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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_small_float,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_iter,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_hmin,
> days_in_year,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_look_poles,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_disp_incr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> sec_in_min,
> glob_percent_done,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_optimal_start,
> glob_dump_analytic,
> glob_hmax,
> glob_h,
> glob_max_sec,
> glob_log10_relerr,
> glob_log10normmin,
> glob_normmax,
> glob_almost_1,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_html_log,
> glob_max_minutes,
> glob_relerr,
> glob_abserr,
> glob_initial_pass,
> years_in_century,
> djd_debug,
> glob_max_opt_iter,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> min_in_hour,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp1_g,
> array_m1,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_tmp3_g,
> array_y_init,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_small_float, glob_reached_optimal_h, glob_not_yet_finished,
glob_clock_start_sec, glob_iter, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_large_float, glob_hmin, days_in_year, djd_debug2, glob_dump,
glob_optimal_expect_sec, glob_subiter_method, glob_log10relerr,
glob_smallish_float, glob_max_trunc_err, glob_look_poles, glob_clock_sec,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec,
glob_disp_incr, glob_not_yet_start_msg, centuries_in_millinium, sec_in_min,
glob_percent_done, glob_current_iter, glob_start, glob_warned,
glob_optimal_start, glob_dump_analytic, glob_hmax, glob_h, glob_max_sec,
glob_log10_relerr, glob_log10normmin, glob_normmax, glob_almost_1,
glob_log10abserr, glob_orig_start_sec, glob_log10_abserr, glob_last_good_h,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_html_log,
glob_max_minutes, glob_relerr, glob_abserr, glob_initial_pass,
years_in_century, djd_debug, glob_max_opt_iter, glob_no_eqs,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, min_in_hour,
glob_display_flag, array_const_1, array_const_0D0, array_tmp1_g, array_m1,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_tmp3_g,
array_y_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_pole, array_norms, array_complex_pole,
array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher,
array_poles, array_y_higher_work2, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_small_float,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_iter,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_hmin,
> days_in_year,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_look_poles,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_disp_incr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> sec_in_min,
> glob_percent_done,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_optimal_start,
> glob_dump_analytic,
> glob_hmax,
> glob_h,
> glob_max_sec,
> glob_log10_relerr,
> glob_log10normmin,
> glob_normmax,
> glob_almost_1,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_html_log,
> glob_max_minutes,
> glob_relerr,
> glob_abserr,
> glob_initial_pass,
> years_in_century,
> djd_debug,
> glob_max_opt_iter,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> min_in_hour,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp1_g,
> array_m1,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_tmp3_g,
> array_y_init,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_small_float, glob_reached_optimal_h, glob_not_yet_finished,
glob_clock_start_sec, glob_iter, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_large_float, glob_hmin, days_in_year, djd_debug2, glob_dump,
glob_optimal_expect_sec, glob_subiter_method, glob_log10relerr,
glob_smallish_float, glob_max_trunc_err, glob_look_poles, glob_clock_sec,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec,
glob_disp_incr, glob_not_yet_start_msg, centuries_in_millinium, sec_in_min,
glob_percent_done, glob_current_iter, glob_start, glob_warned,
glob_optimal_start, glob_dump_analytic, glob_hmax, glob_h, glob_max_sec,
glob_log10_relerr, glob_log10normmin, glob_normmax, glob_almost_1,
glob_log10abserr, glob_orig_start_sec, glob_log10_abserr, glob_last_good_h,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_html_log,
glob_max_minutes, glob_relerr, glob_abserr, glob_initial_pass,
years_in_century, djd_debug, glob_max_opt_iter, glob_no_eqs,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, min_in_hour,
glob_display_flag, array_const_1, array_const_0D0, array_tmp1_g, array_m1,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_tmp3_g,
array_y_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_pole, array_norms, array_complex_pole,
array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher,
array_poles, array_y_higher_work2, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_small_float,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_iter,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_hmin,
> days_in_year,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_look_poles,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_disp_incr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> sec_in_min,
> glob_percent_done,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_optimal_start,
> glob_dump_analytic,
> glob_hmax,
> glob_h,
> glob_max_sec,
> glob_log10_relerr,
> glob_log10normmin,
> glob_normmax,
> glob_almost_1,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_html_log,
> glob_max_minutes,
> glob_relerr,
> glob_abserr,
> glob_initial_pass,
> years_in_century,
> djd_debug,
> glob_max_opt_iter,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> min_in_hour,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp1_g,
> array_m1,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_tmp3_g,
> array_y_init,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_small_float, glob_reached_optimal_h, glob_not_yet_finished,
glob_clock_start_sec, glob_iter, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_large_float, glob_hmin, days_in_year, djd_debug2, glob_dump,
glob_optimal_expect_sec, glob_subiter_method, glob_log10relerr,
glob_smallish_float, glob_max_trunc_err, glob_look_poles, glob_clock_sec,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec,
glob_disp_incr, glob_not_yet_start_msg, centuries_in_millinium, sec_in_min,
glob_percent_done, glob_current_iter, glob_start, glob_warned,
glob_optimal_start, glob_dump_analytic, glob_hmax, glob_h, glob_max_sec,
glob_log10_relerr, glob_log10normmin, glob_normmax, glob_almost_1,
glob_log10abserr, glob_orig_start_sec, glob_log10_abserr, glob_last_good_h,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_html_log,
glob_max_minutes, glob_relerr, glob_abserr, glob_initial_pass,
years_in_century, djd_debug, glob_max_opt_iter, glob_no_eqs,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, min_in_hour,
glob_display_flag, array_const_1, array_const_0D0, array_tmp1_g, array_m1,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_tmp3_g,
array_y_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_pole, array_norms, array_complex_pole,
array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher,
array_poles, array_y_higher_work2, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_small_float,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_iter,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_hmin,
> days_in_year,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_look_poles,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_disp_incr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> sec_in_min,
> glob_percent_done,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_optimal_start,
> glob_dump_analytic,
> glob_hmax,
> glob_h,
> glob_max_sec,
> glob_log10_relerr,
> glob_log10normmin,
> glob_normmax,
> glob_almost_1,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_html_log,
> glob_max_minutes,
> glob_relerr,
> glob_abserr,
> glob_initial_pass,
> years_in_century,
> djd_debug,
> glob_max_opt_iter,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> min_in_hour,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp1_g,
> array_m1,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_tmp3_g,
> array_y_init,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_small_float, glob_reached_optimal_h, glob_not_yet_finished,
glob_clock_start_sec, glob_iter, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_large_float, glob_hmin, days_in_year, djd_debug2, glob_dump,
glob_optimal_expect_sec, glob_subiter_method, glob_log10relerr,
glob_smallish_float, glob_max_trunc_err, glob_look_poles, glob_clock_sec,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec,
glob_disp_incr, glob_not_yet_start_msg, centuries_in_millinium, sec_in_min,
glob_percent_done, glob_current_iter, glob_start, glob_warned,
glob_optimal_start, glob_dump_analytic, glob_hmax, glob_h, glob_max_sec,
glob_log10_relerr, glob_log10normmin, glob_normmax, glob_almost_1,
glob_log10abserr, glob_orig_start_sec, glob_log10_abserr, glob_last_good_h,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_html_log,
glob_max_minutes, glob_relerr, glob_abserr, glob_initial_pass,
years_in_century, djd_debug, glob_max_opt_iter, glob_no_eqs,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, min_in_hour,
glob_display_flag, array_const_1, array_const_0D0, array_tmp1_g, array_m1,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_tmp3_g,
array_y_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_pole, array_norms, array_complex_pole,
array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher,
array_poles, array_y_higher_work2, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_small_float,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_iter,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_hmin,
> days_in_year,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_look_poles,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_disp_incr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> sec_in_min,
> glob_percent_done,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_optimal_start,
> glob_dump_analytic,
> glob_hmax,
> glob_h,
> glob_max_sec,
> glob_log10_relerr,
> glob_log10normmin,
> glob_normmax,
> glob_almost_1,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_html_log,
> glob_max_minutes,
> glob_relerr,
> glob_abserr,
> glob_initial_pass,
> years_in_century,
> djd_debug,
> glob_max_opt_iter,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> min_in_hour,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp1_g,
> array_m1,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_tmp3_g,
> array_y_init,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_small_float, glob_reached_optimal_h, glob_not_yet_finished,
glob_clock_start_sec, glob_iter, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_large_float, glob_hmin, days_in_year, djd_debug2, glob_dump,
glob_optimal_expect_sec, glob_subiter_method, glob_log10relerr,
glob_smallish_float, glob_max_trunc_err, glob_look_poles, glob_clock_sec,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec,
glob_disp_incr, glob_not_yet_start_msg, centuries_in_millinium, sec_in_min,
glob_percent_done, glob_current_iter, glob_start, glob_warned,
glob_optimal_start, glob_dump_analytic, glob_hmax, glob_h, glob_max_sec,
glob_log10_relerr, glob_log10normmin, glob_normmax, glob_almost_1,
glob_log10abserr, glob_orig_start_sec, glob_log10_abserr, glob_last_good_h,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_html_log,
glob_max_minutes, glob_relerr, glob_abserr, glob_initial_pass,
years_in_century, djd_debug, glob_max_opt_iter, glob_no_eqs,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, min_in_hour,
glob_display_flag, array_const_1, array_const_0D0, array_tmp1_g, array_m1,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_tmp3_g,
array_y_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_pole, array_norms, array_complex_pole,
array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher,
array_poles, array_y_higher_work2, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_small_float,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_iter,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_hmin,
> days_in_year,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_look_poles,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_disp_incr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> sec_in_min,
> glob_percent_done,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_optimal_start,
> glob_dump_analytic,
> glob_hmax,
> glob_h,
> glob_max_sec,
> glob_log10_relerr,
> glob_log10normmin,
> glob_normmax,
> glob_almost_1,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_html_log,
> glob_max_minutes,
> glob_relerr,
> glob_abserr,
> glob_initial_pass,
> years_in_century,
> djd_debug,
> glob_max_opt_iter,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> min_in_hour,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp1_g,
> array_m1,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_tmp3_g,
> array_y_init,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> 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 cos $eq_no = 1
> array_tmp3_g[1] := sin(array_x[1]);
> array_tmp3[1] := cos(array_x[1]);
> #emit pre sub $eq_no = 1 i = 1
> array_tmp4[1] := (array_tmp2[1] - (array_tmp3[1]));
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * (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 cos $eq_no = 1
> array_tmp3_g[2] := (att(1,array_tmp3,array_x,1));
> array_tmp3[2] := (-att(1,array_tmp3_g,array_x,1));
> #emit pre sub $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp2[2] - (array_tmp3[2]));
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * (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 cos $eq_no = 1
> array_tmp3_g[3] := (att(2,array_tmp3,array_x,1));
> array_tmp3[3] := (-att(2,array_tmp3_g,array_x,1));
> #emit pre sub $eq_no = 1 i = 3
> array_tmp4[3] := (array_tmp2[3] - (array_tmp3[3]));
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * (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 cos $eq_no = 1
> array_tmp3_g[4] := (att(3,array_tmp3,array_x,1));
> array_tmp3[4] := (-att(3,array_tmp3_g,array_x,1));
> #emit pre sub $eq_no = 1 i = 4
> array_tmp4[4] := (array_tmp2[4] - (array_tmp3[4]));
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * (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 cos $eq_no = 1
> array_tmp3_g[5] := (att(4,array_tmp3,array_x,1));
> array_tmp3[5] := (-att(4,array_tmp3_g,array_x,1));
> #emit pre sub $eq_no = 1 i = 5
> array_tmp4[5] := (array_tmp2[5] - (array_tmp3[5]));
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * (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 cos $eq_no = 1
> array_tmp3_g[kkk] := (att(kkk-1,array_tmp3,array_x,1));
> array_tmp3[kkk] := (-att(kkk-1,array_tmp3_g,array_x,1));
> #emit sub $eq_no = 1
> array_tmp4[kkk] := (array_tmp2[kkk] - (array_tmp3[kkk]));
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp4[kkk] * (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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_small_float, glob_reached_optimal_h, glob_not_yet_finished,
glob_clock_start_sec, glob_iter, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_large_float, glob_hmin, days_in_year, djd_debug2, glob_dump,
glob_optimal_expect_sec, glob_subiter_method, glob_log10relerr,
glob_smallish_float, glob_max_trunc_err, glob_look_poles, glob_clock_sec,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec,
glob_disp_incr, glob_not_yet_start_msg, centuries_in_millinium, sec_in_min,
glob_percent_done, glob_current_iter, glob_start, glob_warned,
glob_optimal_start, glob_dump_analytic, glob_hmax, glob_h, glob_max_sec,
glob_log10_relerr, glob_log10normmin, glob_normmax, glob_almost_1,
glob_log10abserr, glob_orig_start_sec, glob_log10_abserr, glob_last_good_h,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_html_log,
glob_max_minutes, glob_relerr, glob_abserr, glob_initial_pass,
years_in_century, djd_debug, glob_max_opt_iter, glob_no_eqs,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, min_in_hour,
glob_display_flag, array_const_1, array_const_0D0, array_tmp1_g, array_m1,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_tmp3_g,
array_y_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_pole, array_norms, array_complex_pole,
array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher,
array_poles, array_y_higher_work2, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3_g[1] := sin(array_x[1]);
array_tmp3[1] := cos(array_x[1]);
array_tmp4[1] := array_tmp2[1] - array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*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];
array_tmp3_g[2] := att(1, array_tmp3, array_x, 1);
array_tmp3[2] := -att(1, array_tmp3_g, array_x, 1);
array_tmp4[2] := array_tmp2[2] - array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*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];
array_tmp3_g[3] := att(2, array_tmp3, array_x, 1);
array_tmp3[3] := -att(2, array_tmp3_g, array_x, 1);
array_tmp4[3] := array_tmp2[3] - array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*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];
array_tmp3_g[4] := att(3, array_tmp3, array_x, 1);
array_tmp3[4] := -att(3, array_tmp3_g, array_x, 1);
array_tmp4[4] := array_tmp2[4] - array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*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];
array_tmp3_g[5] := att(4, array_tmp3, array_x, 1);
array_tmp3[5] := -att(4, array_tmp3_g, array_x, 1);
array_tmp4[5] := array_tmp2[5] - array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*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];
array_tmp3_g[kkk] := att(kkk - 1, array_tmp3, array_x, 1);
array_tmp3[kkk] := -att(kkk - 1, array_tmp3_g, array_x, 1);
array_tmp4[kkk] := array_tmp2[kkk] - array_tmp3[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_tmp4[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)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! 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) - sin(x);
> end;
exact_soln_y := proc(x) 2.0 - cos(x) - sin(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,
> 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_small_float,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_iter,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_hmin,
> days_in_year,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_look_poles,
> glob_clock_sec,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_disp_incr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> sec_in_min,
> glob_percent_done,
> glob_current_iter,
> glob_start,
> glob_warned,
> glob_optimal_start,
> glob_dump_analytic,
> glob_hmax,
> glob_h,
> glob_max_sec,
> glob_log10_relerr,
> glob_log10normmin,
> glob_normmax,
> glob_almost_1,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_log10_abserr,
> glob_last_good_h,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_html_log,
> glob_max_minutes,
> glob_relerr,
> glob_abserr,
> glob_initial_pass,
> years_in_century,
> djd_debug,
> glob_max_opt_iter,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> min_in_hour,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp1_g,
> array_m1,
> array_last_rel_error,
> array_1st_rel_error,
> array_y,
> array_x,
> array_tmp3_g,
> array_y_init,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_pole,
> array_norms,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> glob_iolevel := 5;
> INFO := 2;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_max_terms := 30;
> glob_small_float := 0.1e-50;
> glob_reached_optimal_h := false;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> glob_iter := 0;
> MAX_UNCHANGED := 10;
> glob_unchanged_h_cnt := 0;
> glob_large_float := 9.0e100;
> glob_hmin := 0.00000000001;
> days_in_year := 365.0;
> djd_debug2 := true;
> glob_dump := false;
> glob_optimal_expect_sec := 0.1;
> glob_subiter_method := 3;
> glob_log10relerr := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_max_trunc_err := 0.1e-10;
> glob_look_poles := false;
> glob_clock_sec := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_warned2 := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_disp_incr := 0.1;
> glob_not_yet_start_msg := true;
> centuries_in_millinium := 10.0;
> sec_in_min := 60.0;
> glob_percent_done := 0.0;
> glob_current_iter := 0;
> glob_start := 0;
> glob_warned := false;
> glob_optimal_start := 0.0;
> glob_dump_analytic := false;
> glob_hmax := 1.0;
> glob_h := 0.1;
> glob_max_sec := 10000.0;
> glob_log10_relerr := 0.1e-10;
> glob_log10normmin := 0.1;
> glob_normmax := 0.0;
> glob_almost_1 := 0.9990;
> glob_log10abserr := 0.0;
> glob_orig_start_sec := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> hours_in_day := 24.0;
> glob_html_log := true;
> glob_max_minutes := 0.0;
> glob_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_initial_pass := true;
> years_in_century := 100.0;
> djd_debug := true;
> glob_max_opt_iter := 10;
> glob_no_eqs := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_max_hours := 0.0;
> min_in_hour := 60.0;
> glob_display_flag := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/subpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 10.0;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> 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) - sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 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_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_tmp3_g:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[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_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_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_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_tmp3_g[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_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[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_norms[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_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 <=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 <=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
> ;
> 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 <=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_higher_work2[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_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_tmp3_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3_g[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_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 10.0;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> 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)) / (convfp(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)) / (convfp(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)) / (convfp(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 ) - cos ( 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,"2012-06-13T19:35:38-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_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," 090 | ")
> ;
> logitem_str(html_log_file,"sub diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> 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, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_small_float, glob_reached_optimal_h, glob_not_yet_finished,
glob_clock_start_sec, glob_iter, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_large_float, glob_hmin, days_in_year, djd_debug2, glob_dump,
glob_optimal_expect_sec, glob_subiter_method, glob_log10relerr,
glob_smallish_float, glob_max_trunc_err, glob_look_poles, glob_clock_sec,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec,
glob_disp_incr, glob_not_yet_start_msg, centuries_in_millinium, sec_in_min,
glob_percent_done, glob_current_iter, glob_start, glob_warned,
glob_optimal_start, glob_dump_analytic, glob_hmax, glob_h, glob_max_sec,
glob_log10_relerr, glob_log10normmin, glob_normmax, glob_almost_1,
glob_log10abserr, glob_orig_start_sec, glob_log10_abserr, glob_last_good_h,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_html_log,
glob_max_minutes, glob_relerr, glob_abserr, glob_initial_pass,
years_in_century, djd_debug, glob_max_opt_iter, glob_no_eqs,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, min_in_hour,
glob_display_flag, array_const_1, array_const_0D0, array_tmp1_g, array_m1,
array_last_rel_error, array_1st_rel_error, array_y, array_x, array_tmp3_g,
array_y_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_pole, array_norms, array_complex_pole,
array_y_set_initial, array_real_pole, array_y_higher_work, array_y_higher,
array_poles, array_y_higher_work2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
glob_iolevel := 5;
INFO := 2;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_max_terms := 30;
glob_small_float := 0.1*10^(-50);
glob_reached_optimal_h := false;
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
glob_iter := 0;
