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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
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_dump,
> glob_normmax,
> glob_warned2,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> glob_hmax,
> glob_clock_sec,
> glob_almost_1,
> glob_optimal_start,
> glob_last_good_h,
> glob_h,
> centuries_in_millinium,
> sec_in_min,
> glob_max_minutes,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> days_in_year,
> djd_debug,
> glob_start,
> glob_dump_analytic,
> glob_display_flag,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_relerr,
> glob_optimal_done,
> years_in_century,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> min_in_hour,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_iter,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_disp_incr,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_html_log,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_fact_1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_m1,
> array_norms,
> array_y_init,
> array_type_pole,
> array_tmp1_g,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, INFO,
glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump,
glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err,
glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec,
glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h,
centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float,
glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr,
days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag,
glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr,
glob_optimal_done, years_in_century, glob_log10relerr,
glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float,
glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour,
glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter,
glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h,
glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr,
glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log,
glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error,
array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y,
array_x, array_1st_rel_error, array_m1, array_norms, array_y_init,
array_type_pole, array_tmp1_g, array_poles, array_y_set_initial,
array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2,
array_complex_pole, array_real_pole, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
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_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_dump,
> glob_normmax,
> glob_warned2,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> glob_hmax,
> glob_clock_sec,
> glob_almost_1,
> glob_optimal_start,
> glob_last_good_h,
> glob_h,
> centuries_in_millinium,
> sec_in_min,
> glob_max_minutes,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> days_in_year,
> djd_debug,
> glob_start,
> glob_dump_analytic,
> glob_display_flag,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_relerr,
> glob_optimal_done,
> years_in_century,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> min_in_hour,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_iter,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_disp_incr,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_html_log,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_fact_1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_m1,
> array_norms,
> array_y_init,
> array_type_pole,
> array_tmp1_g,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_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 (abs(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");
> newline();
> 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
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, INFO,
glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump,
glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err,
glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec,
glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h,
centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float,
glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr,
days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag,
glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr,
glob_optimal_done, years_in_century, glob_log10relerr,
glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float,
glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour,
glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter,
glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h,
glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr,
glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log,
glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error,
array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y,
array_x, array_1st_rel_error, array_m1, array_norms, array_y_init,
array_type_pole, array_tmp1_g, array_poles, array_y_set_initial,
array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2,
array_complex_pole, array_real_pole, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(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");
newline();
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
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_dump,
> glob_normmax,
> glob_warned2,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> glob_hmax,
> glob_clock_sec,
> glob_almost_1,
> glob_optimal_start,
> glob_last_good_h,
> glob_h,
> centuries_in_millinium,
> sec_in_min,
> glob_max_minutes,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> days_in_year,
> djd_debug,
> glob_start,
> glob_dump_analytic,
> glob_display_flag,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_relerr,
> glob_optimal_done,
> years_in_century,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> min_in_hour,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_iter,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_disp_incr,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_html_log,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_fact_1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_m1,
> array_norms,
> array_y_init,
> array_type_pole,
> array_tmp1_g,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_real_pole,
> 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));
> 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));
> 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 Function number 5
> 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 DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, INFO,
glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump,
glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err,
glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec,
glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h,
centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float,
glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr,
days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag,
glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr,
glob_optimal_done, years_in_century, glob_log10relerr,
glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float,
glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour,
glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter,
glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h,
glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr,
glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log,
glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error,
array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y,
array_x, array_1st_rel_error, array_m1, array_norms, array_y_init,
array_type_pole, array_tmp1_g, array_poles, array_y_set_initial,
array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2,
array_complex_pole, array_real_pole, 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));
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))
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
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_dump,
> glob_normmax,
> glob_warned2,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> glob_hmax,
> glob_clock_sec,
> glob_almost_1,
> glob_optimal_start,
> glob_last_good_h,
> glob_h,
> centuries_in_millinium,
> sec_in_min,
> glob_max_minutes,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> days_in_year,
> djd_debug,
> glob_start,
> glob_dump_analytic,
> glob_display_flag,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_relerr,
> glob_optimal_done,
> years_in_century,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> min_in_hour,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_iter,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_disp_incr,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_html_log,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_fact_1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_m1,
> array_norms,
> array_y_init,
> array_type_pole,
> array_tmp1_g,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #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 ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_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_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(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
> #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 (abs(array_y_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 (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_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_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(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 (abs(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 (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * 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
> 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 2
> 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 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> 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 2
> 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 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> 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 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> 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 2
> 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 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> 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 2
> 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 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> 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 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> 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;
global DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, INFO,
glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump,
glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err,
glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec,
glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h,
centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float,
glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr,
days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag,
glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr,
glob_optimal_done, years_in_century, glob_log10relerr,
glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float,
glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour,
glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter,
glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h,
glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr,
glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log,
glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error,
array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y,
array_x, array_1st_rel_error, array_m1, array_norms, array_y_init,
array_type_pole, array_tmp1_g, array_poles, array_y_set_initial,
array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2,
array_complex_pole, array_real_pole, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(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 - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_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 <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(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 < abs(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 < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*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;
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
omniout_str(ALWAYS, "Complex estimate of poles used")
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
omniout_str(ALWAYS, "Real estimate of pole used")
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 glob_display_flag 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
omniout_str(ALWAYS, "Real estimate of pole used")
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
omniout_str(ALWAYS, "Complex estimate of poles used")
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 glob_display_flag 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;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_dump,
> glob_normmax,
> glob_warned2,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> glob_hmax,
> glob_clock_sec,
> glob_almost_1,
> glob_optimal_start,
> glob_last_good_h,
> glob_h,
> centuries_in_millinium,
> sec_in_min,
> glob_max_minutes,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> days_in_year,
> djd_debug,
> glob_start,
> glob_dump_analytic,
> glob_display_flag,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_relerr,
> glob_optimal_done,
> years_in_century,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> min_in_hour,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_iter,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_disp_incr,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_html_log,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_fact_1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_m1,
> array_norms,
> array_y_init,
> array_type_pole,
> array_tmp1_g,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, INFO,
glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump,
glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err,
glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec,
glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h,
centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float,
glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr,
days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag,
glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr,
glob_optimal_done, years_in_century, glob_log10relerr,
glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float,
glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour,
glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter,
glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h,
glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr,
glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log,
glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error,
array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y,
array_x, array_1st_rel_error, array_m1, array_norms, array_y_init,
array_type_pole, array_tmp1_g, array_poles, array_y_set_initial,
array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2,
array_complex_pole, array_real_pole, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_dump,
> glob_normmax,
> glob_warned2,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> glob_hmax,
> glob_clock_sec,
> glob_almost_1,
> glob_optimal_start,
> glob_last_good_h,
> glob_h,
> centuries_in_millinium,
> sec_in_min,
> glob_max_minutes,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> days_in_year,
> djd_debug,
> glob_start,
> glob_dump_analytic,
> glob_display_flag,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_relerr,
> glob_optimal_done,
> years_in_century,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> min_in_hour,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_iter,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_disp_incr,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_html_log,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_fact_1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_m1,
> array_norms,
> array_y_init,
> array_type_pole,
> array_tmp1_g,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin $eq_no = 1 iii = 1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := -att(1,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := -att(2,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := -att(3,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := -att(4,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[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_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 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
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, INFO,
glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump,
glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err,
glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec,
glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h,
centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float,
glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr,
days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag,
glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr,
glob_optimal_done, years_in_century, glob_log10relerr,
glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float,
glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour,
glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter,
glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h,
glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr,
glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log,
glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error,
array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y,
array_x, array_1st_rel_error, array_m1, array_norms, array_y_init,
array_type_pole, array_tmp1_g, array_poles, array_y_set_initial,
array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2,
array_complex_pole, array_real_pole, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= 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);
> fi;
> fi;
> # End Function number 1
> 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
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> 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
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> 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
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_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,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= 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)
> fi;
> # End Function number 1
> 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
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> 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 5
> 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 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> 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 10
> 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 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 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
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> 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 + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_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 + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_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 11
> 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 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_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
+ array_aa[iii_att]*array_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
> # Begin Function number 5
> 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 11
> 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 11
> # End Function number 5
> 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
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> 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
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> 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 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> 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
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> 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 (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> 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 < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 17
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 13
> if array_fact_1[nnn] = 0 then # if number 14
> ret := nnn!;
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> 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 := nnn!; array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> 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 13
> if array_fact_2[mmm,nnn] = 0 then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> 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 := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 - cos(x);
> end;
exact_soln_y := proc(x) 2.0 - cos(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := 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;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_initial_pass,
> glob_dump,
> glob_normmax,
> glob_warned2,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> glob_hmax,
> glob_clock_sec,
> glob_almost_1,
> glob_optimal_start,
> glob_last_good_h,
> glob_h,
> centuries_in_millinium,
> sec_in_min,
> glob_max_minutes,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> days_in_year,
> djd_debug,
> glob_start,
> glob_dump_analytic,
> glob_display_flag,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_relerr,
> glob_optimal_done,
> years_in_century,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_no_eqs,
> glob_not_yet_start_msg,
> min_in_hour,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_iter,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_hmin,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_disp_incr,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_html_log,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_fact_1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_m1,
> array_norms,
> array_y_init,
> array_type_pole,
> array_tmp1_g,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_real_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_max_terms := 30;
> glob_iolevel := 5;
> DEBUGL := 3;
> INFO := 2;
> glob_orig_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_initial_pass := true;
> glob_dump := false;
> glob_normmax := 0.0;
> glob_warned2 := false;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_look_poles := false;
> glob_hmax := 1.0;
> glob_clock_sec := 0.0;
> glob_almost_1 := 0.9990;
> glob_optimal_start := 0.0;
> glob_last_good_h := 0.1;
> glob_h := 0.1;
> centuries_in_millinium := 10.0;
> sec_in_min := 60.0;
> glob_max_minutes := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_iter := 1000;
> glob_max_hours := 0.0;
> glob_abserr := 0.1e-10;
> days_in_year := 365.0;
> djd_debug := true;
> glob_start := 0;
> glob_dump_analytic := false;
> glob_display_flag := true;
> glob_log10abserr := 0.0;
> MAX_UNCHANGED := 10;
> glob_current_iter := 0;
> glob_relerr := 0.1e-10;
> glob_optimal_done := false;
> years_in_century := 100.0;
> glob_log10relerr := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_log10_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_clock_start_sec := 0.0;
> glob_no_eqs := 0;
> glob_not_yet_start_msg := true;
> min_in_hour := 60.0;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> glob_percent_done := 0.0;
> glob_iter := 0;
> glob_warned := false;
> glob_unchanged_h_cnt := 0;
> glob_hmin := 0.00000000001;
> glob_reached_optimal_h := false;
> glob_log10normmin := 0.1;
> glob_subiter_method := 3;
> glob_max_sec := 10000.0;
> glob_disp_incr := 0.1;
> glob_not_yet_finished := true;
> hours_in_day := 24.0;
> djd_debug2 := true;
> glob_html_log := true;
> glob_hmin_init := 0.001;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , 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 := 0.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.05;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"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_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_pole:= 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_fact_1:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> 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_pole[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_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[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_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_m1[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_y_init[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_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 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 <= max_terms do # do number 3
> array_y_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_y_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 <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_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_y_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 <=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
> ;
> ord := 1;
> while ord <=1 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 <=1 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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> 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_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_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_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_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_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_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 := 0.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.05;
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #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 := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (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();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> 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 (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (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_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_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 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , 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 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-18T01:33:12-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_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 3
> 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 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 092 | ")
> ;
> logitem_str(html_log_file,"sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"sin maple results")
> ;
> logitem_str(html_log_file,"Mostly affecting speed of factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := 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;
global DEBUGMASSIVE, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, INFO,
glob_orig_start_sec, glob_max_trunc_err, glob_initial_pass, glob_dump,
glob_normmax, glob_warned2, glob_small_float, glob_max_rel_trunc_err,
glob_log10_relerr, glob_look_poles, glob_hmax, glob_clock_sec,
glob_almost_1, glob_optimal_start, glob_last_good_h, glob_h,
centuries_in_millinium, sec_in_min, glob_max_minutes, glob_smallish_float,
glob_optimal_clock_start_sec, glob_max_iter, glob_max_hours, glob_abserr,
days_in_year, djd_debug, glob_start, glob_dump_analytic, glob_display_flag,
glob_log10abserr, MAX_UNCHANGED, glob_current_iter, glob_relerr,
glob_optimal_done, years_in_century, glob_log10relerr,
glob_curr_iter_when_opt, glob_log10_abserr, glob_large_float,
glob_clock_start_sec, glob_no_eqs, glob_not_yet_start_msg, min_in_hour,
glob_max_opt_iter, glob_optimal_expect_sec, glob_percent_done, glob_iter,
glob_warned, glob_unchanged_h_cnt, glob_hmin, glob_reached_optimal_h,
glob_log10normmin, glob_subiter_method, glob_max_sec, glob_disp_incr,
glob_not_yet_finished, hours_in_day, djd_debug2, glob_html_log,
glob_hmin_init, array_const_0D0, array_const_1, array_last_rel_error,
array_pole, array_tmp0, array_tmp1, array_tmp2, array_fact_1, array_y,
array_x, array_1st_rel_error, array_m1, array_norms, array_y_init,
array_type_pole, array_tmp1_g, array_poles, array_y_set_initial,
array_y_higher_work2, array_y_higher_work, array_y_higher, array_fact_2,
array_complex_pole, array_real_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_max_terms := 30;
glob_iolevel := 5;
DEBUGL := 3;
INFO := 2;
glob_orig_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_initial_pass := true;
glob_dump := false;
glob_normmax := 0.;
glob_warned2 := false;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_look_poles := false;
glob_hmax := 1.0;
glob_clock_sec := 0.;
glob_almost_1 := 0.9990;
glob_optimal_start := 0.;
glob_last_good_h := 0.1;
glob_h := 0.1;
centuries_in_millinium := 10.0;
sec_in_min := 60.0;
glob_max_minutes := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_clock_start_sec := 0.;
glob_max_iter := 1000;
glob_max_hours := 0.;
glob_abserr := 0.1*10^(-10);
days_in_year := 365.0;
djd_debug := true;
glob_start := 0;
glob_dump_analytic := false;
glob_display_flag := true;
glob_log10abserr := 0.;
MAX_UNCHANGED := 10;
glob_current_iter := 0;
glob_relerr := 0.1*10^(-10);
glob_optimal_done := false;
years_in_century := 100.0;
glob_log10relerr := 0.;
glob_curr_iter_when_opt := 0;
glob_log10_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_clock_start_sec := 0.;
glob_no_eqs := 0;
glob_not_yet_start_msg := true;
min_in_hour := 60.0;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_percent_done := 0.;
glob_iter := 0;
glob_warned := false;
glob_unchanged_h_cnt := 0;
glob_hmin := 0.1*10^(-10);
glob_reached_optimal_h := false;
glob_log10normmin := 0.1;
glob_subiter_method := 3;
glob_max_sec := 10000.0;
glob_disp_incr := 0.1;
glob_not_yet_finished := true;
hours_in_day := 24.0;
djd_debug2 := true;
glob_html_log := true;
glob_hmin_init := 0.001;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , 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 := 0.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.05;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "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_last_rel_error := Array(0 .. max_terms + 1, []);
array_pole := 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_fact_1 := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
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_pole[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_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[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_y_init[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_tmp1_g[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 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 <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[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;
ord := 1;
while ord <= 1 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 <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[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_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
glob_h := 0.001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
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 := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
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();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_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 array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() 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_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
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 ( y , 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, "2012-06-18T01:33:12-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_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_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 092 | ");
logitem_str(html_log_file,
"sin diffeq.mxt");
logitem_str(html_log_file,
"sin maple results");
logitem_str(html_log_file, "Mostly affecting speed of factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/sinpostode.ode#################
