536459620261957
relative error = 0.0095903989367707146232072044084547 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1618970448196456082334218877795
y1[1] (numeric) = 1.1618970448196456299006761222519
absolute error = 2.16672542344724e-17
relative error = 1.8648170533763324489887405377339e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.578
y2[1] (analytic) = 1.162442975866669943160820883031
y2[1] (numeric) = 1.1623313358094133520397550415451
absolute error = 0.0001116400572565911210658414859
relative error = 0.0096039168866203402402046005371736 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.162442975866669943160820883031
y1[1] (numeric) = 1.1624429758666699648688110367176
absolute error = 2.17079901536866e-17
relative error = 1.8674455955572367167881799550071e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1247.4MB, alloc=4.6MB, time=164.03
NO POLE
NO POLE
x[1] = 0.579
y2[1] (analytic) = 1.1629897444706486150019254872046
y2[1] (numeric) = 1.1628778950544974885872582929441
absolute error = 0.0001118494161511264146671942605
relative error = 0.0096174034795153136270227028182717 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1629897444706486150019254872046
y1[1] (numeric) = 1.1629897444706486367506250138121
absolute error = 2.17486995266075e-17
relative error = 1.8700680405833441870318716019746e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1251.2MB, alloc=4.6MB, time=164.52
NO POLE
NO POLE
x[1] = 0.58
y2[1] (analytic) = 1.16353735008481306534211267195
y2[1] (numeric) = 1.1634252914465060646924353070688
absolute error = 0.0001120586383070006496773648812
relative error = 0.0096308587170693251214196364475119 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.16353735008481306534211267195
y1[1] (numeric) = 1.1635373500848130871314949844758
absolute error = 2.17893823125258e-17
relative error = 1.8726843887682263887534388865088e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.581
y2[1] (analytic) = 1.1640857921615577256507317563242
y2[1] (numeric) = 1.1639735244380427339630744589114
absolute error = 0.0001122677235149916876572974128
relative error = 0.0096442826010722931348753873332334 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1640857921615577256507317563242
y1[1] (numeric) = 1.1640857921615577474807702270829
absolute error = 2.18300384707587e-17
relative error = 1.8752946404597142123372998290945e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1255.0MB, alloc=4.6MB, time=165.00
NO POLE
NO POLE
x[1] = 0.582
y2[1] (analytic) = 1.1646350701524405648866273036464
y2[1] (numeric) = 1.1645225934808745505485875830191
absolute error = 0.0001124766715660143380397206273
relative error = 0.0096576751334898513326851268882624 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1646350701524405648866273036464
y1[1] (numeric) = 1.1646350701524405867572952642964
absolute error = 2.18706679606500e-17
relative error = 1.8778987960398033065686190193843e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1258.8MB, alloc=4.6MB, time=165.48
NO POLE
NO POLE
x[1] = 0.583
y2[1] (analytic) = 1.165185183508183637940124459152
y2[1] (numeric) = 1.1650724980259325173729101380051
absolute error = 0.0001126854822511205672143211469
relative error = 0.0096710363164628349925395253174159 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.165185183508183637940124459152
y1[1] (numeric) = 1.1651851835081836598513952007223
absolute error = 2.19112707415703e-17
relative error = 1.8804968559245678861514384742644e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.584
y2[1] (analytic) = 1.1657361316786736349109282865074
y2[1] (numeric) = 1.1656232375233121352034525268648
absolute error = 0.0001128941553614997074757596426
relative error = 0.0096843661523067665552021656041132 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1657361316786736349109282865074
y1[1] (numeric) = 1.1657361316786736568627750594241
absolute error = 2.19518467729167e-17
relative error = 1.8830888205640314542911563668162e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1262.6MB, alloc=4.6MB, time=165.96
NO POLE
NO POLE
x[1] = 0.585
y2[1] (analytic) = 1.1662879141129624312213878253303
y2[1] (numeric) = 1.166174811422273952555553504192
absolute error = 0.0001131026906884786658343211383
relative error = 0.0096976646435113403808550309287528 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1662879141129624312213878253303
y1[1] (numeric) = 1.1662879141129624532137838394435
absolute error = 2.19923960141132e-17
relative error = 1.8856746904420974754909642195197e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1266.5MB, alloc=4.6MB, time=166.45
NO POLE
NO POLE
x[1] = 0.586