MAX_UNCHANGED := 10;
glob_unchanged_h_cnt := 0;
glob_large_float := 0.90*10^101;
glob_hmin := 0.1*10^(-10);
days_in_year := 365.0;
djd_debug2 := true;
glob_dump := false;
glob_optimal_expect_sec := 0.1;
glob_subiter_method := 3;
glob_log10relerr := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_max_trunc_err := 0.1*10^(-10);
glob_look_poles := false;
glob_clock_sec := 0.;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_optimal_clock_start_sec := 0.;
glob_disp_incr := 0.1;
glob_not_yet_start_msg := true;
centuries_in_millinium := 10.0;
sec_in_min := 60.0;
glob_percent_done := 0.;
glob_current_iter := 0;
glob_start := 0;
glob_warned := false;
glob_optimal_start := 0.;
glob_dump_analytic := false;
glob_hmax := 1.0;
glob_h := 0.1;
glob_max_sec := 10000.0;
glob_log10_relerr := 0.1*10^(-10);
glob_log10normmin := 0.1;
glob_normmax := 0.;
glob_almost_1 := 0.9990;
glob_log10abserr := 0.;
glob_orig_start_sec := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_hmin_init := 0.001;
glob_optimal_done := false;
hours_in_day := 24.0;
glob_html_log := true;
glob_max_minutes := 0.;
glob_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_initial_pass := true;
years_in_century := 100.0;
djd_debug := true;
glob_max_opt_iter := 10;
glob_no_eqs := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_max_hours := 0.;
min_in_hour := 60.0;
glob_display_flag := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/subpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 10.0;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
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) - sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*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_tmp1_g := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_tmp3_g := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[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_tmp3_g[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_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 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 <= 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 <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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 <= 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_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_tmp3_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp3_g[term] := 0.; term := term + 1
end do;
array_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_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_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_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.;
x_end := 10.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.0001;
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)/convfp(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)/convfp(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)/convfp(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 ) - cos ( x );");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T19:35:38-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sub");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) - cos ( x );");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_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, " 090 | ");
logitem_str(html_log_file,
"sub diffeq.mxt");
logitem_str(html_log_file,
"sub maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/subpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) - cos ( x );
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 10.0;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
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) - sin(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 = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0001
y[1] (analytic) = 0.99990000500016666249991666805555
y[1] (numeric) = 0.99990000500016666249991671666764
absolute error = 4.861209e-26
relative error = 4.8616951452052345351606107523812e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0002
y[1] (analytic) = 0.99980002000133326666400008889141
y[1] (numeric) = 0.99980002000133326666400018612042
absolute error = 9.722901e-26
relative error = 9.7248457746450477039559607500392e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0003
y[1] (analytic) = 0.99970004500449966247975101254339
y[1] (numeric) = 0.99970004500449966247975115839417
absolute error = 1.4585078e-25
relative error = 1.4589454179662813139542996271201e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0004
y[1] (analytic) = 0.99960008001066559991467235588061
y[1] (numeric) = 0.99960008001066559991467255035804
absolute error = 1.9447743e-25
relative error = 1.9455523652811727634704336194274e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0005
y[1] (analytic) = 0.99950012502083072890627170293887
y[1] (numeric) = 0.99950012502083072890627194604782
absolute error = 2.4310895e-25
relative error = 2.4323053485854574622152664968593e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0006
y[1] (analytic) = 0.99940018003599459935206480555389
y[1] (numeric) = 0.99940018003599459935206509729916
absolute error = 2.9174527e-25
relative error = 2.9192036966562527860579249228149e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0007
y[1] (analytic) = 0.99930024505715666109958008439427
y[1] (numeric) = 0.99930024505715666109958042478078
absolute error = 3.4038651e-25
relative error = 3.4062486393219189102684261665569e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0008
y[1] (analytic) = 0.99920032008531626393636413049493
y[1] (numeric) = 0.99920032008531626393636451952748
absolute error = 3.8903255e-25
relative error = 3.8934390049713217968462337698187e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0009
y[1] (analytic) = 0.99910040512147265757998820738948
y[1] (numeric) = 0.99910040512147265757998864507303
absolute error = 4.3768355e-25
relative error = 4.3807764240350352430381678634084e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 0.99900050016662499166805575394343
y[1] (numeric) = 0.99900050016662499166805624028277
absolute error = 4.8633934e-25
relative error = 4.8682592242834977032702452373881e-23 %
memory used=3.8MB, alloc=2.9MB, time=0.21
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0011
y[1] (analytic) = 0.99890060522177231574821088798598
y[1] (numeric) = 0.99890060522177231574821142298591
absolute error = 5.3499993e-25
relative error = 5.3558875347885212448369407482226e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0012
y[1] (analytic) = 0.99880072028791357926814791084196
y[1] (numeric) = 0.99880072028791357926814849450739
absolute error = 5.8366543e-25
relative error = 5.8436624858635766879102918976600e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0013
y[1] (analytic) = 0.99870084536604763156562181286346
y[1] (numeric) = 0.99870084536604763156562244519931
absolute error = 6.3233585e-25
relative error = 6.3315842069627352693218106889102e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0014
y[1] (analytic) = 0.99860098045717322185845978006059
y[1] (numeric) = 0.99860098045717322185846046107165
absolute error = 6.8101106e-25
relative error = 6.8196514256197084703419773277264e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0015
y[1] (analytic) = 0.99850112556228899923457370193126
y[1] (numeric) = 0.99850112556228899923457443162235
absolute error = 7.2969109e-25
relative error = 7.3078644712502133634739975151081e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0016
y[1] (analytic) = 0.99840128068239351264197368059046
y[1] (numeric) = 0.99840128068239351264197445896652
absolute error = 7.7837606e-25
relative error = 7.7962245748321826340553059955079e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0017
y[1] (analytic) = 0.99830144581848521087878254129878
y[1] (numeric) = 0.99830144581848521087878336836463
absolute error = 8.2706585e-25
relative error = 8.2847305637417669544312088116337e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0018
y[1] (analytic) = 0.99820162097156244258325134448921
y[1] (numeric) = 0.99820162097156244258325222024965
absolute error = 8.7576044e-25
relative error = 8.7733822666768576224819691042557e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0019
y[1] (analytic) = 0.99810180614262345622377589939282
y[1] (numeric) = 0.9981018061426234562237768238528
absolute error = 9.2445998e-25
relative error = 9.2621812154891499143084445805360e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 0.99800200133266640008891427936365
y[1] (numeric) = 0.99800200133266640008891525252795
absolute error = 9.7316430e-25
relative error = 9.7511257362259818800857681884205e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0021
y[1] (analytic) = 0.99790220654268932227740533900086
y[1] (numeric) = 0.99790220654268932227740636087436
absolute error = 1.02187350e-24
relative error = 1.0240216859930204074837788016508e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0022
y[1] (analytic) = 0.99780242177369017068818823317004
y[1] (numeric) = 0.99780242177369017068818930375758
absolute error = 1.07058754e-24
relative error = 1.0729454214962990891594742777538e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0023
y[1] (analytic) = 0.99770264702666679301042293802206
y[1] (numeric) = 0.99770264702666679301042405732841
absolute error = 1.11930635e-24
relative error = 1.1218837128835270688088795119122e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0024
y[1] (analytic) = 0.99760288230261693671351177410946
y[1] (numeric) = 0.99760288230261693671351294213957
absolute error = 1.16803011e-24
relative error = 1.1708367434785387591702053812940e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0025
y[1] (analytic) = 0.99750312760253824903712193170132
y[1] (numeric) = 0.99750312760253824903712314846004
absolute error = 1.21675872e-24
relative error = 1.2198044159765538088681481864983e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.0MB, time=0.46
NO POLE
x[1] = 0.0026
y[1] (analytic) = 0.99740338292742827698120899839452
y[1] (numeric) = 0.99740338292742827698121026388667
absolute error = 1.26549215e-24
relative error = 1.2687867032150201130766020492461e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0027
y[1] (analytic) = 0.99730364827828446729604148912252
y[1] (numeric) = 0.99730364827828446729604280335296
absolute error = 1.31423044e-24
relative error = 1.3177836482086960935761150141478e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0028
y[1] (analytic) = 0.99720392365610416647222637866104
y[1] (numeric) = 0.99720392365610416647222774163465
absolute error = 1.36297361e-24
relative error = 1.3667952739323909840439028140966e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0029
y[1] (analytic) = 0.99710420906188462073073563673046
y[1] (numeric) = 0.997104209061884620730737048452
absolute error = 1.41172154e-24
relative error = 1.4158214629624358809041336450736e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 0.99700450449662297601293376579399
y[1] (numeric) = 0.99700450449662297601293522626837
absolute error = 1.46047438e-24
relative error = 1.4648623686383223109666926033106e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0031
y[1] (analytic) = 0.99690480996131627797060634165279
y[1] (numeric) = 0.99690480996131627797060785088487
absolute error = 1.50923208e-24
relative error = 1.5139179437388450166178902357066e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0032
y[1] (analytic) = 0.99680512545696147195598955693624
y[1] (numeric) = 0.99680512545696147195599111493083
absolute error = 1.55799459e-24
relative error = 1.5629881410228249362466451324919e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0033
y[1] (analytic) = 0.99670545098455540301180076758782
y[1] (numeric) = 0.99670545098455540301180237434974
absolute error = 1.60676192e-24
relative error = 1.6120729734274301840756709872199e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0034
y[1] (analytic) = 0.99660578654509481586127004244619
y[1] (numeric) = 0.99660578654509481586127169798038
absolute error = 1.65553419e-24
relative error = 1.6611725642685596920327689923896e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0035
y[1] (analytic) = 0.99650613213957635489817271602167
y[1] (numeric) = 0.99650613213957635489817442033283
absolute error = 1.70431116e-24
relative error = 1.7102866756481578981213100102844e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0036
y[1] (analytic) = 0.99640648776899656417686294456594
y[1] (numeric) = 0.99640648776899656417686469765901
absolute error = 1.75309307e-24
relative error = 1.7594155513030250736300481155479e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0037
y[1] (analytic) = 0.99630685343435188740230826553763
y[1] (numeric) = 0.99630685343435188740231006741747
absolute error = 1.80187984e-24
relative error = 1.8085591138801982479262237081609e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0038
y[1] (analytic) = 0.99620722913663866792012516056053
y[1] (numeric) = 0.996207229136638667920127011232
absolute error = 1.85067147e-24
relative error = 1.8577173662992601850480909080882e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0039
y[1] (analytic) = 0.99610761487685314870661562197591
y[1] (numeric) = 0.99610761487685314870661752144375
absolute error = 1.89946784e-24
relative error = 1.9068901910109657406697375063058e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 0.99600801065599147235880472308743
y[1] (numeric) = 0.99600801065599147235880667135655
absolute error = 1.94826912e-24
relative error = 1.9560777615802805332184394654214e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.1MB, time=0.72
x[1] = 0.0041
y[1] (analytic) = 0.9959084164750496810844791921997
y[1] (numeric) = 0.99590841647504968108448118927494
absolute error = 1.99707524e-24
relative error = 2.0052800106545061774570803544170e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0042
y[1] (analytic) = 0.99580883233502371669222699054842
y[1] (numeric) = 0.99580883233502371669222903643461
absolute error = 2.04588619e-24
relative error = 2.0544969311054421359141757040502e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0043
y[1] (analytic) = 0.99570925823690942058147789422278
y[1] (numeric) = 0.9957092582369094205814799889248
absolute error = 2.09470202e-24
relative error = 2.1037285760595055971499714438420e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0044
y[1] (analytic) = 0.99560969418170253373254508017966
y[1] (numeric) = 0.99560969418170253373254722370233
absolute error = 2.14352267e-24
relative error = 2.1529748881782171636382992308003e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0045
y[1] (analytic) = 0.99551014017039869669666771644858
y[1] (numeric) = 0.99551014017039869669666990879674
absolute error = 2.19234816e-24
relative error = 2.2022358904598820806054377349318e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0046
y[1] (analytic) = 0.99541059620399344958605455662774
y[1] (numeric) = 0.99541059620399344958605679780622
absolute error = 2.24117848e-24
relative error = 2.2515115757726034763600338034440e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0047
y[1] (analytic) = 0.99531106228348223206392853877018
y[1] (numeric) = 0.99531106228348223206393082878379
absolute error = 2.29001361e-24
relative error = 2.3008019269334349407802744207543e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0048
y[1] (analytic) = 0.99521153840986038333457238875987
y[1] (numeric) = 0.99521153840986038333457472761341
absolute error = 2.33885354e-24
relative error = 2.3501069367995854867250184618373e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0049
y[1] (analytic) = 0.99511202458412314213337522827694
y[1] (numeric) = 0.99511202458412314213337761597539
absolute error = 2.38769845e-24
relative error = 2.3994267891575986871989276917034e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 0.99501252080726564671688018745277
y[1] (numeric) = 0.99501252080726564671688262400084
absolute error = 2.43654807e-24
relative error = 2.4487612156108339155618931059089e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0051
y[1] (analytic) = 0.99491302708028293485283302231195
y[1] (numeric) = 0.9949130270802829348528355077145
absolute error = 2.48540255e-24
relative error = 2.4981103698016453531932976652756e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0052
y[1] (analytic) = 0.99481354340416994381023173710369
y[1] (numeric) = 0.9948135434041699438102342713656
absolute error = 2.53426191e-24
relative error = 2.5474742747550105130748672920956e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0053
y[1] (analytic) = 0.99471406977992151034937721162006
y[1] (numeric) = 0.99471406977992151034937979474615
absolute error = 2.58312609e-24
relative error = 2.5968528730789054367674581536710e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0054
y[1] (analytic) = 0.99461460620853237071192483360115
y[1] (numeric) = 0.99461460620853237071192746559624
absolute error = 2.63199509e-24
relative error = 2.6462461676821303518700785985449e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0055
y[1] (analytic) = 0.99451515269099716061093713632677
y[1] (numeric) = 0.99451515269099716061093981719575
absolute error = 2.68086898e-24
relative error = 2.6956542318596173382345286013840e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0056
y[1] (analytic) = 0.99441570922831041522093744149437
y[1] (numeric) = 0.99441570922831041522094017124205
absolute error = 2.72974768e-24
relative error = 2.7450769880921806043545053264145e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.98
NO POLE
x[1] = 0.0057
y[1] (analytic) = 0.99431627582146656916796450748184
y[1] (numeric) = 0.99431627582146656916796728611302
absolute error = 2.77863118e-24
relative error = 2.7945144292286675276748878819699e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0058
y[1] (analytic) = 0.99421685247145995651962818309545
y[1] (numeric) = 0.99421685247145995651963101061497
absolute error = 2.82751952e-24
relative error = 2.8439665984048152416277801532183e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0059
y[1] (analytic) = 0.99411743917928481077516606690205
y[1] (numeric) = 0.99411743917928481077516894331481
absolute error = 2.87641276e-24
relative error = 2.8934335588908739703777939034817e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 0.99401803594593526485550117224524
y[1] (numeric) = 0.99401803594593526485550409755598
absolute error = 2.92531074e-24
relative error = 2.9429151526573587526747376206602e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0061
y[1] (analytic) = 0.99391864277240535109330059804392
y[1] (numeric) = 0.99391864277240535109330357225749
absolute error = 2.97421357e-24
relative error = 2.9924114932624891343279173177545e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0062
y[1] (analytic) = 0.99381925965968900122303520547423
y[1] (numeric) = 0.99381925965968900122303822859554
absolute error = 3.02312131e-24
relative error = 3.0419226439978630854680541193578e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0063
y[1] (analytic) = 0.99371988660878004637104030063336
y[1] (numeric) = 0.99371988660878004637104337266709
absolute error = 3.07203373e-24
relative error = 3.0914483763465592094370791706034e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0064
y[1] (analytic) = 0.99362052362067221704557732328367
y[1] (numeric) = 0.99362052362067221704558044423479
absolute error = 3.12095112e-24
relative error = 3.1409889850377772470193483482817e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0065
y[1] (analytic) = 0.9935211706963591431268965417794
y[1] (numeric) = 0.99352117069635914312689971165265
absolute error = 3.16987325e-24
relative error = 3.1905442415265649003353468790451e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0066
y[1] (analytic) = 0.99342182783683435385730075427149
y[1] (numeric) = 0.99342182783683435385730397307181
absolute error = 3.21880032e-24
relative error = 3.2401143500227934910019926484908e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0067
y[1] (analytic) = 0.99332249504309127783120999629368
y[1] (numeric) = 0.99332249504309127783121326402579
absolute error = 3.26773211e-24
relative error = 3.2896990919935248848319173189751e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0068
y[1] (analytic) = 0.99322317231612324298522725482584
y[1] (numeric) = 0.99322317231612324298523057149459
absolute error = 3.31666875e-24
relative error = 3.3392986012053795467539920785601e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0069
y[1] (analytic) = 0.99312385965692347658820518893663
y[1] (numeric) = 0.99312385965692347658820855454691
absolute error = 3.36561028e-24
relative error = 3.3889129208542592693644378011696e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 0.99302455706648510523131385710335
y[1] (numeric) = 0.99302455706648510523131727165991
absolute error = 3.41455656e-24
relative error = 3.4385419128878483305014260164373e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0071
y[1] (analytic) = 0.99292526454580115481810945130806
y[1] (numeric) = 0.99292526454580115481811291481579
absolute error = 3.46350773e-24
relative error = 3.4881857211925511094187101294764e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0072
y[1] (analytic) = 0.99282598209586455055460403801082
y[1] (numeric) = 0.99282598209586455055460755047451
absolute error = 3.51246369e-24
relative error = 3.5378442479770298267994873239889e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=1.24
NO POLE
x[1] = 0.0073
y[1] (analytic) = 0.99272670971766811693933630609745
y[1] (numeric) = 0.99272670971766811693933986752193
absolute error = 3.56142448e-24
relative error = 3.5875175364354511843193723542744e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0074
y[1] (analytic) = 0.99262744741220457775344332190259
y[1] (numeric) = 0.99262744741220457775344693229269
absolute error = 3.61039010e-24
relative error = 3.6372055894810726564419596734804e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0075
y[1] (analytic) = 0.99252819518046655605073329140666
y[1] (numeric) = 0.99252819518046655605073695076714
absolute error = 3.65936048e-24
relative error = 3.6869083395002560602277510439037e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0076
y[1] (analytic) = 0.99242895302344657414775932970573
y[1] (numeric) = 0.9924289530234465741477630380415
absolute error = 3.70833577e-24
relative error = 3.7366259405295574068393113363145e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0077
y[1] (analytic) = 0.99232972094213705361389423785477
y[1] (numeric) = 0.99232972094213705361389799517062
absolute error = 3.75731585e-24
relative error = 3.7863582745790699196850485574182e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0078
y[1] (analytic) = 0.99223049893753031526140628718168
y[1] (numeric) = 0.99223049893753031526141009348252
absolute error = 3.80630084e-24
relative error = 3.8361054654898693041012322471931e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0079
y[1] (analytic) = 0.99213128701061857913553601117342
y[1] (numeric) = 0.99213128701061857913553986646396
absolute error = 3.85529054e-24
relative error = 3.8858673146135120425948059151736e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 0.99203208516239396450457400503119
y[1] (numeric) = 0.99203208516239396450457790931632
absolute error = 3.90428513e-24
relative error = 3.9356440062731188446819678272268e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0081
y[1] (analytic) = 0.99193289339384848984993973299648
y[1] (numeric) = 0.99193289339384848984994368628095
absolute error = 3.95328447e-24
relative error = 3.9854354022619777015748513931071e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0082
y[1] (analytic) = 0.9918337117059740728562613435446
y[1] (numeric) = 0.99183371170597407285626534583326
absolute error = 4.00228866e-24
relative error = 4.0352416062930372087809206327107e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0083
y[1] (analytic) = 0.99173454009976253040145649254701
y[1] (numeric) = 0.99173454009976253040146054384469
absolute error = 4.05129768e-24
relative error = 4.0850626011195131088849256336369e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0084
y[1] (analytic) = 0.99163537857620557854681417450018
y[1] (numeric) = 0.99163537857620557854681827481181
absolute error = 4.10031163e-24
relative error = 4.1348984904988418263650999272684e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0085
y[1] (analytic) = 0.99153622713629483252707756192143
y[1] (numeric) = 0.99153622713629483252708171125166
absolute error = 4.14933023e-24
relative error = 4.1847489949851729790208055694202e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0086
y[1] (analytic) = 0.99143708578102180674052785300887
y[1] (numeric) = 0.99143708578102180674053205136264
absolute error = 4.19835377e-24
relative error = 4.2346144099427890602831430439636e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0087
y[1] (analytic) = 0.99133795451137791473906912766789
y[1] (numeric) = 0.9913379545113779147390733750499
absolute error = 4.24738201e-24
relative error = 4.2844944962220261555838320842535e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=1.50