diff ( y , x , 1 ) = sin(x);
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 - cos(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 1.0000004999999583333347222221974
y[1] (numeric) = 1.000000499999958333383333331746
absolute error = 4.86111095486e-20
relative error = 4.8611085243059403932115646022377e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 1.000001999999333333422222215873
y[1] (numeric) = 1.0000019999993333335194444011408
absolute error = 9.72221852678e-20
relative error = 9.7221990823883166885573530174913e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 1.0000044999966250010124998372768
y[1] (numeric) = 1.0000044999966250011583330158234
absolute error = 1.458331785466e-19
relative error = 1.4583252230074183127686885267156e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 1.0000079999893333390222205968257
y[1] (numeric) = 1.0000079999893333392166646375997
absolute error = 1.944440407740e-19
relative error = 1.9444248523619216253239107952973e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 1.0000124999739583550347125341049
y[1] (numeric) = 1.000012499973958355277767257444
absolute error = 2.430547233391e-19
relative error = 2.4305168519936447363825618573404e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 1.0000179999460000647999583428738
y[1] (numeric) = 1.0000179999460000650916235205051
absolute error = 2.916651776313e-19
relative error = 2.9165992776834978690377545086004e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 1.0000244998999584967345792460848
y[1] (numeric) = 1.0000244998999584970748546011248
absolute error = 3.402753550400e-19
relative error = 3.4026701853208678791928872200746e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 1.0000319998293336974218061209308
y[1] (numeric) = 1.000031999829333697810691327886
absolute error = 3.888852069552e-19
relative error = 3.8887276309314849589860483133446e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 1.0000404997266257381114323739519
y[1] (numeric) = 1.0000404997266257385489270587189
absolute error = 4.374946847670e-19
relative error = 4.3747696706942863110629445287519e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 1.0000499995833347222197420662478
y[1] (numeric) = 1.0000499995833347227058458061136
absolute error = 4.861037398658e-19
relative error = 4.8607943609652759688458657701332e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 1.0000604993899607938294057888689
y[1] (numeric) = 1.0000604993899607943641181125116
absolute error = 5.347123236427e-19
relative error = 5.3467997583033801256109195451551e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 1.0000719991360041471893357884913
y[1] (numeric) = 1.0000719991360041477726561759804
absolute error = 5.833203874891e-19
relative error = 5.8327839194882979593255491368521e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 1.0000844988099650372144908435208
y[1] (numeric) = 1.0000844988099650378464187263176
absolute error = 6.319278827968e-19
relative error = 6.3187449015433469409427529332133e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 1.0000979983993437909856203908218
y[1] (numeric) = 1.0000979983993437916661551517803
absolute error = 6.805347609585e-19
relative error = 6.8046807617623018060985291621422e-17 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.20
NO POLE
x[1] = 0.015
y[1] (analytic) = 1.0001124978906408202489364033288
y[1] (numeric) = 1.0001124978906408209780773766959
absolute error = 7.291409733671e-19
relative error = 7.2905895577242280337290526502902e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 1.0001279972693566349157005188684
y[1] (numeric) = 1.000127997269356635693446990285
absolute error = 7.777464714166e-19
relative error = 7.7764693473243069157673332951171e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 1.0001444965199918575617129206072
y[1] (numeric) = 1.0001444965199918583880641271087
absolute error = 8.263512065015e-19
relative error = 8.2623181887896544673334282992764e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 1.0001619956260472389266884696369
y[1] (numeric) = 1.0001619956260472398016435996539
absolute error = 8.749551300170e-19
relative error = 8.7481341407031315716535560447777e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 1.0001804945700236744135045903217
y[1] (numeric) = 1.0001804945700236753370627836809
absolute error = 9.235581933592e-19
relative error = 9.2339152620271453655407396532496e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 1.0001999933334222215873044091625
y[1] (numeric) = 1.0001999933334222225594647570875
absolute error = 9.721603479250e-19
relative error = 9.7196596121244418955450553667846e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 1.0002204918967441186744376480752
y[1] (numeric) = 1.0002204918967441196951991931874
absolute error = 1.0207615451122e-18
relative error = 1.0205365250780888803484591400136e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 1.0002419902394908040612207731441
y[1] (numeric) = 1.0002419902394908051305825094639
absolute error = 1.0693617363198e-18
relative error = 1.0691030238230247234475142776005e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 1.0002644883401639367924969000924
y[1] (numeric) = 1.0002644883401639379104577730398
absolute error = 1.1179608729474e-18
relative error = 1.1176652635169935013686460405559e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 1.0002879861762654180699749579101
y[1] (numeric) = 1.0002879861762654192365338643062
absolute error = 1.1665589063961e-18
relative error = 1.1662230502791775072660918184101e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 1.0003124837242974137503266123044
y[1] (numeric) = 1.000312483724297414965482400372
absolute error = 1.2151557880676e-18
relative error = 1.2147761902794736463316759263114e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 1.0003379809597623778430184508743
y[1] (numeric) = 1.0003379809597623791067699202396
absolute error = 1.2637514693653e-18
relative error = 1.2633244897417657617459700190888e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 1.0003644778571630770078559321828
y[1] (numeric) = 1.0003644778571630783202018338761
absolute error = 1.3123459016933e-18
relative error = 1.3118677549450962746889635576401e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 1.0003919743900026160522146011815
y[1] (numeric) = 1.0003919743900026174131536376388
absolute error = 1.3609390364573e-18
relative error = 1.3604057922267358995614927715761e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 1.0004204705307844644279330737607
y[1] (numeric) = 1.0004204705307844658374638988248
absolute error = 1.4095308250641e-18
relative error = 1.4089384079838524112829740814420e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 1.0004499662510124837278412935334
y[1] (numeric) = 1.0004499662510124851859625124553
absolute error = 1.4581212189219e-18
relative error = 1.4574654086759776928422921137229e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 1.000480461521190956181896564327
y[1] (numeric) = 1.0004804615211909576886067337674
absolute error = 1.5067101694404e-18
relative error = 1.5059866008272733309458496592849e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 1.00051195631082461415289886225
y[1] (numeric) = 1.0005119563108246157081964902805
absolute error = 1.5552976280305e-18
relative error = 1.5545017910283948476909644778028e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 1.0005444505884186706317559316192
y[1] (numeric) = 1.0005444505884186722356394777242
absolute error = 1.6038835461050e-18
relative error = 1.6030107859393538431293073870928e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 1.0005779443214788507322676694872
y[1] (numeric) = 1.000577944321478852384735544565
absolute error = 1.6524678750778e-18
relative error = 1.6515133922908792127816275573293e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 1.0006124374765114241853983039858
y[1] (numeric) = 1.0006124374765114258864488703503
absolute error = 1.7010505663645e-18
relative error = 1.7000094168871759602469375195198e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 1.0006479300190232388330038722177
y[1] (numeric) = 1.0006479300190232405826354436003
absolute error = 1.7496315713826e-18
relative error = 1.7484986666082823878583567664127e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 1.0006844219135217551209815039716
y[1] (numeric) = 1.0006844219135217569191923455226
absolute error = 1.7982108415510e-18
relative error = 1.7969809484117259082301174627635e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=0.44
NO POLE
x[1] = 0.038
y[1] (analytic) = 1.0007219131235150815918060181131
y[1] (numeric) = 1.0007219131235150834385943464036
absolute error = 1.8467883282905e-18
relative error = 1.8454560693351763778375182492343e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 1.0007604036115120113764183391194
y[1] (numeric) = 1.0007604036115120132717823221429
absolute error = 1.8953639830235e-18
relative error = 1.8939238364982980100474488106273e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 1.0007998933390220596854292418709
y[1] (numeric) = 1.0007998933390220616293669990454
absolute error = 1.9439377571745e-18
relative error = 1.9423840571053987475396215943732e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 1.0008403822665555022996009335004
y[1] (numeric) = 1.00084038226655550429211053567
absolute error = 1.9925096021696e-18
relative error = 1.9908365384470783339134294132678e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 1.0008818703536234150595679818205
y[1] (numeric) = 1.0008818703536234171006474512575
absolute error = 2.0410794694370e-18
relative error = 2.0392810879028735503315639117806e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 1.0009243575587377143547581006123
y[1] (numeric) = 1.0009243575587377164444054110191
absolute error = 2.0896473104068e-18
relative error = 2.0877175129432018493678391796163e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 1.0009678438394111986114723028572
y[1] (numeric) = 1.0009678438394112007496853793684
absolute error = 2.1382130765112e-18
relative error = 2.1361456211317024734401878570621e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 1.001012329152157590780082933836
y[1] (numeric) = 1.0010123291521575929668596530206
absolute error = 2.1867767191846e-18
relative error = 2.1845652201274753921671646118860e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 1.0010578134524915818213070969007
y[1] (numeric) = 1.0010578134524915840566452867638
absolute error = 2.2353381898631e-18
relative error = 2.2329761176867185635149081263174e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 1.0011042966949288751915119856476
y[1] (numeric) = 1.0011042966949288774754094256329
absolute error = 2.2838974399853e-18
relative error = 2.2813781216656615646211925042762e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 1.0011517788329862323270076371929
y[1] (numeric) = 1.0011517788329862346594620581849
absolute error = 2.3324544209920e-18
relative error = 2.3297710400223978817996652150347e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 1.0012002598191815191272816222591
y[1] (numeric) = 1.0012002598191815215082907065854
absolute error = 2.3810090843263e-18
relative error = 2.3781546808191143664565735427898e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 1.0012497396050337534371291888435
y[1] (numeric) = 1.0012497396050337558666905702769
absolute error = 2.4295613814334e-18
relative error = 2.4265288522240185479992550313008e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 1.0013002181410631535276313773408
y[1] (numeric) = 1.0013002181410631560057426411019
absolute error = 2.4781112637611e-18
relative error = 2.4748933625139625582695888730663e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 1.0013516953767911875759326261474
y[1] (numeric) = 1.0013516953767911901025913089069
absolute error = 2.5266586827595e-18
relative error = 2.5232480200762653944145401110923e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 1.0014041712607406241437683879725
y[1] (numeric) = 1.0014041712607406267189719778537
absolute error = 2.5752035898812e-18
relative error = 2.5715926334110319296052648044776e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 1.0014576457404355836546922783338
y[1] (numeric) = 1.001457645740435586278438214915
absolute error = 2.6237459365812e-18
relative error = 2.6199270111331696053694992648674e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 1.0015121187624015908699512790137
y[1] (numeric) = 1.001512118762401593542236953331
absolute error = 2.6722856743173e-18
relative error = 2.6682509619749016574056641611207e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 1.0015675902721656283629565206066
y[1] (numeric) = 1.0015675902721656310837792751562
absolute error = 2.7208227545496e-18
relative error = 2.7165642947873788245492460387047e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 1.0016240602142561909922961696895
y[1] (numeric) = 1.0016240602142561937616532984307
absolute error = 2.7693571287412e-18
relative error = 2.7648668185434864322826714984863e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 1.0016815285322033413732359476087
y[1] (numeric) = 1.0016815285322033441911246959663
absolute error = 2.8178887483576e-18
relative error = 2.8131583423393505269820689696233e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 1.0017399951685387663476518093861
y[1] (numeric) = 1.0017399951685387692140693742533
absolute error = 2.8664175648672e-18
relative error = 2.8614386753969393581706208580082e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 1.0017994600647958344523383128172
y[1] (numeric) = 1.0017994600647958373672818425585
absolute error = 2.9149435297413e-18
relative error = 2.9097076270661625893588670760757e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.1MB, time=0.69
x[1] = 0.061
y[1] (analytic) = 1.0018599231615096543856352094576
y[1] (numeric) = 1.0018599231615096573491018039114
absolute error = 2.9634665944538e-18
relative error = 2.9579650068266680172040595295802e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 1.0019213843982171344723137908757
y[1] (numeric) = 1.0019213843982171374843005013574
absolute error = 3.0119867104817e-18
relative error = 3.0062106242904337687784473365934e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 1.0019838437134570431266635252906
y[1] (numeric) = 1.0019838437134570461871673545955
absolute error = 3.0605038293049e-18
relative error = 3.0544442892036585554300542357018e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 1.0020473010447700703137185215135
y[1] (numeric) = 1.0020473010447700734227364239198
absolute error = 3.1090179024063e-18
relative error = 3.1026658114489481903823420976132e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 1.0021117563286988900085623589714
y[1] (numeric) = 1.0021117563286988931660912402431
absolute error = 3.1575288812717e-18
relative error = 3.1508750010472992441374223117299e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 1.0021772095007882236536488245129
y[1] (numeric) = 1.0021772095007882268596855419032
absolute error = 3.2060367173903e-18
relative error = 3.1990716681606781400684386151655e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 1.0022436604955849046140750986816
y[1] (numeric) = 1.0022436604955849078686164609358
absolute error = 3.2545413622542e-18
relative error = 3.2472556230935989475569641072760e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 1.0023111092466379436307429361887
y[1] (numeric) = 1.0023111092466379469337857035474
absolute error = 3.3030427673587e-18
relative error = 3.2954266762954961333992207360567e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 1.0023795556864985952713423874285
y[1] (numeric) = 1.002379555686498598622883271631
absolute error = 3.3515408842025e-18
relative error = 3.3435846383629939884328200295394e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 1.0024489997467204253790916100603
y[1] (numeric) = 1.0024489997467204287791272743477
absolute error = 3.4000356642874e-18
relative error = 3.3917293200416737005168521973011e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 1.0025194413578593795191653219204
y[1] (numeric) = 1.0025194413578593829676923810391
absolute error = 3.4485270591187e-18
relative error = 3.4398605322285352512223556853121e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 1.0025908804494738524227434488436
y[1] (numeric) = 1.0025908804494738559197584690486
absolute error = 3.4970150202050e-18
relative error = 3.4879780859738571056333799783596e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 1.0026633169501247584286105233492
y[1] (numeric) = 1.0026633169501247619741100224075
absolute error = 3.5454994990583e-18
relative error = 3.5360817924833515512129771791641e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 1.0027367507873756029222353925998
y[1] (numeric) = 1.002736750787375606516215839794
absolute error = 3.5939804471942e-18
relative error = 3.5841714631204160346660196205819e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 1.0028111818877925547722597965581
y[1] (numeric) = 1.0028111818877925584147176126897
absolute error = 3.6424578161316e-18
relative error = 3.6322469094078820773869407858923e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 1.0028866101769445197643233798592
y[1] (numeric) = 1.0028866101769445234552549372525
absolute error = 3.6909315573933e-18
relative error = 3.6803079430306579508880026034915e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 1.0029630355794032150321517035803
y[1] (numeric) = 1.0029630355794032187715533260857
absolute error = 3.7394016225054e-18
relative error = 3.7283543758371707964897748991073e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 1.0030404580187432444858328258248
y[1] (numeric) = 1.0030404580187432482737007888229
absolute error = 3.7878679629981e-18
relative error = 3.7763860198422008951080779791445e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 1.0031188774175421752372070228519
y[1] (numeric) = 1.0031188774175421790735375532566
absolute error = 3.8363305304047e-18
relative error = 3.8244026872279172381598353073707e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 1.0031982936973806150222932253665
y[1] (numeric) = 1.0031982936973806189070825016294
absolute error = 3.8847892762629e-18
relative error = 3.8724041903472022595644135983094e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 1.0032787067788422906206747475516
y[1] (numeric) = 1.0032787067788422945539188996655
absolute error = 3.9332441521139e-18
relative error = 3.9203903417247791224663978793350e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 1.0033601165815141272717658894624
y[1] (numeric) = 1.0033601165815141312534609989652
absolute error = 3.9816951095028e-18
relative error = 3.9683609540596310119832004780790e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 1.0034425230239863290878799965224
y[1] (numeric) = 1.0034425230239863331180220965011
absolute error = 4.0301420999787e-18
relative error = 4.0163158402271171505210838182049e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 1.0035259260238524604640185630608
y[1] (numeric) = 1.0035259260238524645426036381554
absolute error = 4.0785850750946e-18
relative error = 4.0642548132808853039542902015182e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.93
NO POLE
x[1] = 0.085
y[1] (analytic) = 1.0036103254977095284842999701085
y[1] (numeric) = 1.003610325497709532611323956516
absolute error = 4.1270239864075e-18
relative error = 4.1121776864549794090956892800184e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 1.00369572136115806632494545103
y[1] (numeric) = 1.0036957213611580705004042365085
absolute error = 4.1754587854785e-18
relative error = 4.1600842731659428965071496065134e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 1.0037821135288022176537388820139
y[1] (numeric) = 1.0037821135288022218776283058867
absolute error = 4.2238894238728e-18
relative error = 4.2079743870148180378229470785932e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 1.0038695019142498220258759979679
y[1] (numeric) = 1.0038695019142498262981918511276
absolute error = 4.2723158531597e-18
relative error = 4.2558478417891409453977120269454e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 1.0039578864301125012761176379763
y[1] (numeric) = 1.0039578864301125055968556628892
absolute error = 4.3207380249129e-18
relative error = 4.3037044514652309963797900521872e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 1.0040472669880057469071606281749
y[1] (numeric) = 1.0040472669880057512763165188851
absolute error = 4.3691558907102e-18
relative error = 4.3515440302098780778245687262037e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 1.0041376434985490084741389136785
y[1] (numeric) = 1.0041376434985490128917083158122
absolute error = 4.4175694021337e-18
relative error = 4.3993663923825234457057829645061e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 1.0042290158713657829651665550681
y[1] (numeric) = 1.0042290158713657874311450658381
absolute error = 4.4659785107700e-18
relative error = 4.4471713525374359477314628147883e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 1.0043213840150837051778332089018
y[1] (numeric) = 1.0043213840150837096922163771117
absolute error = 4.5143831682099e-18
relative error = 4.4949587254253857127860921344015e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 1.0044147478373346390915617157617
y[1] (numeric) = 1.0044147478373346436543450418104
absolute error = 4.5627833260487e-18
relative error = 4.5427283259959107476756310098774e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 1.0045091072447547702357364234864
y[1] (numeric) = 1.0045091072447547748469153593727
absolute error = 4.6111789358863e-18
relative error = 4.5904799693993796014612981278123e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 1.0046044621429846990535098774693
y[1] (numeric) = 1.0046044621429847037130798267964
absolute error = 4.6595699493271e-18
relative error = 4.6382134709888501796289292115453e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 1.0047008124366695352611945142231
y[1] (numeric) = 1.0047008124366695399691508322031
absolute error = 4.7079563179800e-18
relative error = 4.6859286463220233923165613292625e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 1.0047981580294589932031449988264
y[1] (numeric) = 1.0047981580294589979594829922852
absolute error = 4.7563379934588e-18
relative error = 4.7336253111635900950091079578346e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 1.0048964988240074882020358513791
y[1] (numeric) = 1.0048964988240074930067507787609
absolute error = 4.8047149273818e-18
relative error = 4.7813032814867768528037296644333e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 1.0049958347219742339044380121961
y[1] (numeric) = 1.0049958347219742387575250835681
absolute error = 4.8530870713720e-18
relative error = 4.8289623734754840683814025794168e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.005096165624023340621597000171
y[1] (numeric) = 1.0050961656240233455230513772282
absolute error = 4.9014543770572e-18
relative error = 4.8766024035263195708922010048718e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.0051974914298239146653143235401
y[1] (numeric) = 1.0051974914298239196151311196103
absolute error = 4.9498167960702e-18
relative error = 4.9242231882507266550074960705896e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.0052998120380501586788328071734
y[1] (numeric) = 1.0052998120380501636770070872219
absolute error = 4.9981742800485e-18
relative error = 4.9718245444766096177876827897370e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.0054031273463814729626255055154
y[1] (numeric) = 1.0054031273463814780091522861501
absolute error = 5.0465267806347e-18
relative error = 5.0194062892506506558055426978071e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.0055074372515025577949868753959
y[1] (numeric) = 1.0055074372515025628898611248723
absolute error = 5.0948742494764e-18
relative error = 5.0669682398401241535663015244907e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.0056127416491035167473238881278
y[1] (numeric) = 1.0056127416491035218905405263537
absolute error = 5.1432166382259e-18
relative error = 5.1145102137345070032528797831376e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.0057190404338799609940437656082
y[1] (numeric) = 1.0057190404338799661855976641492
absolute error = 5.1915538985410e-18
relative error = 5.1620320286481776707340889779728e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.0058263334995331146169340305467
y[1] (numeric) = 1.005826333499533119856820012631
absolute error = 5.2398859820843e-18
relative error = 5.2095335025216182163567502254740e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=1.18
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.0059346207387699209039295664461
y[1] (numeric) = 1.00593462073876992619214240697
absolute error = 5.2882128405239e-18
relative error = 5.2570144535240032279426446436829e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.0060439020433031496421603885802
y[1] (numeric) = 1.006043902043303154978694814113
absolute error = 5.3365344255328e-18
relative error = 5.3044747000544908012279632525564e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.006154177303851505405172832928
y[1] (numeric) = 1.0061541773038515107900235217175
absolute error = 5.3848506887895e-18
relative error = 5.3519140607447012127681212559792e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.0062654464101397368342158758533
y[1] (numeric) = 1.006265446410139742267377457831
absolute error = 5.4331615819777e-18
relative error = 5.3993323544602954090318502791544e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.0063777092508987469134833032516
y[1] (numeric) = 1.006377709250898752394950360038
absolute error = 5.4814670567864e-18
relative error = 5.4467294003029457190482768676650e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.0064909657138657042392014539315
y[1] (numeric) = 1.0064909657138657097689685188419
absolute error = 5.5297670649104e-18
relative error = 5.4941050176126984432868512815493e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.0066052156857841552824512681535
y[1] (numeric) = 1.006605215685784160860512826203
absolute error = 5.5780615580495e-18
relative error = 5.5414590259690391161380058261190e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.006720459052404137645612378511
y[1] (numeric) = 1.0067204590524041432719628664203
absolute error = 5.6263504879093e-18
relative error = 5.5887912451935420677829735266697e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 1.006836695698482294312315986721
y[1] (numeric) = 1.0068366956984822999869497929217
absolute error = 5.6746338062007e-18
relative error = 5.6361014953512226692830291157337e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.00695392550778198889079227638
y[1] (numeric) = 1.0069539255077819946137037410205
absolute error = 5.7229114646405e-18
relative error = 5.6833895967529766835354811276700e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.0070721483630734218504971183478
y[1] (numeric) = 1.007072148363073427621680533299
absolute error = 5.7711834149512e-18
relative error = 5.7306553699572191379715388033321e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.0071913641461337477519018321424
y[1] (numeric) = 1.007191364146133753571351441003
absolute error = 5.8194496088606e-18
relative error = 5.7778986357713190422313195519583e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 1.0073115727377471934693287735644
y[1] (numeric) = 1.0073115727377471993370387716671
absolute error = 5.8677099981027e-18
relative error = 5.8251192152543191942223286363424e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.007432774017705177406714525728
y[1] (numeric) = 1.007432774017705183322679060145
absolute error = 5.9159645344170e-18
relative error = 5.8723169297180613532143124109338e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.0075549678648064297061814777427
y[1] (numeric) = 1.0075549678648064356703946472916
absolute error = 5.9642131695489e-18
relative error = 5.9194916007293978265877382590281e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.007678154156857113449297582485
y[1] (numeric) = 1.007678154156857119461753437735
absolute error = 6.0124558552500e-18
relative error = 5.9666430501122976554844240138183e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.0078023327706709468509030922118
y[1] (numeric) = 1.0078023327706709529115956354892
absolute error = 6.0606925432774e-18
relative error = 6.0137710999489544069220732173360e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 1.0079275035820693264453820781963
y[1] (numeric) = 1.0079275035820693325543052635909
absolute error = 6.1089231853946e-18
relative error = 6.0608755725824759420198585362060e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.0080536664658814512652555481279
y[1] (numeric) = 1.0080536664658814574224032814988
absolute error = 6.1571477333709e-18
relative error = 6.1079562906180795131021349172827e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.0081808212959444480119719826911
y[1] (numeric) = 1.0081808212959444542173381216728
absolute error = 6.2053661389817e-18
relative error = 6.1550130769251739737696420045352e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.0083089679451034972187701205446
y[1] (numeric) = 1.0083089679451035034723484745532
absolute error = 6.2535783540086e-18
relative error = 6.2020457546392373473552878878999e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.0084381062852119604054878288482
y[1] (numeric) = 1.0084381062852119667072721590876
absolute error = 6.3017843302394e-18
relative error = 6.2490541471635890522441532244981e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.0085682361871315082251899045384
y[1] (numeric) = 1.0085682361871315145751739240066
absolute error = 6.3499840194682e-18
relative error = 6.2960380781712551361657070174903e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.008699357520732249602486659737
y[1] (numeric) = 1.0086993575207322560006640332321
absolute error = 6.3981773734951e-18
relative error = 6.3429973716064307052599056002448e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.2MB, time=1.42
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.0088314701548928618634141529829
y[1] (numeric) = 1.00883147015489286830977849711
absolute error = 6.4463643441271e-18
relative error = 6.3899318516871258669002423172483e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.0089645739575007218567459364203
y[1] (numeric) = 1.0089645739575007283512908195972
absolute error = 6.4945448831769e-18
relative error = 6.4368413429057233783474218834531e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.0090986687954520380666051976395
y[1] (numeric) = 1.0090986687954520446093241401037
absolute error = 6.5427189424642e-18
relative error = 6.4837256700320084076340030975263e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.009233754534651983716245183572
y[1] (numeric) = 1.0092337545346519903071316573868
absolute error = 6.5908864738148e-18
relative error = 6.5305846581140110754881342693607e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 1.0093698310400148308628648026684
y[1] (numeric) = 1.0093698310400148375019122317296
absolute error = 6.6390474290612e-18
relative error = 6.5774181324803294283465259827352e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.0095068981754640854833253105562
y[1] (numeric) = 1.0095068981754640921705270705986
absolute error = 6.6872017600424e-18
relative error = 6.6242259187416530730165010153160e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.0096449558039326235506329934705
y[1] (numeric) = 1.0096449558039326302859824120748
absolute error = 6.7353494186043e-18
relative error = 6.6710078427928748113406613211533e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.0097840037873628281010517729886
y[1] (numeric) = 1.0097840037873628348845421295876
absolute error = 6.7834903565990e-18
relative error = 6.7177637308141061434417799041824e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.0099240419867067272917086649643
y[1] (numeric) = 1.00992404198670673412333319085
absolute error = 6.8316245258857e-18
relative error = 6.7644934092732711235157514777423e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 1.0100650702619261334485540350706
y[1] (numeric) = 1.0100650702619261403283059134008
absolute error = 6.8797518783302e-18
relative error = 6.8111967049273068941200577240674e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 1.0102070884719927831045376030009
y[1] (numeric) = 1.0102070884719927900324099688059
absolute error = 6.9278723658050e-18
relative error = 6.8578734448239520039863750163814e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.0103500964748884780278601571639
y[1] (numeric) = 1.0103500964748884850038460973538
absolute error = 6.9759859401899e-18