y2[1] (analytic) = 1.1668405302592676385645747564984
y2[1] (numeric) = 1.1667272191712441164318857658875
absolute error = 0.0001133110880235221326889906109
relative error = 0.0097109317927399067246436262999046 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1668405302592676385645747564984
y1[1] (numeric) = 1.1668405302592676605974931811091
absolute error = 2.20329184246107e-17
relative error = 1.8882544660764455307113372505364e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.587
y2[1] (analytic) = 1.1673939795649731566866257272142
y2[1] (numeric) = 1.1672804602178149238962629820001
absolute error = 0.0001135193471582327903627452141
relative error = 0.0097241676028289549449136130543167 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1673939795649731566866257272142
y1[1] (numeric) = 1.1673939795649731787600396911007
absolute error = 2.20734139638865e-17
relative error = 1.8908281480183845050156172751767e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1270.3MB, alloc=4.6MB, time=166.93
NO POLE
NO POLE
x[1] = 0.588
y2[1] (analytic) = 1.1679482614766297260027965535271
y2[1] (numeric) = 1.1678345340087453744812966989392
absolute error = 0.0001137274678843515214998545879
relative error = 0.0097373720767875959575908858571508 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1679482614766297260027965535271
y1[1] (numeric) = 1.1679482614766297481166791449725
absolute error = 2.21138825914454e-17
relative error = 1.8933957368528427551029732410279e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1274.1MB, alloc=4.6MB, time=167.41
NO POLE
NO POLE
x[1] = 0.589
y2[1] (analytic) = 1.1685033754399554810466756843086
y2[1] (numeric) = 1.1683894399899617234293507034482
absolute error = 0.0001139354499937576173249808604
relative error = 0.0097505452177970439501168102643483 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1685033754399554810466756843086
y1[1] (numeric) = 1.1685033754399555032009999511272
absolute error = 2.21543242668186e-17
relative error = 1.8959572331981696017132813358620e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1277.9MB, alloc=4.6MB, time=167.90
x[1] = 0.59
y2[1] (analytic) = 1.1690593208998365047520034775093
y2[1] (numeric) = 1.1689451776065580357662396074299
absolute error = 0.0001141432932784689857638700794
relative error = 0.0097636870292100973683098659555804 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1690593208998365047520034775093
y1[1] (numeric) = 1.1690593208998365269467424270738
absolute error = 2.21947389495645e-17
relative error = 1.8985126377060994850620897100715e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.591
y2[1] (analytic) = 1.1696160973003273835665430069271
y2[1] (numeric) = 1.1695017463027967412071175799726
absolute error = 0.0001143509975306423594254269545
relative error = 0.0097767975145506191894842118488574 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1696160973003273835665430069271
y1[1] (numeric) = 1.1696160973003274058016696061954
absolute error = 2.22351265992683e-17
relative error = 1.9010619510616132006259129670551e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1281.7MB, alloc=4.6MB, time=168.38
NO POLE
NO POLE
x[1] = 0.592
y2[1] (analytic) = 1.1701737040846517633974472856612
y2[1] (numeric) = 1.170059145522109189894002320733
absolute error = 0.0001145585625425735034449649282
relative error = 0.0097898766775130164951147061546044 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1701737040846517633974472856612
y1[1] (numeric) = 1.1701737040846517856729344612037
absolute error = 2.22754871755425e-17
relative error = 1.9036051739828760202680516769703e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1285.5MB, alloc=4.6MB, time=168.87
NO POLE
NO POLE
x[1] = 0.593
y2[1] (analytic) = 1.1707321406952029063875669609314
y2[1] (numeric) = 1.1706173747070962089643785371992
absolute error = 0.0001147659881066974231884237322
relative error = 0.0098029245219617193562966806715749 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1707321406952029063875669609314
y1[1] (numeric) = 1.1707321406952029287033875989578
absolute error = 2.23158206380264e-17
relative error = 1.9061423072210901530657521369391e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.594
y2[1] (analytic) = 1.1712914065735442485221417040005
y2[1] (numeric) = 1.1711764332995286599503243572767
absolute error = 0.0001149732740155885718173467238
relative error = 0.0098159410519306590452072875556885 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1712914065735442485221417040005
y1[1] (numeric) = 1.1712914065735442708782686503871
absolute error = 2.23561269463866e-17