NO POLE
x[1] = 0.0088
y[1] (analytic) = 0.99123883332835446921831421199941
y[1] (numeric) = 0.99123883332835446921831850841461
absolute error = 4.29641520e-24
relative error = 4.3343895089073692832384131975182e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0089
y[1] (analytic) = 0.991139722232942682007671551353
y[1] (numeric) = 0.99113972223294268200767589680607
absolute error = 4.34545307e-24
relative error = 4.3842991785357075928270192608263e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 0.99104062122613366406043309203996
y[1] (numeric) = 0.99104062122613366406043748653587
absolute error = 4.39449591e-24
relative error = 4.4342238005976474749432846220775e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0091
y[1] (analytic) = 0.99094153030891842544386317180982
y[1] (numeric) = 0.99094153030891842544386761535327
absolute error = 4.44354345e-24
relative error = 4.4841631055817787695205521710904e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0092
y[1] (analytic) = 0.99084244948228787532928841918495
y[1] (numeric) = 0.99084244948228787532929291178078
absolute error = 4.49259583e-24
relative error = 4.5341172376570740066834454939784e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0093
y[1] (analytic) = 0.99074337874723282198218866175607
y[1] (numeric) = 0.99074337874723282198219320340917
absolute error = 4.54165310e-24
relative error = 4.5840862502081949772539192185871e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0094
y[1] (analytic) = 0.9906443181047439727522888435358
y[1] (numeric) = 0.99064431810474397275229343425092
absolute error = 4.59071512e-24
relative error = 4.6340700048456837741436928825457e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0095
y[1] (analytic) = 0.99054526755581193406365195146936
y[1] (numeric) = 0.99054526755581193406365659125123
absolute error = 4.63978187e-24
relative error = 4.6840684842690170932610583391699e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0096
y[1] (analytic) = 0.99044622710142721140477295120203
y[1] (numeric) = 0.99044622710142721140477764005565
absolute error = 4.68885362e-24
relative error = 4.7340819639669698775410645503047e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0097
y[1] (analytic) = 0.99034719674258020931867373220325
y[1] (numeric) = 0.99034719674258020931867847013336
absolute error = 4.73793011e-24
relative error = 4.7841101843715569603993410518688e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0098
y[1] (analytic) = 0.99024817648026123139299906234389
y[1] (numeric) = 0.99024817648026123139300384935524
absolute error = 4.78701135e-24
relative error = 4.8341531584687752571749551613633e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0099
y[1] (analytic) = 0.99014916631546048025011355202817
y[1] (numeric) = 0.99014916631546048025011838812565
absolute error = 4.83609748e-24
relative error = 4.8842110305420632376337311394167e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 0.9900501662491680575371996279787
y[1] (numeric) = 0.99005016624916805753720451316705
absolute error = 4.88518835e-24
relative error = 4.9342836520170172135392181205512e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0101
y[1] (analytic) = 0.98995117628237396391635651677235
y[1] (numeric) = 0.98995117628237396391636145105642
absolute error = 4.93428407e-24
relative error = 4.9843711368979103717372224714700e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0102
y[1] (analytic) = 0.98985219641606809905470023822783
y[1] (numeric) = 0.98985219641606809905470522161251
absolute error = 4.98338468e-24
relative error = 5.0344735285158837686199233806860e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0103
y[1] (analytic) = 0.98975322665124026161446460874293
y[1] (numeric) = 0.98975322665124026161446964123294
absolute error = 5.03249001e-24
relative error = 5.0845906580442000495715811901458e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=1.77
NO POLE
x[1] = 0.0104
y[1] (analytic) = 0.98965426698888014924310325467999
y[1] (numeric) = 0.98965426698888014924310833628011
absolute error = 5.08160012e-24
relative error = 5.1347225889918760375209458158027e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0105
y[1] (analytic) = 0.98955531742997735856339263589985
y[1] (numeric) = 0.98955531742997735856339776661491
absolute error = 5.13071506e-24
relative error = 5.1848693747866786124630513129369e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0106
y[1] (analytic) = 0.98945637797552138516353607954229
y[1] (numeric) = 0.9894563779755213851635412593772
absolute error = 5.17983491e-24
relative error = 5.2350310991963167778318540340725e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0107
y[1] (analytic) = 0.98935744862650162358726882415252
y[1] (numeric) = 0.98935744862650162358727405311201
absolute error = 5.22895949e-24
relative error = 5.2852075832240653108363498844364e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0108
y[1] (analytic) = 0.98925852938390736732396407425162
y[1] (numeric) = 0.98925852938390736732396935234046
absolute error = 5.27808884e-24
relative error = 5.3353988701892718946903153558945e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0109
y[1] (analytic) = 0.98915962024872780879874006545122
y[1] (numeric) = 0.98915962024872780879874539267426
absolute error = 5.32722304e-24
relative error = 5.3856050438658729906340081288411e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 0.98906072122195203936256814021067
y[1] (numeric) = 0.98906072122195203936257351657275
absolute error = 5.37636208e-24
relative error = 5.4358260970647800218690544890603e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0111
y[1] (analytic) = 0.98896183230456904928238183433552
y[1] (numeric) = 0.98896183230456904928238725984147
absolute error = 5.42550595e-24
relative error = 5.4860620225929157046322642029776e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0112
y[1] (analytic) = 0.98886295349756772773118697431652
y[1] (numeric) = 0.98886295349756772773119244897102
absolute error = 5.47465450e-24
relative error = 5.5363126716764658529426816284874e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0113
y[1] (analytic) = 0.98876408480193686277817278560725
y[1] (numeric) = 0.98876408480193686277817830941529
absolute error = 5.52380804e-24
relative error = 5.5865783607082525013612818956207e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0114
y[1] (analytic) = 0.98866522621866514137882401194157
y[1] (numeric) = 0.98866522621866514137882958490777
absolute error = 5.57296620e-24
relative error = 5.6368587184105284708438860998053e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0115
y[1] (analytic) = 0.98856637774874114936503404578567
y[1] (numeric) = 0.98856637774874114936503966791495
absolute error = 5.62212928e-24
relative error = 5.6871540511050516329260043894629e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0116
y[1] (analytic) = 0.9884675393931533714352190700285
y[1] (numeric) = 0.98846753939315337143522474132564
absolute error = 5.67129714e-24
relative error = 5.7374642201015127097442807110435e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0117
y[1] (analytic) = 0.98836871115289019114443321100526
y[1] (numeric) = 0.98836871115289019114443893147504
absolute error = 5.72046978e-24
relative error = 5.7877892283005545271469410468554e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0118
y[1] (analytic) = 0.98826989302893989089448470295516
y[1] (numeric) = 0.98826989302893989089449047260242
absolute error = 5.76964726e-24
relative error = 5.8381291393150283691585768004931e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0119
y[1] (analytic) = 0.98817108502229065192405306401174
y[1] (numeric) = 0.98817108502229065192405888284128
absolute error = 5.81882954e-24
relative error = 5.8884839155850647610047285040928e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.1MB, time=2.04
NO POLE
x[1] = 0.012
y[1] (analytic) = 0.9880722871339305542988072838242
y[1] (numeric) = 0.9880722871339305542988131518408
absolute error = 5.86801660e-24
relative error = 5.9388535397760893313247582508626e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0121
y[1] (analytic) = 0.9879734993648475769015250229089
y[1] (numeric) = 0.98797349936484757690153094011738
absolute error = 5.91720848e-24
relative error = 5.9892380552758541229314923526399e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0122
y[1] (analytic) = 0.98787472171602959742221282382999
y[1] (numeric) = 0.9878747217160295974222187902351
absolute error = 5.96640511e-24
relative error = 6.0396373941381995016138108968430e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0123
y[1] (analytic) = 0.98777595418846439234822733430724
y[1] (numeric) = 0.98777595418846439234823334991386
absolute error = 6.01560662e-24
relative error = 6.0900516908637382245003214105064e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0124
y[1] (analytic) = 0.98767719678313963695439754235125
y[1] (numeric) = 0.98767719678313963695440360716409
absolute error = 6.06481284e-24
relative error = 6.1404807762628004566707574853251e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0125
y[1] (analytic) = 0.98757844950104290529314802352272
y[1] (numeric) = 0.98757844950104290529315413754665
absolute error = 6.11402393e-24
relative error = 6.1909248152275962070198228747558e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0126
y[1] (analytic) = 0.98747971234316167018462320041706
y[1] (numeric) = 0.98747971234316167018462936365683
absolute error = 6.16323977e-24
relative error = 6.2413836891650451943290739260920e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0127
y[1] (analytic) = 0.98738098531048330320681261447066
y[1] (numeric) = 0.98738098531048330320681882693115
absolute error = 6.21246049e-24
relative error = 6.2918575326285864113160035308902e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0128
y[1] (analytic) = 0.98728226840399507468567721018971
y[1] (numeric) = 0.98728226840399507468568347187567
absolute error = 6.26168596e-24
relative error = 6.3423462168751554711717958826120e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0129
y[1] (analytic) = 0.98718356162468415368527663189837
y[1] (numeric) = 0.98718356162468415368528294281461
absolute error = 6.31091624e-24
relative error = 6.3928498055758122876266052821962e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 0.98708486497353760799789753310667
y[1] (numeric) = 0.987084864973537607997903893258
absolute error = 6.36015133e-24
relative error = 6.4433683016409201429827852143190e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0131
y[1] (analytic) = 0.98698617845154240413418289859578
y[1] (numeric) = 0.98698617845154240413418930798701
absolute error = 6.40939123e-24
relative error = 6.4939017079808872567283648704460e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0132
y[1] (analytic) = 0.98688750205968540731326237931994
y[1] (numeric) = 0.98688750205968540731326883795577
absolute error = 6.45863583e-24
relative error = 6.5444499160446271829670314787116e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0133
y[1] (analytic) = 0.98678883579895338145288364022292
y[1] (numeric) = 0.98678883579895338145289014810828
absolute error = 6.50788536e-24
relative error = 6.5950131617884508529758989583965e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0134
y[1] (analytic) = 0.98669017967033298915954472106964
y[1] (numeric) = 0.98669017967033298915955127820917
absolute error = 6.55713953e-24
relative error = 6.6455911542474580735044210842280e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.2MB, time=2.30
NO POLE
x[1] = 0.0135
y[1] (analytic) = 0.9865915336748107917186274103883
y[1] (numeric) = 0.98659153367481079171863401678694
absolute error = 6.60639864e-24
relative error = 6.6961842003577610657062219698531e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0136
y[1] (analytic) = 0.98649289781337324908453163262588
y[1] (numeric) = 0.98649289781337324908453828828834
absolute error = 6.65566246e-24
relative error = 6.7467920699203370069385740025594e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0137
y[1] (analytic) = 0.98639427208700671987081084861151
y[1] (numeric) = 0.98639427208700671987081755354263
absolute error = 6.70493112e-24
relative error = 6.7974148976085895459844002845498e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0138
y[1] (analytic) = 0.98629565649669746134030846942969
y[1] (numeric) = 0.98629565649669746134031522363423
absolute error = 6.75420454e-24
relative error = 6.8480526052307683040804062545966e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0139
y[1] (analytic) = 0.9861970510434316293952952837997
y[1] (numeric) = 0.98619705104343162939530208728253
absolute error = 6.80348283e-24
relative error = 6.8987053072219924816925636189370e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 0.98609845572819527856760789906152
y[1] (numeric) = 0.98609845572819527856761475182739
absolute error = 6.85276587e-24
relative error = 6.9493728848195989479251452851324e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0141
y[1] (analytic) = 0.98599987055197436200878819586535
y[1] (numeric) = 0.98599987055197436200879509791898
absolute error = 6.90205363e-24
relative error = 7.0000553104902021295052918365784e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0142
y[1] (analytic) = 0.9859012955157547314802237966643
y[1] (numeric) = 0.9859012955157547314802307480106
absolute error = 6.95134630e-24
relative error = 7.0507527798343554192238793305636e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0143
y[1] (analytic) = 0.98580273062052213734328954810928
y[1] (numeric) = 0.985802730620522137343296548753
absolute error = 7.00064372e-24
relative error = 7.1014651334891146802753178983063e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0144
y[1] (analytic) = 0.98570417586726222854949001744296
y[1] (numeric) = 0.98570417586726222854949706738887
absolute error = 7.04994591e-24
relative error = 7.1521923946372385861226517462474e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0145
y[1] (analytic) = 0.98560563125696055263060300299314
y[1] (numeric) = 0.98560563125696055263061010224597
absolute error = 7.09925283e-24
relative error = 7.2029345255933607422150368720277e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0146
y[1] (analytic) = 0.98550709679060255568882405886299
y[1] (numeric) = 0.98550709679060255568883120742759
absolute error = 7.14856460e-24
relative error = 7.2536916510088861323974565995758e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0147
y[1] (analytic) = 0.98540857246917358238691203391758
y[1] (numeric) = 0.98540857246917358238691923179882
absolute error = 7.19788124e-24
relative error = 7.3044637941032022545721321138438e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0148
y[1] (analytic) = 0.98531005829365887593833562516456
y[1] (numeric) = 0.98531005829365887593834287236714
absolute error = 7.24720258e-24
relative error = 7.3552507852711530142045021041045e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0149
y[1] (analytic) = 0.98521155426504357809742094562725
y[1] (numeric) = 0.98521155426504357809742824215597
absolute error = 7.29652872e-24
relative error = 7.4060527288914369402091329103432e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 0.98511306038431272914950010681
y[1] (numeric) = 0.9851130603843127291495074526696
absolute error = 7.34585960e-24
relative error = 7.4568695669654710554823512066397e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.2MB, time=2.56
NO POLE
x[1] = 0.0151
y[1] (analytic) = 0.98501457665245126790106081585275
y[1] (numeric) = 0.98501457665245126790106821104808
absolute error = 7.39519533e-24
relative error = 7.5077014140566288365017710606416e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0152
y[1] (analytic) = 0.98491610307044403166989698747472
y[1] (numeric) = 0.98491610307044403166990443201057
absolute error = 7.44453585e-24
relative error = 7.5585482121694434214804308802633e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0153
y[1] (analytic) = 0.98481763963927575627526037080439
y[1] (numeric) = 0.98481763963927575627526786468559
absolute error = 7.49388120e-24
relative error = 7.6094100048257651733190334347952e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0154
y[1] (analytic) = 0.98471918635993107602801319119546
y[1] (numeric) = 0.98471918635993107602802073442671
absolute error = 7.54323125e-24
relative error = 7.6602866629256726787591241771640e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0155
y[1] (analytic) = 0.98462074323339452372078180712598
y[1] (numeric) = 0.98462074323339452372078939971213
absolute error = 7.59258615e-24
relative error = 7.7111783416899365521647040746056e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0156
y[1] (analytic) = 0.98452231026065053061811138228092
y[1] (numeric) = 0.98452231026065053061811902422664
absolute error = 7.64194572e-24
relative error = 7.7620848612123461805778606708701e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0157
y[1] (analytic) = 0.98442388744268342644662157291415
y[1] (numeric) = 0.98442388744268342644662926422435
absolute error = 7.69131020e-24
relative error = 7.8130064681590883885426457567516e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0158
y[1] (analytic) = 0.98432547478047743938516323059134
y[1] (numeric) = 0.9843254747804774393851709712707
absolute error = 7.74067936e-24
relative error = 7.8639429318095347363835887359795e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0159
y[1] (analytic) = 0.98422707227501669605497612040879
y[1] (numeric) = 0.98422707227501669605498391046216
absolute error = 7.79005337e-24
relative error = 7.9148944277599304694328942945632e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 0.9841286799272852215098476547899
y[1] (numeric) = 0.98412867992728522150985549422204
absolute error = 7.83943214e-24
relative error = 7.9658608674825286145124485884273e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0161
y[1] (analytic) = 0.98403029773826693922627264295501
y[1] (numeric) = 0.9840302977382669392262805317708
absolute error = 7.88881579e-24
relative error = 8.0168423758211077894719241842070e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0162
y[1] (analytic) = 0.9839319257089456710936140561652
y[1] (numeric) = 0.98393192570894567109362199436932
absolute error = 7.93820412e-24
relative error = 8.0678387524424930529361477559237e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0163
y[1] (analytic) = 0.98383356384030513740426480883621
y[1] (numeric) = 0.98383356384030513740427279643344
absolute error = 7.98759723e-24
relative error = 8.1188501018618822517140754375712e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0164
y[1] (analytic) = 0.98373521213332895684381055562309
y[1] (numeric) = 0.98373521213332895684381859261825
absolute error = 8.03699516e-24
relative error = 8.1698764676431231507308763572038e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0165
y[1] (analytic) = 0.98363687058900064648119350457262
y[1] (numeric) = 0.98363687058900064648120159097043
absolute error = 8.08639781e-24
relative error = 8.2209177510374068531715855363292e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0166
y[1] (analytic) = 0.98353853920830362175887724644171
y[1] (numeric) = 0.98353853920830362175888538224703
absolute error = 8.13580532e-24
relative error = 8.2719740972721739340430533159026e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.2MB, time=2.83
NO POLE
x[1] = 0.0167
y[1] (analytic) = 0.98344021799222119648301260028138
y[1] (numeric) = 0.983440217992221196483020785499
absolute error = 8.18521762e-24
relative error = 8.3230454380957026664186157830792e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0168
y[1] (analytic) = 0.98334190694173658281360447538328
y[1] (numeric) = 0.98334190694173658281361271001792
absolute error = 8.23463464e-24
relative error = 8.3741317052278394651144582645866e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0169
y[1] (analytic) = 0.98324360605783289125467974968764
y[1] (numeric) = 0.98324360605783289125468803374409
absolute error = 8.28405645e-24
relative error = 8.4252329727458654002087110150504e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 0.98314531534149313064445616475145
y[1] (numeric) = 0.98314531534149313064446449823451
absolute error = 8.33348306e-24
relative error = 8.4763492537269375655917033935729e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0171
y[1] (analytic) = 0.9830470347937002081455122373744
y[1] (numeric) = 0.98304703479370020814552062028885
absolute error = 8.38291445e-24
relative error = 8.5274805307349484641228959142178e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0172
y[1] (analytic) = 0.98294876441543692923495818798127
y[1] (numeric) = 0.98294876441543692923496662033188
absolute error = 8.43235061e-24
relative error = 8.5786267964991526522837821723534e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0173
y[1] (analytic) = 0.98285050420768599769460788585902
y[1] (numeric) = 0.98285050420768599769461636765056
absolute error = 8.48179154e-24
relative error = 8.6297880539192498171917018304548e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0174
y[1] (analytic) = 0.98275225417143001560115181134692
y[1] (numeric) = 0.98275225417143001560116034258407
absolute error = 8.53123715e-24
relative error = 8.6809642143154241692605329382015e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0175
y[1] (analytic) = 0.98265401430765148331633103507741
y[1] (numeric) = 0.98265401430765148331633961576511
absolute error = 8.58068770e-24
relative error = 8.7321555451495254300012692388593e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0176
y[1] (analytic) = 0.98255578461733279947711221436775
y[1] (numeric) = 0.98255578461733279947712084451067
absolute error = 8.63014292e-24
relative error = 8.7833617745796534712358746730345e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0177
y[1] (analytic) = 0.98245756510145626098586360685758
y[1] (numeric) = 0.98245756510145626098587228646055
absolute error = 8.67960297e-24
relative error = 8.8345830683319907405039095528621e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0178
y[1] (analytic) = 0.98235935576100406300053210149414
y[1] (numeric) = 0.98235935576100406300054083056188
absolute error = 8.72906774e-24
relative error = 8.8858193173493577575881324999439e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0179
y[1] (analytic) = 0.98226115659695829892482126696044
y[1] (numeric) = 0.98226115659695829892483004549781
absolute error = 8.77853737e-24
relative error = 8.9370706670446219877090657863219e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 0.98216296761030096039837041764696
y[1] (numeric) = 0.98216296761030096039837924565867
absolute error = 8.82801171e-24
relative error = 8.9883369676209847528050164586128e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0181
y[1] (analytic) = 0.98206478880201393728693469726293
y[1] (numeric) = 0.98206478880201393728694357475377
absolute error = 8.87749084e-24
relative error = 9.0396183034210367523148112346227e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=4.2MB, time=3.10
x[1] = 0.0182
y[1] (analytic) = 0.98196662017307901767256618018731
y[1] (numeric) = 0.98196662017307901767257510716201
absolute error = 8.92697470e-24
relative error = 9.0909146162489244578135071533031e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0183
y[1] (analytic) = 0.98186846172447788784379599065615
y[1] (numeric) = 0.98186846172447788784380496711955
absolute error = 8.97646340e-24
relative error = 9.1422260210236648003486325305596e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0184
y[1] (analytic) = 0.98177031345719213228581743988583
y[1] (numeric) = 0.9817703134571921322858264658427
absolute error = 9.02595687e-24
relative error = 9.1935524493668206408605101065113e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0185
y[1] (analytic) = 0.98167217537220323367067018122906
y[1] (numeric) = 0.98167217537220323367067925668413
absolute error = 9.07545507e-24
relative error = 9.2448938634315682922240667201786e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0186
y[1] (analytic) = 0.9815740474704925728474253834627
y[1] (numeric) = 0.98157404747049257284743450842068
absolute error = 9.12495798e-24
relative error = 9.2962502457302472913211258777883e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0187
y[1] (analytic) = 0.98147592975304142883237192230504
y[1] (numeric) = 0.98147592975304142883238109677081
absolute error = 9.17446577e-24
relative error = 9.3476217723530676057595470039738e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0188
y[1] (analytic) = 0.98137782222083097879920359026159
y[1] (numeric) = 0.9813778222208309787992128142399
absolute error = 9.22397831e-24
relative error = 9.3990083137668540000173486475344e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0189
y[1] (analytic) = 0.98127972487484229806920732489591
y[1] (numeric) = 0.98127972487484229806921659839149
absolute error = 9.27349558e-24
relative error = 9.4504098524840015210148350278758e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 0.98118163771605636010145245562489
y[1] (numeric) = 0.98118163771605636010146177864257