relative error = 6.9045234563040229219002538113355e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.010494094127605227240159951634
y[1] (numeric) = 1.0104940941276052342642525050051
absolute error = 7.0240925533711e-18
relative error = 6.9511465670021989883476020249364e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.0106390812861453900244917671803
y[1] (numeric) = 1.0106390812861453970966839244224
absolute error = 7.0721921572421e-18
relative error = 6.9977426048495825118841938372796e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.0107850578055218199229556284092
y[1] (numeric) = 1.0107850578055218270432403321124
absolute error = 7.1202847037032e-18
relative error = 7.0443113980748663387875091187441e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.0109320235397580097238311794022
y[1] (numeric) = 1.0109320235397580168922013240642
absolute error = 7.1683701446620e-18
relative error = 7.0908527752064843026639815342552e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.0110799783418882374380727307282
y[1] (numeric) = 1.0110799783418882446545211627612
absolute error = 7.2164484320330e-18
relative error = 7.1373665650738643398568664809413e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.0112289220639577132650190013457
y[1] (numeric) = 1.0112289220639577205295385190836
absolute error = 7.2645195177379e-18
relative error = 7.1838525968093673802924559987601e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.0113788545570227275471705896988
y[1] (numeric) = 1.0113788545570227348597539434045
absolute error = 7.3125833537057e-18
relative error = 7.2303106998500213975761542081552e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.0115297756711507997138872192414
y[1] (numeric) = 1.0115297756711508070745271111139
absolute error = 7.3606398918725e-18
relative error = 7.2767407039389519277776848241306e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.0116816852554208282138558147042
y[1] (numeric) = 1.0116816852554208356225448988859
absolute error = 7.4086890841817e-18
relative error = 7.3231424391272012530997771953301e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.0118345831579232414361794766499
y[1] (numeric) = 1.0118345831579232488929103592341
absolute error = 7.4567308825842e-18
relative error = 7.3695157357755404839640626134360e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.0119884692257601496199364332395
y[1] (numeric) = 1.0119884692257601571247016722778
absolute error = 7.5047652390383e-18
relative error = 7.4158604245559780592635162461508e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=26.7MB, alloc=4.2MB, time=1.67
x[1] = 0.156
y[1] (analytic) = 1.0121433433050454977520570596639
y[1] (numeric) = 1.0121433433050455053048491651733
absolute error = 7.5527921055094e-18
relative error = 7.4621763364530637486325428090468e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.0122992052409052194533660673757
y[1] (numeric) = 1.0122992052409052270541775013464
absolute error = 7.6008114339707e-18
relative error = 7.5084633027661737621235898574411e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.0124560548774773918526359770927
y[1] (numeric) = 1.0124560548774773995014591534958
absolute error = 7.6488231764031e-18
relative error = 7.5547211551109980173413710365212e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 1.0126138920579123914484970015328
y[1] (numeric) = 1.0126138920579123991453242863275
absolute error = 7.6968272847947e-18
relative error = 7.6009497254206254007436577234661e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.0127727166243730509590474759817
y[1] (numeric) = 1.012772716624373058703871187123
absolute error = 7.7448237111413e-18
relative error = 7.6471488459476097734032281596417e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.0129325284180348171590079870976
y[1] (numeric) = 1.0129325284180348249518203945443
absolute error = 7.7928124074467e-18
relative error = 7.6933183492658309325402740121549e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.0130933272790859097042613628125
y[1] (numeric) = 1.0130933272790859175450546885345
absolute error = 7.8407933257220e-18
relative error = 7.7394580682713610494430804362193e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.0132551130467274809436196988004
y[1] (numeric) = 1.0132551130467274888323861167868
absolute error = 7.8887664179864e-18
relative error = 7.7855678361848049488198497488158e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 1.0134178855591737767176586097624
y[1] (numeric) = 1.0134178855591737846543902460292
absolute error = 7.9367316362668e-18
relative error = 7.8316474865524482992749915945101e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.0135816446536522981444579067051
y[1] (numeric) = 1.013581644653652306129146839303
absolute error = 7.9846889325979e-18
relative error = 7.8776968532478922317471949817439e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.0137463901664039643920869144861
y[1] (numeric) = 1.0137463901664039724247251735087
absolute error = 8.0326382590226e-18
relative error = 7.9237157704739765170231884929469e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.0139121219326832764376716571557
y[1] (numeric) = 1.013912121932683284518251224747
absolute error = 8.0805795675913e-18
relative error = 7.9697040727636101444497674846524e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.014078839786758481812880152039
y[1] (numeric) = 1.0140788397867584899413929624019
absolute error = 8.1285128103629e-18
relative error = 8.0156615949822716424969582908310e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 1.0142465435619117403356610670895
y[1] (numeric) = 1.0142465435619117485120990064937
absolute error = 8.1764379394042e-18
relative error = 8.0615881723289235408488579215938e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.0144152330904392908280700097875
y[1] (numeric) = 1.0144152330904392990524249165774
absolute error = 8.2243549067899e-18
relative error = 8.1074836403375115022229718843012e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.0145849082036516188200167297711
y[1] (numeric) = 1.0145849082036516270922803943742
absolute error = 8.2722636646031e-18
relative error = 8.1533478348789488544454315926107e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.0147555687318736252387655314679
y[1] (numeric) = 1.014755568731873633558929696403
absolute error = 8.3201641649351e-18
relative error = 8.1991805921624033661146400805366e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.0149272145044447960840202072392
y[1] (numeric) = 1.0149272145044448044520765671246
absolute error = 8.3680563598854e-18
relative error = 8.2449817487367738107000940090576e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.0150998453497193730884238159675
y[1] (numeric) = 1.0150998453497193815043640175293
absolute error = 8.4159402015618e-18
relative error = 8.2907511414922575506502944563689e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.0152734610950665253633026466005
y[1] (numeric) = 1.0152734610950665338271182886809
absolute error = 8.4638156420804e-18
relative error = 8.3364886076618120074536596034688e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 1.0154480615668705220294827209227
y[1] (numeric) = 1.0154480615668705305411653544886
absolute error = 8.5116826335659e-18
relative error = 8.3821939848229040245033767730041e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.0156236465905309058330062047525
y[1] (numeric) = 1.0156236465905309143925473329037
absolute error = 8.5595411281512e-18
relative error = 8.4278671108985621242230029265938e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.0158002159904626677455741118622
y[1] (numeric) = 1.01580021599046267635296518984
absolute error = 8.6073910779778e-18
relative error = 8.4735078241592091367299765884266e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.0159777695900964225495407001936
y[1] (numeric) = 1.0159777695900964312047731353893
absolute error = 8.6552324351957e-18
relative error = 8.5191159632239946648053439959577e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.3MB, time=1.91
x[1] = 0.18
y[1] (analytic) = 1.0161563072118785854072839753885
y[1] (numeric) = 1.0161563072118785941103491273522
absolute error = 8.7030651519637e-18
relative error = 8.5646913670625136499761128317704e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.0163358286772715494147757322793
y[1] (numeric) = 1.0163358286772715581656649127284
absolute error = 8.7508891804491e-18
relative error = 8.6102338749959266049390126970759e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.016516333806753864139173580784
y[1] (numeric) = 1.0165163338067538729378780536117
absolute error = 8.7987044728277e-18
relative error = 8.6557433266983675944429972947291e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.0166978224198204151402564186277
y[1] (numeric) = 1.0166978224198204239867673999121
absolute error = 8.8465109812844e-18
relative error = 8.7012195621989346517662974283919e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.0168802943349826044755238294719
y[1] (numeric) = 1.0168802943349826133698324874844
absolute error = 8.8943086580125e-18
relative error = 8.7466624218823934073105785494897e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.0170637493697685321887789013652
y[1] (numeric) = 1.0170637493697685411308763565796
absolute error = 8.9420974552144e-18
relative error = 8.7920717464912502111030373707372e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.0172481873407231787820129769491
y[1] (numeric) = 1.0172481873407231877718903020505
absolute error = 8.9898773251014e-18
relative error = 8.8374473771269319916188247680875e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.0174336080634085886704098635492
y[1] (numeric) = 1.0174336080634085977080580834427
absolute error = 9.0376482198935e-18
relative error = 8.8827891552509585236825737614701e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.0176200113524040546202860481617
y[1] (numeric) = 1.0176200113524040637056961399817
absolute error = 9.0854100918200e-18
relative error = 8.9280969226868932360276082396935e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.0178073970213063031697824794125
y[1] (numeric) = 1.0178073970213063123029453725313
absolute error = 9.1331628931188e-18
relative error = 8.9733705216210082694177488383870e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.0179957648827296810321224958101
y[1] (numeric) = 1.0179957648827296902130290718473
absolute error = 9.1809065760372e-18
relative error = 9.0186097946044159105711840336598e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 1.0181851147483063424812494970519
y[1] (numeric) = 1.0181851147483063517098905898835
absolute error = 9.2286410928316e-18
relative error = 9.0638145845541109131792977198331e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.0183754464286864377196569727608
y[1] (numeric) = 1.0183754464286864469960233685282
absolute error = 9.2763663957674e-18
relative error = 9.1089847347542016275355944259232e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 1.0185667597335383022282225208382
y[1] (numeric) = 1.0185667597335383115523049579576
absolute error = 9.3240824371194e-18
relative error = 9.1541200888576241978323905457759e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.0187590544715486470978565056148
y[1] (numeric) = 1.0187590544715486564696456747862
absolute error = 9.3717891691714e-18
relative error = 9.1992204908870630985992945044625e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 1.0189523304504227503427750241667
y[1] (numeric) = 1.0189523304504227597622615683834
absolute error = 9.4194865442167e-18
relative error = 9.2442857852367474066809823660632e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.0191465874768846491952058675394
y[1] (numeric) = 1.0191465874768846586623803820975
absolute error = 9.4671745145581e-18
relative error = 9.2893158166737479203294063748437e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.019341825356677333381335182191
y[1] (numeric) = 1.0193418253566773428961882146984
absolute error = 9.5148530325074e-18
relative error = 9.3343104303387757553784101898360e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.0195380438945629393783015557216
y[1] (numeric) = 1.0195380438945629489408236061079
absolute error = 9.5625220503863e-18
relative error = 9.3792694717483466501030107413054e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.0197352428943229456520432699139
y[1] (numeric) = 1.0197352428943229552622247904396
absolute error = 9.6101815205257e-18
relative error = 9.4241927867953671709233999763464e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.0199334221587583688758034832518
y[1] (numeric) = 1.0199334221587583785336348785179
absolute error = 9.6578313952661e-18
relative error = 9.4690802217507921504710850568479e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.020132581489689961129097124429
y[1] (numeric) = 1.0201325814896899708345687513867
absolute error = 9.7054716269577e-18
relative error = 9.5139316232649795087943419749428e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.0203327206879584080769422978976
y[1] (numeric) = 1.0203327206879584178300444658577
absolute error = 9.7531021679601e-18
relative error = 9.5587468383686448297623953870986e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.0205338395534245281291580222406
y[1] (numeric) = 1.0205338395534245379298809928836
absolute error = 9.8007229706430e-18
relative error = 9.6035257144747880457989940988477e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.3MB, time=2.16
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.020735937884969472579529142089
y[1] (numeric) = 1.0207359378849694824278631294744
absolute error = 9.8483339873854e-18
relative error = 9.6482680993791416484502053475560e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 1.0209390154804949267246382744327
y[1] (numeric) = 1.0209390154804949366205734450091
absolute error = 9.8959351705764e-18
relative error = 9.6929738412621788622691569706754e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.0211430721369233119621636705127
y[1] (numeric) = 1.0211430721369233219056901431275
absolute error = 9.9435264726148e-18
relative error = 9.7376427886899375630960499419323e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.0213481076501979888684408950116
y[1] (numeric) = 1.021348107650197998859548740921
absolute error = 9.9911078459094e-18
relative error = 9.7822747906155218483048884118121e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.0215541218152834612550852449989
y[1] (numeric) = 1.0215541218152834712937644878776
absolute error = 1.00386792428787e-17
relative error = 9.8268696963800077124182035157584e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 1.0217611144261655812044708520248
y[1] (numeric) = 1.021761114426165591290711467976
absolute error = 1.00862406159512e-17
relative error = 9.8714273557139280832275449136885e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.0219690852758517550838614319006
y[1] (numeric) = 1.0219690852758517652176533494665
absolute error = 1.01337919175659e-17
relative error = 9.9159476187389449711692850052267e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.0221780341563711505379866680538
y[1] (numeric) = 1.0221780341563711607193197682249
absolute error = 1.01813331001711e-17
relative error = 9.9604303359678496559350269284352e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.022387960858774904459857235895
y[1] (numeric) = 1.0223879608587749146887213521208
absolute error = 1.02288641162258e-17
relative error = 1.0004875358307099117283267914551e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.0225988651731363319396104974034
y[1] (numeric) = 1.0225988651731363422159954156025
absolute error = 1.02763849181991e-17
relative error = 1.0049282537057386703542939260458e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.0228107468885511361911779170994
y[1] (numeric) = 1.0228107468885511465150733756695
absolute error = 1.03238954585701e-17
relative error = 1.0093651723914694080069390369464e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.0230236057931376194565642727558
y[1] (numeric) = 1.0230236057931376298279599625839
absolute error = 1.03713956898281e-17
relative error = 1.0137982770971628244042227869148e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.0232374416740368948875277565849
y[1] (numeric) = 1.023237441674036905306413321058
absolute error = 1.04188855644731e-17
relative error = 1.0182275530719043165255797553963e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.0234522543174130994044490852411
y[1] (numeric) = 1.0234522543174131098708141202562
absolute error = 1.04663650350151e-17
relative error = 1.0226529856046479977990406826224e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 1.023668043508453607532176759785
y[1] (numeric) = 1.0236680435084536180460108137596
absolute error = 1.05138340539746e-17
relative error = 1.0270745600243771942689063667821e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.0238848090313692462126346397834
y[1] (numeric) = 1.0238848090313692567739272136662
absolute error = 1.05612925738828e-17
relative error = 1.0314922617002347431802730970857e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.0241025506693945105939770189553
y[1] (numeric) = 1.0241025506693945212027175662363
absolute error = 1.06087405472810e-17
relative error = 1.0359060760415743122666994830223e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 1.0243212682047877807960754132258
y[1] (numeric) = 1.0243212682047877914522533399471
absolute error = 1.06561779267213e-17
relative error = 1.0403159884981378687812140900401e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.0245409614188315396521202957203
y[1] (numeric) = 1.0245409614188315503557249604866
absolute error = 1.07036046647663e-17
relative error = 1.0447219845601346169099237905780e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.024761630091832591426120037115
y[1] (numeric) = 1.0247616300918326021771407511042
absolute error = 1.07510207139892e-17
relative error = 1.0491240497583581654820782729116e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.0249832740031222815060783338625
y[1] (numeric) = 1.0249832740031222923045043608366
absolute error = 1.07984260269741e-17
relative error = 1.0535221696643223538235157246340e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.0252058929310567170726304311345
y[1] (numeric) = 1.0252058929310567279184509874502
absolute error = 1.08458205563157e-17
relative error = 1.0579163298903376717569394520885e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 1.0254294866530169887429174718627
y[1] (numeric) = 1.025429486653016999636121726482
absolute error = 1.08932042546193e-17
relative error = 1.0623065160896161296274439934312e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.0256540549454093931894773280223
y[1] (numeric) = 1.0256540549454094041300544025236
absolute error = 1.09405770745013e-17
relative error = 1.0666927139564240327946097519581e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=2.41
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.0258795975836656567339292952864
y[1] (numeric) = 1.0258795975836656677218682638753
absolute error = 1.09879389685889e-17
relative error = 1.0710749092261558640738636621016e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.0261061143422431599152290573844
y[1] (numeric) = 1.0261061143422431709505189469045
absolute error = 1.10352898895201e-17
relative error = 1.0754530876754365942052740732433e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.0263336049946251630322693519284
y[1] (numeric) = 1.0263336049946251741148991418726
absolute error = 1.10826297899442e-17
relative error = 1.0798272351222718614403136115307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.0265620693133210326606007951267
y[1] (numeric) = 1.0265620693133210437905594176479
absolute error = 1.11299586225212e-17
relative error = 1.0841973374260900834334096247966e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.0267915070698664691430463486806
y[1] (numeric) = 1.0267915070698664803203226886028
absolute error = 1.11772763399222e-17
relative error = 1.0885633804878811879059428441720e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.0270219180348237350539819382704
y[1] (numeric) = 1.0270219180348237462785648331
absolute error = 1.12245828948296e-17
relative error = 1.0929253502503149666656896207963e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.027253301977781884637054759369
y[1] (numeric) = 1.0272533019777818959089329993057
absolute error = 1.12718782399367e-17
relative error = 1.0972832326978001434060177017227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.0274856586673569942161098326828
y[1] (numeric) = 1.027485658667357005535272160631
absolute error = 1.13191623279482e-17
relative error = 1.1016370138566302340693385223682e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.0277189878711923935790943983139
y[1] (numeric) = 1.0277189878711924049455295098941
absolute error = 1.13664351115802e-17
relative error = 1.1059866797950798365105314111757e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.0279532893559588983347087647578
y[1] (numeric) = 1.0279532893559589097484053083175
absolute error = 1.14136965435597e-17
relative error = 1.1103322166234514255104261113191e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.0281885628873550432415712561047
y[1] (numeric) = 1.0281885628873550547025178327301
absolute error = 1.14609465766254e-17
relative error = 1.1146736104942477955319234449033e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.0284248082301073165096639283
y[1] (numeric) = 1.0284248082301073280178490918271
absolute error = 1.15081851635271e-17
relative error = 1.1190108476022074106880661251532e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.0286620251479703950738247530366
y[1] (numeric) = 1.0286620251479704066292370100631
absolute error = 1.15554122570265e-17
relative error = 1.1233439141844750779191508822471e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 1.0289002134037273808390509958078
y[1] (numeric) = 1.0289002134037273924416788057041
absolute error = 1.16026278098963e-17
relative error = 1.1276727965206064306814245618820e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.0291393727591900378973775428355
y[1] (numeric) = 1.0291393727591900495472093177564
absolute error = 1.16498317749209e-17
relative error = 1.1319974809327271462615337248835e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.0293795029751990307160929600163
y[1] (numeric) = 1.0293795029751990424131170649128
absolute error = 1.16970241048965e-17
relative error = 1.1363179537856329228546816921657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.0296206038116241632970550956892
y[1] (numeric) = 1.0296206038116241750412598483199
absolute error = 1.17442047526307e-17
relative error = 1.1406342014868400225575506566546e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.0298626750273646193068670679285
y[1] (numeric) = 1.0298626750273646310982407388714
absolute error = 1.17913736709429e-17
relative error = 1.1449462104867126899449880695300e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.0301057163803492031776735062069
y[1] (numeric) = 1.0301057163803492150162043188711
absolute error = 1.18385308126642e-17
relative error = 1.1492539672785411175184924661272e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 1.0303497276275365821783359466519
y[1] (numeric) = 1.0303497276275365940640120772892
absolute error = 1.18856761306373e-17
relative error = 1.1535574583986185645975358724871e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.0305947085249155294557453097401
y[1] (numeric) = 1.0305947085249155413885548874572
absolute error = 1.19328095777171e-17
relative error = 1.1578566704263855513696926783043e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.0308406588275051680460284191387
y[1] (numeric) = 1.0308406588275051800259595259087
absolute error = 1.19799311067700e-17
relative error = 1.1621515899844469980490050374069e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.0310875782893552158554045505058
y[1] (numeric) = 1.0310875782893552278824452211804
absolute error = 1.20270406706746e-17
relative error = 1.1664422037387243786136735269837e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.0313354666635462316104470294153
y[1] (numeric) = 1.0313354666635462436845852517365
absolute error = 1.20741382223212e-17
relative error = 1.1707284983984905612164066875177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=2.65
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.0315843237021898617775039281638
y[1] (numeric) = 1.0315843237021898738987276427762
absolute error = 1.21212237146124e-17
relative error = 1.1750104607165104883067831295166e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.0318341491564290884510309420608
y[1] (numeric) = 1.0318341491564291006193280425234
absolute error = 1.21682971004626e-17
relative error = 1.1792880774890743037592714564710e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.0320849427764384782105885568886
y[1] (numeric) = 1.032084942776438490425946889687
absolute error = 1.22153583327984e-17
relative error = 1.1835613355561168896037598085624e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.0323367043114244319462546505563
y[1] (numeric) = 1.0323367043114244442086620151151
absolute error = 1.22624073645588e-17
relative error = 1.1878302218013171097391604053614e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.0325894335096254356522027035565
y[1] (numeric) = 1.0325894335096254479616468522511
absolute error = 1.23094441486946e-17
relative error = 1.1920947231521186866289668314084e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.032843130118312312188194824666
y[1] (numeric) = 1.0328431301183123245446634628349
absolute error = 1.23564686381689e-17
relative error = 1.1963548265798568019422565189612e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.0330977938837884740087378304194
y[1] (numeric) = 1.0330977938837884864122186163768
absolute error = 1.24034807859574e-17
relative error = 1.2006105190998644031038911090368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.0333534245513901768596496492213
y[1] (numeric) = 1.0333534245513901893101301942692
absolute error = 1.24504805450479e-17
relative error = 1.2048617877715001849640543234032e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.0336100218654867744417823535499
y[1] (numeric) = 1.0336100218654867869392502219905
absolute error = 1.24974678684406e-17
relative error = 1.2091086196982531778178291791034e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.0338675855694809740416471565521
y[1] (numeric) = 1.0338675855694809865860898657003
absolute error = 1.25444427091482e-17
relative error = 1.2133510020278270833984841862593e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.0341261154058090931286857424248
y[1] (numeric) = 1.0341261154058091057200907626208
absolute error = 1.25914050201960e-17
relative error = 1.2175889219522237321886353904889e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.0343856111159413169189313333344
y[1] (numeric) = 1.0343856111159413295572860879559
absolute error = 1.26383547546215e-17
relative error = 1.2218223667077773240243718481899e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.0346460724403819569048019292326
y[1] (numeric) = 1.0346460724403819695900937947076
absolute error = 1.26852918654750e-17
relative error = 1.2260513235752845141601172477931e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.0349074991186697103507671907983
y[1] (numeric) = 1.0349074991186697230829834966178
absolute error = 1.27322163058195e-17
relative error = 1.2302757798800659087214405860783e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.0351698908893779207546294698607
y[1] (numeric) = 1.0351698908893779335337574985911
absolute error = 1.27791280287304e-17
relative error = 1.2344957229920073899221367788621e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.0354332474901148392741585260421
y[1] (numeric) = 1.0354332474901148521001855133383
absolute error = 1.28260269872962e-17
relative error = 1.2387111403256971992441356185331e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.0356975686575238871188185030108
y[1] (numeric) = 1.0356975686575238999917316376286
absolute error = 1.28729131346178e-17
relative error = 1.2429220193404268788026266840797e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.0359628541272839189063247726353
y[1] (numeric) = 1.0359628541272839318261111964443
absolute error = 1.29197864238090e-17
relative error = 1.2471283475403072864868383684542e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.0362291036341094869837672905078
y[1] (numeric) = 1.0362291036341094999504140985045
absolute error = 1.29666468079967e-17
relative error = 1.2513301124743547222409435692315e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.0364963169117511067130361417346
y[1] (numeric) = 1.036496316911751119726530382055
absolute error = 1.30134942403204e-17
relative error = 1.2555273017365086255967997062914e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.0367644936929955227202839915894
y[1] (numeric) = 1.036764493692995535780612665522
absolute error = 1.30603286739326e-17
relative error = 1.2597199029657352929457575883229e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 1.0370336337096659761091591915901
y[1] (numeric) = 1.0370336337096659892163092535892
absolute error = 1.31071500619991e-17
relative error = 1.2639079038461210290418432370001e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.0373037366926224726375423277883
y[1] (numeric) = 1.0373037366926224857915006854866
absolute error = 1.31539583576983e-17
relative error = 1.2680912921068679865728403515018e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.0375748023717620518575180345561
y[1] (numeric) = 1.0375748023717620650582715487781
absolute error = 1.32007535142220e-17
relative error = 1.2722700555224338164315806220354e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=2.90
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.0378468304760190572183129339225
y[1] (numeric) = 1.0378468304760190704658484186975
absolute error = 1.32475354847750e-17
relative error = 1.2764441819125547109241399096467e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 1.0381198207333654071319295975428
y[1] (numeric) = 1.0381198207333654204262338201182
absolute error = 1.32943042225754e-17
relative error = 1.2806136591423350750440072727843e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.0383937728708108670012054656899
y[1] (numeric) = 1.0383937728708108803422651465443
absolute error = 1.33410596808544e-17
relative error = 1.2847784751222881392380631285945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 1.0386686866144033222100246952314
y[1] (numeric) = 1.038668686614403335597826508088
absolute error = 1.33878018128566e-17
relative error = 1.2889386178084238799259488489212e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.0389445616892290520754099464035
y[1] (numeric) = 1.0389445616892290655099405182433
absolute error = 1.34345305718398e-17
relative error = 1.2930940752022879075488978303081e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.0392213978194130047612201563121
y[1] (numeric) = 1.0392213978194130182424660673874
absolute error = 1.34812459110753e-17
relative error = 1.2972448353510476377864877085795e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.0394991947281190731531793854871
y[1] (numeric) = 1.0394991947281190866811271693349
absolute error = 1.35279477838478e-17
relative error = 1.3013908863475390766129206209429e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.0397779521375503716949608624835
y[1] (numeric) = 1.0397779521375503852695970059389
absolute error = 1.35746361434554e-17
relative error = 1.3055322163303223786611106206690e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.0400576697689495141850493904688
y[1] (numeric) = 1.0400576697689495278063603336784
absolute error = 1.36213109432096e-17
relative error = 1.3096688134837365466590975349957e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.040338347342598892534104318956
y[1] (numeric) = 1.0403383473425989062020764553919
absolute error = 1.36679721364359e-17
relative error = 1.3138006660380109460723442985934e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.0406199845778209564825443233454
y[1] (numeric) = 1.0406199845778209701971639998182
absolute error = 1.37146196764728e-17
relative error = 1.3179277622692221138727418370657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.0409025811929784942780742747098
y[1] (numeric) = 1.0409025811929785080393277913828
absolute error = 1.37612535166730e-17
relative error = 1.3220500904994612211219237486844e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 1.0411861369054749143128735223236
y[1] (numeric) = 1.0411861369054749281207471327261
absolute error = 1.38078736104025e-17