relative error = 1.9086733515604325853860436418979e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1289.3MB, alloc=4.6MB, time=169.35
NO POLE
NO POLE
x[1] = 0.595
y2[1] (analytic) = 1.1718515011604099580653176885558
y2[1] (numeric) = 1.1717363207403479970076032781168
absolute error = 0.000115180420061961057714410439
relative error = 0.0098289262716227455857335117614873 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1718515011604099580653176885558
y1[1] (numeric) = 1.1718515011604099804617237488727
absolute error = 2.23964060603169e-17
relative error = 1.9111983078179414812973114752193e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1293.2MB, alloc=4.6MB, time=169.84
NO POLE
NO POLE
x[1] = 0.596
y2[1] (analytic) = 1.172412423895705494825932721079
y2[1] (numeric) = 1.1722970364696668259741634221424
absolute error = 0.0001153874260386688517692989366
relative error = 0.0098418801854093446563899759447221 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.172412423895705494825932721079
y1[1] (numeric) = 1.172412423895705517262590660617
absolute error = 2.24366579395380e-17
relative error = 1.9137171768433854348186213762318e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.597
y2[1] (analytic) = 1.1729741742185081702520097574644
y2[1] (numeric) = 1.1728585799267694642574850418188
absolute error = 0.0001155942917387059945247156456
relative error = 0.0098548027978297538586074603632873 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1729741742185081702520097574644
y1[1] (numeric) = 1.1729741742185081927288923012625
absolute error = 2.24768825437981e-17
relative error = 1.9162299595192094125026957533703e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1297.0MB, alloc=4.6MB, time=170.32
NO POLE
NO POLE
x[1] = 0.598
y2[1] (analytic) = 1.1735367515670677083533987114403
y2[1] (numeric) = 1.173420950550112501550216385868
absolute error = 0.0001158010169552068031823255723
relative error = 0.0098676941135906783634306218805876 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1735367515670677083533987114403
y1[1] (numeric) = 1.173536751567067730870478544313
absolute error = 2.25170798328727e-17
relative error = 1.9187366567604122703075118664513e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1300.8MB, alloc=4.6MB, time=170.81
NO POLE
NO POLE
x[1] = 0.599
y2[1] (analytic) = 1.1741001553788068074520056321979
y2[1] (numeric) = 1.1739841477773253613735372113378
absolute error = 0.0001160076014814460784684208601
relative error = 0.009880554137565705949620725556507 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1741001553788068074520056321979
y1[1] (numeric) = 1.1741001553788068300092553987623
absolute error = 2.25572497665644e-17
relative error = 1.9212372695144242133052375388753e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.6
y2[1] (analytic) = 1.1746643850903217027590475010446
y2[1] (numeric) = 1.174548171045210863447688398209
absolute error = 0.0001162140451108393113591028356
relative error = 0.0098933828747947814461163036377223 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1746643850903217027590475010446
y1[1] (numeric) = 1.1746643850903217253564398057478
absolute error = 2.25973923047032e-17
relative error = 1.9237317987610267661977159175383e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1304.6MB, alloc=4.6MB, time=171.28
NO POLE
NO POLE
x[1] = 0.601
y2[1] (analytic) = 1.1752294401373827297787700698751
y2[1] (numeric) = 1.1751130197897457868891052960577
absolute error = 0.0001164203476369428896647738174
relative error = 0.0099061803304836805917615330179044 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1752294401373827297787700698751
y1[1] (numeric) = 1.1752294401373827524162774770217
absolute error = 2.26375074071466e-17
relative error = 1.9262202455122555511512659640700e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1308.4MB, alloc=4.6MB, time=171.77
NO POLE
NO POLE
x[1] = 0.602
y2[1] (analytic) = 1.1757953199549348885380653377883
y2[1] (numeric) = 1.1756786934460814342335916056863
absolute error = 0.000116626508853454304473732102
relative error = 0.0099189465100034833251687759669172 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1757953199549348885380653377883
y1[1] (numeric) = 1.175795319954934911215660371568
absolute error = 2.26775950337797e-17
relative error = 1.9287026108123029424314946425358e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.603
y2[1] (analytic) = 1.1763620239770984086414244362806
y2[1] (numeric) = 1.1762451914485441962849697725968
absolute error = 0.0001168325285542123564546636838
relative error = 0.0099316814188900465175381640531228 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1763620239770984086414244362806