absolute error = 9.32301768e-24
relative error = 9.5018264933102867546681248022869e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0191
y[1] (analytic) = 0.98108356074545403648298096913657
y[1] (numeric) = 0.98108356074545403648299034168108
absolute error = 9.37254451e-24
relative error = 9.5532581372360221386581215759215e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0192
y[1] (analytic) = 0.98098549396401609691899879352764
y[1] (numeric) = 0.98098549396401609691900821560366
absolute error = 9.42207602e-24
relative error = 9.6047047361799365856355181742219e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0193
y[1] (analytic) = 0.98088743737272320922306810125927
y[1] (numeric) = 0.98088743737272320922307757287174
absolute error = 9.47161247e-24
relative error = 9.6561665580807337954310870423941e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0194
y[1] (analytic) = 0.98078939097255593930730063103056
y[1] (numeric) = 0.98078939097255593930731015218414
absolute error = 9.52115358e-24
relative error = 9.7076433204062024284970120012703e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0195
y[1] (analytic) = 0.98069135476449475117255202866458
y[1] (numeric) = 0.98069135476449475117256159936407
absolute error = 9.57069949e-24
relative error = 9.7591351687793021855118402831852e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0196
y[1] (analytic) = 0.98059332874952000689861720710866
y[1] (numeric) = 0.98059332874952000689862682735878
absolute error = 9.62025012e-24
relative error = 9.8106420245261219257422045309271e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0197
y[1] (analytic) = 0.98049531292861196663442672564423
y[1] (numeric) = 0.98049531292861196663443639544977
absolute error = 9.66980554e-24
relative error = 9.8621639619240489831597882651964e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.2MB, time=3.36
NO POLE
x[1] = 0.0198
y[1] (analytic) = 0.98039730730275078858824418840594
y[1] (numeric) = 0.98039730730275078858825390777165
absolute error = 9.71936571e-24
relative error = 9.9137009430796194768154591547577e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0199
y[1] (analytic) = 0.98029931187291652901786466230702
y[1] (numeric) = 0.98029931187291652901787443123767
absolute error = 9.76893065e-24
relative error = 9.9652529912888676385688376201528e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 0.98020132664008914222081411446952
y[1] (numeric) = 0.98020132664008914222082393296995
absolute error = 9.81850043e-24
relative error = 1.0016820180865927702947616948590e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0201
y[1] (analytic) = 0.98010335160524848052454986925751
y[1] (numeric) = 0.98010335160524848052455973733237
absolute error = 9.86807486e-24
relative error = 1.0068402320875357147901781529291e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0202
y[1] (analytic) = 0.98000538676937429427666208501003
y[1] (numeric) = 0.98000538676937429427667200266417
absolute error = 9.91765414e-24
relative error = 1.0119999618261212735437139474456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0203
y[1] (analytic) = 0.97990743213344623183507625057412
y[1] (numeric) = 0.97990743213344623183508621781221
absolute error = 9.96723809e-24
relative error = 1.0171611892257427762104570569387e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0204
y[1] (analytic) = 0.97980948769844383955825670173296
y[1] (numeric) = 0.97980948769844383955826671855989
absolute error = 1.001682693e-23
relative error = 1.0223239370267131779167484354811e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0205
y[1] (analytic) = 0.97971155346534656179541115763024
y[1] (numeric) = 0.97971155346534656179542122405066
absolute error = 1.006642042e-23
relative error = 1.0274881810257288123193705781966e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0206
y[1] (analytic) = 0.97961362943513374087669627728543
y[1] (numeric) = 0.9796136294351337408767063933041
absolute error = 1.011601867e-23
relative error = 1.0326539327380646632639424253626e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0207
y[1] (analytic) = 0.97951571560878461710342423630073
y[1] (numeric) = 0.97951571560878461710343440192253
absolute error = 1.016562180e-23
relative error = 1.0378212047043986581391582871911e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0208
y[1] (analytic) = 0.9794178119872783287382703238565
y[1] (numeric) = 0.97941781198727832873828053908603
absolute error = 1.021522953e-23
relative error = 1.0429899686297195660049819880663e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0209
y[1] (analytic) = 0.97931991857159391199548156009172
y[1] (numeric) = 0.97931991857159391199549182493385
absolute error = 1.026484213e-23
relative error = 1.0481602523690097978281153178870e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 0.97922203536271030103108633397068
y[1] (numeric) = 0.97922203536271030103109664843012
absolute error = 1.031445944e-23
relative error = 1.0533320398758649449008128086355e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0211
y[1] (analytic) = 0.97912416236160632793310506173016
y[1] (numeric) = 0.9791241623616063279331154258117
absolute error = 1.036408154e-23
relative error = 1.0585053396090513095175631563601e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0212
y[1] (analytic) = 0.97902629956926072271176186600772
y[1] (numeric) = 0.97902629956926072271177227971614
absolute error = 1.041370842e-23
relative error = 1.0636801508377954907214608594165e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0213
y[1] (analytic) = 0.97892844698665211328969727574759
y[1] (numeric) = 0.97892844698665211328970773908759
absolute error = 1.046334000e-23
relative error = 1.0688564656802408511614888506160e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.2MB, time=3.62
NO POLE
x[1] = 0.0214
y[1] (analytic) = 0.97883060461475902549218194698223
y[1] (numeric) = 0.97883060461475902549219245995857
absolute error = 1.051297634e-23
relative error = 1.0740342905540453720772793379123e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0215
y[1] (analytic) = 0.97873277245455988303733140458792
y[1] (numeric) = 0.9787327724545598830373419672054
absolute error = 1.056261748e-23
relative error = 1.0792136298358596074981719187380e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0216
y[1] (analytic) = 0.97863495050703300752632180511189
y[1] (numeric) = 0.97863495050703300752633241737519
absolute error = 1.061226330e-23
relative error = 1.0843944715546652096808127260683e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0217
y[1] (analytic) = 0.97853713877315661843360672076828
y[1] (numeric) = 0.97853713877315661843361738268225
absolute error = 1.066191397e-23
relative error = 1.0895768333706170076782271047819e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0218
y[1] (analytic) = 0.97843933725390883309713494470236
y[1] (numeric) = 0.9784393372539088330971456562717
absolute error = 1.071156934e-23
relative error = 1.0947607002456715291282480486136e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0219
y[1] (analytic) = 0.97834154595026766670856931761867
y[1] (numeric) = 0.97834154595026766670858007884813
absolute error = 1.076122946e-23
relative error = 1.0999460775784154268480096066488e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 0.97824376486321103230350657587276
y[1] (numeric) = 0.97824376486321103230351738676712
absolute error = 1.081089436e-23
relative error = 1.1051329687249987204970876840256e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0221
y[1] (analytic) = 0.97814599399371674075169822112346
y[1] (numeric) = 0.97814599399371674075170908168744
absolute error = 1.086056398e-23
relative error = 1.1103213678417175391540565396039e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0222
y[1] (analytic) = 0.97804823334276250074727241164332
y[1] (numeric) = 0.97804823334276250074728332188165
absolute error = 1.091023833e-23
relative error = 1.1155112762395273049323715924880e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0223
y[1] (analytic) = 0.97795048291132591879895687538548
y[1] (numeric) = 0.977950482911325918798967835303
absolute error = 1.095991752e-23
relative error = 1.1207027054552590089633079642392e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0224
y[1] (analytic) = 0.97785274270038449922030284490487
y[1] (numeric) = 0.97785274270038449922031385450627
absolute error = 1.100960140e-23
relative error = 1.1258956404413704100398673666915e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0225
y[1] (analytic) = 0.97775501271091564411991001423039
y[1] (numeric) = 0.97775501271091564411992107352043
absolute error = 1.105929004e-23
relative error = 1.1310900886447108911097039112162e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0226
y[1] (analytic) = 0.97765729294389665339165251778736
y[1] (numeric) = 0.97765729294389665339166362677078
absolute error = 1.110898342e-23
relative error = 1.1362860483093122591931882793840e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0227
y[1] (analytic) = 0.97755958340030472470490593146672
y[1] (numeric) = 0.97755958340030472470491709014833
absolute error = 1.115868161e-23
relative error = 1.1414835268849886063825938141369e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0228
y[1] (analytic) = 0.97746188408111695349477529593972
y[1] (numeric) = 0.97746188408111695349478650432422
absolute error = 1.120838450e-23
relative error = 1.1466825134093766953336254500173e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=57.2MB, alloc=4.2MB, time=3.88
x[1] = 0.0229
y[1] (analytic) = 0.97736419498731033295232416231472
y[1] (numeric) = 0.9773641949873103329523354204068
absolute error = 1.125809208e-23
relative error = 1.1518830071472149763359949617433e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 0.97726651611986175401480466023464
y[1] (numeric) = 0.97726651611986175401481596803913
absolute error = 1.130780449e-23
relative error = 1.1570850227117673595127119624193e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0231
y[1] (analytic) = 0.97716884747974800535588858851294
y[1] (numeric) = 0.9771688474797480053558999460346
absolute error = 1.135752166e-23
relative error = 1.1622885532313684013089187987567e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0232
y[1] (analytic) = 0.97707118906794577337589952840477
y[1] (numeric) = 0.97707118906794577337591093564836
absolute error = 1.140724359e-23
relative error = 1.1674935989957572523457356355340e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0233
y[1] (analytic) = 0.97697354088543164219204597961208
y[1] (numeric) = 0.97697354088543164219205743658223
absolute error = 1.145697015e-23
relative error = 1.1727001469882737899465721813740e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0234
y[1] (analytic) = 0.97687590293318209362865551911913
y[1] (numeric) = 0.97687590293318209362866702582072
absolute error = 1.150670159e-23
relative error = 1.1779082230864541669058116197846e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0235
y[1] (analytic) = 0.97677827521217350720740998295824
y[1] (numeric) = 0.97677827521217350720742153939593
absolute error = 1.155643769e-23
relative error = 1.1831178050606968565724285342975e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0236
y[1] (analytic) = 0.97668065772338216013758167100031
y[1] (numeric) = 0.97668065772338216013759327717885
absolute error = 1.160617854e-23
relative error = 1.1883289024125559923102723627194e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0237
y[1] (analytic) = 0.97658305046778422730627057487056
y[1] (numeric) = 0.97658305046778422730628223079477
absolute error = 1.165592421e-23
relative error = 1.1935415225993120616755852236417e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0238
y[1] (analytic) = 0.9764854534463557812686426290859
y[1] (numeric) = 0.97648545344635578126865433476042
absolute error = 1.170567452e-23
relative error = 1.1987556474790910033344580559422e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0239
y[1] (analytic) = 0.97638786666007279223816898551073
y[1] (numeric) = 0.97638786666007279223818074094045
absolute error = 1.175542972e-23
relative error = 1.2039713029425247899302562846225e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 0.97629029010991112807686631123128
y[1] (numeric) = 0.97629029010991112807687811642084
absolute error = 1.180518956e-23
relative error = 1.2091884636762050884474282901894e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0241
y[1] (analytic) = 0.97619272379684655428553810994272
y[1] (numeric) = 0.97619272379684655428554996489687
absolute error = 1.185495415e-23
relative error = 1.2144071412344505399550875993821e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0242
y[1] (analytic) = 0.97609516772185473399401706694983
y[1] (numeric) = 0.97609516772185473399402897167323
absolute error = 1.190472340e-23
relative error = 1.2196273266862781634109274547230e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0243
y[1] (analytic) = 0.97599762188591122795140841787627
y[1] (numeric) = 0.9759976218859112279514203723738
absolute error = 1.195449753e-23
relative error = 1.2248490428593908226189516478924e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0244
y[1] (analytic) = 0.97590008628999149451633434118237
y[1] (numeric) = 0.97590008628999149451634634545874
absolute error = 1.200427637e-23
relative error = 1.2300722726273942589832685771652e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.2MB, time=4.15
NO POLE
x[1] = 0.0245
y[1] (analytic) = 0.97580256093507088964717937458648
y[1] (numeric) = 0.97580256093507088964719142864639
absolute error = 1.205405991e-23
relative error = 1.2352970152536899687660450599916e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0246
y[1] (analytic) = 0.9757050458221246668923368554893
y[1] (numeric) = 0.97570504582212466689234895933757
absolute error = 1.210384827e-23
relative error = 1.2405232833249675458265904950025e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0247
y[1] (analytic) = 0.97560754095212797738045638549853
y[1] (numeric) = 0.97560754095212797738046853913976
absolute error = 1.215364123e-23
relative error = 1.2457510545827531920064421403991e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0248
y[1] (analytic) = 0.97551004632605586981069231914972
y[1] (numeric) = 0.97551004632605586981070452258873
absolute error = 1.220343901e-23
relative error = 1.2509803518641677968499801962806e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0249
y[1] (analytic) = 0.97541256194488329044295327692348
y[1] (numeric) = 0.97541256194488329044296553016512
absolute error = 1.225324164e-23
relative error = 1.2562111785364091165659056046466e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 0.97531508780958508308815268265467
y[1] (numeric) = 0.97531508780958508308816498570348
absolute error = 1.230304881e-23
relative error = 1.2614435031073749366965400742808e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0251
y[1] (analytic) = 0.97521762392113598909846032543042
y[1] (numeric) = 0.97521762392113598909847267829128
absolute error = 1.235286086e-23
relative error = 1.2666773607240462024144824955701e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0252
y[1] (analytic) = 0.97512017028051064735755494607771
y[1] (numeric) = 0.9751201702805106473575673487553
absolute error = 1.240267759e-23
relative error = 1.2719127311695490171199248709014e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0253
y[1] (analytic) = 0.97502272688868359427087784833396
y[1] (numeric) = 0.97502272688868359427089030083298
absolute error = 1.245249902e-23
relative error = 1.2771496167823867606303919909559e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0254
y[1] (analytic) = 0.97492529374662926375588753480087
y[1] (numeric) = 0.97492529374662926375590003712614
absolute error = 1.250232527e-23
relative error = 1.2823880301590776034907579214593e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0255
y[1] (analytic) = 0.97482787085532198723231536777832
y[1] (numeric) = 0.9748278708553219872323279199345
absolute error = 1.255215618e-23
relative error = 1.2876279551780392763711574489570e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0256
y[1] (analytic) = 0.9747304582157359936124222550746
y[1] (numeric) = 0.9747304582157359936124348570665
absolute error = 1.260199190e-23
relative error = 1.2928694075147916776790540766713e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0257
y[1] (analytic) = 0.97463305582884540929125636089242
y[1] (numeric) = 0.97463305582884540929126901272478
absolute error = 1.265183236e-23
relative error = 1.2981123802784069465631829741277e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0258
y[1] (analytic) = 0.97453566369562425813691184188633
y[1] (numeric) = 0.97453566369562425813692454356385
absolute error = 1.270167752e-23
relative error = 1.3033568696534744921486306854814e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0259
y[1] (analytic) = 0.97443828181704646148078860848986
y[1] (numeric) = 0.97443828181704646148080136001725
absolute error = 1.275152739e-23
relative error = 1.3086028769541030068594670928568e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 0.97434091019408583810785311160966
y[1] (numeric) = 0.97434091019408583810786591299167
absolute error = 1.280138201e-23
relative error = 1.3138504065738143363925647760456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.2MB, time=4.42
NO POLE
x[1] = 0.0261
y[1] (analytic) = 0.97424354882771610424690015478399
y[1] (numeric) = 0.97424354882771610424691300602539
absolute error = 1.285124140e-23
relative error = 1.3190994608548951182245857093980e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0262
y[1] (analytic) = 0.974146197718910873560815731903
y[1] (numeric) = 0.97414619771891087356082863300847
absolute error = 1.290110547e-23
relative error = 1.3243500308485117069367393795506e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0263
y[1] (analytic) = 0.97404885686864365713684089058768
y[1] (numeric) = 0.97404885686864365713685384156197
absolute error = 1.295097429e-23
relative error = 1.3296021240284168543256771434048e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0264
y[1] (analytic) = 0.97395152627788786347683662132588
y[1] (numeric) = 0.97395152627788786347684962217369
absolute error = 1.300084781e-23
relative error = 1.3348557355502924604464637393507e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0265
y[1] (analytic) = 0.97385420594761679848754977246157
y[1] (numeric) = 0.97385420594761679848756282318764
absolute error = 1.305072607e-23
relative error = 1.3401108698093966005238473796503e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0266
y[1] (analytic) = 0.97375689587880366547087999113559
y[1] (numeric) = 0.9737568958788036654708930917447
absolute error = 1.310060911e-23
relative error = 1.3453675312026274095585454351866e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0267
y[1] (analytic) = 0.97365959607242156511414769027491
y[1] (numeric) = 0.97365959607242156511416084077173
absolute error = 1.315049682e-23
relative error = 1.3506257087227285667206581313776e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0268
y[1] (analytic) = 0.97356230652944349548036304172717
y[1] (numeric) = 0.97356230652944349548037624211647
absolute error = 1.320038930e-23
relative error = 1.3558854129281945386949494922267e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0269
y[1] (analytic) = 0.97346502725084235199849599563905
y[1] (numeric) = 0.97346502725084235199850924592556
absolute error = 1.325028651e-23
relative error = 1.3611466400000076997193941915149e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 0.97336775823759092745374732617445
y[1] (numeric) = 0.97336775823759092745376062636292
absolute error = 1.330018847e-23
relative error = 1.3664093922816719445994699871344e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0271
y[1] (analytic) = 0.9732704994906619119778207036708
y[1] (numeric) = 0.97327049949066191197783405376589
absolute error = 1.335009509e-23
relative error = 1.3716736608154111727316350431285e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0272
y[1] (analytic) = 0.97317325101102789303919579332974
y[1] (numeric) = 0.97317325101102789303920919333625
absolute error = 1.340000651e-23
relative error = 1.3769394602737753001707327247235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0273
y[1] (analytic) = 0.97307601279966135543340238054092
y[1] (numeric) = 0.97307601279966135543341583046358
absolute error = 1.344992266e-23
relative error = 1.3822067837540143264923287478069e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0274
y[1] (analytic) = 0.97297878485753468127329552293462
y[1] (numeric) = 0.97297878485753468127330902277802
absolute error = 1.349984340e-23
relative error = 1.3874756171560998177608515472241e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0275
y[1] (analytic) = 0.9728815671856201499793317292608
y[1] (numeric) = 0.97288156718562014997934527902986
absolute error = 1.354976906e-23
relative error = 1.3927459946843440190121091191652e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0276
y[1] (analytic) = 0.97278435978488993826984616519374
y[1] (numeric) = 0.97278435978488993826985976489305
memory used=68.6MB, alloc=4.2MB, time=4.68
absolute error = 1.359969931e-23
relative error = 1.3980178827101288029030758371762e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0277
y[1] (analytic) = 0.9726871626563161201513308861556
y[1] (numeric) = 0.97268716265631612015134453578996
absolute error = 1.364963436e-23
relative error = 1.4032913031075836246128284527362e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0278
y[1] (analytic) = 0.97258997580087066690871409726045
y[1] (numeric) = 0.97258997580087066690872779683457
absolute error = 1.369957412e-23
relative error = 1.4085662469139892280391734417450e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0279
y[1] (analytic) = 0.97249279921952544709564044047266
y[1] (numeric) = 0.97249279921952544709565418999127
absolute error = 1.374951861e-23
relative error = 1.4138427164740636249617272267958e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 0.97239563291325222652475230907875
y[1] (numeric) = 0.97239563291325222652476610854652
absolute error = 1.379946777e-23
relative error = 1.4191207059062404916518050097760e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0281
y[1] (analytic) = 0.97229847688302266825797218956885
y[1] (numeric) = 0.97229847688302266825798603899053
absolute error = 1.384942168e-23
relative error = 1.4244002237253556219487316515358e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0282
y[1] (analytic) = 0.97220133112980833259678603102578
y[1] (numeric) = 0.97220133112980833259679993040612
absolute error = 1.389938034e-23
relative error = 1.4296812702207825491732279213164e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0283
y[1] (analytic) = 0.97210419565458067707252764211828
y[1] (numeric) = 0.97210419565458067707254159146197
absolute error = 1.394934369e-23
relative error = 1.4349638395097146950992604892528e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0284
y[1] (analytic) = 0.97200707045831105643666411579561
y[1] (numeric) = 0.97200707045831105643667811510737
absolute error = 1.399931176e-23
relative error = 1.4402479349660681453633638622424e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0285
y[1] (analytic) = 0.97190995554197072265108228178104
y[1] (numeric) = 0.97190995554197072265109633106565
absolute error = 1.404928461e-23
relative error = 1.4455335630516955968585368831041e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0286
y[1] (analytic) = 0.97181285090653082487837618696133
y[1] (numeric) = 0.97181285090653082487839028622339
absolute error = 1.409926206e-23
relative error = 1.4508207055348015917477409287850e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0287
y[1] (analytic) = 0.9717157565529624094721356037682
y[1] (numeric) = 0.97171575655296240947214975301258
absolute error = 1.414924438e-23
relative error = 1.4561093904860242309190726698569e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0288
y[1] (analytic) = 0.97161867248223641996723556665158
y[1] (numeric) = 0.97161867248223641996724976588283
absolute error = 1.419923125e-23
relative error = 1.4613995852636927255972227686200e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0289
y[1] (analytic) = 0.97152159869532369707012693673771
y[1] (numeric) = 0.9715215986953236970701411859607
absolute error = 1.424922299e-23
relative error = 1.4666913230890156358305372624104e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 0.97142453519319497864912799477387
y[1] (numeric) = 0.97142453519319497864914229399327
absolute error = 1.429921940e-23
relative error = 1.4719845836667281311632312212850e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0291
y[1] (analytic) = 0.97132748197682089972471706245251
y[1] (numeric) = 0.97132748197682089972473141167306
absolute error = 1.434922055e-23
relative error = 1.4772793744903451694532812214875e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=4.94
NO POLE
x[1] = 0.0292
y[1] (analytic) = 0.97123043904717199245982615221499