relative error = 1.3261676390967987981587187885165e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.0414706514317545277201639517677
y[1] (numeric) = 1.0414706514317545415746438628091
absolute error = 1.38544799110414e-17
relative error = 1.3302803964754119755645097367945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.0417561244873028319298752220681
y[1] (numeric) = 1.0417561244873028458309475940514
absolute error = 1.39010723719833e-17
relative error = 1.3343883510955763554665592981956e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 1.0420425557866467951831236262249
y[1] (numeric) = 1.0420425557866468091307745728605
absolute error = 1.39476509466356e-17
relative error = 1.3384914914637434916083315887576e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.0423299450433551420052200606774
y[1] (numeric) = 1.0423299450433551559994356490973
absolute error = 1.39942155884199e-17
relative error = 1.3425898061326270620579351029185e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.0426182919700386396369216307212
y[1] (numeric) = 1.0426182919700386536776878814928
absolute error = 1.40407662507716e-17
relative error = 1.3466832837012113951650348540287e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 1.0429075962783503854236404606493
y[1] (numeric) = 1.0429075962783503995109433477892
absolute error = 1.40873028871399e-17
relative error = 1.3507719128147975608843614462022e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.043197857678986095162322319432
y[1] (numeric) = 1.0431978576789861092961477704202
absolute error = 1.41338254509882e-17
relative error = 1.3548556821650869542173945884513e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.0434890758816843924057067150814
y[1] (numeric) = 1.0434890758816844065860406108755
absolute error = 1.41803338957941e-17
relative error = 1.3589345804902256308542295644602e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.0437812505952270987236791534653
y[1] (numeric) = 1.0437812505952271129505073285142
absolute error = 1.42268281750489e-17
relative error = 1.3630085965747998898479429615160e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.0440743815274395249214253002402
y[1] (numeric) = 1.0440743815274395391947335424988
absolute error = 1.42733082422586e-17
relative error = 1.3670777192499747556090332609914e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 1.0443684683851907632140958277764
y[1] (numeric) = 1.0443684683851907775338698787193
absolute error = 1.43197740509429e-17
relative error = 1.3711419373934399469637825828625e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=3.15
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.044663510874393980357689772432
y[1] (numeric) = 1.044663510874393994723915327068
absolute error = 1.43662255546360e-17
relative error = 1.3752012399295274648055718362085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.0449595087000067117358632713184
y[1] (numeric) = 1.0449595087000067261485259782051
absolute error = 1.44126627068867e-17
relative error = 1.3792556158292612154691603318577e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.0452564615660311564023695917739
y[1] (numeric) = 1.0452564615660311708614550530314
absolute error = 1.44590854612575e-17
relative error = 1.3833050541103101017470761481076e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 1.0455543691755144730788354111266
y[1] (numeric) = 1.0455543691755144875843291824524
absolute error = 1.45054937713258e-17
relative error = 1.3873495438371412666702380553958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.0458532312305490771075773489994
y[1] (numeric) = 1.0458532312305490916594649396827
absolute error = 1.45518875906833e-17
relative error = 1.3913890741210001894269970199959e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.0461530474322729383591617993617
y[1] (numeric) = 1.0461530474322729529574286722978
absolute error = 1.45982668729361e-17
relative error = 1.3954236341199569487304148740260e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.0464538174808698800944101547946
y[1] (numeric) = 1.0464538174808698947390417264996
absolute error = 1.46446315717050e-17
relative error = 1.3994532130389707405962026417600e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.0467555410755698787805505609892
y[1] (numeric) = 1.0467555410755698934715322016146
absolute error = 1.46909816406254e-17
relative error = 1.4034778001299152929661812346049e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.0470582179146493648612163853508
y[1] (numeric) = 1.0470582179146493795985334186978
absolute error = 1.47373170333470e-17
relative error = 1.4074973846915843563338553335589e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.0473618476954315244799906297348
y[1] (numeric) = 1.0473618476954315392636283332695
absolute error = 1.47836377035347e-17
relative error = 1.4115119560698109796323693919798e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.0476664301142866021571945637978
y[1] (numeric) = 1.0476664301142866169871381686653
absolute error = 1.48299436048675e-17
relative error = 1.4155215036573948991250521213064e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 1.0479719648666322044196179021966
y[1] (numeric) = 1.0479719648666322192958525932363
absolute error = 1.48762346910397e-17
relative error = 1.4195260168942487460933043099293e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.0482784516469336043828868959338
y[1] (numeric) = 1.048278451646933619305397811694
absolute error = 1.49225109157602e-17
relative error = 1.4235254852673619701117822203200e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.0485858901487040472861657555049
y[1] (numeric) = 1.0485858901487040622549379882577
absolute error = 1.49687722327528e-17
relative error = 1.4275198983108594123268618759886e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.0488942800645050569788858711721
y[1] (numeric) = 1.0488942800645050719939044669283
absolute error = 1.50150185957562e-17
relative error = 1.4315092456060303947375717221699e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.0492036210859467433591963436608
y[1] (numeric) = 1.0492036210859467584204463021848
absolute error = 1.50612499585240e-17
relative error = 1.4354935167813569784843532311850e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.0495139129036881107638283868539
y[1] (numeric) = 1.0495139129036881258712946616787
absolute error = 1.51074662748248e-17
relative error = 1.4394727015125509206913863240767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.0498251552074373673090652126448
y[1] (numeric) = 1.0498251552074373824627327110872
absolute error = 1.51536674984424e-17
relative error = 1.4434467895225993114355405428388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.0501373476859522351825080570062
y[1] (numeric) = 1.0501373476859522503823616401816
absolute error = 1.51998535831754e-17
relative error = 1.4474157705817522142949123953204e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.0504504900270402618853280555329
y[1] (numeric) = 1.0504504900270402771313525383708
absolute error = 1.52460244828379e-17
relative error = 1.4513796345076142661306030654504e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.0507645819175591324246927262339
y[1] (numeric) = 1.0507645819175591477168728774929
absolute error = 1.52921801512590e-17
relative error = 1.4553383711651211307524706203901e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.0510796230434169824560548671731
y[1] (numeric) = 1.051079623043416997794375409456
absolute error = 1.53383205422829e-17
relative error = 1.4592919704665722989855651431798e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.0513956130895727123749907266948
y[1] (numeric) = 1.0513956130895727277594363364641
absolute error = 1.53844456097693e-17
relative error = 1.4632404223716915837192489060769e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.3MB, time=3.39
x[1] = 0.323
y[1] (analytic) = 1.051712551740036302358273354424
y[1] (numeric) = 1.0517125517400363177888286620171
absolute error = 1.54305553075931e-17
relative error = 1.4671837168876201680645511184351e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.0520304386778691283538660919921
y[1] (numeric) = 1.0520304386778691438305156816367
absolute error = 1.54766495896446e-17
relative error = 1.4711218440689564134632427872118e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.0523492735851842790195202135225
y[1] (numeric) = 1.0523492735851842945422486233521
absolute error = 1.55227284098296e-17
relative error = 1.4750547940177853136108123709810e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.0526690561431468736096597773046
y[1] (numeric) = 1.0526690561431468891784514993737
absolute error = 1.55687917220691e-17
relative error = 1.4789825568836691166676433252307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.0529897860319743808102358017967
y[1] (numeric) = 1.0529897860319743964250752820967
absolute error = 1.56148394803000e-17
relative error = 1.4829051228637321529499674735795e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 1.0533114629309369385212309311322
y[1] (numeric) = 1.0533114629309369541821025696066
absolute error = 1.56608716384744e-17
relative error = 1.4868224822026118142572374240488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.0536340865183576745864948076487
y[1] (numeric) = 1.053634086518357690293382958209
absolute error = 1.57068881505603e-17
relative error = 1.4907346251925417172386582755701e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.0539576564716130284705894216338
y[1] (numeric) = 1.0539576564716130442234783921749
absolute error = 1.57528889705411e-17
relative error = 1.4946415421733200786367154754268e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.0542821724671330738823227614669
y[1] (numeric) = 1.0542821724671330896811968138829
absolute error = 1.57988740524160e-17
relative error = 1.4985432235323627360416018540031e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.0546076341804018423446481406519
y[1] (numeric) = 1.0546076341804018581894914908518
absolute error = 1.58448433501999e-17
relative error = 1.5024396597047078813176924973591e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.0549340412859576477106056318672
y[1] (numeric) = 1.0549340412859576636014024497906
absolute error = 1.58907968179234e-17
relative error = 1.5063308411730294861005652097449e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.0552613934573934116249810921192
y[1] (numeric) = 1.0552613934573934275617155017524
absolute error = 1.59367344096332e-17
relative error = 1.5102167584676878295984852838191e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.0555896903673569899313573173679
y[1] (numeric) = 1.0555896903673570059140133967597
absolute error = 1.59826560793918e-17
relative error = 1.5140974021667128407413192905303e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.0559189316875515000242309195995
y[1] (numeric) = 1.0559189316875515160527927008768
absolute error = 1.60285617812773e-17
relative error = 1.5179727628957961639908027444788e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.056249117088735649145867574257
y[1] (numeric) = 1.0562491170887356652203190436411
absolute error = 1.60744514693841e-17
relative error = 1.5218428313283676699765631524667e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.0565802462407240636275673412012
y[1] (numeric) = 1.0565802462407240797478924390237
absolute error = 1.61203250978225e-17
relative error = 1.5257075981855669361599200656694e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.0569123188123876190750108179637
y[1] (numeric) = 1.0569123188123876352411934386826
absolute error = 1.61661826207189e-17
relative error = 1.5295670542362707732141485432481e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.0572453344716537714973559399734
y[1] (numeric) = 1.0572453344716537877093799321892
absolute error = 1.62120239922158e-17
relative error = 1.5334211902971010059831652685117e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 1.0575792928855068893797542986879
y[1] (numeric) = 1.0575792928855069056376034651597
absolute error = 1.62578491664718e-17
relative error = 1.5372699972324314635066494051129e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.0579141937199885866989549051396
y[1] (numeric) = 1.0579141937199886030026130028014
absolute error = 1.63036580976618e-17
relative error = 1.5411134659544130850929553281818e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.0582500366401980568816623833228
y[1] (numeric) = 1.0582500366401980732311131232995
absolute error = 1.63494507399767e-17
relative error = 1.5449515874229509553785520021448e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 1.0585868213102924077053156350886
y[1] (numeric) = 1.0585868213102924241005426827127
absolute error = 1.63952270476241e-17
relative error = 1.5487843526457750735602855334836e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 1.0589245473934869971409520758003
y[1] (numeric) = 1.0589245473934870135819390506277
absolute error = 1.64409869748274e-17
relative error = 1.5526117526783591160937002200486e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.0592632145520557701378215979091
y[1] (numeric) = 1.059263214552055786624552073736
absolute error = 1.64867304758269e-17
relative error = 1.5564337786240273908664148397628e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=57.2MB, alloc=4.3MB, time=3.64
x[1] = 0.347
y[1] (analytic) = 1.0596028224473315963494134778678
y[1] (numeric) = 1.0596028224473316128818709827469
absolute error = 1.65324575048791e-17
relative error = 1.5602504216338909374721032151827e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.0599433707397066088005585003816
y[1] (numeric) = 1.0599433707397066253787265166384
absolute error = 1.65781680162568e-17
relative error = 1.5640616729068584522389525083699e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.0602848590886325434952676329222
y[1] (numeric) = 1.0602848590886325601191295971719
absolute error = 1.66238619642497e-17
relative error = 1.5678675236896935764992902518008e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.0606272871526210799649676426963
y[1] (numeric) = 1.0606272871526210966345069458601
absolute error = 1.66695393031638e-17
relative error = 1.5716679652769581608860562721814e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.0609706545892441827567931078597
y[1] (numeric) = 1.0609706545892441994719930951814
absolute error = 1.67151999873217e-17
relative error = 1.5754629890110396951437408881376e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.0613149610551344438615933347137
y[1] (numeric) = 1.0613149610551344606224373057764
absolute error = 1.67608439710627e-17
relative error = 1.5792525862821590686483785624714e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.0616602062059854260813117529063
y[1] (numeric) = 1.0616602062059854428877829616492
absolute error = 1.68064712087429e-17
relative error = 1.5830367485283775446058376473118e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.0620063896965520073353944212866
y[1] (numeric) = 1.0620063896965520241874760760217
absolute error = 1.68520816547351e-17
relative error = 1.5868154672355841175887710085651e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.062353511180650725905883338033
y[1] (numeric) = 1.0623535111806507428035586014617
absolute error = 1.68976752634287e-17
relative error = 1.5905887339374821255675917068671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.0627015703111601266208493099901
y[1] (numeric) = 1.0627015703111601435641012992203
absolute error = 1.69432519892302e-17
relative error = 1.5943565402156315785509988970633e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.0630505667400211079758181978111
y[1] (numeric) = 1.063050566740021124964629984374
absolute error = 1.69888117865629e-17
relative error = 1.5981188776994153798774305287428e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.0634005001182372701928434155077
y[1] (numeric) = 1.0634005001182372872271980253746
absolute error = 1.70343546098669e-17
relative error = 1.6018757380660330567297325730945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.0637513700958752642168766253644
y[1] (numeric) = 1.0637513700958752812967570389639
absolute error = 1.70798804135995e-17
relative error = 1.6056271130405313379793421327402e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.0641031763220651416490876318753
y[1] (numeric) = 1.0641031763220651587744767841102
absolute error = 1.71253891522349e-17
relative error = 1.6093729943957681210733559774159e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 1.064455918445000705616783541413
y[1] (numeric) = 1.0644559184450007227876643216774
absolute error = 1.71708807802644e-17
relative error = 1.6131133739524227158754933762230e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 1.0648095961119398625795763177395
y[1] (numeric) = 1.0648095961119398797959315699357
absolute error = 1.72163552521962e-17
relative error = 1.6168482435789677366898382216452e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.0651642089692049750714469272204
y[1] (numeric) = 1.0651642089692049923332594497763
absolute error = 1.72618125225559e-17
relative error = 1.6205775951917060024334550060336e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.0655197566621832153783533317088
y[1] (numeric) = 1.0655197566621832326856058775951
absolute error = 1.73072525458863e-17
relative error = 1.6243014207547409026745423276160e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.0658762388353269201510286515192
y[1] (numeric) = 1.0658762388353269375037039282665
absolute error = 1.73526752767473e-17
relative error = 1.6280197122799554405640301198872e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.0662336551321539459526148857234
y[1] (numeric) = 1.0662336551321539633506955554396
absolute error = 1.73980806697162e-17
relative error = 1.6317324618270280695937924603617e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.0665920051952480257407766421643
y[1] (numeric) = 1.066592005195248043184245321552
absolute error = 1.74434686793877e-17
relative error = 1.6354396615034196087690468762990e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.0669512886662591262839383951033
y[1] (numeric) = 1.066951288666259143772777655477
absolute error = 1.74888392603737e-17
relative error = 1.6391413034643406769081405873740e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.0673115051859038065112878542941
y[1] (numeric) = 1.0673115051859038240454802215977
absolute error = 1.75341923673036e-17
relative error = 1.6428373799127652780199218295709e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.0676726543939655767961870955091
y[1] (numeric) = 1.0676726543939655943757150503335
absolute error = 1.75795279548244e-17
relative error = 1.6465278830994248662509344033261e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=61.0MB, alloc=4.3MB, time=3.89
x[1] = 0.371
y[1] (analytic) = 1.0680347359292952591726321691378
y[1] (numeric) = 1.0680347359292952767974781467382
absolute error = 1.76248459776004e-17
relative error = 1.6502128053227642108358820726683e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.0683977494298113484844009704265
y[1] (numeric) = 1.0683977494298113661545473607402
absolute error = 1.76701463903137e-17
relative error = 1.6538921389289714700804639556698e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.0687616945325003744665282222431
y[1] (numeric) = 1.0687616945325003921819573699069
absolute error = 1.77154291476638e-17
relative error = 1.6575658763119232360520603338693e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.0691265708734172647587454889206
y[1] (numeric) = 1.0691265708734172825194396932885
absolute error = 1.77606942043679e-17
relative error = 1.6612340099131944077841176950546e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.0694923780876857088505232077704
y[1] (numeric) = 1.0694923780876857266564647229316
absolute error = 1.78059415151612e-17
relative error = 1.6648965322220672875233245257205e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.0698591158094985229573507932542
y[1] (numeric) = 1.0698591158094985408085218280503
absolute error = 1.78511710347961e-17
relative error = 1.6685534357754370847832340996014e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.070226783672118015827889937563
y[1] (numeric) = 1.0702267836721180337242726556061
absolute error = 1.78963827180431e-17
relative error = 1.6722047131578757043069466375293e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 1.0705953813078763554816353004824
y[1] (numeric) = 1.0705953813078763734232118201731
absolute error = 1.79415765196907e-17
relative error = 1.6758503570016012424340448280506e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 1.070964908348175936876715850913
y[1] (numeric) = 1.070964908348175954863468245458
absolute error = 1.79867523945450e-17
relative error = 1.6794903599864187804333882747342e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 1.0713353644234897505074691922754
y[1] (numeric) = 1.0713353644234897685393794897056
absolute error = 1.80319102974302e-17
relative error = 1.6831247148397445549455056995802e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.0717067491633617519314202742562
y[1] (numeric) = 1.0717067491633617700084704574445
absolute error = 1.80770501831883e-17
relative error = 1.6867534143365546792480594861933e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.0720790621964072322252949639468
y[1] (numeric) = 1.0720790621964072503474669706262
absolute error = 1.81221720066794e-17
relative error = 1.6903764512993891860761579401315e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.072452303150313189369698020393
y[1] (numeric) = 1.0724523031503132075369737431748
absolute error = 1.81672757227818e-17
relative error = 1.6939938185983366631400952334698e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.0728264716518387005620840879077
y[1] (numeric) = 1.0728264716518387187744453742995
absolute error = 1.82123612863918e-17
relative error = 1.6976055091509902078543915747221e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.0732015673268152954576493952072
y[1] (numeric) = 1.073201567326815313715078047631
absolute error = 1.82574286524238e-17
relative error = 1.7012115159224306795927881821201e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.0735775898001473303377709195101
y[1] (numeric) = 1.0735775898001473486402486953204
absolute error = 1.83024777758103e-17
relative error = 1.7048118319251999251232568903181e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.0739545386958123632056188471909
y[1] (numeric) = 1.0739545386958123815531274586932
absolute error = 1.83475086115023e-17
relative error = 1.7084064502193105594542206651281e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.0743324136368615298085672354074
y[1] (numeric) = 1.0743324136368615482010883498765
absolute error = 1.83925211144691e-17
relative error = 1.7119953639121991319028574079474e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.0747112142454199205870268523226
y[1] (numeric) = 1.0747112142454199390245420920206
absolute error = 1.84375152396980e-17
relative error = 1.7155785661586693414111281222010e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.0750909401426869585493232471189
y[1] (numeric) = 1.0750909401426869770318141893138
absolute error = 1.84824909421949e-17
relative error = 1.7191560501609183423412262849750e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 1.0754715909489367780722421749589
y[1] (numeric) = 1.075471590948936796599690351943
absolute error = 1.85274481769841e-17
relative error = 1.7227278091684878661203897179609e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.0758531662835186046268635763786
y[1] (numeric) = 1.0758531662835186231992504754871
absolute error = 1.85723868991085e-17
relative error = 1.7262938364782518847053623124932e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.0762356657648571354293043853106
y[1] (numeric) = 1.07623566576485715404661144894
absolute error = 1.86173070636294e-17
relative error = 1.7298541254343663930796290123430e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.0766190890104529210159895150267
y[1] (numeric) = 1.076619089010452939678198140653
absolute error = 1.86622086256263e-17
relative error = 1.7334086694282185591918622875753e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=64.8MB, alloc=4.3MB, time=4.15
x[1] = 0.395
y[1] (analytic) = 1.0770034356368827477430694467592
y[1] (numeric) = 1.0770034356368827664501609869571
absolute error = 1.87070915401979e-17
relative error = 1.7369574618984866644861387630783e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 1.0773887052598000212096019216175
y[1] (numeric) = 1.0773887052598000399615576840789
absolute error = 1.87519557624614e-17
relative error = 1.7405004963310413896884808861996e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.0777748974939351506041143126486
y[1] (numeric) = 1.077774897493935169400915560201
absolute error = 1.87968012475524e-17
relative error = 1.7440377662589022457661175272349e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 1.0781620119530959339741623305114
y[1] (numeric) = 1.0781620119530959528157902811368
absolute error = 1.88416279506254e-17
relative error = 1.7475692652622490136506359789358e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.0785500482501679444184997932385
y[1] (numeric) = 1.0785500482501679633049356200924
absolute error = 1.88864358268539e-17
relative error = 1.7510949869683953383205234953046e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.0789390059971149172014732679482
y[1] (numeric) = 1.078939005997114936132698099378
absolute error = 1.89312248314298e-17
relative error = 1.7546149250516967678692903994661e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.0793288848049791377892544701431
y[1] (numeric) = 1.0793288848049791567652493897073
absolute error = 1.89759949195642e-17
relative error = 1.7581290732335879695648034994197e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.0797196842838818308075223843972
y[1] (numeric) = 1.0797196842838818498282684308841
absolute error = 1.90207460464869e-17
relative error = 1.7616374252824987327838271944083e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.0801114040430235499202061487794
y[1] (numeric) = 1.0801114040430235689856843162264
absolute error = 1.90654781674470e-17
relative error = 1.7651399750138712656058941818750e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.0805040436906845686288988243055
y[1] (numeric) = 1.0805040436906845877390900620178
absolute error = 1.91101912377123e-17
relative error = 1.7686367162900656657218670689240e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.0808976028342252719925512500355
y[1] (numeric) = 1.0808976028342252911474364626051
absolute error = 1.91548852125696e-17
relative error = 1.7721276430203481337687631508781e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.0812920810800865492670542641556
y[1] (numeric) = 1.0812920810800865684666143114807
absolute error = 1.91995600473251e-17
relative error = 1.7756127491608877343522475121381e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.0816874780337901874643166514964
y[1] (numeric) = 1.0816874780337902067085323488003
absolute error = 1.92442156973039e-17
relative error = 1.7790920287146692353902426366225e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.0820837932999392658304452584406
y[1] (numeric) = 1.0820837932999392851192973762909
absolute error = 1.92888521178503e-17
relative error = 1.7825654757314793457168078114833e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.0824810264822185512426327970737
y[1] (numeric) = 1.0824810264822185705761020614016
absolute error = 1.93334692643279e-17
relative error = 1.7860330843078737840284750294211e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.082879177183394894524357941723
y[1] (numeric) = 1.0828791771833949139024250338427
absolute error = 1.93780670921197e-17
relative error = 1.7894948485871436984806652128701e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.0832782450053176276785014027179
y[1] (numeric) = 1.0832782450053176471011469593456
absolute error = 1.94226455566277e-17
relative error = 1.7929507627592352834499702229514e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 1.0836782295489189620379807442877
y[1] (numeric) = 1.0836782295489189815051853575612
absolute error = 1.94672046132735e-17
relative error = 1.7964008210607611329055782108663e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 1.084079130414214387333505795996
y[1] (numeric) = 1.0840791304142144068452500134941
absolute error = 1.95117442174981e-17
relative error = 1.7998450177749370552563737652351e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.0844809472003030716780555899898
y[1] (numeric) = 1.0844809472003030912343199147516
absolute error = 1.95562643247618e-17
relative error = 1.8032833472315275322616058217767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.0848836795053682624676768396186
y[1] (numeric) = 1.0848836795053682820684417301632
absolute error = 1.96007648905446e-17
relative error = 1.8067158038068366714338292026479e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.0852873269266776881982030586595
y[1] (numeric) = 1.0852873269266777078434489290054
absolute error = 1.96452458703459e-17
relative error = 1.8101423819236339651214337759036e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.0856918890605839611974925044623
y[1] (numeric) = 1.085691889060583980887199724147
absolute error = 1.96897072196847e-17
relative error = 1.8135630760511255555408441127696e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.0860973655025249812727822128099
y[1] (numeric) = 1.0860973655025250010069311069096
absolute error = 1.97341488940997e-17
relative error = 1.8169778807049156449483723330738e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=4.39
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.0865037558470243402727544771743
y[1] (numeric) = 1.0865037558470243600513253263234
absolute error = 1.97785708491491e-17
relative error = 1.8203867904469396700616501538578e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.0869110596876917275639112103343
y[1] (numeric) = 1.0869110596876917473868842507454
absolute error = 1.98229730404111e-17
relative error = 1.8237897998854613197962936444359e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.087319276617223336420850712016
y[1] (numeric) = 1.0873192766172233562882061354994
absolute error = 1.98673554234834e-17
relative error = 1.8271869036749768823644465579641e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 1.0877284062274022713300404523114
y[1] (numeric) = 1.0877284062274022912417584062951
absolute error = 1.99117179539837e-17
relative error = 1.8305780965162110356849424774556e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.0881384481090989562066785671374
y[1] (numeric) = 1.088138448109098976162739154687
absolute error = 1.99560605875496e-17
relative error = 1.8339633731560568019441905205842e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.088549401852271543524235848908
y[1] (numeric) = 1.0885494018522715635246191287461
absolute error = 2.00003832798381e-17
relative error = 1.8373427283874781874912566676584e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.0889612670459663243562691029099
y[1] (numeric) = 1.0889612670459663444009550894367
absolute error = 2.00446859865268e-17
relative error = 1.8407161570495684527200308203967e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.0893740432783181393300958276049
y[1] (numeric) = 1.0893740432783181594190644909179
absolute error = 2.00889686633130e-17
relative error = 1.8440836540274147771685484746661e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.089787730136550790491919265217
y[1] (numeric) = 1.0897877301365508106251505311309
absolute error = 2.01332312659139e-17
relative error = 1.8474452142520634689136824671958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.0902023272069774540829919575135
y[1] (numeric) = 1.0902023272069774742604657075805
absolute error = 2.01774737500670e-17
relative error = 1.8508008327005028999841498055876e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.0906178340750010942264050306518
y[1] (numeric) = 1.0906178340750011144481011021816
absolute error = 2.02216960715298e-17
relative error = 1.8541505043955815995852224157597e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 1.0910342503251148775240895223366
y[1] (numeric) = 1.0910342503251148977899877084164
absolute error = 2.02658981860798e-17
relative error = 1.8574942244059533353151423271170e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.09145157554090258856361515432
y[1] (numeric) = 1.0914515755409026088736952038352
absolute error = 2.03100800495152e-17
relative error = 1.8608319878460857605084994801327e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.0918698093050390463343710434825
y[1] (numeric) = 1.0918698093050390666886126611364
absolute error = 2.03542416176539e-17