y1[1] (numeric) = 1.1763620239770984313590795807953
absolute error = 2.27176551445147e-17
relative error = 1.9311788957373695955952437674715e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1312.2MB, alloc=4.6MB, time=172.25
NO POLE
NO POLE
x[1] = 0.604
y2[1] (analytic) = 1.1769295516371693151506608681084
y2[1] (numeric) = 1.1768125132306361177886430437023
absolute error = 0.0001170384065331973620178244061
relative error = 0.0099443850628434761612133241998685 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1769295516371693151506608681084
y1[1] (numeric) = 1.1769295516371693379083485673999
absolute error = 2.27576876992915e-17
relative error = 1.9336491013956094695102686890316e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1316.0MB, alloc=4.6MB, time=172.73
NO POLE
NO POLE
x[1] = 0.605
y2[1] (analytic) = 1.177497902367619995288838220145
y2[1] (numeric) = 1.1773806582250354639295035137625
absolute error = 0.0001172441425845313593347063825
relative error = 0.0099570574477275990267083522866067 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.177497902367619995288838220145
y1[1] (numeric) = 1.1774979023676200180865308782227
absolute error = 2.27976926580777e-17
relative error = 1.9361132289270236541815852932555e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.606
y2[1] (analytic) = 1.1780670756000997659678356463513
y2[1] (numeric) = 1.1779496258635972876536196636819
absolute error = 0.0001174497365024783142159826694
relative error = 0.009969698579569433800896936404248 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1780670756000997659678356463513
y1[1] (numeric) = 1.1780670756000997888055056272194
absolute error = 2.28376699808681e-17
relative error = 1.9385712795033116674261480097469e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1319.9MB, alloc=4.6MB, time=173.21
NO POLE
NO POLE
x[1] = 0.607
y2[1] (analytic) = 1.1786370707654354421389835933405
y2[1] (numeric) = 1.1785194155773539978131360690308
absolute error = 0.0001176551880814443258475243097
relative error = 0.0099823084645586617190101218366934 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1786370707654354421389835933405
y1[1] (numeric) = 1.178637070765435465016603221026
absolute error = 2.28776196276855e-17
relative error = 1.9410232543278330853122804654344e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1323.7MB, alloc=4.6MB, time=173.69
NO POLE
NO POLE
x[1] = 0.608
y2[1] (analytic) = 1.1792078872936319059662014179512
y2[1] (numeric) = 1.179090026796515928133817133936
absolute error = 0.0001178604971159778323842840152
relative error = 0.0099948871090470967030445969899982 %
Correct digits = 4
h = 0.001
y1[1] (analytic) = 1.1792078872936319059662014179512
y1[1] (numeric) = 1.1792078872936319288837429765315
absolute error = 2.29175415585803e-17
relative error = 1.9434691546354671285690489564375e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.609
y2[1] (analytic) = 1.1797795246138726768210677237362
y2[1] (numeric) = 1.1796614589504719070046658828463
absolute error = 0.0001180656634007698164018408899
relative error = 0.010007434519548155019138565144426 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1797795246138726768210677237362
y1[1] (numeric) = 1.1797795246138726997785034573666
absolute error = 2.29574357336304e-17
relative error = 1.9459089816924976946440616245760e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1327.5MB, alloc=4.6MB, time=174.18
NO POLE
NO POLE
x[1] = 0.61
y2[1] (analytic) = 1.1803519821545204820992534213452
y2[1] (numeric) = 1.1802337114677898280890480205996
absolute error = 0.0001182706867306540102054007456
relative error = 0.010019950702736324466427256438141 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1803519821545204820992534213452
y1[1] (numeric) = 1.1803519821545205050965555342871
absolute error = 2.29973021129419e-17
relative error = 1.9483427367965661119342414810796e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1331.3MB, alloc=4.6MB, time=174.67
NO POLE
NO POLE
x[1] = 0.611
y2[1] (analytic) = 1.1809252593431178288577466964165
y2[1] (numeric) = 1.1808067837762172217567506497169
absolute error = 0.0001184755669006071009960466996
relative error = 0.010032435665446633109844928813051 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1809252593431178288577466964165
y1[1] (numeric) = 1.1809252593431178518948873530648
absolute error = 2.30371406566483e-17
relative error = 1.9507704212764966258137227344923e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.612
y2[1] (analytic) = 1.1814993556063875762722982477992
y2[1] (numeric) = 1.1813806753026818273364042129108
absolute error = 0.0001186803037057489358940348884