y[1] (numeric) = 0.97123043904717199245984055144132
absolute error = 1.439922633e-23
relative error = 1.4825756845230670854093322781967e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0293
y[1] (analytic) = 0.97113340640521868615013564562996
y[1] (numeric) = 0.97113340640521868615015009486683
absolute error = 1.444923687e-23
relative error = 1.4878735274369563228210365552697e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0294
y[1] (analytic) = 0.97103638405193130721437000044495
y[1] (numeric) = 0.97103638405193130721438449969715
absolute error = 1.449925220e-23
relative error = 1.4931729066111466932042401562561e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0295
y[1] (analytic) = 0.97093937198828007918459448640735
y[1] (numeric) = 0.97093937198828007918460903567948
absolute error = 1.454927213e-23
relative error = 1.4984738027675346904280189040679e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0296
y[1] (analytic) = 0.97084237021523512269651294995121
y[1] (numeric) = 0.97084237021523512269652754924809
absolute error = 1.459929688e-23
relative error = 1.5037762388515599465675192264437e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0297
y[1] (analytic) = 0.97074537873376645547976660784904
y[1] (numeric) = 0.97074537873376645547978125717535
absolute error = 1.464932631e-23
relative error = 1.5090802007328100511168143596620e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0298
y[1] (analytic) = 0.97064839754484399234823386992301
y[1] (numeric) = 0.97064839754484399234824856928342
absolute error = 1.469936041e-23
relative error = 1.5143856876682155134448997596868e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0299
y[1] (analytic) = 0.97055142664943754519033119091429
y[1] (numeric) = 0.97055142664943754519034594031354
absolute error = 1.474939925e-23
relative error = 1.5196927071570285847174578296579e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 0.97045446604851682295931495160714
y[1] (numeric) = 0.97045446604851682295932975104995
absolute error = 1.479944281e-23
relative error = 1.5250012574273750459309683464320e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0301
y[1] (analytic) = 0.9703575157430514316635843693043
y[1] (numeric) = 0.97035751574305143166359921879542
absolute error = 1.484949112e-23
relative error = 1.5303113418592939598560544314972e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0302
y[1] (analytic) = 0.97026057573401087435698543775123
y[1] (numeric) = 0.9702605757340108743570003372953
absolute error = 1.489954407e-23
relative error = 1.5356229494049431578982015856273e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0303
y[1] (analytic) = 0.97016364602236455112911589660542
y[1] (numeric) = 0.97016364602236455112913084620718
absolute error = 1.494960176e-23
relative error = 1.5409360906577792505881880132278e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0304
y[1] (analytic) = 0.97006672660908175909563123054878
y[1] (numeric) = 0.97006672660908175909564623021298
absolute error = 1.499966420e-23
relative error = 1.5462507669376620416837592847448e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0305
y[1] (analytic) = 0.96996981749513169238855169813913
y[1] (numeric) = 0.96996981749513169238856674787045
absolute error = 1.504973132e-23
relative error = 1.5515669713171807073225092593080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0306
y[1] (analytic) = 0.96987291868148344214657039049787
y[1] (numeric) = 0.96987291868148344214658549030107
absolute error = 1.509980320e-23
relative error = 1.5568847123319808453653807937090e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0307
y[1] (analytic) = 0.96977603016910599650536231993145
y[1] (numeric) = 0.96977603016910599650537746981119
absolute error = 1.514987974e-23
relative error = 1.5622039799600140036707431964642e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=5.21
NO POLE
x[1] = 0.0308
y[1] (analytic) = 0.96967915195896824058789453858239
y[1] (numeric) = 0.96967915195896824058790973854335
absolute error = 1.519996096e-23
relative error = 1.5675247765503349704933407882553e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0309
y[1] (analytic) = 0.9695822840520389564947372872078
y[1] (numeric) = 0.96958228405203895649475253725468
absolute error = 1.525004688e-23
relative error = 1.5728471044528188573611625991262e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 0.96948542644928682329437617418166
y[1] (numeric) = 0.96948542644928682329439147431927
absolute error = 1.530013761e-23
relative error = 1.5781709753014364301453977968821e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0311
y[1] (analytic) = 0.96938857915168041701352538481839
y[1] (numeric) = 0.96938857915168041701354073505141
absolute error = 1.535023302e-23
relative error = 1.5834963759768151852265947652858e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0312
y[1] (analytic) = 0.96929174216018821062744192111343
y[1] (numeric) = 0.96929174216018821062745732144648
absolute error = 1.540033305e-23
relative error = 1.5888233005759882337649649880427e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0313
y[1] (analytic) = 0.96919491547577857405024087199866
y[1] (numeric) = 0.96919491547577857405025632243648
absolute error = 1.545043782e-23
relative error = 1.5941517617656266262679172918778e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0314
y[1] (analytic) = 0.96909809909941977412521171420962
y[1] (numeric) = 0.96909809909941977412522721475695
absolute error = 1.550054733e-23
relative error = 1.5994817598346974826950292530872e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0315
y[1] (analytic) = 0.96900129303207997461513564386058
y[1] (numeric) = 0.96900129303207997461515119452213
absolute error = 1.555066155e-23
relative error = 1.6048132919761930909326159788603e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0316
y[1] (analytic) = 0.96890449727472723619260393882467
y[1] (numeric) = 0.96890449727472723619261953960521
absolute error = 1.560078054e-23
relative error = 1.6101463646707059708986450978631e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0317
y[1] (analytic) = 0.96880771182832951643033735201637
y[1] (numeric) = 0.9688077118283295164303530029205
absolute error = 1.565090413e-23
relative error = 1.6154809606607780571777889914740e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0318
y[1] (analytic) = 0.96871093669385466979150653567188
y[1] (numeric) = 0.96871093669385466979152223670429
absolute error = 1.570103241e-23
relative error = 1.6208170895217275564621797957256e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0319
y[1] (analytic) = 0.96861417187227044762005349672576
y[1] (numeric) = 0.9686141718722704476200692478912
absolute error = 1.575116544e-23
relative error = 1.6261547577353720768253011106165e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 0.96851741736454449813101408337968
y[1] (numeric) = 0.96851741736454449813102988468283
absolute error = 1.580130315e-23
relative error = 1.6314939583634228580368673196104e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0321
y[1] (analytic) = 0.96842067317164436640084150295985
y[1] (numeric) = 0.96842067317164436640085735440545
absolute error = 1.585144560e-23
relative error = 1.6368346978886174039553939248496e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0322
y[1] (analytic) = 0.9683239392945374943577308711608
y[1] (numeric) = 0.96832393929453749435774677275356
absolute error = 1.590159276e-23
relative error = 1.6421769735017542604952901987265e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0323
y[1] (analytic) = 0.96822721573419122077194479277137
y[1] (numeric) = 0.96822721573419122077196074451598
absolute error = 1.595174461e-23
relative error = 1.6475207834252053168841134463450e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=5.47
NO POLE
x[1] = 0.0324
y[1] (analytic) = 0.96813050249157278124613997398008
y[1] (numeric) = 0.96813050249157278124615597588128
absolute error = 1.600190120e-23
relative error = 1.6528661331109429273194216296770e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0325
y[1] (analytic) = 0.96803379956764930820569486635686
y[1] (numeric) = 0.96803379956764930820571091841929
absolute error = 1.605206243e-23
relative error = 1.6582130125176719481327348538896e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0326
y[1] (analytic) = 0.96793710696338783088903834260702
y[1] (numeric) = 0.96793710696338783088905444483537
absolute error = 1.610222835e-23
relative error = 1.6635614270968398696748612343469e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0327
y[1] (analytic) = 0.96784042467975527533797940419515
y[1] (numeric) = 0.96784042467975527533799555659417
absolute error = 1.615239902e-23
relative error = 1.6689113833351815888879482749074e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0328
y[1] (analytic) = 0.96774375271771846438803792093526
y[1] (numeric) = 0.96774375271771846438805412350962
absolute error = 1.620257436e-23
relative error = 1.6742628732552650173300493986675e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0329
y[1] (analytic) = 0.96764709107824411765877640264336
y[1] (numeric) = 0.96764709107824411765879265539775
absolute error = 1.625275439e-23
relative error = 1.6796158992106967807342963567408e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 0.96755043976229885154413280295004
y[1] (numeric) = 0.96755043976229885154414910588917
absolute error = 1.630293913e-23
relative error = 1.6849704635559045524297972895596e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0331
y[1] (analytic) = 0.96745379877084917920275435536914
y[1] (numeric) = 0.9674537987708491792027707084977
absolute error = 1.635312856e-23
relative error = 1.6903265645115728360204778175919e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0332
y[1] (analytic) = 0.9673571681048615105483324417193
y[1] (numeric) = 0.96735716810486151054834884504197
absolute error = 1.640332267e-23
relative error = 1.6956842013312997885755649204084e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0333
y[1] (analytic) = 0.9672605477653021522399384929951
y[1] (numeric) = 0.96726054776530215223995494651658
absolute error = 1.645352148e-23
relative error = 1.7010433763698084989821194719478e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0334
y[1] (analytic) = 0.9671639377531373076723609227843
y[1] (numeric) = 0.96716393775313730767237742650941
absolute error = 1.650372511e-23
relative error = 1.7064041023221520392318169425792e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0335
y[1] (analytic) = 0.9670673380693330769664430933285
y[1] (numeric) = 0.96706733806933307696645964726179
absolute error = 1.655393329e-23
relative error = 1.7117663515602240014838630635984e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0336
y[1] (analytic) = 0.96697074871485545695942231432195
y[1] (numeric) = 0.96697074871485545695943891846814
absolute error = 1.660414619e-23
relative error = 1.7171301419476860407768914147092e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0337
y[1] (analytic) = 0.96687416969067034119526987454779
y[1] (numeric) = 0.96687416969067034119528652891161
absolute error = 1.665436382e-23
relative error = 1.7224954748070464407118821790718e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0338
y[1] (analytic) = 0.9667776009977435199150321064463
y[1] (numeric) = 0.96677760099774351991504881103246
absolute error = 1.670458616e-23
relative error = 1.7278623483581296656237239163329e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=83.9MB, alloc=4.3MB, time=5.74
x[1] = 0.0339
y[1] (analytic) = 0.96668104263704068004717248371248
y[1] (numeric) = 0.96668104263704068004718923852561
absolute error = 1.675481313e-23
relative error = 1.7332307546131245029656651011101e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 0.96658449460952740519791475201918
y[1] (numeric) = 0.96658449460952740519793155706406
absolute error = 1.680504488e-23
relative error = 1.7386007093760343531217167273266e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0341
y[1] (analytic) = 0.96648795691616917564158709296343
y[1] (numeric) = 0.96648795691616917564160394824472
absolute error = 1.685528129e-23
relative error = 1.7439722005208582513437556703844e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0342
y[1] (analytic) = 0.96639142955793136831096732133083
y[1] (numeric) = 0.96639142955793136831098422685314
absolute error = 1.690552231e-23
relative error = 1.7493452231600715345272860523625e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0343
y[1] (analytic) = 0.96629491253577925678762911577564
y[1] (numeric) = 0.96629491253577925678764607154381
absolute error = 1.695576817e-23
relative error = 1.7547198013807378186274586460921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0344
y[1] (analytic) = 0.96619840585067801129228928301387
y[1] (numeric) = 0.96619840585067801129230628903245
absolute error = 1.700601858e-23
relative error = 1.7600959054602508016553521822923e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0345
y[1] (analytic) = 0.96610190950359269867515605562312
y[1] (numeric) = 0.96610190950359269867517311189687
absolute error = 1.705627375e-23
relative error = 1.7654735574183824604988423623827e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0346
y[1] (analytic) = 0.96600542349548828240627842354935
y[1] (numeric) = 0.96600542349548828240629553008297
absolute error = 1.710653362e-23
relative error = 1.7708527513334293278055092544211e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0347
y[1] (analytic) = 0.96590894782732962256589649941407
y[1] (numeric) = 0.96590894782732962256591365621225
absolute error = 1.715679818e-23
relative error = 1.7762334864576727231206268087839e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0348
y[1] (analytic) = 0.96581248250008147583479291772003
y[1] (numeric) = 0.96581248250008147583481012478748
absolute error = 1.720706745e-23
relative error = 1.7816157651491679093806434094205e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0349
y[1] (analytic) = 0.96571602751470849548464526805157
y[1] (numeric) = 0.96571602751470849548466252539289
absolute error = 1.725734132e-23
relative error = 1.7869995763052777176786069397087e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 0.96561958287217523136837956236555
y[1] (numeric) = 0.96561958287217523136839686998545
absolute error = 1.730761990e-23
relative error = 1.7923849316021081452951874287860e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0351
y[1] (analytic) = 0.96552314857344612991052473647042
y[1] (numeric) = 0.96552314857344612991054209437364
absolute error = 1.735790322e-23
relative error = 1.7977718344346465104959941667708e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0352
y[1] (analytic) = 0.96542672461948553409756818578895
y[1] (numeric) = 0.9654267246194855340975855939802
absolute error = 1.740819125e-23
relative error = 1.8031602819842475063404882259574e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0353
y[1] (analytic) = 0.96533031101125768346831233550142
y[1] (numeric) = 0.9653303110112576834683297939853
absolute error = 1.745848388e-23
relative error = 1.8085502631437001604738745663833e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0354
y[1] (analytic) = 0.96523390774972671410423224516527
y[1] (numeric) = 0.96523390774972671410424975394652
absolute error = 1.750878125e-23
relative error = 1.8139417927016931660497699183384e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.3MB, time=6.00
NO POLE
x[1] = 0.0355
y[1] (analytic) = 0.96513751483585665861983424790886
y[1] (numeric) = 0.96513751483585665861985180699218
absolute error = 1.755908332e-23
relative error = 1.8193348668025112505614321621317e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0356
y[1] (analytic) = 0.96504113227061144615301562429423
y[1] (numeric) = 0.96504113227061144615303323368427
absolute error = 1.760939004e-23
relative error = 1.8247294805525525687433939859742e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0357
y[1] (analytic) = 0.96494476005495490235542531094608
y[1] (numeric) = 0.96494476005495490235544297064754
absolute error = 1.765970146e-23
relative error = 1.8301256394194271019074139251842e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0358
y[1] (analytic) = 0.9648483981898507493828256440435
y[1] (numeric) = 0.96484839818985074938284335406102
absolute error = 1.771001752e-23
relative error = 1.8355233374720538416349895911551e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0359
y[1] (analytic) = 0.96475204667626260588545513777006
y[1] (numeric) = 0.96475204667626260588547289810844
absolute error = 1.776033838e-23
relative error = 1.8409225915806483720940098398575e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 0.96465570551515398699839229782007
y[1] (numeric) = 0.96465570551515398699841010848387
absolute error = 1.781066380e-23
relative error = 1.8463233771564738229268090270367e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0361
y[1] (analytic) = 0.96455937470748830433192047005496
y[1] (numeric) = 0.96455937470748830433193833104896
absolute error = 1.786099400e-23
relative error = 1.8517257172910184295051682597411e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0362
y[1] (analytic) = 0.96446305425422886596189372440935
y[1] (numeric) = 0.96446305425422886596191163573816
absolute error = 1.791132881e-23
relative error = 1.8571295946478671947224235983106e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0363
y[1] (analytic) = 0.96436674415633887642010377413981
y[1] (numeric) = 0.96436674415633887642012173580817
absolute error = 1.796166836e-23
relative error = 1.8625350229920551544987017382975e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0364
y[1] (analytic) = 0.96427044441478143668464793051552
y[1] (numeric) = 0.96427044441478143668466594252807
absolute error = 1.801201255e-23
relative error = 1.8679419922417660836386444147208e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0365
y[1] (analytic) = 0.96417415503051954417029809304497
y[1] (numeric) = 0.96417415503051954417031615540638
absolute error = 1.806236141e-23
relative error = 1.8733505057940763787554203963055e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0366
y[1] (analytic) = 0.96407787600451609271887077533638
y[1] (numeric) = 0.96407787600451609271888888805134
absolute error = 1.811271496e-23
relative error = 1.8787605660100381175922146461313e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0367
y[1] (analytic) = 0.96398160733773387258959816668758
y[1] (numeric) = 0.96398160733773387258961632976081
absolute error = 1.816307323e-23
relative error = 1.8841721762888897467069433560260e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0368
y[1] (analytic) = 0.96388534903113557044950022950172
y[1] (numeric) = 0.96388534903113557044951844293792
absolute error = 1.821343620e-23
relative error = 1.8895853348437674849300250093685e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0369
y[1] (analytic) = 0.96378910108568376936375783262519
y[1] (numeric) = 0.96378910108568376936377609642893
absolute error = 1.826380374e-23
relative error = 1.8950000284736870609371479830732e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 0.96369286350234094878608692070345
y[1] (numeric) = 0.96369286350234094878610523487944
absolute error = 1.831417599e-23
relative error = 1.9004162719894949422700859924869e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.3MB, time=6.28
NO POLE
x[1] = 0.0371
y[1] (analytic) = 0.96359663628206948454911371965217
y[1] (numeric) = 0.96359663628206948454913208420523
absolute error = 1.836455306e-23
relative error = 1.9058340770944974160721533024281e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0372
y[1] (analytic) = 0.9635004194258316488547509783394
y[1] (numeric) = 0.96350041942583164885476939327403
absolute error = 1.841493463e-23
relative error = 1.9112534108676166633519398226842e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0373
y[1] (analytic) = 0.9634042129345896102645752465735
y[1] (numeric) = 0.96340421293458961026459371189443
absolute error = 1.846532093e-23
relative error = 1.9166742974637276293424034053259e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0374
y[1] (analytic) = 0.96330801680930543369020518949613
y[1] (numeric) = 0.9633080168093054336902237052081
absolute error = 1.851571197e-23
relative error = 1.9220967382092631373774673422506e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0375
y[1] (analytic) = 0.96321183105094108038368093847403
y[1] (numeric) = 0.96321183105094108038369950458164
absolute error = 1.856610761e-23
relative error = 1.9275207188581656988798300112870e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0376
y[1] (analytic) = 0.96311565566045840792784447858627
y[1] (numeric) = 0.96311565566045840792786309509419
absolute error = 1.861650792e-23
relative error = 1.9329462469628005362666923599223e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0377
y[1] (analytic) = 0.96301949063881917022672107280411
y[1] (numeric) = 0.96301949063881917022673973971702
absolute error = 1.866691291e-23
relative error = 1.9383733238480250920672366922384e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0378
y[1] (analytic) = 0.96292333598698501749590172295863
y[1] (numeric) = 0.96292333598698501749592044028131
absolute error = 1.871732268e-23
relative error = 1.9438019601856430120863205245863e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0379
y[1] (analytic) = 0.96282719170591749625292666759319
y[1] (numeric) = 0.96282719170591749625294543533024
absolute error = 1.876773705e-23
relative error = 1.9492321375705756629700738434965e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 0.96273105779657804930766991679558
y[1] (numeric) = 0.96273105779657804930768873495159
absolute error = 1.881815601e-23
relative error = 1.9546638552483694094996295727083e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0381
y[1] (analytic) = 0.96263493425992801575272482410724
y[1] (numeric) = 0.96263493425992801575274369268703
absolute error = 1.886857979e-23
relative error = 1.9600971373957179081495239000494e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0382
y[1] (analytic) = 0.96253882109692863095379069560606
y[1] (numeric) = 0.9625388210969286309538096146142
absolute error = 1.891900814e-23
relative error = 1.9655319583307317619172463378988e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0383
y[1] (analytic) = 0.96244271830854102654006043625648
y[1] (numeric) = 0.96244271830854102654007940569771
absolute error = 1.896944123e-23
relative error = 1.9709683360001019887529283346893e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0384
y[1] (analytic) = 0.96234662589572623039460923362627
y[1] (numeric) = 0.96234662589572623039462825350523
absolute error = 1.901987896e-23
relative error = 1.9764062603011478018454588075981e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0385
y[1] (analytic) = 0.96225054385944516664478427906341
y[1] (numeric) = 0.96225054385944516664480334938475
absolute error = 1.907032134e-23
relative error = 1.9818457325585653258674744617996e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=95.3MB, alloc=4.3MB, time=6.55
x[1] = 0.0386
y[1] (analytic) = 0.96215447220065865565259552643068
y[1] (numeric) = 0.96215447220065865565261464719911
absolute error = 1.912076843e-23
relative error = 1.9872867592941289270272568989898e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0387
y[1] (analytic) = 0.96205841092032741400510748849383
y[1] (numeric) = 0.96205841092032741400512665971392
absolute error = 1.917122009e-23
relative error = 1.9927293262433375249703695213368e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0388
y[1] (analytic) = 0.96196236001941205450483207105831
y[1] (numeric) = 0.96196236001941205450485129273489
absolute error = 1.922167658e-23
relative error = 1.9981734607175392474508484956455e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0389
y[1] (analytic) = 0.96186631949887308616012244495318
y[1] (numeric) = 0.96186631949887308616014171709074
absolute error = 1.927213756e-23
relative error = 2.0036191276601383339369578619023e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 0.96177028935967091417556795595438
y[1] (numeric) = 0.96177028935967091417558727855768
absolute error = 1.932260330e-23
relative error = 2.0090663554251230018032606099566e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0391
y[1] (analytic) = 0.96167426960276583994239007274775
y[1] (numeric) = 0.96167426960276583994240944582151
absolute error = 1.937307376e-23
relative error = 2.0145151401422377970222081354974e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0392
y[1] (analytic) = 0.96157826022911806102883937302456
y[1] (numeric) = 0.96157826022911806102885879657339
absolute error = 1.942354883e-23
relative error = 2.0199654706598602052600543418428e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0393
y[1] (analytic) = 0.9614822612396876711705935678068
y[1] (numeric) = 0.96148226123968767117061304183537
absolute error = 1.947402857e-23
relative error = 2.0254173535028249797220138376094e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0394
y[1] (analytic) = 0.96138627263543466026115656409851