relative error = 1.8641637898761126522961894138350e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.0922889511992905215527119353457
y[1] (numeric) = 1.0922889511992905419510947816802
absolute error = 2.03983828463345e-17
relative error = 1.8674896257018688990653314327739e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.0927090008045151548956526349088
y[1] (numeric) = 1.0927090008045151753381563263245
absolute error = 2.04425036914157e-17
relative error = 1.8708094905747782922168438660939e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.0931299577006633761426924011461
y[1] (numeric) = 1.0931299577006633966292965099227
absolute error = 2.04866041087766e-17
relative error = 1.8741233797918232199788737473854e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.0935518214667783242253501633781
y[1] (numeric) = 1.093551821466778344756034217695
absolute error = 2.05306840543169e-17
relative error = 1.8774312886955045994244407820411e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.0939745916809962681839905100158
y[1] (numeric) = 1.0939745916809962887587339939723
absolute error = 2.05747434839565e-17
relative error = 1.8807332126737463692330778804809e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.0943982679205470290315194928856
y[1] (numeric) = 1.0943982679205470496503018465218
absolute error = 2.06187823536362e-17
relative error = 1.8840291471599000311402782905692e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.0948228497617544025235283834771
y[1] (numeric) = 1.094822849761754423186329002794
absolute error = 2.06628006193169e-17
relative error = 1.8873190876326114893032976225487e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.0952483367800365828344626110016
y[1] (numeric) = 1.0952483367800366035412608479822
absolute error = 2.07067982369806e-17
relative error = 1.8906030296158518640122988495613e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 1.0956747285499065871393922061318
y[1] (numeric) = 1.0956747285499066078901673687612
absolute error = 2.07507751626294e-17
relative error = 1.8938809686787650176281278465391e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.0961020246449726811009591686834
y[1] (numeric) = 1.0961020246449727018956905209699
absolute error = 2.07947313522865e-17
relative error = 1.8971529004356972224216304472924e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=4.64
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.0965302246379388052610762723304
y[1] (numeric) = 1.0965302246379388260997430343262
absolute error = 2.08386667619958e-17
relative error = 1.9004188205460984066091353570758e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.0969593281006050023369509146883
y[1] (numeric) = 1.0969593281006050232195322625101
absolute error = 2.08825813478218e-17
relative error = 1.9036787247144503040784562161671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 1.0973893346038678454210067167782
y[1] (numeric) = 1.0973893346038678663474817826281
absolute error = 2.09264750658499e-17
relative error = 1.9069326086902305487754729437309e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.0978202437177208670842746719854
y[1] (numeric) = 1.0978202437177208880546225441718
absolute error = 2.09703478721864e-17
relative error = 1.9101804682678488540380774340109e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 1.0982520550112549893828247411573
y[1] (numeric) = 1.0982520550112550103970244641159
absolute error = 2.10141997229586e-17
relative error = 1.9134222992865917763629127061006e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.0986847680526589547668078874449
y[1] (numeric) = 1.0986847680526589758248384617595
absolute error = 2.10580305743146e-17
relative error = 1.9166580976305396343980599880300e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.0991183824092197578916776418816
y[1] (numeric) = 1.0991183824092197789935180243051
absolute error = 2.11018403824235e-17
relative error = 1.9198878592285193489442832606190e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.0995528976473230783311593885136
y[1] (numeric) = 1.099552897647323099476788491989
absolute error = 2.11456291034754e-17
relative error = 1.9231115800540385389254446316629e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.0999883133324537141915346561489
y[1] (numeric) = 1.0999883133324537353809313498308
absolute error = 2.11893966936819e-17
relative error = 1.9263292561252645636475409851752e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.1004246290291960166268068024775
y[1] (numeric) = 1.1004246290291960378599499117526
absolute error = 2.12331431092751e-17
relative error = 1.9295408835048666402422808968722e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.100861844301234325254313575431
y[1] (numeric) = 1.1008618443012343465311818819397
absolute error = 2.12768683065087e-17
relative error = 1.9327464583000484343667747287228e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.101299958711353404470351136208
y[1] (numeric) = 1.1012999587113534257909233778656
absolute error = 2.13205722416576e-17
relative error = 1.9359459766624437105721670405853e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.1017389718214388806653732283767
y[1] (numeric) = 1.1017389718214389020296280993944
absolute error = 2.13642548710177e-17
relative error = 1.9391394347880297258121010576694e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.1021788831924776803383282778904
y[1] (numeric) = 1.1021788831924777017462444287968
absolute error = 2.14079161509064e-17
relative error = 1.9423268289171036835325894005051e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.1026196923845584691096963097179
y[1] (numeric) = 1.1026196923845584905612523473805
absolute error = 2.14515560376626e-17
relative error = 1.9455081553342132421703980479111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.1030613989568720916327866680871
y[1] (numeric) = 1.1030613989568721131279611557333
absolute error = 2.14951744876462e-17
relative error = 1.9486834103680412077941471463952e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.1035040024677120124028566290802
y[1] (numeric) = 1.103504002467712033941628086319
absolute error = 2.15387714572388e-17
relative error = 1.9518525903913985959738371117902e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.1039475024744747574636100964996
y[1] (numeric) = 1.1039475024744747790459569993432
absolute error = 2.15823469028436e-17
relative error = 1.9550156918211445926036531023548e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.104391898533660357010634674543
y[1] (numeric) = 1.104391898533660378636535455428
absolute error = 2.16259007808850e-17
relative error = 1.9581727111180788940342657410312e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.1048371902008727888913345138855
y[1] (numeric) = 1.1048371902008728105607675616947
absolute error = 2.16694330478092e-17
relative error = 1.9613236447869241707487538669646e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.1052833770308204230009154312754
y[1] (numeric) = 1.1052833770308204447138590913593
absolute error = 2.17129436600839e-17
relative error = 1.9644684893762265006772605765975e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 1.1057304585773164665739779066934
y[1] (numeric) = 1.1057304585773164883304104808919
absolute error = 2.17564325741985e-17
relative error = 1.9676072414783006183088933105014e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.1061784343932794103712726665209
y[1] (numeric) = 1.106178434393279432171172413185
absolute error = 2.17998997466641e-17
relative error = 1.9707398977291565738714583419380e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.1066273040307334757611726659979
y[1] (numeric) = 1.1066273040307334976045178000113
absolute error = 2.18433451340134e-17
relative error = 1.9738664548084168933133008056427e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=4.89
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.1070770670408090626954143895363
y[1] (numeric) = 1.1070770670408090845821830823375
absolute error = 2.18867686928012e-17
relative error = 1.9769869094392874974662252546968e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.107527722973743198578660493185
y[1] (numeric) = 1.1075277229737432205088308727889
absolute error = 2.19301703796039e-17
relative error = 1.9801012583884377633187694740039e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.1079792713788799880314349197206
y[1] (numeric) = 1.1079792713788800100049850707404
absolute error = 2.19735501510198e-17
relative error = 1.9832094984659524455646534272052e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.1084317118046710635459807234666
y[1] (numeric) = 1.1084317118046710855628886871357
absolute error = 2.20169079636691e-17
relative error = 1.9863116265252560163809454438021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.1088850437986760370345899490213
y[1] (numeric) = 1.1088850437986760590948337232153
absolute error = 2.20602437741940e-17
relative error = 1.9894076394630455760122615726981e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.109339266907562952269954015601
y[1] (numeric) = 1.1093392669075629743735115548598
absolute error = 2.21035575392588e-17
relative error = 1.9924975342192232970624858229198e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.1097943806771087382170821666872
y[1] (numeric) = 1.1097943806771087603639313822367
absolute error = 2.21468492155495e-17
relative error = 1.9955813077767833521392201721556e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.1102503846521996632563346530956
y[1] (numeric) = 1.1102503846521996854464534128702
absolute error = 2.21901187597746e-17
relative error = 1.9986589571618065760334046992767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.1107072783768317902971164264731
y[1] (numeric) = 1.1107072783768318125304825551377
absolute error = 2.22333661286646e-17
relative error = 2.0017304794433374728810068440964e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.1111650613941114327817762295659
y[1] (numeric) = 1.111165061394111455058367508538
absolute error = 2.22765912789721e-17
relative error = 2.0047958717333148999689373647552e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.1116237332462556115792550793985
y[1] (numeric) = 1.1116237332462556338990492468703
absolute error = 2.23197941674718e-17
relative error = 2.0078551311864933048412386251498e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.1120832934745925127680272497516
y[1] (numeric) = 1.1120832934745925351310020007126
absolute error = 2.23629747509610e-17
relative error = 2.0109082550004084975615106498371e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.1125437416195619463078759700387
y[1] (numeric) = 1.1125437416195619687140089562978
absolute error = 2.24061329862591e-17
relative error = 2.0139552404152530048446693629628e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.1130050772207158056000451688413
y[1] (numeric) = 1.1130050772207158280493139990491
absolute error = 2.24492688302078e-17
relative error = 2.0169960847138140091972406969851e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 1.1134672998167185279353077019906
y[1] (numeric) = 1.113467299816718550427689941662
absolute error = 2.24923822396714e-17
relative error = 2.0200307852214198081357019662012e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 1.1139304089453475558294896171662
y[1] (numeric) = 1.1139304089453475783649627887024
absolute error = 2.25354731715362e-17
relative error = 2.0230593393058049980885656286752e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.1143944041434937992459891195241
y[1] (numeric) = 1.1143944041434938218245307022356
absolute error = 2.25785415827115e-17
relative error = 2.0260817443771189584297178933042e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.1148592849471620987048280158762
y[1] (numeric) = 1.1148592849471621213264154460051
absolute error = 2.26215874301289e-17
relative error = 2.0290979978877812187128402264347e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.1153250508914716892777725284065
y[1] (numeric) = 1.1153250508914717119423831991489
absolute error = 2.26646106707424e-17
relative error = 2.0321080973324083070455897748276e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.115791701510656665469059482842
y[1] (numeric) = 1.1157917015106566881766707443709
absolute error = 2.27076112615289e-17
relative error = 2.0351120402477760243451894258324e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.1162592363380664469812629903921
y[1] (numeric) = 1.1162592363380664697318521498799
absolute error = 2.27505891594878e-17
relative error = 2.0381098242127005820096128864849e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.1167276549061662453658358576272
y[1] (numeric) = 1.1167276549061662681593801792684
absolute error = 2.27935443216412e-17
relative error = 2.0411014468479731634719569452733e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.117196956746537531557859073795
y[1] (numeric) = 1.1171969567465375543943357788289
absolute error = 2.28364767050339e-17
relative error = 2.0440869058162761473207730771241e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.1176671413898785042945318408633
y[1] (numeric) = 1.1176671413898785271739181075968
absolute error = 2.28793862667335e-17
relative error = 2.0470661988221078892855666748913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=5.13
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.1181382083660045594169337278386
y[1] (numeric) = 1.1181382083660045823392066916691
absolute error = 2.29222729638305e-17
relative error = 2.0500393236117070963861636678289e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.1186101572038487600545896476376
y[1] (numeric) = 1.1186101572038487830197264010758
absolute error = 2.29651367534382e-17
relative error = 2.0530062779729589169561993543880e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.1190829874314623076923674719854
y[1] (numeric) = 1.1190829874314623307003450646782
absolute error = 2.30079775926928e-17
relative error = 2.0559670597353185460115550261008e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.1195566985760150141192372174827
y[1] (numeric) = 1.1195566985760150371700326562361
absolute error = 2.30507954387534e-17
relative error = 2.0589216667697254999096375740971e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.1200312901637957742584198541208
y[1] (numeric) = 1.1200312901637957973520101029231
absolute error = 2.30935902488023e-17
relative error = 2.0618700969885443031180656989125e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.1205067617202130398784529061372
y[1] (numeric) = 1.1205067617202130630148148861819
absolute error = 2.31363619800447e-17
relative error = 2.0648123483454511898474440072582e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.1209831127697952941846991341835
y[1] (numeric) = 1.1209831127697953173638097238922
absolute error = 2.31791105897087e-17
relative error = 2.0677484188353472693732226079357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 1.1214603428361915272908237073372
y[1] (numeric) = 1.121460342836191550512659742383
absolute error = 2.32218360350458e-17
relative error = 2.0706783064943159125679912972366e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.1219384514421717125697643935207
y[1] (numeric) = 1.1219384514421717358343026668513
absolute error = 2.32645382733306e-17
relative error = 2.0736020093995083588731684406010e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 1.1224174381096272838837184173962
y[1] (numeric) = 1.1224174381096273071909356792569
absolute error = 2.33072172618607e-17
relative error = 2.0765195256690468528424583220050e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 1.1228973023595716136926687557886
y[1] (numeric) = 1.1228973023595716370425417137459
absolute error = 2.33498729579573e-17
relative error = 2.0794308534619897879658000244582e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 1.1233780437121404920409717621522
y[1] (numeric) = 1.1233780437121405154334770811168
absolute error = 2.33925053189646e-17
relative error = 2.0823359909781895414793749566977e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 1.1238596616865926064215271335312
y[1] (numeric) = 1.1238596616865926298566414357816
absolute error = 2.34351143022504e-17
relative error = 2.0852349364582568730313187189158e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 1.1243421558013100225170503558855
y[1] (numeric) = 1.124342155801310045994750221091
absolute error = 2.34776998652055e-17
relative error = 2.0881276881834181118676182059851e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 1.1248255255737986658179668865485
y[1] (numeric) = 1.1248255255737986893382288517929
absolute error = 2.35202619652444e-17
relative error = 2.0910142444754877129176110346729e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 1.1253097705206888041164464559634
y[1] (numeric) = 1.1253097705206888276792470157685
absolute error = 2.35628005598051e-17
relative error = 2.0938946036967603354721191805586e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 1.1257948901577355308760949947039
y[1] (numeric) = 1.1257948901577355544814106010529
absolute error = 2.36053156063490e-17
relative error = 2.0967687642499115143848508100926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.508
y[1] (analytic) = 1.1262808839998192494768208161278
y[1] (numeric) = 1.1262808839998192731246278784886
absolute error = 2.36478070623608e-17
relative error = 2.0996367245778980214285992294797e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 1.126767751560946158334390809836
y[1] (numeric) = 1.1267677515609461820246656951854
absolute error = 2.36902748853494e-17
relative error = 2.1024984831639466694013505372486e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 1.1272554923542487368941915264245
y[1] (numeric) = 1.1272554923542487606269105592713
absolute error = 2.37327190328468e-17
relative error = 2.1053540385313651602374972986630e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 1.1277441058919862324987091598053
y[1] (numeric) = 1.1277441058919862562738486222142
absolute error = 2.37751394624089e-17
relative error = 2.1082033892435213407634365137227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 1.1282335916855451481282415596589
y[1] (numeric) = 1.1282335916855451719457776912742
absolute error = 2.38175361316153e-17
relative error = 2.1110465339037333193613043416340e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 1.1287239492454397310143545333464
y[1] (numeric) = 1.1287239492454397548742635314157
absolute error = 2.38599089980693e-17
relative error = 2.1138834711551770303085712941195e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 1.1292151780813124621255938238659
y[1] (numeric) = 1.1292151780813124860278518432639
absolute error = 2.39022580193980e-17
relative error = 2.1167141996808023393462996095889e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=5.38
NO POLE
x[1] = 0.515
y[1] (analytic) = 1.1297072777019345465249632781811
y[1] (numeric) = 1.1297072777019345704695464314335
absolute error = 2.39445831532524e-17
relative error = 2.1195387182032488146890998682984e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 1.1302002476152064045986788484863
y[1] (numeric) = 1.1302002476152064285855632057936
absolute error = 2.39868843573073e-17
relative error = 2.1223570254847434704876545231942e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 1.1306940873281581641557071976931
y[1] (numeric) = 1.1306940873281581881848687869548
absolute error = 2.40291615892617e-17
relative error = 2.1251691203270424487088332514926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 1.1311887963469501533975968096429
y[1] (numeric) = 1.1311887963469501774690116164812
absolute error = 2.40714148068383e-17
relative error = 2.1279750015712927435842360222432e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 1.1316843741768733947581086342535
y[1] (numeric) = 1.1316843741768734188717526020373
absolute error = 2.41136439677838e-17
relative error = 2.1307746680979644338439286717244e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 1.1321808203223500996121524280115
y[1] (numeric) = 1.1321808203223501237680014578806
absolute error = 2.41558490298691e-17
relative error = 2.1335681188267737165578169963604e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 1.1326781342869341638535340809147
y[1] (numeric) = 1.1326781342869341880515640318039
absolute error = 2.41980299508892e-17
relative error = 2.1363553527165791152937066346173e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 1.1331763155733116643410183521593
y[1] (numeric) = 1.1331763155733116885812050408223
absolute error = 2.42401866886630e-17
relative error = 2.1391363687652685965032559615504e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 1.133675363683301356212210568549
y[1] (numeric) = 1.133675363683301380494529769583
absolute error = 2.42823192010340e-17
relative error = 2.1419111660097258331082537979865e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 1.134175278117855171064759971788
y[1] (numeric) = 1.1341752781178551953891874176575
absolute error = 2.43244274458695e-17
relative error = 2.1446797435256637660088878733993e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 1.1346760583770587160043865334936
y[1] (numeric) = 1.1346760583770587403708979145549
absolute error = 2.43665113810613e-17
relative error = 2.1474421004275902672822677431917e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 1.135177703960131773559232189945
y[1] (numeric) = 1.1351777039601317979678031544705
absolute error = 2.44085709645255e-17
relative error = 2.1501982358686940790727092799537e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 1.1356802143654288024600365822581
y[1] (numeric) = 1.1356802143654288269106427364606
absolute error = 2.44506061542025e-17
relative error = 2.1529481490407481345250301699393e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 1.1361835890904394392856365218521
y[1] (numeric) = 1.1361835890904394637782534299092
absolute error = 2.44926169080571e-17
relative error = 2.1556918391740214079016053816359e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 1.1366878276317890009732875357502
y[1] (numeric) = 1.1366878276317890255078907198289
absolute error = 2.45346031840787e-17
relative error = 2.1584293055371992695609170720943e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 1.1371929294852389881933049814358
y[1] (numeric) = 1.1371929294852390127698699217166
absolute error = 2.45765649402808e-17
relative error = 2.1611605474372419727191810670716e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 1.1376988941456875895875213566629
y[1] (numeric) = 1.1376988941456876142060234913647
absolute error = 2.46185021347018e-17
relative error = 2.1638855642193572599233345051654e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 1.138205721107170186871055565808
y[1] (numeric) = 1.1382057211071702115314702912124
absolute error = 2.46604147254044e-17
relative error = 2.1666043552668495209315582720118e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 1.1387134098628598607968890410339
y[1] (numeric) = 1.13871340986285988549919171151
absolute error = 2.47023026704761e-17
relative error = 2.1693169200010654343524504850944e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 1.1392219599050678979827427537335
y[1] (numeric) = 1.1392219599050679227269086817624
absolute error = 2.47441659280289e-17
relative error = 2.1720232578812690140743425224979e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 1.1397313707252442985997482894172
y[1] (numeric) = 1.1397313707252443233857527456168
absolute error = 2.47860044561996e-17
relative error = 2.1747233684045691188029213140681e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 1.1402416418139782849224052974161
y[1] (numeric) = 1.1402416418139783097502235105658
absolute error = 2.48278182131497e-17
relative error = 2.1774172511058115622567700937188e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 1.1407527726609988107393167654858
y[1] (numeric) = 1.1407527726609988356089239225512
absolute error = 2.48696071570654e-17
relative error = 2.1801049055574797675263114590701e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 1.1412647627551750716241927086173
y[1] (numeric) = 1.1412647627551750965355639547751
absolute error = 2.49113712461578e-17
relative error = 2.1827863313696127033033233063495e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.3MB, time=5.63
NO POLE
x[1] = 0.539
y[1] (analytic) = 1.1417776115845170160666120010952
y[1] (numeric) = 1.1417776115845170410197224397579
absolute error = 2.49531104386627e-17
relative error = 2.1854615281896875001993588878506e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 1.1422913186361758574620312210822
y[1] (numeric) = 1.1422913186361758824568559139231
absolute error = 2.49948246928409e-17
relative error = 2.1881304957025456492680911715365e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 1.1428058833964445869605285177651
y[1] (numeric) = 1.1428058833964446119970424847434
absolute error = 2.50365139669783e-17
relative error = 2.1907932336303013950948610131872e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.542
y[1] (analytic) = 1.1433213053507584871737696523608
y[1] (numeric) = 1.1433213053507585122519478717465
absolute error = 2.50781782193857e-17
relative error = 2.1934497417322236349809902996225e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 1.1438375839836956467396825060591
y[1] (numeric) = 1.1438375839836956718594999144576
absolute error = 2.51198174083985e-17
relative error = 2.1961000198046088949966559133889e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 1.1443547187789774757443254902696
y[1] (numeric) = 1.1443547187789775009057569826475
absolute error = 2.51614314923779e-17
relative error = 2.1987440676807852303976008591540e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 1.1448727092194692220004344373497
y[1] (numeric) = 1.1448727092194692472034548670593
absolute error = 2.52030204297096e-17
relative error = 2.2013818852308972545545457024857e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 1.1453915547871804881821316933069
y[1] (numeric) = 1.1453915547871805134267158721116
absolute error = 2.52445841788047e-17
relative error = 2.2040134723618833310047067634551e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 1.1459112549632657498152802778119
y[1] (numeric) = 1.1459112549632657751014029759114
absolute error = 2.52861226980995e-17
relative error = 2.2066388290173563421474907615574e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 1.1464318092280248741229651212096
y[1] (numeric) = 1.146431809228024899450601067265
absolute error = 2.53276359460554e-17
relative error = 2.2092579551774930146460135732834e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 1.1469532170609036397255825330915
y[1] (numeric) = 1.1469532170609036650947064142507
absolute error = 2.53691238811592e-17
relative error = 2.2118708508589579330503489326643e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 1.1474754779404942571950182023822
y[1] (numeric) = 1.1474754779404942826056046643053
absolute error = 2.54105864619231e-17
relative error = 2.2144775161148011299996968563797e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 1.1479985913445358904623931748063
y[1] (numeric) = 1.1479985913445359159144168216906
absolute error = 2.54520236468843e-17
relative error = 2.2170779510343206282871232280249e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 1.1485225567499151790788564000321
y[1] (numeric) = 1.1485225567499152045722917946378
absolute error = 2.54934353946057e-17
relative error = 2.2196721557430206515070144035300e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 1.1490473736326667613289015877443
y[1] (numeric) = 1.1490473736326667868637232514199
absolute error = 2.55348216636756e-17
relative error = 2.2222601304024824400933719579519e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 1.1495730414679737981956852593716
y[1] (numeric) = 1.1495730414679738237718676720793
absolute error = 2.55761824127077e-17
relative error = 2.2248418752102610392313848054898e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 1.150099559730168498177822030195
y[1] (numeric) = 1.1500995597301685237953396305363
absolute error = 2.56175176003413e-17
relative error = 2.2274173903997992831476383997727e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 1.1506269278927326429571323050854
y[1] (numeric) = 1.1506269278927326686159594903265
absolute error = 2.56588271852411e-17
relative error = 2.2299866762403067773511266141482e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 1.1511551454282981139168167201663
y[1] (numeric) = 1.151155145428298139616927846264
absolute error = 2.57001111260977e-17
relative error = 2.2325497330366995494033855005632e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 1.1516842118086474195095308122717
y[1] (numeric) = 1.1516842118086474452509001938987
absolute error = 2.57413693816270e-17
relative error = 2.2351065611294438827848563929601e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 1.1522141265047142234748325481675
y[1] (numeric) = 1.1522141265047142492574344587383
absolute error = 2.57826019105708e-17
relative error = 2.2376571608945042595634970075271e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 1.1527448889865838739054744961337
y[1] (numeric) = 1.1527448889865838997292831678303
absolute error = 2.58238086716966e-17
relative error = 2.2402015327432215804345521283969e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.561
y[1] (analytic) = 1.153276498723493933162011573659
y[1] (numeric) = 1.1532764987234939590270011974566
absolute error = 2.58649896237976e-17
relative error = 2.2427396771222085980116395256501e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 1.1538089551838347086351944566842
y[1] (numeric) = 1.1538089551838347345413391823772
absolute error = 2.59061447256930e-17
relative error = 2.2452715945132711772164866933506e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.3MB, time=5.87
NO POLE
x[1] = 0.563
y[1] (analytic) = 1.1543422578351497843556178880455
y[1] (numeric) = 1.154342257835149810302891824273
absolute error = 2.59472739362275e-17
relative error = 2.2477972854332600091198685396194e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 1.1548764061441365534500922755128
y[1] (numeric) = 1.1548764061441365794384694897847
absolute error = 2.59883772142719e-17
relative error = 2.2503167504340175250072857347615e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 1.1554113995766467514442061230971
y[1] (numeric) = 1.1554113995766467774736606418202
absolute error = 2.60294545187231e-17
relative error = 2.2528299901022725712709032119909e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.566
y[1] (analytic) = 1.1559472375976869904105459931083
y[1] (numeric) = 1.155947237597687016481051801612
absolute error = 2.60705058085037e-17
relative error = 2.2553370050595003179063378941668e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 1.1564839196714192939620398507875
y[1] (numeric) = 1.1564839196714193200735708933499
absolute error = 2.61115310425624e-17
relative error = 2.2578377959618512785861621853049e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 1.157021445261161633089888798216
y[1] (numeric) = 1.1570214452611616592424189780899
absolute error = 2.61525301798739e-17
relative error = 2.2603323635000368628624702955362e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 1.1575598138293884628455513596132
y[1] (numeric) = 1.1575598138293884890390545390523
absolute error = 2.61935031794391e-17
relative error = 2.2628207083992407146270480756400e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 1.158099024837731259866243636084
y[1] (numeric) = 1.1580990248377312861006936363692
absolute error = 2.62344500002852e-17
relative error = 2.2653028314190212158030231090306e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 1.158639077746979060743417804361
y[1] (numeric) = 1.1586390777469790870187884058261
absolute error = 2.62753706014651e-17
relative error = 2.2677787333531534011828980782966e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 1.1591799720170790012336805911064
y[1] (numeric) = 1.1591799720170790275499455331648
absolute error = 2.63162649420584e-17
relative error = 2.2702484150296089005572880127153e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 1.1597217071071368563116125119018
y[1] (numeric) = 1.1597217071071368826687454930725
absolute error = 2.63571329811707e-17
relative error = 2.2727118773103889088133639109807e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 1.1602642824754175810639478221502
y[1] (numeric) = 1.1602642824754176074619225000841
absolute error = 2.63979746779339e-17
relative error = 2.2751691210914433716398052509724e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 1.1608076975793458524245742857562
y[1] (numeric) = 1.1608076975793458788633642772626
absolute error = 2.64387899915064e-17
relative error = 2.2776201473025813458761047146203e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 1.1613519518755066117498110266296