relative error = 0.010044889414674117569294810211948 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1814993556063875762722982477992
y1[1] (numeric) = 1.1814993556063875993492495727102
absolute error = 2.30769513249110e-17
relative error = 1.9531920364922320376528018525291e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1335.1MB, alloc=4.6MB, time=175.15
NO POLE
NO POLE
x[1] = 0.613
y2[1] (analytic) = 1.1820742703702335089145143387088
y2[1] (numeric) = 1.1819553854732921661876954084352
absolute error = 0.0001188848969413427268189302736
relative error = 0.010057311957573290877562849513024 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1820742703702335089145143387088
y1[1] (numeric) = 1.1820742703702335320312484166282
absolute error = 2.31167340779194e-17
relative error = 1.9556075838347353099708622180174e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1338.9MB, alloc=4.6MB, time=175.64
NO POLE
NO POLE
x[1] = 0.614
y2[1] (analytic) = 1.1826500030597409108480243837716
y2[1] (numeric) = 1.18253091371333811559279800611
absolute error = 0.0001190893464027952552263776616
relative error = 0.010069703301457609919305373967022 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1826500030597409108480243837716
y1[1] (numeric) = 1.1826500030597409340045132596622
absolute error = 2.31564888758906e-17
relative error = 1.9580170647258572552485776912588e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1342.7MB, alloc=4.6MB, time=176.13
NO POLE
NO POLE
x[1] = 0.615
y2[1] (analytic) = 1.1832265530991771405431489758368
y2[1] (numeric) = 1.1831072594472914834664476726389
absolute error = 0.0001192936518856570767013031979
relative error = 0.010082063453798942463394798495706 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1832265530991771405431489758368
y1[1] (numeric) = 1.1832265530991771637393646549069
absolute error = 2.31962156790701e-17
relative error = 1.9604204806182887466607185869625e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.616
y2[1] (analytic) = 1.1838039199119922066094934379379
y2[1] (numeric) = 1.1836844220988065838840860961925
absolute error = 0.0001194978131856227254073417454
relative error = 0.010094392422227033800861401447851 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1838039199119922066094934379379
y1[1] (numeric) = 1.1838039199119922298454078856687
absolute error = 2.32359144477308e-17
relative error = 1.9628178329953690863850647296643e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1346.6MB, alloc=4.6MB, time=176.61
NO POLE
NO POLE
x[1] = 0.617
y2[1] (analytic) = 1.1843821029208193443458911678558
y2[1] (numeric) = 1.1842624010907208134274988821612
absolute error = 0.0001197018300985309183922856946
relative error = 0.010106690214528973000622873640075 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1843821029208193443458911678558
y1[1] (numeric) = 1.18438210292081936762147631003
absolute error = 2.32755851421742e-17
relative error = 1.9652091233710803099546317541808e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1350.4MB, alloc=4.6MB, time=177.09
NO POLE
NO POLE
x[1] = 0.618
y2[1] (analytic) = 1.1849611015474755931071202253905
y2[1] (numeric) = 1.1848411958450552283473708744875
absolute error = 0.000119905702420364759749350903
relative error = 0.010118956838648658795146867500589 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1849611015474755931071202253905
y1[1] (numeric) = 1.1849611015474756164223479481199
absolute error = 2.33152277227294e-17
relative error = 1.9675943532898554738620198157556e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.619
y2[1] (analytic) = 1.1855409152129623744868157956707
y2[1] (numeric) = 1.1854208057830151225421817400708
absolute error = 0.0001201094299472519446340555999
relative error = 0.010131192302686265108145122054645 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1855409152129623744868157956707
y1[1] (numeric) = 1.1855409152129623978416579454246
absolute error = 2.33548421497539e-17
relative error = 1.9699735243265389626668930971579e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1354.2MB, alloc=4.6MB, time=177.57
NO POLE
NO POLE
x[1] = 0.62
y2[1] (analytic) = 1.1861215433374660713160003456393
y2[1] (numeric) = 1.1860012303249906063528638373972
absolute error = 0.0001203130124754649631365082421
relative error = 0.01014339661489770623635092207683 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1861215433374660713160003456393
y1[1] (numeric) = 1.1861215433374660947104287292725
absolute error = 2.33944283836332e-17
relative error = 1.9723466380862453728923744836766e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1358.0MB, alloc=4.6MB, time=178.05
NO POLE
NO POLE
x[1] = 0.621