y[1] (numeric) = 0.96138627263543466026117608861158
absolute error = 1.952451307e-23
relative error = 2.0308707983189448998455195709212e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0395
y[1] (analytic) = 0.96129029441731891434225856595915
y[1] (numeric) = 0.96129029441731891434227814096122
absolute error = 1.957500207e-23
relative error = 2.0363257783503665927284088039454e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0396
y[1] (analytic) = 0.96119432658630021559425721409335
y[1] (numeric) = 0.96119432658630021559427683958923
absolute error = 1.962549588e-23
relative error = 2.0417823261296515206370884451773e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0397
y[1] (analytic) = 0.96109836914333824232653976405651
y[1] (numeric) = 0.96109836914333824232655944005074
absolute error = 1.967599423e-23
relative error = 2.0472404138546115433666105160916e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0398
y[1] (analytic) = 0.96100242208939256896792630316788
y[1] (numeric) = 0.96100242208939256896794602966518
absolute error = 1.972649730e-23
relative error = 2.0527000605379367797971023102409e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0399
y[1] (analytic) = 0.96090648542542266605707400623101
y[1] (numeric) = 0.96090648542542266605709378323606
absolute error = 1.977700505e-23
relative error = 2.0581612623047408704031426385521e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 0.96081055915238790023288243015498
y[1] (numeric) = 0.96081055915238790023290225767242
absolute error = 1.982751744e-23
relative error = 2.0636240152784672607262267642449e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0401
y[1] (analytic) = 0.96071464327124753422489984757332
y[1] (numeric) = 0.96071464327124753422491972560782
absolute error = 1.987803450e-23
relative error = 2.0690883228671314155547404781758e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.3MB, time=6.84
NO POLE
x[1] = 0.0402
y[1] (analytic) = 0.96061873778296072684373061955662
y[1] (numeric) = 0.96061873778296072684375054811286
absolute error = 1.992855624e-23
relative error = 2.0745541863979960515189501217945e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0403
y[1] (analytic) = 0.96052284268848653297144360751441
y[1] (numeric) = 0.96052284268848653297146358659709
absolute error = 1.997908268e-23
relative error = 2.0800216082398310465554471464352e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0404
y[1] (analytic) = 0.96042695798878390355198162438269
y[1] (numeric) = 0.96042695798878390355200165399637
absolute error = 2.002961368e-23
relative error = 2.0854905741029720902738052342598e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0405
y[1] (analytic) = 0.96033108368481168558157192519199
y[1] (numeric) = 0.9603310836848116855815920053414
absolute error = 2.008014941e-23
relative error = 2.0909611019724594327982810472621e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0406
y[1] (analytic) = 0.96023521977752862209913773711366
y[1] (numeric) = 0.96023521977752862209915786780344
absolute error = 2.013068978e-23
relative error = 2.0964331827636944819067658422398e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0407
y[1] (analytic) = 0.96013936626789335217671082907821
y[1] (numeric) = 0.96013936626789335217673101031307
absolute error = 2.018123486e-23
relative error = 2.1019068240525752330640838436978e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0408
y[1] (analytic) = 0.96004352315686441090984512106337
y[1] (numeric) = 0.96004352315686441090986535284786
absolute error = 2.023178449e-23
relative error = 2.1073820094606552150281510330617e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0409
y[1] (analytic) = 0.95994769044540022940803133314598
y[1] (numeric) = 0.95994769044540022940805161548483
absolute error = 2.028233885e-23
relative error = 2.1128587580214211718874919604747e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 0.95985186813445913478511267441565
y[1] (numeric) = 0.95985186813445913478513300731352
absolute error = 2.033289787e-23
relative error = 2.1183370627301526816032270493117e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0411
y[1] (analytic) = 0.95975605622499935014970157184396
y[1] (numeric) = 0.95975605622499935014972195530553
absolute error = 2.038346157e-23
relative error = 2.1238169259565917985964029019640e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0412
y[1] (analytic) = 0.95966025471797899459559743920656
y[1] (numeric) = 0.95966025471797899459561787323641
absolute error = 2.043402985e-23
relative error = 2.1292983375668786637063906286885e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0413
y[1] (analytic) = 0.95956446361435608319220548615273
y[1] (numeric) = 0.95956446361435608319222597075563
absolute error = 2.048460290e-23
relative error = 2.1347813176450284103734100878135e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0414
y[1] (analytic) = 0.95946868291508852697495656751998
y[1] (numeric) = 0.95946868291508852697497710270052
absolute error = 2.053518054e-23
relative error = 2.1402658477199438991956069202988e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0415
y[1] (analytic) = 0.95937291262113413293572807298713
y[1] (numeric) = 0.95937291262113413293574865874993
absolute error = 2.058576280e-23
relative error = 2.1457519312023271246139566898471e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0416
y[1] (analytic) = 0.95927715273345060401326585716371
y[1] (numeric) = 0.95927715273345060401328649351347
absolute error = 2.063634976e-23
relative error = 2.1512395767163774094351937774581e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0417
y[1] (analytic) = 0.95918140325299553908360721021064
y[1] (numeric) = 0.95918140325299553908362789715199
absolute error = 2.068694135e-23
relative error = 2.1567287772512800066685440105702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.3MB, time=7.12
NO POLE
x[1] = 0.0418
y[1] (analytic) = 0.95908566418072643295050486908762
y[1] (numeric) = 0.95908566418072643295052560662522
absolute error = 2.073753760e-23
relative error = 2.1622195362198947183544633432481e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0419
y[1] (analytic) = 0.95898993551760067633585206952368
y[1] (numeric) = 0.9589899355176006763358728576622
absolute error = 2.078813852e-23
relative error = 2.1677118549507934906284755010469e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 0.95889421726457555587010863880622
y[1] (numeric) = 0.95889421726457555587012947755035
absolute error = 2.083874413e-23
relative error = 2.1732057358158234511768048841891e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0421
y[1] (analytic) = 0.95879850942260825408272812948448
y[1] (numeric) = 0.95879850942260825408274901883882
absolute error = 2.088935434e-23
relative error = 2.1787011697149634412904179327695e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0422
y[1] (analytic) = 0.95870281199265584939258599408278
y[1] (numeric) = 0.95870281199265584939260693405196
absolute error = 2.093996918e-23
relative error = 2.1841981600613486885693281017424e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0423
y[1] (analytic) = 0.95860712497567531609840880091983
y[1] (numeric) = 0.95860712497567531609842979150851
absolute error = 2.099058868e-23
relative error = 2.1896967102693542782896133492308e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0424
y[1] (analytic) = 0.9585114483726235243692044911294
y[1] (numeric) = 0.95851144837262352436922553234234
absolute error = 2.104121294e-23
relative error = 2.1951968310575858872028966844831e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0425
y[1] (analytic) = 0.95841578218445724023469367697864
y[1] (numeric) = 0.95841578218445724023471476882033
absolute error = 2.109184169e-23
relative error = 2.2006984945434310775027216963210e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0426
y[1] (analytic) = 0.95832012641213312557574198157794
y[1] (numeric) = 0.95832012641213312557576312405314
absolute error = 2.114247520e-23
relative error = 2.2062017291816233709170487694122e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0427
y[1] (analytic) = 0.95822448105660773811479342008115
y[1] (numeric) = 0.95822448105660773811481461319451
absolute error = 2.119311336e-23
relative error = 2.2117065237814564834886525781046e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0428
y[1] (analytic) = 0.95812884611883753140630482246873
y[1] (numeric) = 0.95812884611883753140632606622481
absolute error = 2.124375608e-23
relative error = 2.2172128692350338610072683648714e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0429
y[1] (analytic) = 0.95803322159977885482718129801092
y[1] (numeric) = 0.95803322159977885482720259241445
absolute error = 2.129440353e-23
relative error = 2.2227207835696326796062436537948e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 0.95793760750038795356721274150717
y[1] (numeric) = 0.95793760750038795356723408656276
absolute error = 2.134505559e-23
relative error = 2.2282302545462341607923326399191e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0431
y[1] (analytic) = 0.95784200382162096861951138139576
y[1] (numeric) = 0.95784200382162096861953277710811
absolute error = 2.139571235e-23
relative error = 2.2337412918450928656433498879340e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0432
y[1] (analytic) = 0.95774641056443393677095036983098
y[1] (numeric) = 0.95774641056443393677097181620472
absolute error = 2.144637374e-23
relative error = 2.2392538884443211980462691119844e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0433
y[1] (analytic) = 0.95765082772978279059260341482216
y[1] (numeric) = 0.9576508277297827905926249118619
absolute error = 2.149703974e-23
relative error = 2.2447680425402137867959120845438e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.3MB, time=7.39
NO POLE
x[1] = 0.0434
y[1] (analytic) = 0.95755525531862335843018545453098
y[1] (numeric) = 0.9575552553186233584302070022413
absolute error = 2.154771032e-23
relative error = 2.2502837512838953964542224762698e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0435
y[1] (analytic) = 0.95745969333191136439449437382202
y[1] (numeric) = 0.9574596933319113643945159722077
absolute error = 2.159838568e-23
relative error = 2.2558010358471288674806551308339e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0436
y[1] (analytic) = 0.95736414177060242835185376316342
y[1] (numeric) = 0.95736414177060242835187541222901
absolute error = 2.164906559e-23
relative error = 2.2613198724950169352280300468853e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0437
y[1] (analytic) = 0.95726860063565206591455671997081
y[1] (numeric) = 0.95726860063565206591457841972099
absolute error = 2.169975018e-23
relative error = 2.2668402750900617611824728961576e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0438
y[1] (analytic) = 0.95717306992801568843131069249286
y[1] (numeric) = 0.95717306992801568843133244293229
absolute error = 2.175043943e-23
relative error = 2.2723622418290293432646889728989e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0439
y[1] (analytic) = 0.95707754964864860297768336633201
y[1] (numeric) = 0.95707754964864860297770516746533
absolute error = 2.180113332e-23
relative error = 2.2778857709078416350542616520657e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 0.95698203979850601234654959369677
y[1] (numeric) = 0.95698203979850601234657144552859
absolute error = 2.185183182e-23
relative error = 2.2834108594766246182918308284283e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0441
y[1] (analytic) = 0.95688654037854301503853936548079
y[1] (numeric) = 0.95688654037854301503856126801582
absolute error = 2.190253503e-23
relative error = 2.2889375182699703254256807180855e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0442
y[1] (analytic) = 0.95679105138971460525248682626479
y[1] (numeric) = 0.9567910513897146052525087795077
absolute error = 2.195324291e-23
relative error = 2.2944657433943884039815315856281e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0443
y[1] (analytic) = 0.95669557283297567287588033233612
y[1] (numeric) = 0.95669557283297567287590233629144
absolute error = 2.200395532e-23
relative error = 2.2999955205020638307065173312639e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0444
y[1] (analytic) = 0.95660010470928100347531355282148
y[1] (numeric) = 0.95660010470928100347533560749388
absolute error = 2.205467240e-23
relative error = 2.3055268645096588783156727343456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0445
y[1] (analytic) = 0.95650464701958527828693761402935
y[1] (numeric) = 0.9565046470195852782869597194235
absolute error = 2.210539415e-23
relative error = 2.3110597757030418809403947426893e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0446
y[1] (analytic) = 0.95640919976484307420691428709638
y[1] (numeric) = 0.95640919976484307420693644321686
absolute error = 2.215612048e-23
relative error = 2.3165942449578728236347453851530e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0447
y[1] (analytic) = 0.95631376294600886378187021903346
y[1] (numeric) = 0.95631376294600886378189242588494
absolute error = 2.220685148e-23
relative error = 2.3221302819683192746960347191333e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0448
y[1] (analytic) = 0.95621833656403701519935220726764
y[1] (numeric) = 0.95621833656403701519937446485483
absolute error = 2.225758719e-23
relative error = 2.3276678912033633605937090503909e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.3MB, time=7.65
x[1] = 0.0449
y[1] (analytic) = 0.95612292061988179227828351777474
y[1] (numeric) = 0.9561229206198817922783058261022
absolute error = 2.230832746e-23
relative error = 2.3332070572617247033344440799461e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 0.95602751511449735445942124689761
y[1] (numeric) = 0.95602751511449735445944360597005
absolute error = 2.235907244e-23
relative error = 2.3387477961157002522013714370923e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0451
y[1] (analytic) = 0.95593212004883775679581472694711
y[1] (numeric) = 0.95593212004883775679583713676906
absolute error = 2.240982195e-23
relative error = 2.3442900892225591611710984758538e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0452
y[1] (analytic) = 0.95583673542385694994326497567888
y[1] (numeric) = 0.95583673542385694994328743625506
absolute error = 2.246057618e-23
relative error = 2.3498339567415836410832215047760e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0453
y[1] (analytic) = 0.955741361240508780150785189744
y[1] (numeric) = 0.95574136124050878015080770107898
absolute error = 2.251133498e-23
relative error = 2.3553793832655010289321418247358e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0454
y[1] (analytic) = 0.95564599749974698925106228220618
y[1] (numeric) = 0.95564599749974698925108484430464
absolute error = 2.256209846e-23
relative error = 2.3609263805874908608631924463422e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0455
y[1] (analytic) = 0.9555506442025252146509194642232
y[1] (numeric) = 0.95555064420252521465094207708986
absolute error = 2.261286666e-23
relative error = 2.3664749531796968284406883940560e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0456
y[1] (analytic) = 0.95545530134979698932177987098674
y[1] (numeric) = 0.95545530134979698932180253462614
absolute error = 2.266363940e-23
relative error = 2.3720250824902511766473140238865e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0457
y[1] (analytic) = 0.95535996894251574179013123201561
y[1] (numeric) = 0.95535996894251574179015394643241
absolute error = 2.271441680e-23
relative error = 2.3775767813615322599031517737753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0458
y[1] (analytic) = 0.95526464698163479612799158589925
y[1] (numeric) = 0.95526464698163479612801435109808
absolute error = 2.276519883e-23
relative error = 2.3831300469384654922391720208820e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0459
y[1] (analytic) = 0.95516933546810737194337603958541
y[1] (numeric) = 0.9551693354681073719433988555708
absolute error = 2.281598539e-23
relative error = 2.3886848690361683392553340955285e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 0.95507403440288658437076457230754
y[1] (numeric) = 0.95507403440288658437078743908426
absolute error = 2.286677672e-23
relative error = 2.3942412730649028526885594690762e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0461
y[1] (analytic) = 0.95497874378692544406157088424873
y[1] (numeric) = 0.95497874378692544406159380182134
absolute error = 2.291757261e-23
relative error = 2.3997992373234813662345574253151e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0462
y[1] (analytic) = 0.9548834636211768571746122900347
y[1] (numeric) = 0.95488346362117685717463525840789
absolute error = 2.296837319e-23
relative error = 2.4053587757083680852561824709493e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0463
y[1] (analytic) = 0.95478819390659362536658065715418
y[1] (numeric) = 0.95478819390659362536660367633252
absolute error = 2.301917834e-23
relative error = 2.4109198759376315509227874855667e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0464
y[1] (analytic) = 0.95469293464412844578251438939944
y[1] (numeric) = 0.95469293464412844578253745938762
absolute error = 2.306998818e-23
relative error = 2.4164825508632861110626652463607e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.3MB, time=7.92
NO POLE
x[1] = 0.0465
y[1] (analytic) = 0.95459768583473391104627145542427
y[1] (numeric) = 0.95459768583473391104629457622691
absolute error = 2.312080264e-23
relative error = 2.4220467934386782085856947893590e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0466
y[1] (analytic) = 0.95450244747936250925100346251307
y[1] (numeric) = 0.95450244747936250925102663413479
absolute error = 2.317162172e-23
relative error = 2.4276126039478802202402123995423e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0467
y[1] (analytic) = 0.95440721957896662394963077565737
y[1] (numeric) = 0.95440721957896662394965399810278
absolute error = 2.322244541e-23
relative error = 2.4331799816271821395092420381366e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0468
y[1] (analytic) = 0.95431200213449853414531868203444
y[1] (numeric) = 0.95431200213449853414534195530824
absolute error = 2.327327380e-23
relative error = 2.4387489361911973972363690603012e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0469
y[1] (analytic) = 0.95421679514691041428195460098393
y[1] (numeric) = 0.95421679514691041428197792509065
absolute error = 2.332410672e-23
relative error = 2.4443194501108147199890573592093e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 0.95412159861715433423462633957639
y[1] (numeric) = 0.95412159861715433423464971452068
absolute error = 2.337494429e-23
relative error = 2.4498915362442500960995266004911e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0471
y[1] (analytic) = 0.95402641254618225930010139387075
y[1] (numeric) = 0.95402641254618225930012481965725
absolute error = 2.342578650e-23
relative error = 2.4554651938282694764661446207571e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0472
y[1] (analytic) = 0.95393123693494605018730729595437
y[1] (numeric) = 0.95393123693494605018733077258777
absolute error = 2.347663340e-23
relative error = 2.4610404283889703472572455761254e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0473
y[1] (analytic) = 0.95383607178439746300781300686197
y[1] (numeric) = 0.9538360717843974630078365343468
absolute error = 2.352748483e-23
relative error = 2.4666172234381684520334362900874e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0474
y[1] (analytic) = 0.95374091709548814926631135546735
y[1] (numeric) = 0.95374091709548814926633493380832
absolute error = 2.357834097e-23
relative error = 2.4721955981300680819068163947676e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0475
y[1] (analytic) = 0.95364577286916965585110252344505
y[1] (numeric) = 0.95364577286916965585112615264669
absolute error = 2.362920164e-23
relative error = 2.4777755338765269458398618606505e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0476
y[1] (analytic) = 0.95355063910639342502457857639466
y[1] (numeric) = 0.95355063910639342502460225646162
absolute error = 2.368006696e-23
relative error = 2.4833570435432188290720923447890e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0477
y[1] (analytic) = 0.95345551580811079441370904122519
y[1] (numeric) = 0.95345551580811079441373277216213
absolute error = 2.373093694e-23
relative error = 2.4889401284638440793317178794077e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0478
y[1] (analytic) = 0.95336040297527299700052752989331
y[1] (numeric) = 0.95336040297527299700055131170484
absolute error = 2.378181153e-23
relative error = 2.4945247836789820206202633770052e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0479
y[1] (analytic) = 0.95326530060883116111261940959076
y[1] (numeric) = 0.9532653006088311611126432422815
absolute error = 2.383269074e-23
relative error = 2.5001110105212625599126449631034e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 0.95317020870973631041361051947653
y[1] (numeric) = 0.95317020870973631041363440305111
absolute error = 2.388357458e-23
relative error = 2.5056988103237219216078019837798e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.3MB, time=8.18
NO POLE
x[1] = 0.0481
y[1] (analytic) = 0.9530751272789393638936569340485
y[1] (numeric) = 0.95307512727893936389368086851157
absolute error = 2.393446307e-23
relative error = 2.5112881854690379208601575495674e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0482
y[1] (analytic) = 0.9529800563173911358599357732499
y[1] (numeric) = 0.95298005631739113585995975860604
absolute error = 2.398535614e-23
relative error = 2.5168791288966543434748703495822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0483
y[1] (analytic) = 0.95288499582604233592713705940519
y[1] (numeric) = 0.95288499582604233592716109565908
absolute error = 2.403625389e-23
relative error = 2.5224716513836295898237789792777e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0484
y[1] (analytic) = 0.95278994580584356900795662108154
y[1] (numeric) = 0.95278994580584356900798070823771
absolute error = 2.408715617e-23
relative error = 2.5280657374724651228644702007435e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0485
y[1] (analytic) = 0.95269490625774533530359004396916
y[1] (numeric) = 0.95269490625774533530361418203234
absolute error = 2.413806318e-23
relative error = 2.5336614084372574473874355683303e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0486
y[1] (analytic) = 0.95259987718269803029422766887806
y[1] (numeric) = 0.95259987718269803029425185785275
absolute error = 2.418897469e-23
relative error = 2.5392586404208431868058213368656e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0487
y[1] (analytic) = 0.95250485858165194472955063694315
y[1] (numeric) = 0.9525048585816519447295748768341
absolute error = 2.423989095e-23
relative error = 2.5448574599498564545490868980477e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0488
y[1] (analytic) = 0.95240985045555726461922798213632
y[1] (numeric) = 0.95240985045555726461925227294804
absolute error = 2.429081172e-23
relative error = 2.5504578421129521097669923245924e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0489
y[1] (analytic) = 0.95231485280536407122341477117682
y[1] (numeric) = 0.95231485280536407122343911291393
absolute error = 2.434173711e-23
relative error = 2.5560597987412688951691677405771e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 0.95221986563202234104325129093804
y[1] (numeric) = 0.95221986563202234104327568360523
absolute error = 2.439266719e-23
relative error = 2.5616633374698306052328045033098e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0491
y[1] (analytic) = 0.95212488893648194581136328344417
y[1] (numeric) = 0.95212488893648194581138772704599
absolute error = 2.444360182e-23
relative error = 2.5672684438806513502822509157131e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0492
y[1] (analytic) = 0.95202992271969265248236322855136
y[1] (numeric) = 0.95202992271969265248238772309251
absolute error = 2.449454115e-23
relative error = 2.5728751340110932671900206649341e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0493
y[1] (analytic) = 0.95193496698260412322335267441012
y[1] (numeric) = 0.95193496698260412322337721989515
absolute error = 2.454548503e-23
relative error = 2.5784833923900339080249886484918e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0494
y[1] (analytic) = 0.95184002172616591540442561580171
y[1] (numeric) = 0.9518400217261659154044502122352
absolute error = 2.459643349e-23
relative error = 2.5840932224507920534564794825415e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0495
y[1] (analytic) = 0.95174508695132748158917292044518
y[1] (numeric) = 0.95174508695132748158919756783188
absolute error = 2.464738670e-23
relative error = 2.5897046423377517754213409251777e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=122.0MB, alloc=4.3MB, time=8.44