y[1] (numeric) = 1.1613519518755066382293899077025
absolute error = 2.64795788810729e-17
relative error = 2.2800649569073467333491998192395e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 1.1618970448196456082334218877795
y[1] (numeric) = 1.1618970448196456347537631936239
absolute error = 2.65203413058444e-17
relative error = 2.2825035509029111435842831518829e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 1.162442975866669943160820883031
y[1] (numeric) = 1.1624429758666699697218981080896
absolute error = 2.65610772250586e-17
relative error = 2.2849359303200010367333909998906e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 1.1629897444706486150019254872046
y[1] (numeric) = 1.1629897444706486416037120851841
absolute error = 2.66017865979795e-17
relative error = 2.2873620962227558538167632710177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 1.16353735008481306534211267195
y[1] (numeric) = 1.1635373500848130919845820558478
absolute error = 2.66424693838978e-17
relative error = 2.2897820497086548750659900757028e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 1.1640857921615577256507317563242
y[1] (numeric) = 1.1640857921615577523338572984549
absolute error = 2.66831255421307e-17
relative error = 2.2921957919083923164256798483829e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.582
y[1] (analytic) = 1.1646350701524405648866273036464
y[1] (numeric) = 1.1646350701524405916103823356684
absolute error = 2.67237550320220e-17
relative error = 2.2946033239857781142558890126848e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 1.165185183508183637940124459152
y[1] (numeric) = 1.1651851835081836647044822720943
absolute error = 2.67643578129423e-17
relative error = 2.2970046471376471511929778629224e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 1.1657361316786736349109282865074
y[1] (numeric) = 1.1657361316786736617158621307961
absolute error = 2.68049338442887e-17
relative error = 2.2993997625937254277376350897578e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 1.1662879141129624312213878253303
y[1] (numeric) = 1.1662879141129624580668709108155
absolute error = 2.68454830854852e-17
relative error = 2.3017886716165562146915509593124e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 1.1668405302592676385645747564984
y[1] (numeric) = 1.1668405302592676654505802524811
absolute error = 2.68860054959827e-17
relative error = 2.3041713755013917185630037295337e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.3MB, time=6.12
NO POLE
x[1] = 0.587
y[1] (analytic) = 1.1673939795649731566866257272142
y[1] (numeric) = 1.1673939795649731836131267624727
absolute error = 2.69265010352585e-17
relative error = 2.3065478755760418100348736064321e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 1.1679482614766297260027965535271
y[1] (numeric) = 1.1679482614766297529697662163445
absolute error = 2.69669696628174e-17
relative error = 2.3089181732008597628661537559322e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 1.1685033754399554810466756843086
y[1] (numeric) = 1.1685033754399555080540870224992
absolute error = 2.70074113381906e-17
relative error = 2.3112822697685393481805988201206e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 1.1690593208998365047520034775093
y[1] (numeric) = 1.1690593208998365317998294984458
absolute error = 2.70478260209365e-17
relative error = 2.3136401667040746222690931015165e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 1.1696160973003273835665430069271
y[1] (numeric) = 1.1696160973003274106547566775674
absolute error = 2.70882136706403e-17
relative error = 2.3159918654646168251937238465629e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 1.1701737040846517633974472856612
y[1] (numeric) = 1.1701737040846517905260215325757
absolute error = 2.71285742469145e-17
relative error = 2.3183373675394081951508228647807e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 1.1707321406952029063875669609314
y[1] (numeric) = 1.1707321406952029335564746703298
absolute error = 2.71689077093984e-17
relative error = 2.3206766744496301529201919416373e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 1.1712914065735442485221417040005
y[1] (numeric) = 1.1712914065735442757313557217591
absolute error = 2.72092140177586e-17
relative error = 2.3230097877483368959135863520524e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 1.1718515011604099580653176885558
y[1] (numeric) = 1.1718515011604099853148108202447
absolute error = 2.72494931316889e-17
relative error = 2.3253367090203375828745930908170e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 1.172412423895705494825932721079
y[1] (numeric) = 1.172412423895705522115677731989
absolute error = 2.72897450109100e-17
relative error = 2.3276574398820614006963439078890e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 1.1729741742185081702520097574644
y[1] (numeric) = 1.1729741742185081975819793726345
absolute error = 2.73299696151701e-17
relative error = 2.3299719819814993518167382334032e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 1.1735367515670677083533987114403
y[1] (numeric) = 1.173536751567067735723565615685
absolute error = 2.73701669042447e-17
relative error = 2.3322803369980776461092760809517e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 1.1741001553788068074520056321979
y[1] (numeric) = 1.1741001553788068348623424701343
absolute error = 2.74103368379364e-17
relative error = 2.3345825066425310657807059694496e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 1.1746643850903217027590475010446
y[1] (numeric) = 1.1746643850903217302095268771198
absolute error = 2.74504793760752e-17
relative error = 2.3368784926568188712065530424257e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 1.1752294401373827297787700698751
y[1] (numeric) = 1.1752294401373827572693645483937
absolute error = 2.74905944785186e-17
relative error = 2.3391682968140235441785164793617e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 1.1757953199549348885380653377883
y[1] (numeric) = 1.17579531995493491606874744294
absolute error = 2.75306821051517e-17
relative error = 2.3414519209182494380050278946711e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 1.1763620239770984086414244362806
y[1] (numeric) = 1.1763620239770984362121666521673
absolute error = 2.75707422158867e-17
relative error = 2.3437293668044703321820673084113e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 1.1769295516371693151506608681084
y[1] (numeric) = 1.1769295516371693427614356387719
absolute error = 2.76107747706635e-17
relative error = 2.3460006363384705098641899464283e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 1.177497902367619995288838220145
y[1] (numeric) = 1.1774979023676200229396179495947
absolute error = 2.76507797294497e-17
relative error = 2.3482657314167346710734434608052e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 1.1780670756000997659678356463513
y[1] (numeric) = 1.1780670756000997936585926985914
absolute error = 2.76907570522401e-17
relative error = 2.3505246539662953446459729791033e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 1.1786370707654354421389835933405
y[1] (numeric) = 1.178637070765435469869690292398
absolute error = 2.77307066990575e-17
relative error = 2.3527774059446906637902665118109e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 1.1792078872936319059662014179512
y[1] (numeric) = 1.1792078872936319337368300479035
absolute error = 2.77706286299523e-17
relative error = 2.3550239893398201274191625261911e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.609
y[1] (analytic) = 1.1797795246138726768210677237362
y[1] (numeric) = 1.1797795246138727046315905287386
absolute error = 2.78105228050024e-17
relative error = 2.3572644061698258368904395248988e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 1.1803519821545204820992534213452
y[1] (numeric) = 1.1803519821545205099496426056591
absolute error = 2.78503891843139e-17
relative error = 2.3594986584830414846362826088381e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.3MB, time=6.37
NO POLE
x[1] = 0.611
y[1] (analytic) = 1.1809252593431178288577466964165
y[1] (numeric) = 1.1809252593431178567479744244368
absolute error = 2.78902277280203e-17
relative error = 2.3617267483578141042609377715714e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 1.1814993556063875762722982477992
y[1] (numeric) = 1.1814993556063876042023366440822
absolute error = 2.79300383962830e-17
relative error = 2.3639486779024360032550656657878e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.613
y[1] (analytic) = 1.1820742703702335089145143387088
y[1] (numeric) = 1.1820742703702335368843354880002
absolute error = 2.79698211492914e-17
relative error = 2.3661644492550426914237175986224e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 1.1826500030597409108480243837716
y[1] (numeric) = 1.1826500030597409388576003310342
absolute error = 2.80095759472626e-17
relative error = 2.3683740645834769225066711144518e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 1.1832265530991771405431489758368
y[1] (numeric) = 1.1832265530991771685924517262789
absolute error = 2.80493027504421e-17
relative error = 2.3705775260852372872053134309594e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 1.1838039199119922066094934379379
y[1] (numeric) = 1.1838039199119922346984949570407
absolute error = 2.80890015191028e-17
relative error = 2.3727748359872829932238794208833e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 1.1843821029208193443458911678558
y[1] (numeric) = 1.184382102920819372474563381402
absolute error = 2.81286722135462e-17
relative error = 2.3749659965460246107439941624209e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 1.1849611015474755931071202253905
y[1] (numeric) = 1.1849611015474756212754350194919
absolute error = 2.81683147941014e-17
relative error = 2.3771510100471288304925194616960e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 1.1855409152129623744868157956707
y[1] (numeric) = 1.1855409152129624026947450167966
absolute error = 2.82079292211259e-17
relative error = 2.3793298788054752706043539071446e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 1.1861215433374660713160003456393
y[1] (numeric) = 1.1861215433374660995635158006445
absolute error = 2.82475154550052e-17
relative error = 2.3815026051650118895160674816305e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 1.1867029853403586074766524752305
y[1] (numeric) = 1.1867029853403586357637259313837
absolute error = 2.82870734561532e-17
relative error = 2.3836691914986778880450123174037e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 1.1872852406401980285297346497202
y[1] (numeric) = 1.1872852406401980568563378347321
absolute error = 2.83266031850119e-17
relative error = 2.3858296402082675330242132777745e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 1.1878683086547290831570991852689
y[1] (numeric) = 1.1878683086547291115232037873204
absolute error = 2.83661046020515e-17
relative error = 2.3879839537243277100580800662601e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 1.1884521888008838054166910457999
y[1] (numeric) = 1.1884521888008838338222687135705
absolute error = 2.84055776677706e-17
relative error = 2.3901321345060638490473839156874e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 1.1890368804947820978104651960589
y[1] (numeric) = 1.1890368804947821262554875387551
absolute error = 2.84450223426962e-17
relative error = 2.3922741850412289652340133762027e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 1.189622383151732315164435442986
y[1] (numeric) = 1.1896223831517323436488740303695
absolute error = 2.84844385873835e-17
relative error = 2.3944101078459958758891320351839e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 1.1902086961862318493202708853993
y[1] (numeric) = 1.1902086961862318778440972478157
absolute error = 2.85238263624164e-17
relative error = 2.3965399054648882698429273579352e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 1.1907958190119677146378552804441
y[1] (numeric) = 1.1907958190119677432010409088511
absolute error = 2.85631856284070e-17
relative error = 2.3986635804706276674932726748706e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 1.1913837510418171343082238242947
y[1] (numeric) = 1.1913837510418171629107401702907
absolute error = 2.86025163459960e-17
relative error = 2.4007811354640560418501540176261e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 1.1919724916878481274762910342229
y[1] (numeric) = 1.1919724916878481561181095100758
absolute error = 2.86418184758529e-17
relative error = 2.4028925730740415577965999329371e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 1.1925620403613200971727826093538
y[1] (numeric) = 1.1925620403613201258538745880292
absolute error = 2.86810919786754e-17
relative error = 2.4049978959573171778403783818987e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
y[1] (analytic) = 1.1931523964726844190547833382246
y[1] (numeric) = 1.1931523964726844477751201534147
absolute error = 2.87203368151901e-17
relative error = 2.4070971067984283731552219247111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 1.1937435594315850309543123126502
y[1] (numeric) = 1.1937435594315850597138652588022
absolute error = 2.87595529461520e-17
relative error = 2.4091902083095801393738734526272e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 1.1943355286468590232343358993664
y[1] (numeric) = 1.1943355286468590520330762317117
absolute error = 2.87987403323453e-17
relative error = 2.4112772032305929892517083048887e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.3MB, time=6.62
NO POLE
x[1] = 0.635
y[1] (analytic) = 1.1949283035265372299516281134903
y[1] (numeric) = 1.1949283035265372587895270480726
absolute error = 2.88378989345823e-17
relative error = 2.4133580943286997480474160373181e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 1.1955218834778448208258872309833
y[1] (numeric) = 1.1955218834778448497029159446878
absolute error = 2.88770287137045e-17
relative error = 2.4154328843985266525963122390651e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 1.1961162679072018940145166710524
y[1] (numeric) = 1.1961162679072019229306463016345
absolute error = 2.89161296305821e-17
relative error = 2.4175015762619404215761644969583e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 1.1967114562202240696924773737563
y[1] (numeric) = 1.1967114562202240986476790198706
absolute error = 2.89552016461143e-17
relative error = 2.4195641727679623140424978954741e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 1.1973074478217230844366180930148
y[1] (numeric) = 1.1973074478217231134308628142439
absolute error = 2.89942447212291e-17
relative error = 2.4216206767926403686107373939151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 1.1979042421157073864138892207397
y[1] (numeric) = 1.1979042421157074154471480376229
absolute error = 2.90332588168832e-17
relative error = 2.4236710912389300584059911545274e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 1.198501838505382731372844953923
y[1] (numeric) = 1.1985018385053827604450888479857
absolute error = 2.90722438940627e-17
relative error = 2.4257154190366417410484078491662e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 1.1991002363931527794378378132311
y[1] (numeric) = 1.1991002363931528085490377270136
absolute error = 2.91111999137825e-17
relative error = 2.4277536631422795412953455302388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 1.1996994351806196927053087189588
y[1] (numeric) = 1.1996994351806197218554355560454
absolute error = 2.91501268370866e-17
relative error = 2.4297858265389554265071561996711e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 1.2002994342685847336415750281037
y[1] (numeric) = 1.2002994342685847628305996531517
absolute error = 2.91890246250480e-17
relative error = 2.4318119122362699083682249056272e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 1.2009002330570488642815181348221
y[1] (numeric) = 1.200900233057048893509411373591
absolute error = 2.92278932387689e-17
relative error = 2.4338319232702177791361383532667e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 1.2015018309452133462275714356296
y[1] (numeric) = 1.2015018309452133754943040750103
absolute error = 2.92667326393807e-17
relative error = 2.4358458627030771823458969446853e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 1.2021042273314803414484086604078
y[1] (numeric) = 1.2021042273314803707539514484519
absolute error = 2.93055427880441e-17
relative error = 2.4378537336233070345715274584658e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 1.2027074216134535138767317705792
y[1] (numeric) = 1.2027074216134535432210554165281
absolute error = 2.93443236459489e-17
relative error = 2.4398555391454195127641392637949e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 1.203311413187938631805556826712
y[1] (numeric) = 1.2033114131879386611886320010263
absolute error = 2.93830751743143e-17
relative error = 2.4418512824098941799958147131743e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 1.2039162014509441710823954293201
y[1] (numeric) = 1.2039162014509442005041927637087
absolute error = 2.94217973343886e-17
relative error = 2.4438409665830422370626524944639e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 1.2045217857976819191007285387257
y[1] (numeric) = 1.2045217857976819485612186261755
absolute error = 2.94604900874498e-17
relative error = 2.4458245948569456079955828773293e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 1.2051281656225675795881686825627
y[1] (numeric) = 1.2051281656225676090873220773678
absolute error = 2.94991533948051e-17
relative error = 2.4478021704493046409156908964155e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 1.2057353403192213781907057628076
y[1] (numeric) = 1.2057353403192214077284929805988
absolute error = 2.95377872177912e-17
relative error = 2.4497736966033523279784915227968e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 1.2063433092804686688524308781435
y[1] (numeric) = 1.2063433092804686984288223959179
absolute error = 2.95763915177744e-17
relative error = 2.4517391765877519172853291428726e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 1.2069520718983405409901317819836
y[1] (numeric) = 1.2069520718983405706050980381338
absolute error = 2.96149662561502e-17
relative error = 2.4536986136964531211655644329372e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.656
y[1] (analytic) = 1.207561627564074427462152801609
y[1] (numeric) = 1.207561627564074457115664195953
absolute error = 2.96535113943440e-17
relative error = 2.4556520112486395675345848205212e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 1.2081719756681147133309112496125
y[1] (numeric) = 1.2081719756681147430229381434231
absolute error = 2.96920268938106e-17
relative error = 2.4575993725885768039775592891913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 1.2087831156001133454184615651814
y[1] (numeric) = 1.2087831156001133751489742812159
absolute error = 2.97305127160345e-17
relative error = 2.4595407010855266634649311853581e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.3MB, time=6.87
NO POLE
x[1] = 0.659
y[1] (analytic) = 1.2093950467489304426544976297072
y[1] (numeric) = 1.2093950467489304724234664522371
absolute error = 2.97689688225299e-17
relative error = 2.4614760001336368047570893729932e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 1.2100077685026349072161829087698
y[1] (numeric) = 1.2100077685026349370235780836105
absolute error = 2.98073951748407e-17
relative error = 2.4634052731518303104757208943682e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 1.2106212802485050364591972807178
y[1] (numeric) = 1.2106212802485050663049890152584
absolute error = 2.98457917345406e-17
relative error = 2.4653285235837036049481409516718e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 1.2112355813730291356393886208484
y[1] (numeric) = 1.2112355813730291655235470840814
absolute error = 2.98841584632330e-17
relative error = 2.4672457548974078962766773759363e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 1.2118506712619061314244164195866
y[1] (numeric) = 1.2118506712619061613469117421377
absolute error = 2.99224953225511e-17
relative error = 2.4691569705855472105063576473650e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 1.2124665493000461861947739230711
y[1] (numeric) = 1.2124665493000462161555761972293
absolute error = 2.99608022741582e-17
relative error = 2.4710621741650929610855578737093e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 1.2130832148715713131335744951767
y[1] (numeric) = 1.213083214871571343132653774924
absolute error = 2.99990792797473e-17
relative error = 2.4729613691772408056234054318110e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.666
y[1] (analytic) = 1.213700667359815992104487111237
y[1] (numeric) = 1.2137006673598160221418134122783
absolute error = 3.00373263010413e-17
relative error = 2.4748545591873171076305442761021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 1.2143189061473277863172051055833
y[1] (numeric) = 1.2143189061473278163927484053766
absolute error = 3.00755432997933e-17
relative error = 2.4767417477846936536286420560054e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.668
y[1] (analytic) = 1.2149379306158679597798315074841
y[1] (numeric) = 1.2149379306158679898935617452702
absolute error = 3.01137302377861e-17
relative error = 2.4786229385826365201649610452178e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 1.2155577401464120955375635131482
y[1] (numeric) = 1.2155577401464121256894505899812
absolute error = 3.01518870768330e-17
relative error = 2.4804981352182620876945554832764e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 1.2161783341191507146970578551619
y[1] (numeric) = 1.216178334119150744887071633939
absolute error = 3.01900137787771e-17
relative error = 2.4823673413523695918243761303967e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 1.2167997119134898962358580450436
y[1] (numeric) = 1.2167997119134899264639683505353
absolute error = 3.02281103054917e-17
relative error = 2.4842305606693643296798867538666e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 1.2174218729080518975962636795423
y[1] (numeric) = 1.2174218729080519278624402984225
absolute error = 3.02661766188802e-17
relative error = 2.4860877968771397746456773813143e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 1.2180448164806757760630212168607
y[1] (numeric) = 1.2180448164806758063672338977371
absolute error = 3.03042126808764e-17
relative error = 2.4879390537069926370934882669366e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 1.2186685420084180109242148451658
y[1] (numeric) = 1.21866854200841804126643329861
absolute error = 3.03422184534442e-17
relative error = 2.4897843349134886984468983358834e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 1.219293048867553126414735282546
y[1] (numeric) = 1.2192930488675531567949291811238
absolute error = 3.03801938985778e-17
relative error = 2.4916236442743698129909244188139e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 1.2199183364335743154417035649992
y[1] (numeric) = 1.219918336433574345859842543301
absolute error = 3.04181389783018e-17
relative error = 2.4934569855904527484610951362392e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 1.2205444040811940640912260970796
y[1] (numeric) = 1.2205444040811940945472797517507
absolute error = 3.04560536546711e-17
relative error = 2.4952843626855117034564506490214e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 1.2211712511843447769158564585004
y[1] (numeric) = 1.2211712511843448074097943482714
absolute error = 3.04939378897710e-17
relative error = 2.4971057794061773176807880598624e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 1.221798877116179403002138679282
y[1] (numeric) = 1.2217988771161794335339303249993
absolute error = 3.05317916457173e-17
relative error = 2.4989212396218357485291507481794e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.68
y[1] (analytic) = 1.2224272812490720628176059159557
y[1] (numeric) = 1.2224272812490720933872208006119
absolute error = 3.05696148846562e-17
relative error = 2.5007307472245114547941587552550e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 1.2230564629546186758366076818755
y[1] (numeric) = 1.2230564629546187064440152506401
absolute error = 3.06074075687646e-17
relative error = 2.5025343061287828054888749315950e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 1.223686421603637588944338005864
y[1] (numeric) = 1.2236864216036376195895076661136
absolute error = 3.06451696602496e-17
relative error = 2.5043319202716323332731398691473e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.3MB, time=7.11
NO POLE
x[1] = 0.683
y[1] (analytic) = 1.2243171565661702056184361152149
y[1] (numeric) = 1.2243171565661702363013372365643
absolute error = 3.06829011213494e-17
relative error = 2.5061235936124115618447209899295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 1.2249486672114816158875304615069
y[1] (numeric) = 1.2249486672114816466081323758392
absolute error = 3.07206019143323e-17
relative error = 2.5079093301326505973202001633411e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.685
y[1] (analytic) = 1.2255809529080612270660961307334
y[1] (numeric) = 1.225580952908061257824368132231
absolute error = 3.07582720014976e-17
relative error = 2.5096891338360231022702879800158e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 1.2262140130236233952649949029474
y[1] (numeric) = 1.2262140130236234260609062481226
absolute error = 3.07959113451752e-17
relative error = 2.5114630087482051280806295910917e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 1.2268478469251080576770664509304
y[1] (numeric) = 1.2268478469251080885105863586562
absolute error = 3.08335199077258e-17
relative error = 2.5132309589167830589341260773887e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 1.2274824539786813656371383923497
y[1] (numeric) = 1.2274824539786813965082360438905
absolute error = 3.08710976515408e-17
relative error = 2.5149929884111371712895357393700e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 1.2281178335497363184558221354451
y[1] (numeric) = 1.2281178335497363493644666744875
absolute error = 3.09086445390424e-17
relative error = 2.5167491013223416116310535175980e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 1.2287539850028933980264606845022
y[1] (numeric) = 1.2287539850028934289726212171861
absolute error = 3.09461605326839e-17
relative error = 2.5184993017630807350672690516518e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 1.2293909077020012042045937982186
y[1] (numeric) = 1.2293909077020012351882393931677
absolute error = 3.09836455949491e-17
relative error = 2.5202435938674922721029261681513e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.692
y[1] (analytic) = 1.2300286010101370909593051215486
y[1] (numeric) = 1.2300286010101371219804048099016
absolute error = 3.10210996883530e-17
relative error = 2.5219819817911164483994424287184e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 1.2306670642896078032958151397345
y[1] (numeric) = 1.2306670642896078343543379151761
absolute error = 3.10585227754416e-17
relative error = 2.5237144697107719105101526898875e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 1.2313062969019501149486830319832
y[1] (numeric) = 1.231306296901950146044597850775
absolute error = 3.10959148187918e-17
relative error = 2.5254410618244399393465963931802e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 1.2319462982079314668449797316401
y[1] (numeric) = 1.2319462982079314979782555126515
absolute error = 3.11332757810114e-17
relative error = 2.5271617623511569234000651758595e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 1.2325870675675506063367937297397
y[1] (numeric) = 1.2325870675675506375073993544793
absolute error = 3.11706056247396e-17
relative error = 2.5288765755309475157802350945325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 1.2332286043400382272024303894814
y[1] (numeric) = 1.233228604340038258410334702128
absolute error = 3.12079043126466e-17
relative error = 2.5305855056246848057079417545797e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 1.2338709078838576104156647704838
y[1] (numeric) = 1.2338709078838576416608365779174
absolute error = 3.12451718074336e-17
relative error = 2.5322885569139831313026288512516e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 1.234513977556705265682407193618
y[1] (numeric) = 1.2345139775567052969648152654511
absolute error = 3.12824080718331e-17
relative error = 2.5339857337011153166429407495074e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 1.2351578127155115737441400098081
y[1] (numeric) = 1.235157812715511605063753078417
absolute error = 3.13196130686089e-17
relative error = 2.5356770403089056691176007889228e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 1.2358024127164414294474832694162
y[1] (numeric) = 1.2358024127164414608042700299721
absolute error = 3.13567867605559e-17
relative error = 2.5373624810806069190842437488106e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 1.2364477769148948855792462226979
y[1] (numeric) = 1.2364477769148949169731753331985
absolute error = 3.13939291105006e-17
relative error = 2.5390420603798339515860783414102e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 1.2370939046655077974663208163335
y[1] (numeric) = 1.237093904665507828897360897634
absolute error = 3.14310400813005e-17
relative error = 2.5407157825904086223193753177054e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 1.2377407953221524683397725861917
y[1] (numeric) = 1.2377407953221524998078922220364
absolute error = 3.14681196358447e-17
relative error = 2.5423836521163018069579323199770e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 1.2383884482379382954624835822915
y[1] (numeric) = 1.2383884482379383269676513193452
absolute error = 3.15051677370537e-17
relative error = 2.5440456733815108301921894801149e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 1.2390368627652124170197011983717
y[1] (numeric) = 1.239036862765212448561885546251
absolute error = 3.15421843478793e-17
relative error = 2.5457018508299451495373596390926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.3MB, time=7.36
NO POLE
x[1] = 0.707
y[1] (analytic) = 1.2396860382555603597718460155734
y[1] (numeric) = 1.2396860382555603913510154468783
absolute error = 3.15791694313049e-17
relative error = 2.5473521889253444654287858543521e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 1.2403359740598066874689310074817
y[1] (numeric) = 1.2403359740598067190850539578272
absolute error = 3.16161229503455e-17
relative error = 2.5489966921511727043346852652610e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.709
y[1] (analytic) = 1.2409866695280156500259436921618
y[1] (numeric) = 1.2409866695280156816789885602093
absolute error = 3.16530448680475e-17
relative error = 2.5506353650104960231162827961088e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 1.2416381240094918334585420558604
y[1] (numeric) = 1.2416381240094918651484772033495
absolute error = 3.16899351474891e-17
relative error = 2.5522682120259093262103469077702e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 1.2422903368527808105784143127322
y[1] (numeric) = 1.242290336852780842305208064512
absolute error = 3.17267937517798e-17
relative error = 2.5538952377393903747056521806713e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 1.2429433074056697924476518052839
y[1] (numeric) = 1.2429433074056698242112724493451
absolute error = 3.17636206440612e-17
relative error = 2.5555164467122587542648695854828e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 1.2435970350151882805914835912195
y[1] (numeric) = 1.2435970350151883123918993787258
absolute error = 3.18004157875063e-17
relative error = 2.5571318435250141650998101421387e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 1.2442515190276087199687205040045
y[1] (numeric) = 1.2442515190276087518058996493246
absolute error = 3.18371791453201e-17
relative error = 2.5587414327772795142636184396163e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 1.2449067587884471526992557167609
y[1] (numeric) = 1.2449067587884471845731663975
absolute error = 3.18739106807391e-17
relative error = 2.5603452190876556411811091156640e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 1.2455627536424638725479680820458
y[1] (numeric) = 1.2455627536424639044585784390776
absolute error = 3.19106103570318e-17
relative error = 2.5619432070936566019188343595174e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 1.2462195029336640801643737636656
y[1] (numeric) = 1.2462195029336641121116519011641
absolute error = 3.19472781374985e-17
relative error = 2.5635354014515888048066300536800e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 1.2468770060052985390773709209283