y2[1] (analytic) = 1.1867029853403586074766524752305
y2[1] (numeric) = 1.1865824688905571861726435747845
absolute error = 0.000120516449801421304008900446
relative error = 0.010155569783694101697384667282511 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1867029853403586074766524752305
y1[1] (numeric) = 1.1867029853403586309106388600117
absolute error = 2.34339863847812e-17
relative error = 1.9747136962042858569154403088850e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.622
y2[1] (analytic) = 1.1872852406401980285297346497202
y2[1] (numeric) = 1.1871645208984763448714866484498
absolute error = 0.0001207197417216836582480012704
relative error = 0.010167711817641240755665184415647 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1872852406401980285297346497202
y1[1] (numeric) = 1.1872852406401980520032507633601
absolute error = 2.34735161136399e-17
relative error = 1.9770747003460353592725976038554e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1361.8MB, alloc=4.6MB, time=178.53
NO POLE
NO POLE
x[1] = 0.623
y2[1] (analytic) = 1.1878683086547290831570991852689
y2[1] (numeric) = 1.1877473857666961230345667360021
absolute error = 0.0001209228880329601225324492668
relative error = 0.010179822725459046638277113176518 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1878683086547290831570991852689
y1[1] (numeric) = 1.1878683086547291066701167159484
absolute error = 2.35130175306795e-17
relative error = 1.9794296522068335529973951926105e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1365.6MB, alloc=4.6MB, time=179.02
NO POLE
NO POLE
x[1] = 0.624
y2[1] (analytic) = 1.1884521888008838054166910457999
y2[1] (numeric) = 1.1883310629123517010141764069405
absolute error = 0.0001211258885321044025146388594
relative error = 0.010191902516021040452657239825053 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1884521888008838054166910457999
y1[1] (numeric) = 1.1884521888008838289691816421985
absolute error = 2.35524905963986e-17
relative error = 1.9817785535118941196902476876576e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.625
y2[1] (analytic) = 1.1890368804947820978104651960589
y2[1] (numeric) = 1.1889155517517659817944981982947
absolute error = 0.0001213287430161160159669977642
relative error = 0.010203951198353804817915042816598 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1890368804947820978104651960589
y1[1] (numeric) = 1.1890368804947821214024004673831
absolute error = 2.35919352713242e-17
relative error = 1.9841214060161971161236447355505e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1369.4MB, alloc=4.6MB, time=179.51
NO POLE
NO POLE
x[1] = 0.626
y2[1] (analytic) = 1.189622383151732315164435442986
y2[1] (numeric) = 1.1895008517004501746686529906863
absolute error = 0.0001215314512821404957824522997
relative error = 0.010215968781636447221554955386678 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.189622383151732315164435442986
y1[1] (numeric) = 1.1896223831517323387957869589975
absolute error = 2.36313515160115e-17
relative error = 1.9864582115043644875594434807444e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
memory used=1373.3MB, alloc=4.6MB, time=180.03
NO POLE
NO POLE
x[1] = 0.627
y2[1] (analytic) = 1.1902086961862318493202708853993
y2[1] (numeric) = 1.1900869621731043797274420078101
absolute error = 0.0001217340131274695928288775892
relative error = 0.010227955275200063113319944210588 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1902086961862318493202708853993
y1[1] (numeric) = 1.1902086961862318729910101764437
absolute error = 2.36707392910444e-17
relative error = 1.9887889717905944050300213554098e-15 %
Correct digits = 16
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.628
y2[1] (analytic) = 1.1907958190119677146378552804441
y2[1] (numeric) = 1.1906738825836181731591979506428
absolute error = 0.0001219364283495414786573298013
relative error = 0.010239910688527198747827953559696 %
Correct digits = 3
h = 0.001
y1[1] (analytic) = 1.1907958190119677146378552804441
y1[1] (numeric) = 1.1907958190119677383479538374791
absolute error = 2.37100985570350e-17
relative error = 1.9911136887185114642747074072286e-15 %
Correct digits = 16
h = 0.001
Finished!
Maximum Time Reached before Solution Completed!
diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;
diff ( y1 , x , 1 ) = sin ( x ) ;
Iterations = 528
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 3 Minutes 0 Seconds
Expected Time Remaining = 24 Minutes 50 Seconds
Optimized Time Remaining = 24 Minutes 47 Seconds
Expected Total Time = 27 Minutes 47 Seconds
Time to Timeout Unknown
Percent Done = 10.8 %
> quit
memory used=1376.7MB, alloc=4.6MB, time=180.47