x[1] = 0.0496
y[1] (analytic) = 0.95165016265903816952518780336999
y[1] (numeric) = 0.95165016265903816952521250171433
absolute error = 2.469834434e-23
relative error = 2.5953176187129011671696435006663e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0497
y[1] (analytic) = 0.95155524885024722213457234944688
y[1] (numeric) = 0.95155524885024722213459709875359
absolute error = 2.474930671e-23
relative error = 2.6009321833812897389639012090228e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0498
y[1] (analytic) = 0.95146034552590377750444508417578
y[1] (numeric) = 0.95146034552590377750446988444948
absolute error = 2.480027370e-23
relative error = 2.6065483250688775574754962784345e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0499
y[1] (analytic) = 0.95136545268695686887744959282206
y[1] (numeric) = 0.95136545268695686887747444406734
absolute error = 2.485124528e-23
relative error = 2.6121660409059657503216060200883e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 0.95127057033435542464226418799801
y[1] (numeric) = 0.95127057033435542464228909021949
absolute error = 2.490222148e-23
relative error = 2.6177853343289378466929303391499e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0501
y[1] (analytic) = 0.95117569846904826832411262578409
y[1] (numeric) = 0.95117569846904826832413757898638
absolute error = 2.495320229e-23
relative error = 2.6234062045701002157391764394717e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0502
y[1] (analytic) = 0.95108083709198411857527587048448
y[1] (numeric) = 0.95108083709198411857530087467223
absolute error = 2.500418775e-23
relative error = 2.6290286561185031176879841167087e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0503
y[1] (analytic) = 0.95098598620411158916560490811233
y[1] (numeric) = 0.95098598620411158916562996329013
absolute error = 2.505517780e-23
relative error = 2.6346526829494592089433390017423e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0504
y[1] (analytic) = 0.95089114580637918897303460869901
y[1] (numeric) = 0.95089114580637918897305971487145
absolute error = 2.510617244e-23
relative error = 2.6402782853456212778171190840152e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0505
y[1] (analytic) = 0.95079631589973532197409863752269
y[1] (numeric) = 0.95079631589973532197412379469438
absolute error = 2.515717169e-23
relative error = 2.6459054656931283898713529737432e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0506
y[1] (analytic) = 0.95070149648512828723444541535096
y[1] (numeric) = 0.95070149648512828723447062352652
absolute error = 2.520817556e-23
relative error = 2.6515342253270902002699243398208e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0507
y[1] (analytic) = 0.95060668756350627889935512779223
y[1] (numeric) = 0.95060668756350627889938038697627
absolute error = 2.525918404e-23
relative error = 2.6571645634791027768255763257626e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0508
y[1] (analytic) = 0.95051188913581738618425778385084
y[1] (numeric) = 0.95051188913581738618428309404794
absolute error = 2.531019710e-23
relative error = 2.6627964772761994800421662151954e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0509
y[1] (analytic) = 0.95041710120300959336525232378066
y[1] (numeric) = 0.95041710120300959336527768499536
absolute error = 2.536121470e-23
relative error = 2.6684299627919711835340245436170e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 0.95032232376603077976962677633175
y[1] (numeric) = 0.95032232376603077976965218856879
absolute error = 2.541223704e-23
relative error = 2.6740650413529051355533977155886e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0511
y[1] (analytic) = 0.95022755682582871976637946548598
y[1] (numeric) = 0.95022755682582871976640492874992
absolute error = 2.546326394e-23
relative error = 2.6797016943034489103340472236892e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.3MB, time=8.71
NO POLE
x[1] = 0.0512
y[1] (analytic) = 0.95013280038335108275674126677433
y[1] (numeric) = 0.9501328003833510827567667810698
absolute error = 2.551429547e-23
relative error = 2.6853399292925915519764963320424e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0513
y[1] (analytic) = 0.95003805443954543316469891327287
y[1] (numeric) = 0.95003805443954543316472447860443
absolute error = 2.556533156e-23
relative error = 2.6909797392359950087642342440268e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0514
y[1] (analytic) = 0.94994331899535923042751935137053
y[1] (numeric) = 0.94994331899535923042754496774279
absolute error = 2.561637226e-23
relative error = 2.6966211296787007533942362595247e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0515
y[1] (analytic) = 0.94984859405173982898627514640442
y[1] (numeric) = 0.94984859405173982898630081382204
absolute error = 2.566741762e-23
relative error = 2.7022641061678355416622604623322e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0516
y[1] (analytic) = 0.94975387960963447827637093825718
y[1] (numeric) = 0.94975387960963447827639665672473
absolute error = 2.571846755e-23
relative error = 2.7079086595119507978744089800470e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0517
y[1] (analytic) = 0.94965917566999032271807094701058
y[1] (numeric) = 0.94965917566999032271809671653262
absolute error = 2.576952204e-23
relative error = 2.7135547889398789320863494196129e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0518
y[1] (analytic) = 0.94956448223375440170702752875072
y[1] (numeric) = 0.94956448223375440170705334933194
absolute error = 2.582058122e-23
relative error = 2.7192025084236190339343257457338e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0519
y[1] (analytic) = 0.94946979930187364960481078161983
y[1] (numeric) = 0.94946979930187364960483665326475
absolute error = 2.587164492e-23
relative error = 2.7248518003440350001042075820366e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 0.94937512687529489572943920220786
y[1] (numeric) = 0.94937512687529489572946512492114
absolute error = 2.592271328e-23
relative error = 2.7305026797278918192961173127794e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0521
y[1] (analytic) = 0.94928046495496486434591139238071
y[1] (numeric) = 0.94928046495496486434593736616693
absolute error = 2.597378622e-23
relative error = 2.7361551384323737430222305739906e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0522
y[1] (analytic) = 0.94918581354183017465673881663779
y[1] (numeric) = 0.94918581354183017465676484150158
absolute error = 2.602486379e-23
relative error = 2.7418091820072378726519884432402e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0523
y[1] (analytic) = 0.94909117263683734079247961009501
y[1] (numeric) = 0.94909117263683734079250568604096
absolute error = 2.607594595e-23
relative error = 2.7474648065215717955217454351150e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0524
y[1] (analytic) = 0.94899654224093277180227343718692
y[1] (numeric) = 0.94899654224093277180229956421964
absolute error = 2.612703272e-23
relative error = 2.7531220143652353603298223368118e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0525
y[1] (analytic) = 0.94890192235506277164437740118339
y[1] (numeric) = 0.94890192235506277164440357930742
absolute error = 2.617812403e-23
relative error = 2.7587807984442670813191692952505e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0526
y[1] (analytic) = 0.94880731298017353917670300461462
y[1] (numeric) = 0.9488073129801735391767292338346
absolute error = 2.622921998e-23
relative error = 2.7644411695789797148696375688577e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0527
y[1] (analytic) = 0.94871271411721116814735416070022
y[1] (numeric) = 0.94871271411721116814738044102077
absolute error = 2.628032055e-23
relative error = 2.7701031259451562243102087423163e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.3MB, time=9.00
NO POLE
x[1] = 0.0528
y[1] (analytic) = 0.94861812576712164718516625587605
y[1] (numeric) = 0.94861812576712164718519258730167
absolute error = 2.633142562e-23
relative error = 2.7757666551760744728334917242708e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0529
y[1] (analytic) = 0.94852354793085085979024626351329
y[1] (numeric) = 0.94852354793085085979027264604869
absolute error = 2.638253540e-23
relative error = 2.7814317796908650032984826744725e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 0.94842898060934458432451390892596
y[1] (numeric) = 0.9484289806093445843245403425757
absolute error = 2.643364974e-23
relative error = 2.7870984839599657033043547470199e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0531
y[1] (analytic) = 0.94833442380354849400224388575905
y[1] (numeric) = 0.94833442380354849400227037052774
absolute error = 2.648476869e-23
relative error = 2.7927667735370990166248118808092e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0532
y[1] (analytic) = 0.94823987751440815688060912385388
y[1] (numeric) = 0.94823987751440815688063565974613
absolute error = 2.653589225e-23
relative error = 2.7984366487051475914595357123888e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0533
y[1] (analytic) = 0.94814534174286903585022510868433
y[1] (numeric) = 0.94814534174286903585025169570465
absolute error = 2.658702032e-23
relative error = 2.8041080992000728714517139420822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0534
y[1] (analytic) = 0.94805081648987648862569525245821
y[1] (numeric) = 0.94805081648987648862572189061124
absolute error = 2.663815303e-23
relative error = 2.8097811390139178803398186269069e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0535
y[1] (analytic) = 0.94795630175637576773615731697949
y[1] (numeric) = 0.94795630175637576773618400626986
absolute error = 2.668929037e-23
relative error = 2.8154557673755654295968593992650e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0536
y[1] (analytic) = 0.94786179754331202051583088836463
y[1] (numeric) = 0.94786179754331202051585762879698
absolute error = 2.674043235e-23
relative error = 2.8211319856234748964664432785906e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0537
y[1] (analytic) = 0.94776730385163028909456590370844
y[1] (numeric) = 0.94776730385163028909459269528725
absolute error = 2.679157881e-23
relative error = 2.8268097771596190760995351470808e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0538
y[1] (analytic) = 0.94767282068227551038839222979303
y[1] (numeric) = 0.94767282068227551038841907252291
absolute error = 2.684272988e-23
relative error = 2.8324891559805018101435227384411e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0539
y[1] (analytic) = 0.94757834803619251609007029393574
y[1] (numeric) = 0.94757834803619251609009718782134
absolute error = 2.689388560e-23
relative error = 2.8381701265901861679378809995058e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 0.94748388591432603265964276706948
y[1] (numeric) = 0.94748388591432603265966971211532
absolute error = 2.694504584e-23
relative error = 2.8438526755521456343227372411135e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0541
y[1] (analytic) = 0.94738943431762068131498729914969
y[1] (numeric) = 0.9473894343176206813150142953605
absolute error = 2.699621081e-23
relative error = 2.8495368253124598095444988560793e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0542
y[1] (analytic) = 0.9472949932470209780223703069843
y[1] (numeric) = 0.94729499324702097802239735436449
absolute error = 2.704738019e-23
relative error = 2.8552225423772509426854458444340e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0543
memory used=133.5MB, alloc=4.3MB, time=9.28
y[1] (analytic) = 0.94720056270347133348700181457779
y[1] (numeric) = 0.94720056270347133348702891313206
absolute error = 2.709855427e-23
relative error = 2.8609098576394551668987121529327e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0544
y[1] (analytic) = 0.94710614268791605314359134608795
y[1] (numeric) = 0.94710614268791605314361849582091
absolute error = 2.714973296e-23
relative error = 2.8665987618819820659338953695364e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0545
y[1] (analytic) = 0.94701173320129933714690487148623
y[1] (numeric) = 0.94701173320129933714693207240244
absolute error = 2.720091621e-23
relative error = 2.8722892501077492752237417201851e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0546
y[1] (analytic) = 0.94691733424456528036232280501795
y[1] (numeric) = 0.94691733424456528036235005712197
absolute error = 2.725210402e-23
relative error = 2.8779813225978453690038050928107e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0547
y[1] (analytic) = 0.9468229458186578723563990565564
y[1] (numeric) = 0.9468229458186578723564263598528
absolute error = 2.730329640e-23
relative error = 2.8836749806895066064768301387951e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0548
y[1] (analytic) = 0.94672856792452099738742113594513
y[1] (numeric) = 0.94672856792452099738744849043854
absolute error = 2.735449341e-23
relative error = 2.8893702310017191571792585392957e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0549
y[1] (analytic) = 0.94663420056309843439597131042305
y[1] (numeric) = 0.94663420056309843439599871611808
absolute error = 2.740569503e-23
relative error = 2.8950670717049862179621157238227e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 0.94653984373533385699548881522648
y[1] (numeric) = 0.94653984373533385699551627212767
absolute error = 2.745690119e-23
relative error = 2.9007654956865549713762810500002e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0551
y[1] (analytic) = 0.9464454974421708334628331174624
y[1] (numeric) = 0.94644549744217083346286062557435
absolute error = 2.750811195e-23
relative error = 2.9064655095663112687450254570467e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0552
y[1] (analytic) = 0.94635116168455282672884823334788
y[1] (numeric) = 0.94635116168455282672887579267525
absolute error = 2.755932737e-23
relative error = 2.9121671199666523853083952873980e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0553
y[1] (analytic) = 0.94625683646342319436892809890971
y[1] (numeric) = 0.94625683646342319436895570945699
absolute error = 2.761054728e-23
relative error = 2.9178703092061902108714756823864e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0554
y[1] (analytic) = 0.94616252177972518859358299423786
y[1] (numeric) = 0.94616252177972518859361065600963
absolute error = 2.766177177e-23
relative error = 2.9235750870757803604253484631051e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0555
y[1] (analytic) = 0.94606821763440195623900702138852
y[1] (numeric) = 0.94606821763440195623903473438939
absolute error = 2.771300087e-23
relative error = 2.9292814570280169482606953123861e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0556
y[1] (analytic) = 0.94597392402839653875764663602997
y[1] (numeric) = 0.9459739240283965387576744002646
absolute error = 2.776423463e-23
relative error = 2.9349894246309652601483165139109e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0557
y[1] (analytic) = 0.94587964096265187220877023292619
y[1] (numeric) = 0.94587964096265187220879804839909
absolute error = 2.781547290e-23
relative error = 2.9406989743104425281610271062445e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0558
y[1] (analytic) = 0.94578536843811078724903878535159
y[1] (numeric) = 0.94578536843811078724906665206733
absolute error = 2.786671574e-23
relative error = 2.9464101126896963645677673915085e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.3MB, time=9.55
NO POLE
x[1] = 0.0559
y[1] (analytic) = 0.94569110645571600912307753853254
y[1] (numeric) = 0.94569110645571600912310545649573
absolute error = 2.791796319e-23
relative error = 2.9521228442796313651318381978854e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 0.94559685501641015765404875720903
y[1] (numeric) = 0.94559685501641015765407672642421
absolute error = 2.796921518e-23
relative error = 2.9578371619599574766534444007729e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0561
y[1] (analytic) = 0.9455026141211357472342255274106
y[1] (numeric) = 0.94550261412113574723425354788243
absolute error = 2.802047183e-23
relative error = 2.9635530787025489739609299021639e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0562
y[1] (analytic) = 0.94540838377083518681556661254192
y[1] (numeric) = 0.94540838377083518681559468427493
absolute error = 2.807173301e-23
relative error = 2.9692705810407244473920717789108e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0563
y[1] (analytic) = 0.94531416396645077990029236387066
y[1] (numeric) = 0.9453141639664507799003204868694
absolute error = 2.812299874e-23
relative error = 2.9749896713700447455467836618808e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0564
y[1] (analytic) = 0.94521995470892472453146168551317
y[1] (numeric) = 0.9452199547089247245314898597823
absolute error = 2.817426913e-23
relative error = 2.9807103616084904699214880780514e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0565
y[1] (analytic) = 0.94512575599919911328355005401213
y[1] (numeric) = 0.94512575599919911328357827955614
absolute error = 2.822554401e-23
relative error = 2.9864326340529775957414344894632e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0566
y[1] (analytic) = 0.94503156783821593325302859259904
y[1] (numeric) = 0.94503156783821593325305686942259
absolute error = 2.827682355e-23
relative error = 2.9921565069708689858719723585611e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0567
y[1] (analytic) = 0.94493739022691706604894420023796
y[1] (numeric) = 0.9449373902269170660489725283456
absolute error = 2.832810764e-23
relative error = 2.9978819690050887067050372472022e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0568
y[1] (analytic) = 0.94484322316624428778350073554249
y[1] (numeric) = 0.94484322316624428778352911493879
absolute error = 2.837939630e-23
relative error = 3.0036090225527999127804645111943e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0569
y[1] (analytic) = 0.94474906665713926906264125566174
y[1] (numeric) = 0.94474906665713926906266968635124
absolute error = 2.843068950e-23
relative error = 3.0093376647195817885502924047962e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 0.9446549207005435749766313102286
y[1] (numeric) = 0.94465492070054357497665979221593
absolute error = 2.848198733e-23
relative error = 3.0150679053127818895125009971309e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0571
y[1] (analytic) = 0.94456078529739866509064329046522
y[1] (numeric) = 0.94456078529739866509067182375493
absolute error = 2.853328971e-23
relative error = 3.0207997361457454439674709040705e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0572
y[1] (analytic) = 0.94446666044864589343534183353883
y[1] (numeric) = 0.94446666044864589343537041813551
absolute error = 2.858459668e-23
relative error = 3.0265331617340079803792714771724e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0573
y[1] (analytic) = 0.94437254615522650849747028226307
y[1] (numeric) = 0.94437254615522650849749891817133
absolute error = 2.863590826e-23
relative error = 3.0322681844769676276629892617608e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0574
y[1] (analytic) = 0.94427844241808165321043820023849
y[1] (numeric) = 0.94427844241808165321046688746287
absolute error = 2.868722438e-23
relative error = 3.0380047972437624832560623842062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.3MB, time=9.82
NO POLE
x[1] = 0.0575
y[1] (analytic) = 0.94418434923815236494490994252613
y[1] (numeric) = 0.94418434923815236494493868107118
absolute error = 2.873854505e-23
relative error = 3.0437430013734800913739647731020e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0576
y[1] (analytic) = 0.94409026661637957549939428194876
y[1] (numeric) = 0.94409026661637957549942307181906
absolute error = 2.878987030e-23
relative error = 3.0494828003240540624783387199012e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0577
y[1] (analytic) = 0.94399619455370411109083509111364
y[1] (numeric) = 0.94399619455370411109086393231381
absolute error = 2.884120017e-23
relative error = 3.0552241986139933535825567211354e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0578
y[1] (analytic) = 0.94390213305106669234520308025106
y[1] (numeric) = 0.94390213305106669234523197278566
absolute error = 2.889253460e-23
relative error = 3.0609671901691597620543472041699e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0579
y[1] (analytic) = 0.94380808210940793428808859096232
y[1] (numeric) = 0.94380808210940793428811753483588
absolute error = 2.894387356e-23
relative error = 3.0667117720914763261780460604633e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 0.9437140417296683463352954459716
y[1] (numeric) = 0.94371404172966834633532444118872
absolute error = 2.899521712e-23
relative error = 3.0724579520780116133956184761416e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0581
y[1] (analytic) = 0.94362001191278833228343585497598
y[1] (numeric) = 0.94362001191278833228346490154121
absolute error = 2.904656523e-23
relative error = 3.0782057251117894422757057554187e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0582
y[1] (analytic) = 0.94352599265970819030052637668689
y[1] (numeric) = 0.94352599265970819030055547460487
absolute error = 2.909791798e-23
relative error = 3.0839551010116630272370056372962e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0583
y[1] (analytic) = 0.94343198397136811291658493715814
y[1] (numeric) = 0.94343198397136811291661408643339
absolute error = 2.914927525e-23
relative error = 3.0897060673411132892448695823757e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0584
y[1] (analytic) = 0.94333798584870818701422890449321
y[1] (numeric) = 0.94333798584870818701425810513027
absolute error = 2.920063706e-23
relative error = 3.0954586264994501637990295809260e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0585
y[1] (analytic) = 0.94324399829266839381927422002703
y[1] (numeric) = 0.94324399829266839381930347203051
absolute error = 2.925200348e-23
relative error = 3.1012127861876657655389179348235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0586
y[1] (analytic) = 0.94315002130418860889133558607578
y[1] (numeric) = 0.94315002130418860889136488945024
absolute error = 2.930337446e-23
relative error = 3.1069685413863714068947019254852e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0587
y[1] (analytic) = 0.94305605488420860211442771034839
y[1] (numeric) = 0.94305605488420860211445706509845
absolute error = 2.935475006e-23
relative error = 3.1127258987382535633574047924912e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0588
y[1] (analytic) = 0.9429620990336680376875676071145
y[1] (numeric) = 0.94296209903366803768759701324464
absolute error = 2.940613014e-23
relative error = 3.1184848436787561010497361057614e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0589
y[1] (analytic) = 0.9428681537535064741153779552217
y[1] (numeric) = 0.94286815375350647411540741273651
absolute error = 2.945751481e-23
relative error = 3.1242453881522296716094333927636e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 0.94277421904466336419869151305751
y[1] (numeric) = 0.94277421904466336419872102196153
absolute error = 2.950890402e-23
relative error = 3.1300075271364663121646713124406e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.3MB, time=10.10
NO POLE
x[1] = 0.0591
y[1] (analytic) = 0.94268029490807805502515659054856
y[1] (numeric) = 0.94268029490807805502518615084647
absolute error = 2.956029791e-23
relative error = 3.1357712757624218661156249816441e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0592
y[1] (analytic) = 0.94258638134468978795984357829246
y[1] (numeric) = 0.94258638134468978795987318998872
absolute error = 2.961169626e-23
relative error = 3.1415366109741664214594980146126e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0593
y[1] (analytic) = 0.94249247835543769863585253391426
y[1] (numeric) = 0.94249247835543769863588219701345
absolute error = 2.966309919e-23
relative error = 3.1473035457810090562644677089317e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0594
y[1] (analytic) = 0.9423985859412608169449218257437
y[1] (numeric) = 0.94239858594126081694495154025038
absolute error = 2.971450668e-23
relative error = 3.1530720783416040460777636077116e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0595
y[1] (analytic) = 0.94230470410309806702803783390548
y[1] (numeric) = 0.94230470410309806702806759982428
absolute error = 2.976591880e-23
relative error = 3.1588422163647922036121206326429e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0596
y[1] (analytic) = 0.94221083284188826726604570891751
y[1] (numeric) = 0.94221083284188826726607552625289
absolute error = 2.981733538e-23
relative error = 3.1646139420903501688118830492092e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0597
y[1] (analytic) = 0.94211697215857013027026118788969
y[1] (numeric) = 0.94211697215857013027029105664631
absolute error = 2.986875662e-23
relative error = 3.1703872770241010757155849727456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0598