y[1] (numeric) = 1.2468770060052985710612849063998
absolute error = 3.19839139854715e-17
relative error = 2.5651218068364624264057209670955e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 1.2475352621998642324444214506442
y[1] (numeric) = 1.2475352621998642644649393149592
absolute error = 3.20205178643150e-17
relative error = 2.5667024279418788799944665777431e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 1.248194270859105020554513037748
y[1] (numeric) = 1.248194270859105052611602775173
absolute error = 3.20570897374250e-17
relative error = 2.5682772694799184614216872106964e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 1.2488540313240122990842440116342
y[1] (numeric) = 1.2488540313240123311778735798638
absolute error = 3.20936295682296e-17
relative error = 2.5698463361810602029603839575852e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 1.249514542934825658106372752177
y[1] (numeric) = 1.2495145429348256902365100723661
absolute error = 3.21301373201891e-17
relative error = 2.5714096327940857992529089306031e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 1.2501758050310335418501726369398
y[1] (numeric) = 1.2501758050310335740167855937355
absolute error = 3.21666129567957e-17
relative error = 2.5729671640859516680809693103396e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 1.2508378169513739092129327692739
y[1] (numeric) = 1.2508378169513739414159892108478
absolute error = 3.22030564415739e-17
relative error = 2.5745189348417172067788840806603e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 1.2515005780338348950219439758613
y[1] (numeric) = 1.2515005780338349272614117139412
absolute error = 3.22394677380799e-17
relative error = 2.5760649498643932011445134823770e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 1.2521640876156554720463088117698
y[1] (numeric) = 1.2521640876156555043221556216725
absolute error = 3.22758468099027e-17
relative error = 2.5776052139749263111083299349557e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 1.2528283450333261137579135612673
y[1] (numeric) = 1.2528283450333261460701071819304
absolute error = 3.23121936206631e-17
relative error = 2.5791397320120158168144039431322e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 1.2534933496225894578408994734763
y[1] (numeric) = 1.2534933496225894901894076074906
absolute error = 3.23485081340143e-17
relative error = 2.5806685088320584238051399915622e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 1.2541591007184409704489697234547
y[1] (numeric) = 1.2541591007184410028337600370965
absolute error = 3.23847903136418e-17
relative error = 2.5821915493090372644342225896008e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 1.2548255976551296112098678414497
y[1] (numeric) = 1.2548255976551296436309079647131
absolute error = 3.24210401232634e-17
relative error = 2.5837088583344190580453074177755e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.3MB, time=7.61
NO POLE
x[1] = 0.731
y[1] (analytic) = 1.2554928397661584989763626059028
y[1] (numeric) = 1.2554928397661585314336201325322
absolute error = 3.24572575266294e-17
relative error = 2.5852204408170673664356800105472e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 1.2561608263842855783230736492765
y[1] (numeric) = 1.2561608263842856108165161367987
absolute error = 3.24934424875222e-17
relative error = 2.5867263016831082003461563817539e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 1.2568295568415242867884712799312
y[1] (numeric) = 1.2568295568415243193180662496882
absolute error = 3.25295949697570e-17
relative error = 2.5882264458758834169931291338633e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 1.2574990304691442228613832781104
y[1] (numeric) = 1.2574990304691442554270982152917
absolute error = 3.25657149371813e-17
relative error = 2.5897208783558086808988355542746e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 1.2581692465976718147113406795812
y[1] (numeric) = 1.2581692465976718473131430332564
absolute error = 3.26018023536752e-17
relative error = 2.5912096041002953060735692674571e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 1.2588402045568909896620938166407
y[1] (numeric) = 1.2588402045568910222999509997919
absolute error = 3.26378571831512e-17
relative error = 2.5926926281036324737891459650757e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 1.2595119036758438444076291430284
y[1] (numeric) = 1.2595119036758438770815085325828
absolute error = 3.26738793895544e-17
relative error = 2.5941699553769014315629752265256e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 1.2601843432828313159700166267826
y[1] (numeric) = 1.2601843432828313486798855636453
absolute error = 3.27098689368627e-17
relative error = 2.5956415909478898144393948615493e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 1.2608575227054138533984167532507
y[1] (numeric) = 1.2608575227054138861442425423372
absolute error = 3.27458257890865e-17
relative error = 2.5971075398609664340937273875009e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 1.2615314412704120902085754393012
y[1] (numeric) = 1.2615314412704121229903253495702
absolute error = 3.27817499102690e-17
relative error = 2.5985678071770038807241681412357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 1.2622060983039075175621344192991
y[1] (numeric) = 1.2622060983039075503797756837853
absolute error = 3.28176412644862e-17
relative error = 2.6000223979732774571225319296504e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 1.2628814931312431581850839235906
y[1] (numeric) = 1.2628814931312431910385837394371
absolute error = 3.28534998158465e-17
relative error = 2.6014713173433326165497543946012e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 1.2635576250770242410246837310994
y[1] (numeric) = 1.2635576250770242739140092595909
absolute error = 3.28893255284915e-17
relative error = 2.6029145703969476506962509091408e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 1.2642344934651188766441779391716
y[1] (numeric) = 1.2642344934651189095692963057671
absolute error = 3.29251183665955e-17
relative error = 2.6043521622599935247169339677672e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 1.2649120976186587333546280560096
y[1] (numeric) = 1.2649120976186587663155063503751
absolute error = 3.29608782943655e-17
relative error = 2.6057840980743335483253749909333e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 1.2655904368600397140831882839174
y[1] (numeric) = 1.2655904368600397470797935599592
absolute error = 3.29966052760418e-17
relative error = 2.6072103829977706371130300806465e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 1.266269510510922633977146125141
y[1] (numeric) = 1.2662695105109226670094454010383
absolute error = 3.30322992758973e-17
relative error = 2.6086310222038919400824018670847e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 1.2669493178922338987430507063167
y[1] (numeric) = 1.2669493178922339318110109645548
absolute error = 3.30679602582381e-17
relative error = 2.6100460208820164373549700067941e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 1.2676298583241661837202504824584
y[1] (numeric) = 1.2676298583241662168238386698614
absolute error = 3.31035881874030e-17
relative error = 2.6114553842370557937237963479519e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 1.2683111311261791136881612469999
y[1] (numeric) = 1.2683111311261791468273442747642
absolute error = 3.31391830277643e-17
relative error = 2.6128591174894780233251351065035e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.751
y[1] (analytic) = 1.2689931356169999434065846406836
y[1] (numeric) = 1.2689931356169999765813293844106
absolute error = 3.31747447437270e-17
relative error = 2.6142572258751450531564779050194e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 1.2696758711146242388883966190315
y[1] (numeric) = 1.2696758711146242720986699187611
absolute error = 3.32102732997296e-17
relative error = 2.6156497146452766938186016418440e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 1.270359336936316559403924605769
y[1] (numeric) = 1.2703593369363165926496932660123
absolute error = 3.32457686602433e-17
relative error = 2.6170365890662886466095685221021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 1.2710435323986111402163313278786
y[1] (numeric) = 1.2710435323986111734975621176515
absolute error = 3.32812307897729e-17
relative error = 2.6184178544197646516853820568219e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.3MB, time=7.86
NO POLE
x[1] = 0.755
y[1] (analytic) = 1.2717284568173125760473225969591
y[1] (numeric) = 1.2717284568173126093639822498153
absolute error = 3.33166596528562e-17
relative error = 2.6197935160023106479297643629313e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 1.2724141095074965052724955712377
y[1] (numeric) = 1.2724141095074965386245507853021
absolute error = 3.33520552140644e-17
relative error = 2.6211635791254878672885483417175e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 1.2731004897835102948456433029448
y[1] (numeric) = 1.2731004897835103282330607409467
absolute error = 3.33874174380019e-17
relative error = 2.6225280491156988904403673045923e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 1.2737875969589737259513306468032
y[1] (numeric) = 1.2737875969589737593740769361097
absolute error = 3.34227462893065e-17
relative error = 2.6238869313141053486932441421071e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 1.274475430346779680385055877114
y[1] (numeric) = 1.2744754303467797138430976097633
absolute error = 3.34580417326493e-17
relative error = 2.6252402310765222298034363721110e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 1.275163989259094827660311633333
y[1] (numeric) = 1.275163989259094861153615366068
absolute error = 3.34933037327350e-17
relative error = 2.6265879537733437724788548088533e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 1.2758532730073603128418580871366
y[1] (numeric) = 1.275853273007360346370390341438
absolute error = 3.35285322543014e-17
relative error = 2.6279301047894067771084622680424e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 1.2765432809022924451045204977583
y[1] (numeric) = 1.2765432809022924786682477598785
absolute error = 3.35637272621202e-17
relative error = 2.6292666895239560776016630799543e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 1.2772340122538833870168225968583
y[1] (numeric) = 1.2772340122538834206157113178544
absolute error = 3.35988887209961e-17
relative error = 2.6305977133904769070976767759705e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 1.277925466371401844548766519348
y[1] (numeric) = 1.2779254663714018781827831151159
absolute error = 3.36340165957679e-17
relative error = 2.6319231818166841942897981943794e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 1.2786176425633937578030692724491
y[1] (numeric) = 1.2786176425633937914721801237568
absolute error = 3.36691108513077e-17
relative error = 2.6332431002443631812052879437537e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 1.2793105401376829924691650118068
y[1] (numeric) = 1.279310540137683026173336464328
absolute error = 3.37041714525212e-17
relative error = 2.6345574741292964280040041603049e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 1.2800041584013720319992816707128
y[1] (numeric) = 1.2800041584013720657384800350605
absolute error = 3.37391983643477e-17
relative error = 2.6358663089411675047869940201539e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 1.2806984966608426705058997664195
y[1] (numeric) = 1.28069849666084270428009131818
absolute error = 3.37741915517605e-17
relative error = 2.6371696101634961178579791188806e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 1.2813935542217567063799004861449
y[1] (numeric) = 1.2813935542217567401890514659111
absolute error = 3.38091509797662e-17
relative error = 2.6384673832934874925943647604766e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
y[1] (analytic) = 1.2820893303890566366287094346757
y[1] (numeric) = 1.2820893303890566704727860480813
absolute error = 3.38440766134056e-17
relative error = 2.6397596338420069335958011910559e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 1.2827858244669663519337417054856
y[1] (numeric) = 1.2827858244669663858127101232386
absolute error = 3.38789684177530e-17
relative error = 2.6410463673334296314756029182422e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 1.2834830357589918324264532179796
y[1] (numeric) = 1.2834830357589918663402795758961
absolute error = 3.39138263579165e-17
relative error = 2.6423275893055687651703114655550e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 1.2841809635679218441823025448716
y[1] (numeric) = 1.2841809635679218781309529439098
absolute error = 3.39486503990382e-17
relative error = 2.6436033053095959463792048668210e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 1.2848796071958286364319267357915
y[1] (numeric) = 1.2848796071958286704153672420856
absolute error = 3.39834405062941e-17
relative error = 2.6448735209099384708853097113048e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 1.2855789659440686394888339260045
y[1] (numeric) = 1.2855789659440686735070305708985
absolute error = 3.40181966448940e-17
relative error = 2.6461382416841768022191028872820e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.776
y[1] (analytic) = 1.2862790391132831633929148026071
y[1] (numeric) = 1.286279039113283197445833582689
absolute error = 3.40529187800819e-17
relative error = 2.6473974732229811602137840903335e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 1.2869798260033990972690742847478
y[1] (numeric) = 1.2869798260033991313566811618834
absolute error = 3.40876068771356e-17
relative error = 2.6486512211299860553272781409686e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 1.2876813259136296094002840592981
y[1] (numeric) = 1.287681325913629643522544960665
absolute error = 3.41222609013669e-17
relative error = 2.6498994910217117290784829681778e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=8.12
NO POLE
x[1] = 0.779
y[1] (analytic) = 1.28838353814247484801435589898
y[1] (numeric) = 1.288383538142474882171236717102
absolute error = 3.41568808181220e-17
relative error = 2.6511422885275012768578331376384e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 1.2890864619877226427837349762354
y[1] (numeric) = 1.2890864619877226769752015690162
absolute error = 3.41914665927808e-17
relative error = 2.6523796192893725479673501174941e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 1.289790096746449207037611673102
y[1] (numeric) = 1.2897900967464492412636298638596
absolute error = 3.42260181907576e-17
relative error = 2.6536114889619789794683264258548e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 1.2904944417150198406856496750424
y[1] (numeric) = 1.2904944417150198749461852525432
absolute error = 3.42605355775008e-17
relative error = 2.6548379032124929745425993987010e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 1.2911994961890896338526274250576
y[1] (numeric) = 1.2911994961890896681476461435507
absolute error = 3.42950187184931e-17
relative error = 2.6560588677205282933379499439184e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 1.2919052594636041712232893035015
y[1] (numeric) = 1.2919052594636042055527568827527
absolute error = 3.43294675792512e-17
relative error = 2.6572743881780239038069076242601e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
y[1] (analytic) = 1.2926117308328002370967021888034
y[1] (numeric) = 1.2926117308328002714605843141297
absolute error = 3.43638821253263e-17
relative error = 2.6584844702891900128627657058110e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 1.293318909590206521149412344802
y[1] (numeric) = 1.293318909590206555547674667106
absolute error = 3.43982623223040e-17
relative error = 2.6596891197704077929640514595879e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 1.2940267950286443249066968715924
y[1] (numeric) = 1.2940267950286443593393050073962
absolute error = 3.44326081358038e-17
relative error = 2.6608883423500984380939976774143e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 1.2947353864402282689212032486917
y[1] (numeric) = 1.2947353864402283033881227801719
absolute error = 3.44669195314802e-17
relative error = 2.6620821437687161399037041396061e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 1.2954446831163670006582697919461
y[1] (numeric) = 1.2954446831163670351594662669679
absolute error = 3.45011964750218e-17
relative error = 2.6632705297785866141133443317718e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 1.296154684347763903087219138915
y[1] (numeric) = 1.2961546843477639376226580710665
absolute error = 3.45354389321515e-17
relative error = 2.6644535061438309388611487152135e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 1.2968653894244178039779161714986
y[1] (numeric) = 1.2968653894244178385475630401254
absolute error = 3.45696468686268e-17
relative error = 2.6656310786402972709669569768568e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 1.2975767976356236859018810793109
y[1] (numeric) = 1.2975767976356237205057013295508
absolute error = 3.46038202502399e-17
relative error = 2.6668032530554772911200188628288e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.793
y[1] (analytic) = 1.2982889082699733969372475627432
y[1] (numeric) = 1.2982889082699734315752066055606
absolute error = 3.46379590428174e-17
relative error = 2.6679700351883920329028967488842e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 1.2990017206153563620768554708199
y[1] (numeric) = 1.2990017206153563967489186830404
absolute error = 3.46720632122205e-17
relative error = 2.6691314308495164985674149878604e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 1.2997152339589602953387664658126
y[1] (numeric) = 1.2997152339589603300448991901576
absolute error = 3.47061327243450e-17
relative error = 2.6702874458606890562450099813380e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 1.3004294475872719125784906041565
y[1] (numeric) = 1.300429447587271947318658149278
absolute error = 3.47401675451215e-17
relative error = 2.6714380860550364374111534416855e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.797
y[1] (analytic) = 1.3011443607860776450022110215024
y[1] (numeric) = 1.3011443607860776797763786620174
absolute error = 3.47741676405150e-17
relative error = 2.6725833572768527916761740451595e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 1.3018599728404643533802932087375
y[1] (numeric) = 1.301859972840464388188426185263
absolute error = 3.48081329765255e-17
relative error = 2.6737232653815558779951831417084e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 1.3025762830348200429603646655274
y[1] (numeric) = 1.3025762830348200778024281847151
absolute error = 3.48420635191877e-17
relative error = 2.6748578162355742323352359788924e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 1.3032932906528345790792500183577
y[1] (numeric) = 1.3032932906528346139552092529287
absolute error = 3.48759592345710e-17
relative error = 2.6759870157162576529288649461045e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 1.3040109949775004034730459911998
y[1] (numeric) = 1.3040109949775004383828660799795
absolute error = 3.49098200887797e-17
relative error = 2.6771108697118032462804798009161e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 1.3047293952911132512846199187868
y[1] (numeric) = 1.3047293952911132862282659667397
absolute error = 3.49436460479529e-17
relative error = 2.6782293841211586532106025684936e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.4MB, time=8.37
x[1] = 0.803
y[1] (analytic) = 1.3054484908752728687678147950589
y[1] (numeric) = 1.3054484908752729037452518733237
absolute error = 3.49774370782648e-17
relative error = 2.6793425648539561655539261633398e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 1.3061682810108837316876431526351
y[1] (numeric) = 1.3061682810108837666988362985593
absolute error = 3.50111931459242e-17
relative error = 2.6804504178303857440328572043595e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 1.3068887649781557644157513731752
y[1] (numeric) = 1.3068887649781557994606655903504
absolute error = 3.50449142171752e-17
relative error = 2.6815529489811602094147477825990e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 1.3076099420566050597204353332294
y[1] (numeric) = 1.3076099420566050947990355915261
absolute error = 3.50786002582967e-17
relative error = 2.6826501642473887119189102237251e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 1.3083318115250545992504875956188
y[1] (numeric) = 1.3083318115250546343627388312213
absolute error = 3.51122512356025e-17
relative error = 2.6837420695804964136614868711113e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 1.3090543726616349747121556625597
y[1] (numeric) = 1.3090543726616350098580227780015
absolute error = 3.51458671154418e-17
relative error = 2.6848286709421749291516086806463e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 1.3097776247437851097384901136346
y[1] (numeric) = 1.3097776247437851449179379778332
absolute error = 3.51794478641986e-17
relative error = 2.6859099743042488829496212887631e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 1.3105015670482529824503607593199
y[1] (numeric) = 1.3105015670482530176633542076122
absolute error = 3.52129934482923e-17
relative error = 2.6869859856486344150934778214311e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 1.311226198851096348708418249117
y[1] (numeric) = 1.3112261988510963839549220832942
absolute error = 3.52465038341772e-17
relative error = 2.6880567109672138721061797279655e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 1.3119515194276834660552778823829
y[1] (numeric) = 1.3119515194276835013352568707258
absolute error = 3.52799789883429e-17
relative error = 2.6891221562617794534250008225834e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 1.3126775280526938183472016797382
y[1] (numeric) = 1.3126775280526938536606205570526
absolute error = 3.53134188773144e-17
relative error = 2.6901823275439541318266146710877e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 1.3134042240001188410745540834314
y[1] (numeric) = 1.313404224000118876421377551083
absolute error = 3.53468234676516e-17
relative error = 2.6912372308350670954409901492368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 1.3141316065432626473703059662622
y[1] (numeric) = 1.3141316065432626827504986922122
absolute error = 3.53801927259500e-17
relative error = 2.6922868721661208613733871837764e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 1.314859674954742754705860940622
y[1] (numeric) = 1.3148596749547427901193875594625
absolute error = 3.54135266188405e-17
relative error = 2.6933312575776899944722736632038e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 1.315588428506490812273477271886
y[1] (numeric) = 1.315588428506490847720302384875
absolute error = 3.54468251129890e-17
relative error = 2.6943703931198049052945468259128e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 1.316317866469753329054558013794
y[1] (numeric) = 1.3163178664697533645346461888911
absolute error = 3.54800881750971e-17
relative error = 2.6954042848519195469484652703388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 1.3170479881150924025730812975917
y[1] (numeric) = 1.3170479881150924380863970694934
absolute error = 3.55133157719017e-17
relative error = 2.6964329388427956466316611245398e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 1.3177787927123864483334420215631
y[1] (numeric) = 1.3177787927123864838799498917383
absolute error = 3.55465078701752e-17
relative error = 2.6974563611704328015405979850834e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.821
y[1] (analytic) = 1.3185102795308309299419755031717
y[1] (numeric) = 1.3185102795308309655216399398973
absolute error = 3.55796644367256e-17
relative error = 2.6984745579219911724279459992861e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 1.3192424478389390899114329723498
y[1] (numeric) = 1.3192424478389391255242184107461
absolute error = 3.56127854383963e-17
relative error = 2.6994875351936916444573337361917e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 1.3199752969045426811476781015192
y[1] (numeric) = 1.3199752969045427167935489435854
absolute error = 3.56458708420662e-17
relative error = 2.7004952990907389995075802268521e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 1.3207088259947926991178730857087
y[1] (numeric) = 1.3207088259947927347967937003587
absolute error = 3.56789206146500e-17
relative error = 2.7014978557272604401957653993353e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 1.3214430343761601146994221046441
y[1] (numeric) = 1.3214430343761601504113568277421
absolute error = 3.57119347230980e-17
relative error = 2.7024952112262064346925992568455e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 1.3221779213144366077089393179268
y[1] (numeric) = 1.3221779213144366434538524523227
absolute error = 3.57449131343959e-17
relative error = 2.7034873717192518463274521731572e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.4MB, time=8.62
x[1] = 0.827
y[1] (analytic) = 1.3229134860747353011105078643946
y[1] (numeric) = 1.32291348607473533688836367996
absolute error = 3.57778558155654e-17
relative error = 2.7044743433467578208695780299045e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 1.3236497279214914959024956574681
y[1] (numeric) = 1.3236497279214915317132583911319
absolute error = 3.58107627336638e-17
relative error = 2.7054561322576582086865873702895e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 1.3243866461184634066821930897261
y[1] (numeric) = 1.3243866461184634425258269455103
absolute error = 3.58436338557842e-17
relative error = 2.7064327446093916271014209638027e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 1.3251242399287328978875370821356
y[1] (numeric) = 1.325124239928732933764006231191
absolute error = 3.58764691490554e-17
relative error = 2.7074041865678110685107064345876e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 1.3258625086147062207151852362717
y[1] (numeric) = 1.325862508614706256624453816914
absolute error = 3.59092685806423e-17
relative error = 2.7083704643071314809281353612941e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 1.3266014514381147507142031715169
y[1] (numeric) = 1.3266014514381147866562352892623
absolute error = 3.59420321177454e-17
relative error = 2.7093315840098096413656229608894e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 1.3273410676600157260546274536119
y[1] (numeric) = 1.327341067660015762029387181213
absolute error = 3.59747597276011e-17
relative error = 2.7102875518664846626327002378584e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 1.3280813565407929864701658460576
y[1] (numeric) = 1.3280813565407930224776172235393
absolute error = 3.60074513774817e-17
relative error = 2.7112383740758960723268970341674e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 1.3288223173401577128742959417292
y[1] (numeric) = 1.3288223173401577489144029764249
absolute error = 3.60401070346957e-17
relative error = 2.7121840568448247052803937632007e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.836
y[1] (analytic) = 1.3295639493171491676490225586661
y[1] (numeric) = 1.3295639493171492037217492252536
absolute error = 3.60727266665875e-17
relative error = 2.7131246063879886302151589499092e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 1.3303062517301354356055536113409
y[1] (numeric) = 1.3303062517301354717108638518782
absolute error = 3.61053102405373e-17
relative error = 2.7140600289279544237209380453126e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 1.3310492238368141656161534967937
y[1] (numeric) = 1.3310492238368142017540112207553
absolute error = 3.61378577239616e-17
relative error = 2.7149903306950937844944449805015e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 1.3317928648942133129164323638407
y[1] (numeric) = 1.3317928648942133490868014481537
absolute error = 3.61703690843130e-17
relative error = 2.7159155179274876991028185676328e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 1.3325371741586918820773289631291
y[1] (numeric) = 1.3325371741586919182801732522092
absolute error = 3.62028442890801e-17
relative error = 2.7168355968708384009689798444108e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 1.3332821508859406706460441061175
y[1] (numeric) = 1.333282150885940706881327411905
absolute error = 3.62352833057875e-17
relative error = 2.7177505737783890934249009446076e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 1.3340277943309830134551810921098
y[1] (numeric) = 1.3340277943309830497228671941063
absolute error = 3.62676861019965e-17
relative error = 2.7186604549108963842714044931368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 1.334774103748175527599348794266
y[1] (numeric) = 1.3347741037481755638994014395701
absolute error = 3.63000526453041e-17
relative error = 2.7195652465364754209886850237608e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.844
y[1] (analytic) = 1.3355210783912088580784824280462
y[1] (numeric) = 1.3355210783912088944108653313901
absolute error = 3.63323829033439e-17
relative error = 2.7204649549305877833094556287828e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 1.3362687175131084241071363588314
y[1] (numeric) = 1.336268717513108460471813202617
absolute error = 3.63646768437856e-17
relative error = 2.7213595863759246196630081625316e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 1.3370170203662351660890026394896
y[1] (numeric) = 1.3370170203662352024859370738248
absolute error = 3.63969344343352e-17
relative error = 2.7222491471623425044008442798328e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 1.3377659862022862932559083034306
y[1] (numeric) = 1.3377659862022863296850639461658
absolute error = 3.64291556427352e-17
relative error = 2.7231336435867994846733758992180e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 1.3385156142722960319705437742155
y[1] (numeric) = 1.3385156142722960684318842109797
absolute error = 3.64613404367642e-17
relative error = 2.7240130819532464914139427552856e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 1.3392659038266363746921740890535
y[1] (numeric) = 1.3392659038266364111856628732911
absolute error = 3.64934887842376e-17
relative error = 2.7248874685726012256544468046123e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 1.3400168541150178296045839705385
y[1] (numeric) = 1.3400168541150178661301846235455
absolute error = 3.65256006530070e-17
relative error = 2.7257568097626250958416587060081e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=137.3MB, alloc=4.4MB, time=8.87
x[1] = 0.851
y[1] (analytic) = 1.3407684643864901709055071187424
y[1] (numeric) = 1.3407684643864902074631831297029
absolute error = 3.65576760109605e-17
relative error = 2.7266211118478676721675591128424e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 1.3415207338894431897567894342973
y[1] (numeric) = 1.3415207338894432263465042603202
absolute error = 3.65897148260229e-17
relative error = 2.7274803811596038521920764805763e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.853
y[1] (analytic) = 1.3422736618716074458945352223685
y[1] (numeric) = 1.3422736618716074825162522885237
absolute error = 3.66217170661552e-17
relative error = 2.7283346240357190669769090370961e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 1.3430272475800550198984847674316
y[1] (numeric) = 1.3430272475800550565521674667868
absolute error = 3.66536826993552e-17
relative error = 2.7291838468206767583366900518746e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 1.3437814902612002661198710095412
y[1] (numeric) = 1.3437814902612003028054827031986
absolute error = 3.66856116936574e-17
relative error = 2.7300280558654338550929396993792e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 1.3445363891608005662670023942965
y[1] (numeric) = 1.3445363891608006029845064114292
absolute error = 3.67175040171327e-17
relative error = 2.7308672575273416408736466019191e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 1.3452919435239570836478183109831
y[1] (numeric) = 1.3452919435239571203971779488718
absolute error = 3.67493596378887e-17
relative error = 2.7317014581700915386963750624349e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 1.3460481525951155180686628763995
y[1] (numeric) = 1.3460481525951155548498414004693
absolute error = 3.67811785240698e-17
relative error = 2.7325306641636462037635517198253e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 1.3468050156180668613885221656564
y[1] (numeric) = 1.3468050156180668982014828095138
absolute error = 3.68129606438574e-17
relative error = 2.7333548818841782580478817271606e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 1.3475625318359481537279693357761
y[1] (numeric) = 1.3475625318359481905726753012451
absolute error = 3.68447059654690e-17
relative error = 2.7341741177139275879185473836355e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 1.3483207004912432403320614332074
y[1] (numeric) = 1.3483207004912432772084758903669
absolute error = 3.68764144571595e-17
relative error = 2.7349883780412222751608730440554e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 1.3490795208257835290864310224247
y[1] (numeric) = 1.349079520825783565994517109645
absolute error = 3.69080860872203e-17
relative error = 2.7357976692603363705437962785945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 1.3498389920807487486858151195816
y[1] (numeric) = 1.3498389920807487856255359435615
absolute error = 3.69397208239799e-17
relative error = 2.7366019977714592593639144544170e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 1.3505991134966677074542632627533
y[1] (numeric) = 1.3505991134966677444255818985568
absolute error = 3.69713186358035e-17
relative error = 2.7374013699805910780200403678056e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 1.3513598843134190528162658986232
y[1] (numeric) = 1.3513598843134190898191453897165
absolute error = 3.70028794910933e-17
relative error = 2.7381957922994902728309855686070e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 1.3521213037702320314180436145485
y[1] (numeric) = 1.352121303770232068452446972837
absolute error = 3.70344033582885e-17
relative error = 2.7389852711455991390303715786423e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 1.3528833711056872498982370947791
y[1] (numeric) = 1.3528833711056872869641273006442
absolute error = 3.70658902058651e-17
relative error = 2.7397698129419548191903656130732e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 1.3536460855577174363072370302028
y[1] (numeric) = 1.353646085557717473404577032539
absolute error = 3.70973400023362e-17
relative error = 2.7405494241171375316378322225974e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 1.3544094463636082021743925623504
y[1] (numeric) = 1.3544094463636082393031452786027
absolute error = 3.71287527162523e-17
relative error = 2.7413241111052189666903109908884e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 1.3551734527599988052223361945172
y[1] (numeric) = 1.3551734527599988423824645107176
absolute error = 3.71601283162004e-17
relative error = 2.7420938803456223012918403493577e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 1.3559381039828829127276624557362
y[1] (numeric) = 1.3559381039828829499191292265414
absolute error = 3.71914667708052e-17
relative error = 2.7428587382831375556644775204428e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
y[1] (analytic) = 1.3567033992676093655271969569926
y[1] (numeric) = 1.3567033992676094027499650057205
absolute error = 3.72227680487279e-17
relative error = 2.7436186913677599939104415417773e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 1.3574693378488829426690918334692
y[1] (numeric) = 1.3574693378488829799231239521367
absolute error = 3.72540321186675e-17
relative error = 2.7443737460547132333975335134916e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 1.3582359189607651267079829217956
y[1] (numeric) = 1.3582359189607651639932418711554
absolute error = 3.72852589493598e-17
relative error = 2.7451239088043029354849681829725e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=141.1MB, alloc=4.4MB, time=9.11
x[1] = 0.875
y[1] (analytic) = 1.359003141836674869643443377204
y[1] (numeric) = 1.359003141836674906959891886782
absolute error = 3.73164485095780e-17
relative error = 2.7458691860818887221961084397752e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 1.3597710057093893595009677922045
y[1] (numeric) = 1.3597710057093893968485685603371
absolute error = 3.73476007681326e-17
relative error = 2.7466095843578047070897776296289e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.877
y[1] (analytic) = 1.3605395098110447875547202358586
y[1] (numeric) = 1.3605395098110448249334359297297
absolute error = 3.73787156938711e-17
relative error = 2.7473451101072655941765475783438e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 1.3613086533731371161912789909656
y[1] (numeric) = 1.3613086533731371536010722466446
absolute error = 3.74097932556790e-17
relative error = 2.7480757698103685910955787017063e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 1.3620784356265228474136101254846
y[1] (numeric) = 1.362078435626522884854443547963
absolute error = 3.74408334224784e-17
relative error = 2.7488015699519191150094978345872e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 1.3628488558014197919845013942779
y[1] (numeric) = 1.3628488558014198294563375575071
absolute error = 3.74718361632292e-17
relative error = 2.7495225170214478672706288886954e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 1.3636199131274078392086873278103
y[1] (numeric) = 1.3636199131274078767114887747391
absolute error = 3.75028014469288e-17
relative error = 2.7502386175131178510696669127575e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 1.3643916068334297273528957257406
y[1] (numeric) = 1.3643916068334297648866249683524
absolute error = 3.75337292426118e-17
relative error = 2.7509498779256317070005185787441e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 1.3651639361477918147030451354242
y[1] (numeric) = 1.3651639361477918522676646547746
absolute error = 3.75646195193504e-17
relative error = 2.7516563047621906423406429826258e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 1.3659369002981648512578222581931
y[1] (numeric) = 1.3659369002981648888532945044474
absolute error = 3.75954722462543e-17
relative error = 2.7523579045304168990437236815457e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 1.3667104985115847510578675899006
y[1] (numeric) = 1.3667104985115847886841549823715
absolute error = 3.76262873924709e-17
relative error = 2.7530546837422984402721693770534e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 1.3674847300144533651497969666091
y[1] (numeric) = 1.3674847300144534028068618937941
absolute error = 3.76570649271850e-17
relative error = 2.7537466489140972668508077627597e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 1.3682595940325392551842860514642
y[1] (numeric) = 1.3682595940325392928720908710832
absolute error = 3.76878048196190e-17
relative error = 2.7544338065662945941528073331121e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 1.3690350897909784676474441647341
y[1] (numeric) = 1.3690350897909785053659512037672
absolute error = 3.77185070390331e-17
relative error = 2.7551161632235362223230362048845e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 1.369811216514275308724703225707
y[1] (numeric) = 1.3698112165142753464738747804321
absolute error = 3.77491715547251e-17
relative error = 2.7557937254145488987446229489962e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 1.3705879734263031197964469426198
y[1] (numeric) = 1.3705879734263031575762452786501
absolute error = 3.77797983360303e-17
relative error = 2.7564664996720642692925536190550e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 1.3713653597503050535646047550548
y[1] (numeric) = 1.371365359750305091374992107377
absolute error = 3.78103873523222e-17
relative error = 2.7571344925328014333307635135595e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 1.3721433747088948508094344022757
y[1] (numeric) = 1.3721433747088948886503729752873
absolute error = 3.78409385730116e-17
relative error = 2.7577977105373329619897560275535e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 1.3729220175240576177757163607833
y[1] (numeric) = 1.3729220175240576556471683283307
absolute error = 3.78714519675474e-17
relative error = 2.7584561602300752060348647186132e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 1.373701287417150604187582764963
y[1] (numeric) = 1.373701287417150642089510270379
absolute error = 3.79019275054160e-17
relative error = 2.7591098481591767336099829127390e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 1.3744811836089039818912027960585
y[1] (numeric) = 1.3744811836089040198235679522006
absolute error = 3.79323651561421e-17
relative error = 2.7597587808765090160314564661391e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 1.3752617053194216241245458968532
y[1] (numeric) = 1.375261705319421662087310786141
absolute error = 3.79627648892878e-17
relative error = 2.7604029649375335450800188706859e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 1.3760428517681818854134435423582
y[1] (numeric) = 1.3760428517681819234065702168118
absolute error = 3.79931266744536e-17
relative error = 2.7610424069013074929016737777650e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 1.3768246221740383820931696705131
y[1] (numeric) = 1.3768246221740384201166201517908
absolute error = 3.80234504812777e-17
relative error = 2.7616771133303658941481712851021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=144.9MB, alloc=4.4MB, time=9.36
x[1] = 0.899
y[1] (analytic) = 1.3776070157552207734547592513822
y[1] (numeric) = 1.3776070157552208115084955308183
absolute error = 3.80537362794361e-17
relative error = 2.7623070907906623155323509442103e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 1.3783900317293355435152838485929
y[1] (numeric) = 1.3783900317293355815992678872361
absolute error = 3.80839840386432e-17
relative error = 2.7629323458515460170521245417304e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 1.3791736693133667834113024028072
y[1] (numeric) = 1.3791736693133668215254961314584
absolute error = 3.81141937286512e-17
relative error = 2.7635528850856521983191114339897e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 1.3799579277236769744147048438388
y[1] (numeric) = 1.3799579277236770125590701630892
absolute error = 3.81443653192504e-17
relative error = 2.7641687150688578547563114152154e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 1.380742806176007771570165515639
y[1] (numeric) = 1.3807428061760078097446642959082
absolute error = 3.81744987802692e-17
relative error = 2.7647798423802160741155038180496e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 1.3815283038854807879534227767624
y[1] (numeric) = 1.3815283038854808261580168583365
absolute error = 3.82045940815741e-17
relative error = 2.7653862736018905748436326818427e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 1.3823144200665983795496005180982
y[1] (numeric) = 1.3823144200665984177842517111682
absolute error = 3.82346511930700e-17
relative error = 2.7659880153191121889086069971163e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 1.3831011539332444307507867196122
y[1] (numeric) = 1.3831011539332444690154568043117
absolute error = 3.82646700846995e-17
relative error = 2.7665850741200632108642299171638e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 1.3838885046986851404720835485838
y[1] (numeric) = 1.3838885046986851787667342750277
absolute error = 3.82946507264439e-17
relative error = 2.7671774565958850034837208313468e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 1.3846764715755698088853428833566
y[1] (numeric) = 1.3846764715755698472099359716791
absolute error = 3.83245930883225e-17
relative error = 2.7677651693405628255548971283166e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 1.3854650537759316247698005289301
y[1] (numeric) = 1.3854650537759316631242976693231
absolute error = 3.83544971403930e-17
relative error = 2.7683482189508904693685204477299e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 1.3862542505111884534788217738253
y[1] (numeric) = 1.3862542505111884918631846265766
absolute error = 3.83843628527513e-17
relative error = 2.7689266120263917585117414426913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 1.3870440609921436255219703215436
y[1] (numeric) = 1.3870440609921436639361605170752
absolute error = 3.84141901955316e-17
relative error = 2.7695003551692639646486658618680e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 1.387834484428986725761612014616
y[1] (numeric) = 1.3878344844289867642055911535227
absolute error = 3.84439791389067e-17
relative error = 2.7700694549843358513737699131723e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 1.3886255200312943832232641547054
y[1] (numeric) = 1.388625520031294421696993807793
absolute error = 3.84737296530876e-17
relative error = 2.7706339180789754752571900576274e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 1.3894171670080310615189006084766
y[1] (numeric) = 1.3894171670080311000223423168004
absolute error = 3.85034417083238e-17
relative error = 2.7711937510630487067419541372034e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 1.390209424567549849882422275997
y[1] (numeric) = 1.3902094245675498884155375509002
absolute error = 3.85331152749032e-17
relative error = 2.7717489605488491448528266374744e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 1.3910022919175932548165018862618
y[1] (numeric) = 1.3910022919175932933792522094142
absolute error = 3.85627503231524e-17
relative error = 2.7722995531510570529303231685558e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 1.3917957682652939923500114730661
y[1] (numeric) = 1.3917957682652940309423582965022
absolute error = 3.85923468234361e-17
relative error = 2.7728455354866337959154115686168e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 1.3925898528171757809052402738607
y[1] (numeric) = 1.3925898528171758195271450200187
absolute error = 3.86219047461580e-17
relative error = 2.7733869141748243779797508554960e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 1.3933845447791541347741101844421
y[1] (numeric) = 1.3933845447791541734255342462022
absolute error = 3.86514240617601e-17
relative error = 2.7739236958370451702388662935039e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.92
y[1] (analytic) = 1.3941798433565371582025952933256
y[1] (numeric) = 1.3941798433565371968835000340488
absolute error = 3.86809047407232e-17
relative error = 2.7744558870968581220952465241987e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 1.3949757477540263400825514114488
y[1] (numeric) = 1.3949757477540263787928981650152
absolute error = 3.87103467535664e-17
relative error = 2.7749834945798734031986359802269e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 1.3957722571757173492501609054418
y[1] (numeric) = 1.3957722571757173879899109762897
absolute error = 3.87397500708479e-17
relative error = 2.7755065249137455456786822735371e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=148.7MB, alloc=4.4MB, time=9.61
x[1] = 0.923
y[1] (analytic) = 1.3965693708251008303901975360864
y[1] (numeric) = 1.3965693708251008691593121992507
absolute error = 3.87691146631643e-17
relative error = 2.7760249847280622228718509174103e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 1.3973670879050632005453153977649
y[1] (numeric) = 1.3973670879050632393437558989159
absolute error = 3.87984405011510e-17
relative error = 2.7765388806543121580167150025001e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 1.3981654076178874462295654496762
y[1] (numeric) = 1.3981654076178874850572930051584
absolute error = 3.88277275554822e-17
relative error = 2.7770482193258245644067805883089e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 1.3989643291652539211453425253694
y[1] (numeric) = 1.3989643291652539600023183222401
absolute error = 3.88569757968707e-17
relative error = 2.7775530073776945275791928236775e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 1.3997638517482411445029651037137
y[1] (numeric) = 1.3997638517482411833891502997822
absolute error = 3.88861851960685e-17
relative error = 2.7780532514467658271075671896951e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 1.4005639745673265999420895217925
y[1] (numeric) = 1.4005639745673266388574452456586
absolute error = 3.89153557238661e-17
relative error = 2.7785489581715210295619926150983e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 1.4013646968223875350541597083728
y[1] (numeric) = 1.4013646968223875739986470594657
absolute error = 3.89444873510929e-17
relative error = 2.7790401341920504854970446475500e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 1.402166017712701761505092915567
y[1] (numeric) = 1.4021660177127018004786729641844
absolute error = 3.89735800486174e-17
relative error = 2.7795267861500072022928652737774e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 1.4029679364369484557574013260696
y[1] (numeric) = 1.4029679364369484947600351134164
absolute error = 3.90026337873468e-17
relative error = 2.7800089206885191388389303738383e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 1.4037704521932089603909488139114
y[1] (numeric) = 1.4037704521932089994225973521388
absolute error = 3.90316485382274e-17
relative error = 2.7804865444521588244438818741600e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 1.4045735641789675860215415380431
y[1] (numeric) = 1.4045735641789676250821658102876
absolute error = 3.90606242722445e-17
relative error = 2.7809596640868775187164881652275e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 1.4053772715911124138165504502244
y[1] (numeric) = 1.4053772715911124529061114106466
absolute error = 3.90895609604222e-17
relative error = 2.7814282862399325169270382156095e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 1.4061815736259360986067632016613
y[1] (numeric) = 1.4061815736259361377252217754854
absolute error = 3.91184585738241e-17
relative error = 2.7818924175598787436313765917215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 1.4069864694791366725936623366093
y[1] (numeric) = 1.4069864694791367117409794201616
absolute error = 3.91473170835523e-17
relative error = 2.7823520646964395858289107815148e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 1.4077919583458183496513260657285
y[1] (numeric) = 1.4077919583458183888274625264771
absolute error = 3.91761364607486e-17
relative error = 2.7828072343005344791409996881145e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.938
y[1] (analytic) = 1.4085980394204923302221473173594
y[1] (numeric) = 1.4085980394204923694270639939527
absolute error = 3.92049166765933e-17
relative error = 2.7832579330241360545678026468112e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 1.409404711897077606805566171065
y[1] (numeric) = 1.4094047118970776460392238733714
absolute error = 3.92336577023064e-17
relative error = 2.7837041675202980979295237493328e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 1.410211974968901770039010184776
y[1] (numeric) = 1.4102119749689018093013696939228
absolute error = 3.92623595091468e-17
relative error = 2.7841459444430416291318522399771e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 1.4110198278287018153702365346646
y[1] (numeric) = 1.4110198278287018546612586030773
absolute error = 3.92910220684127e-17
relative error = 2.7845832704473264561226539330395e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 1.4118282696686249503202692954725
y[1] (numeric) = 1.4118282696686249896399146469141
absolute error = 3.93196453514416e-17
relative error = 2.7850161521889945338681173399150e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 1.4126372996802294023361245984231
y[1] (numeric) = 1.4126372996802294416843539280333
absolute error = 3.93482293296102e-17
relative error = 2.7854445963247064786738701763649e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.944
y[1] (analytic) = 1.41344691705448522723251581406
y[1] (numeric) = 1.4134469170544852666092897883944
absolute error = 3.93767739743344e-17
relative error = 2.7858686095118854157653605440063e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 1.4142571209817751182217303183736
y[1] (numeric) = 1.4142571209817751576270095754432
absolute error = 3.94052792570696e-17
relative error = 2.7862881984086822731410424009382e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 1.4150679106518952155308688124071
y[1] (numeric) = 1.4150679106518952549646139617178
absolute error = 3.94337451493107e-17
relative error = 2.7867033696739200355450230725294e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=152.5MB, alloc=4.4MB, time=9.85
x[1] = 0.947
y[1] (analytic) = 1.4158792852540559166056375781701
y[1] (numeric) = 1.4158792852540559560678092007617
absolute error = 3.94621716225916e-17
relative error = 2.7871141299670029179265158697160e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 1.4166912439768826868998834671338
y[1] (numeric) = 1.4166912439768827263904421156198
absolute error = 3.94905586484860e-17
relative error = 2.7875204859479176563941881753507e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 1.4175037860084168712500608318425
y[1] (numeric) = 1.4175037860084169107689670304492
absolute error = 3.95189061986067e-17
relative error = 2.7879224442771290176514311696376e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 1.4183169105361165058338190262395
y[1] (numeric) = 1.4183169105361165453810332708458
absolute error = 3.95472142446063e-17
relative error = 2.7883200116155744192785126998448e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 1.4191306167468571307118985161905
y[1] (numeric) = 1.4191306167468571702873812743671
absolute error = 3.95754827581766e-17
relative error = 2.7887131946245670067936041713016e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 1.419944903826932602952523058373
y[1] (numeric) = 1.4199449038269326425562347694222
absolute error = 3.96037117110492e-17
relative error = 2.7891019999657836183438215238921e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 1.4207597709620559103374748232099
y[1] (numeric) = 1.4207597709620559499693758982051
absolute error = 3.96319010749952e-17
relative error = 2.7894864343011894889692241854829e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 1.4215752173373599856490387558386
y[1] (numeric) = 1.4215752173373600253090895776638
absolute error = 3.96600508218252e-17
relative error = 2.7898665042929843621134152587651e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 1.4223912421373985215370018882395
y[1] (numeric) = 1.4223912421373985612251628116288
absolute error = 3.96881609233893e-17
relative error = 2.7902422166035488319665465208024e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 1.4232078445461467859648927355918
y[1] (numeric) = 1.4232078445461468256811240871694
absolute error = 3.97162313515776e-17
relative error = 2.7906135778954260482296942908073e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 1.4240250237470024382346453306867
y[1] (numeric) = 1.4240250237470024779789074090063
absolute error = 3.97442620783196e-17
relative error = 2.7909805948312262842838353708451e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 1.4248427789227863455888718718004
y[1] (numeric) = 1.4248427789227863853611249473851
absolute error = 3.97722530755847e-17
relative error = 2.7913432740736090819653489345568e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 1.4256611092557434003899273818234
y[1] (numeric) = 1.425661109255743440190131697205
absolute error = 3.98002043153816e-17
relative error = 2.7917016222851883478310617631329e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 1.4264800139275433378749491996481
y[1] (numeric) = 1.4264800139275433777030649694075
absolute error = 3.98281157697594e-17
relative error = 2.7920556461285569981956138756960e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 1.4272994921192815544860535488458
y[1] (numeric) = 1.4272994921192815943420409596522
absolute error = 3.98559874108064e-17
relative error = 2.7924053522661504238989231172196e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 1.4281195430114799267748708535018
y[1] (numeric) = 1.4281195430114799666586900641529
absolute error = 3.98838192106511e-17
relative error = 2.7927507473602645222815484660859e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 1.4289401657840876308806008967442
y[1] (numeric) = 1.4289401657840876707922120382058
absolute error = 3.99116111414616e-17
relative error = 2.7930918380729617449401238441872e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 1.4297613596164819625807683439772
y[1] (numeric) = 1.4297613596164820025201315194232
absolute error = 3.99393631754460e-17
relative error = 2.7934286310660474600160836981897e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 1.4305831236874691579138585801337
y[1] (numeric) = 1.4305831236874691978809338649861
absolute error = 3.99670752848524e-17
relative error = 2.7937611330010184850218747895319e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 1.4314054571752852143730132383785
y[1] (numeric) = 1.4314054571752852543677606803471
absolute error = 3.99947474419686e-17
relative error = 2.7940893505389908885986730241902e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 1.4322283592575967126699642266353
y[1] (numeric) = 1.4322283592575967526923438457577
absolute error = 4.00223796191224e-17
relative error = 2.7944132903406699842947217561736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 1.4330518291115016390683844880724
y[1] (numeric) = 1.433051829111501679118356276754
absolute error = 4.00499717886816e-17
relative error = 2.7947329590662995443590975022818e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 1.4338758659135302082858331622636
y[1] (numeric) = 1.4338758659135302483633570853178
absolute error = 4.00775239230542e-17
relative error = 2.7950483633756251880538403702358e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 1.4347004688396456869634722451501
y[1] (numeric) = 1.434700468839645727068508239838
absolute error = 4.01050359946879e-17
relative error = 2.7953595099278091571493023077040e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=156.4MB, alloc=4.4MB, time=10.11
x[1] = 0.971
y[1] (analytic) = 1.4355256370652452177027312781524
y[1] (numeric) = 1.435525637065245257835239254223
absolute error = 4.01325079760706e-17
relative error = 2.7956664053814150981663571486684e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 1.4363513697651606436680960298383
y[1] (numeric) = 1.4363513697651606838280358695688
absolute error = 4.01599398397305e-17
relative error = 2.7959690563943651012966093475331e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.973
y[1] (analytic) = 1.4371776661136593337551965674268
y[1] (numeric) = 1.4371776661136593739425281256624
absolute error = 4.01873315582356e-17
relative error = 2.7962674696238551917499831669037e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 1.4380045252844450083233695501071
y[1] (numeric) = 1.4380045252844450485380526543014
absolute error = 4.02146831041943e-17
relative error = 2.7965616517263476606221965419045e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 1.4388319464506585654918690116816
y[1] (numeric) = 1.4388319464506586057338634619366
absolute error = 4.02419944502550e-17
relative error = 2.7968516093574939750700576648748e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 1.4396599287848789079988993363884
y[1] (numeric) = 1.4396599287848789482681649054948
absolute error = 4.02692655691064e-17
relative error = 2.7971373491721066309062823000041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 1.4404884714591237706226435689417
y[1] (numeric) = 1.4404884714591238109191400024189
absolute error = 4.02964964334772e-17
relative error = 2.7974188778240895041515675942701e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 1.4413175736448505481634596378282
y[1] (numeric) = 1.4413175736448505884871466539649
absolute error = 4.03236870161367e-17
relative error = 2.7976962019664309404538967086592e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 1.4421472345129571239864165097351
y[1] (numeric) = 1.4421472345129571643372537996294
absolute error = 4.03508372898943e-17
relative error = 2.7979693282511206483221666613767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 1.4429774532337826991233417326401
y[1] (numeric) = 1.4429774532337827395012889602398
absolute error = 4.03779472275997e-17
relative error = 2.7982382633291154453046794142633e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 1.4438082289771086219335512655861
y[1] (numeric) = 1.4438082289771086623385680677291
absolute error = 4.04050168021430e-17
relative error = 2.7985030138502982521165166431710e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 1.4446395609121592183224319344801
y[1] (numeric) = 1.4446395609121592587544779209348
absolute error = 4.04320459864547e-17
relative error = 2.7987635864634303623128188582759e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 1.4454714482076026225170462954026
y[1] (numeric) = 1.445471448207602662976081048908
absolute error = 4.04590347535054e-17
relative error = 2.7990199878160831787330815287517e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 1.4463038900315516083979291298914
y[1] (numeric) = 1.4463038900315516488839122061979
absolute error = 4.04859830763065e-17
relative error = 2.7992722245546393842387107753136e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 1.4471368855515644213862442404742
y[1] (numeric) = 1.4471368855515644618991351683839
absolute error = 4.05128909279097e-17
relative error = 2.7995203033242112433185188677212e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 1.4479704339346456108854696593607
y[1] (numeric) = 1.4479704339346456514252279407677
absolute error = 4.05397582814070e-17
relative error = 2.7997642307685937743163852457289e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 1.4488045343472468632767788286789
y[1] (numeric) = 1.4488045343472469038433639386102
absolute error = 4.05665851099313e-17
relative error = 2.8000040135302595547642218952852e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 1.4496391859552678354672847569453
y[1] (numeric) = 1.4496391859552678760606561436008
absolute error = 4.05933713866555e-17
relative error = 2.8002396582502501288785418442477e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 1.4504743879240569889903136035916
y[1] (numeric) = 1.4504743879240570296104306883851
absolute error = 4.06201170847935e-17
relative error = 2.8004711715681988402091751279308e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 1.4513101394184124246568735913464
y[1] (numeric) = 1.4513101394184124653036957689458
absolute error = 4.06468221775994e-17
relative error = 2.8006985601222296185765455108838e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 1.4521464396025827177574845950707
y[1] (numeric) = 1.452146439602582758430971233439
absolute error = 4.06734866383683e-17
relative error = 2.8009218305489663574635774816234e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.992
y[1] (analytic) = 1.4529832876402677538135332052885
y[1] (numeric) = 1.4529832876402677945136436457243
absolute error = 4.07001104404358e-17
relative error = 2.8011409894834528475539249660865e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 1.4538206826946195648773175151265
y[1] (numeric) = 1.4538206826946196056040110723045
absolute error = 4.07266935571780e-17
relative error = 2.8013560435591074387787042498041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 1.4546586239282431663799453306873
y[1] (numeric) = 1.454658623928243207133181292699
absolute error = 4.07532359620117e-17
relative error = 2.8015669994076916681806531738709e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=160.2MB, alloc=4.4MB, time=10.35
x[1] = 0.995
y[1] (analytic) = 1.4554971105031973945262489570286
y[1] (numeric) = 1.4554971105031974353059865854232
absolute error = 4.07797376283946e-17
relative error = 2.8017738636592790567305962573527e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 1.4563361415809957442358791649033
y[1] (numeric) = 1.4563361415809957850420776947282
absolute error = 4.08061985298249e-17
relative error = 2.8019766429421828754864747950088e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.997
y[1] (analytic) = 1.4571757163226072076297403972349
y[1] (numeric) = 1.4571757163226072484623590370769
absolute error = 4.08326186398420e-17
relative error = 2.8021753438829597109625527266021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 1.4580158338884571130609287289657
y[1] (numeric) = 1.4580158338884571539199266609912
absolute error = 4.08589979320255e-17
relative error = 2.8023699731062964828347974079823e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 1.4588564934384279646893335494061
y[1] (numeric) = 1.4588564934384280055746699294024
absolute error = 4.08853363799963e-17
relative error = 2.8025605372350418621616920097980e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 1.459697694131860282599063392557
y[1] (numeric) = 1.4596976941318603235106973499728
absolute error = 4.09116339574158e-17
relative error = 2.8027470428901074792482484943784e-15 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = sin(x);
Iterations = 1000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Expected Time Remaining = 41 Seconds
Optimized Time Remaining = 41 Seconds
Time to Timeout = 14 Minutes 49 Seconds
Percent Done = 20.02 %
> quit
memory used=161.1MB, alloc=4.4MB, time=10.41