y[1] (analytic) = 0.9420231220540822628730834684193
y[1] (numeric) = 0.94202312205408226287311338860167
absolute error = 2.992018237e-23
relative error = 3.1761622055262311923095002355174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0599
y[1] (analytic) = 0.94192928252936316611860914027417
y[1] (numeric) = 0.94192928252936316611863911188693
absolute error = 2.997161276e-23
relative error = 3.1819387416767863400073310554463e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 0.94183545358535123525324717496022
y[1] (numeric) = 0.94183545358535123525327719800777
absolute error = 3.002304755e-23
relative error = 3.1877168602762992382276201172434e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0601
y[1] (analytic) = 0.94174163522298475971633497326427
y[1] (numeric) = 0.94174163522298475971636504775131
absolute error = 3.007448704e-23
relative error = 3.1934965934556975698046386186670e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0602
y[1] (analytic) = 0.9416478274432019231307554708695
y[1] (numeric) = 0.94164782744320192313078559680054
absolute error = 3.012593104e-23
relative error = 3.1992779213221440085585839533606e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0603
y[1] (analytic) = 0.94155403024694080329355530213366
y[1] (numeric) = 0.94155403024694080329358547951332
absolute error = 3.017737966e-23
relative error = 3.2050608558369610479548273972619e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0604
y[1] (analytic) = 0.941460243635139372166564022127
y[1] (numeric) = 0.94146024363513937216659425095974
absolute error = 3.022883274e-23
relative error = 3.2108453802872541278840182661253e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0605
y[1] (analytic) = 0.94136646760873549586701438702118
y[1] (numeric) = 0.94136646760873549586704466731163
absolute error = 3.028029045e-23
relative error = 3.2166315130087613593603254141074e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=148.7MB, alloc=4.3MB, time=10.38
x[1] = 0.0606
y[1] (analytic) = 0.94127270216866693465816369292537
y[1] (numeric) = 0.94127270216866693465819402467805
absolute error = 3.033175268e-23
relative error = 3.2224192425974384883070884011060e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0607
y[1] (analytic) = 0.94117894731587134293991617326109
y[1] (numeric) = 0.94117894731587134293994655648052
absolute error = 3.038321943e-23
relative error = 3.2282085693320352435751461183560e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0608
y[1] (analytic) = 0.94108520305128626923944645477097
y[1] (numeric) = 0.94108520305128626923947688946182
absolute error = 3.043469085e-23
relative error = 3.2339995094303275645479662976938e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0609
y[1] (analytic) = 0.94099146937584915620182407225532
y[1] (numeric) = 0.94099146937584915620185455842203
absolute error = 3.048616671e-23
relative error = 3.2397920387334849429677798202539e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 0.94089774629049734058063904212845
y[1] (numeric) = 0.94089774629049734058066957977565
absolute error = 3.053764720e-23
relative error = 3.2455861777111387051294231375673e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0611
y[1] (analytic) = 0.94080403379616805322862849489132
y[1] (numeric) = 0.94080403379616805322865908402353
absolute error = 3.058913221e-23
relative error = 3.2513819149533275762103786009650e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0612
y[1] (analytic) = 0.94071033189379841908830436661149
y[1] (numeric) = 0.9407103318937984190883350072333
absolute error = 3.064062181e-23
relative error = 3.2571792581798895204772645126495e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0613
y[1] (analytic) = 0.94061664058432545718258214950606
y[1] (numeric) = 0.94061664058432545718261284162203
absolute error = 3.069211597e-23
relative error = 3.2629782044822838440207569260874e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0614
y[1] (analytic) = 0.94052295986868608060541070172028
y[1] (numeric) = 0.94052295986868608060544144533494
absolute error = 3.074361466e-23
relative error = 3.2687787509506797680102183253673e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0615
y[1] (analytic) = 0.94042928974781709651240311639576
y[1] (numeric) = 0.94042928974781709651243391151367
absolute error = 3.079511791e-23
relative error = 3.2745809010540211049071368720583e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0616
y[1] (analytic) = 0.94033563022265520611146865012231
y[1] (numeric) = 0.94033563022265520611149949674799
absolute error = 3.084662568e-23
relative error = 3.2803846508183522509374037672892e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0617
y[1] (analytic) = 0.94024198129413700465344571086638
y[1] (numeric) = 0.94024198129413700465347660900448
absolute error = 3.089813810e-23
relative error = 3.2861900143484551690715048114546e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0618
y[1] (analytic) = 0.94014834296319898142273590547104
y[1] (numeric) = 0.94014834296319898142276685512598
absolute error = 3.094965494e-23
relative error = 3.2919969674627707571845334726921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0619
y[1] (analytic) = 0.94005471523077751972793914681892
y[1] (numeric) = 0.94005471523077751972797014799536
absolute error = 3.100117644e-23
relative error = 3.2978055359670640212303535451548e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 0.93996109809780889689248982075491
y[1] (numeric) = 0.93996109809780889689252087345734
absolute error = 3.105270243e-23
relative error = 3.3036157020584239034379242413408e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0621
y[1] (analytic) = 0.93986749156522928424529401285888
y[1] (numeric) = 0.93986749156522928424532511709193
absolute error = 3.110423305e-23
relative error = 3.3094274809100878601444090413545e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.3MB, time=10.65
NO POLE
x[1] = 0.0622
y[1] (analytic) = 0.93977389563397474711136779516509
y[1] (numeric) = 0.93977389563397474711139895093319
absolute error = 3.115576810e-23
relative error = 3.3152408515222919865664914100227e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0623
y[1] (analytic) = 0.93968031030498124480247657291911
y[1] (numeric) = 0.93968031030498124480250778022685
absolute error = 3.120730774e-23
relative error = 3.3210558311976764294899497582663e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0624
y[1] (analytic) = 0.93958673557918463060777549146854
y[1] (numeric) = 0.93958673557918463060780675032047
absolute error = 3.125885193e-23
relative error = 3.3268724159596895848930749061669e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0625
y[1] (analytic) = 0.93949317145752065178445090337897
y[1] (numeric) = 0.93949317145752065178448221377968
absolute error = 3.131040071e-23
relative error = 3.3326906103452935260972767743364e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0626
y[1] (analytic) = 0.93939961794092494954836289587005
y[1] (numeric) = 0.93939961794092494954839425782412
absolute error = 3.136195407e-23
relative error = 3.3385104135705776613536984950808e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0627
y[1] (analytic) = 0.93930607503033305906468887866478
y[1] (numeric) = 0.93930607503033305906472029217663
absolute error = 3.141351185e-23
relative error = 3.3443318088819516957869839823798e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0628
y[1] (analytic) = 0.93921254272668040943856823234496
y[1] (numeric) = 0.93921254272668040943859969741928
absolute error = 3.146507432e-23
relative error = 3.3501548253020540688935011270981e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0629
y[1] (analytic) = 0.93911902103090232370574801730855
y[1] (numeric) = 0.93911902103090232370577953394976
absolute error = 3.151664121e-23
relative error = 3.3559794343642544933284262336990e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 0.93902550994393401882322974341899
y[1] (numeric) = 0.93902550994393401882326131163172
absolute error = 3.156821273e-23
relative error = 3.3618056587072729608602877032069e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0631
y[1] (analytic) = 0.93893200946671060565991720044376
y[1] (numeric) = 0.93893200946671060565994882023253
absolute error = 3.161978877e-23
relative error = 3.3676334868974412988507204419605e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0632
y[1] (analytic) = 0.93883851960016708898726534937268
y[1] (numeric) = 0.93883851960016708898729702074205
absolute error = 3.167136937e-23
relative error = 3.3734629234735932020407267410975e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0633
y[1] (analytic) = 0.93874504034523836746993027471132
y[1] (numeric) = 0.93874504034523836746996199766585
absolute error = 3.172295453e-23
relative error = 3.3792939687152307798502691364289e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0634
y[1] (analytic) = 0.93865157170285923365642019784234
y[1] (numeric) = 0.93865157170285923365645197238648
absolute error = 3.177454414e-23
relative error = 3.3851266111828970712222184753247e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0635
y[1] (analytic) = 0.93855811367396437396974755154779
y[1] (numeric) = 0.93855811367396437396977937768613
absolute error = 3.182613834e-23
relative error = 3.3909608660690498796464613011059e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0636
y[1] (analytic) = 0.93846466625948836869808211578724
y[1] (numeric) = 0.93846466625948836869811399352434
absolute error = 3.187773710e-23
relative error = 3.3967967304573731895992739368272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0637
y[1] (analytic) = 0.93837122946036569198540521482362
y[1] (numeric) = 0.93837122946036569198543714416405
absolute error = 3.192934043e-23
relative error = 3.4026342056929624270512984025072e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.3MB, time=10.92
NO POLE
x[1] = 0.0638
y[1] (analytic) = 0.93827780327753071182216497579136
y[1] (numeric) = 0.9382778032775307118221969567396
absolute error = 3.198094824e-23
relative error = 3.4084732824634923007883154584838e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0639
y[1] (analytic) = 0.93818438771191769003593264879933
y[1] (numeric) = 0.93818438771191769003596468136002
absolute error = 3.203256069e-23
relative error = 3.4143139781000101845157276267883e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 0.9380909827644607822820599886635
y[1] (numeric) = 0.93809098276446078228209207284113
absolute error = 3.208417763e-23
relative error = 3.4201562768944991915915607595184e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0641
y[1] (analytic) = 0.93799758843609403803433769836074
y[1] (numeric) = 0.93799758843609403803436983415976
absolute error = 3.213579902e-23
relative error = 3.4260001748596625916260913631604e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0642
y[1] (analytic) = 0.93790420472775140057565493429867
y[1] (numeric) = 0.93790420472775140057568712172368
absolute error = 3.218742501e-23
relative error = 3.4318456882644162812666618316217e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0643
y[1] (analytic) = 0.93781083164036670698865987349483
y[1] (numeric) = 0.93781083164036670698869211255045
absolute error = 3.223905562e-23
relative error = 3.4376928195219532173692344308663e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0644
y[1] (analytic) = 0.93771746917487368814642134275809
y[1] (numeric) = 0.93771746917487368814645363344874
absolute error = 3.229069065e-23
relative error = 3.4435415475850703057429799088608e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0645
y[1] (analytic) = 0.93762411733220596870309150996513
y[1] (numeric) = 0.93762411733220596870312385229542
absolute error = 3.234233029e-23
relative error = 3.4493918929925427939390575102415e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0646
y[1] (analytic) = 0.93753077611329706708456963752732
y[1] (numeric) = 0.93753077611329706708460203150182
absolute error = 3.239397450e-23
relative error = 3.4552438517586658995541620935928e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0647
y[1] (analytic) = 0.93743744551908039547916689813932
y[1] (numeric) = 0.93743744551908039547919934376251
absolute error = 3.244562319e-23
relative error = 3.4610974145623254736288734751110e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0648
y[1] (analytic) = 0.93734412555048925982827225290354
y[1] (numeric) = 0.93734412555048925982830475017996
absolute error = 3.249727642e-23
relative error = 3.4669525880812234630770790110382e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0649
y[1] (analytic) = 0.93725081620845685981701939192433
y[1] (numeric) = 0.93725081620845685981705194085846
absolute error = 3.254893413e-23
relative error = 3.4728093661921859183320716751289e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 0.93715751749391628886495473746405
y[1] (numeric) = 0.93715751749391628886498733806052
absolute error = 3.260059647e-23
relative error = 3.4786677651776540434336688895866e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0651
y[1] (analytic) = 0.93706422940780053411670650975588
y[1] (numeric) = 0.93706422940780053411673916201921
absolute error = 3.265226333e-23
relative error = 3.4845277735801904276825192706907e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0652
y[1] (analytic) = 0.93697095195104247643265485556496
y[1] (numeric) = 0.93697095195104247643268755949964
absolute error = 3.270393468e-23
relative error = 3.4903893884758135177978452921992e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=160.2MB, alloc=4.3MB, time=11.19
x[1] = 0.0653
y[1] (analytic) = 0.93687768512457489037960303959234
y[1] (numeric) = 0.93687768512457489037963579520294
absolute error = 3.275561060e-23
relative error = 3.4962526186803720416166093085276e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0654
y[1] (analytic) = 0.93678442892933044422144969881497
y[1] (numeric) = 0.93678442892933044422148250610598
absolute error = 3.280729101e-23
relative error = 3.5021174559333896495573789648014e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0655
y[1] (analytic) = 0.93669118336624169990986215985423
y[1] (numeric) = 0.93669118336624169990989501883019
absolute error = 3.285897596e-23
relative error = 3.5079839058496080784238594520471e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0656
y[1] (analytic) = 0.93659794843624111307495081946715
y[1] (numeric) = 0.93659794843624111307498373013263
absolute error = 3.291066548e-23
relative error = 3.5138519719104843742334992553649e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0657
y[1] (analytic) = 0.93650472414026103301594458825308
y[1] (numeric) = 0.93650472414026103301597755061266
absolute error = 3.296235958e-23
relative error = 3.5197216554631284536650676810846e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0658
y[1] (analytic) = 0.9364115104792337026918673976693
y[1] (numeric) = 0.93641151047923370269190041172744
absolute error = 3.301405814e-23
relative error = 3.5255929439722681743583529020037e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0659
y[1] (analytic) = 0.93631830745409125871221577044824
y[1] (numeric) = 0.93631830745409125871224883620944
absolute error = 3.306576120e-23
relative error = 3.5314658419857129106774078496173e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 0.93622511506576573132763745451037
y[1] (numeric) = 0.93622511506576573132767057197924
absolute error = 3.311746887e-23
relative error = 3.5373403615297846652716897489205e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0661
y[1] (analytic) = 0.93613193331518904442061112046578
y[1] (numeric) = 0.93613193331518904442064428964684
absolute error = 3.316918106e-23
relative error = 3.5432164932709511355923163656403e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0662
y[1] (analytic) = 0.93603876220329301549612712279687
y[1] (numeric) = 0.93603876220329301549616034369463
absolute error = 3.322089776e-23
relative error = 3.5490942364184849114171208740784e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0663
y[1] (analytic) = 0.93594560173100935567236932481628
y[1] (numeric) = 0.93594560173100935567240259743523
absolute error = 3.327261895e-23
relative error = 3.5549735891127726419971515597310e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0664
y[1] (analytic) = 0.93585245189926966967139798749276
y[1] (numeric) = 0.93585245189926966967143131183745
absolute error = 3.332434469e-23
relative error = 3.5608545580416837502538775545536e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0665
y[1] (analytic) = 0.93575931270900545580983372223845
y[1] (numeric) = 0.93575931270900545580986709831343
absolute error = 3.337607498e-23
relative error = 3.5667371434837123008298380234633e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0666
y[1] (analytic) = 0.93566618416114810598954250775043
y[1] (numeric) = 0.9356661841611481059895759355602
absolute error = 3.342780977e-23
relative error = 3.5726213403735437740058186695016e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0667
y[1] (analytic) = 0.93557306625662890568832177099967
y[1] (numeric) = 0.93557306625662890568835525054879
absolute error = 3.347954912e-23
relative error = 3.5785071554012133400936933365284e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0668
y[1] (analytic) = 0.93547995899637903395058753246099
y[1] (numeric) = 0.93547995899637903395062106375401
absolute error = 3.353129302e-23
relative error = 3.5843945877764966326873887536928e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.3MB, time=11.45
NO POLE
x[1] = 0.0669
y[1] (analytic) = 0.93538686238132956337806261567659
y[1] (numeric) = 0.93538686238132956337809619871804
absolute error = 3.358304145e-23
relative error = 3.5902836356396447963133044325737e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 0.93529377641241146012046592124661
y[1] (numeric) = 0.93529377641241146012049955604097
absolute error = 3.363479436e-23
relative error = 3.5961742939224867765994217974473e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0671
y[1] (analytic) = 0.93520070109055558386620276533958
y[1] (numeric) = 0.93520070109055558386623645189138
absolute error = 3.368655180e-23
relative error = 3.6020665682475924050739242966616e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0672
y[1] (analytic) = 0.93510763641669268783305628281631
y[1] (numeric) = 0.93510763641669268783309002113003
absolute error = 3.373831372e-23
relative error = 3.6079604535456806611048543764659e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0673
y[1] (analytic) = 0.93501458239175341875887989505962
y[1] (numeric) = 0.93501458239175341875891368513978
absolute error = 3.379008016e-23
relative error = 3.6138559543708373683664002942863e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0674
y[1] (analytic) = 0.93492153901666831689229084260358
y[1] (numeric) = 0.93492153901666831689232468445482
absolute error = 3.384185124e-23
relative error = 3.6197530838356958727921441115924e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0675
y[1] (analytic) = 0.93482850629236781598336478265547
y[1] (numeric) = 0.93482850629236781598339867628226
absolute error = 3.389362679e-23
relative error = 3.6256518240362431723818451733801e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0676
y[1] (analytic) = 0.93473548421978224327433145160229
y[1] (numeric) = 0.93473548421978224327436539700912
absolute error = 3.394540683e-23
relative error = 3.6315521773878109412672345389170e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0677
y[1] (analytic) = 0.93464247279984181949027139259643
y[1] (numeric) = 0.93464247279984181949030538978777
absolute error = 3.399719134e-23
relative error = 3.6374541420268477385530389745038e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0678
y[1] (analytic) = 0.93454947203347665882981374831248
y[1] (numeric) = 0.93454947203347665882984779729291
absolute error = 3.404898043e-23
relative error = 3.6433577299993729559111519320044e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0679
y[1] (analytic) = 0.9344564819216167689558351189689
y[1] (numeric) = 0.93445648192161676895586921974299
absolute error = 3.410077409e-23
relative error = 3.6492629405143780897944983383964e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 0.93436350246519205098615948570697
y[1] (numeric) = 0.93436350246519205098619363827922
absolute error = 3.415257225e-23
relative error = 3.6551697663589219259603440037926e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0681
y[1] (analytic) = 0.93427053366513229948425919942017
y[1] (numeric) = 0.93427053366513229948429340379508
absolute error = 3.420437491e-23
relative error = 3.6610782078095345784045334006240e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0682
y[1] (analytic) = 0.93417757552236720244995703512719
y[1] (numeric) = 0.93417757552236720244999129130932
absolute error = 3.425618213e-23
relative error = 3.6669882715654843193656566052748e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0683
y[1] (analytic) = 0.93408462803782634131012931198174
y[1] (numeric) = 0.93408462803782634131016361997552
absolute error = 3.430799378e-23
relative error = 3.6728999439878028194258674152005e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0684
y[1] (analytic) = 0.9339916912124391909094100790111
y[1] (numeric) = 0.93399169121243919090944443882104
absolute error = 3.435980994e-23
relative error = 3.6788132339160990384870924494994e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.3MB, time=11.72
NO POLE
x[1] = 0.0685
y[1] (analytic) = 0.9338987650471351195008963666777
y[1] (numeric) = 0.93389876504713511950093077830844
absolute error = 3.441163074e-23
relative error = 3.6847281555472663014603752553922e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0686
y[1] (analytic) = 0.93380584954284338873685450435624
y[1] (numeric) = 0.93380584954284338873688896781225
absolute error = 3.446345601e-23
relative error = 3.6906446909571219973555282022184e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0687
y[1] (analytic) = 0.93371294470049315365942750381826
y[1] (numeric) = 0.93371294470049315365946201910404
absolute error = 3.451528578e-23
relative error = 3.6965628436340741528399612823150e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0688
y[1] (analytic) = 0.93362005052101346269134350881875
y[1] (numeric) = 0.93362005052101346269137807593876
absolute error = 3.456712001e-23
relative error = 3.7024826095700887261722864911580e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0689
y[1] (analytic) = 0.93352716700533325762662531087634
y[1] (numeric) = 0.93352716700533325762665992983517
absolute error = 3.461895883e-23
relative error = 3.7084040029659063216834848129652e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 0.93343429415438137362130093134122
y[1] (numeric) = 0.93343429415438137362133560214338
absolute error = 3.467080216e-23
relative error = 3.7143270155302190914187020641232e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0691
y[1] (analytic) = 0.93334143196908653918411526984236
y[1] (numeric) = 0.93334143196908653918414999249229
absolute error = 3.472264993e-23
relative error = 3.7202516400397039840181425621895e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0692
y[1] (analytic) = 0.93324858045037737616724281920756
y[1] (numeric) = 0.93324858045037737616727759370989
absolute error = 3.477450233e-23
relative error = 3.7261778971277017914768766472268e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0693
y[1] (analytic) = 0.93315573959918239975700144695005
y[1] (numeric) = 0.93315573959918239975703627330925
absolute error = 3.482635920e-23
relative error = 3.7321057699284941209875507888001e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0694
y[1] (analytic) = 0.93306290941643001846456724341253
y[1] (numeric) = 0.93306290941643001846460212163308
absolute error = 3.487822055e-23
relative error = 3.7380352597890802106086395888166e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0695
y[1] (analytic) = 0.93297008990304853411669043666333
y[1] (numeric) = 0.93297008990304853411672536674972
absolute error = 3.493008639e-23
relative error = 3.7439663680568613165304401190985e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0696
y[1] (analytic) = 0.93287728105996614184641237423652
y[1] (numeric) = 0.93287728105996614184644735619334
absolute error = 3.498195682e-23
relative error = 3.7498991057272119571708458135486e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0697
y[1] (analytic) = 0.9327844828881109300837835718096
y[1] (numeric) = 0.9327844828881109300838186056413
absolute error = 3.503383170e-23
relative error = 3.7558334580703318929284721901318e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0698
y[1] (analytic) = 0.93269169538841088054658282891018
y[1] (numeric) = 0.93269169538841088054661791462134
absolute error = 3.508571116e-23
relative error = 3.7617694392988969625902911742890e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0699
y[1] (analytic) = 0.9325989185617938682310374117465
y[1] (numeric) = 0.93259891856179386823107254934157
absolute error = 3.513759507e-23
relative error = 3.7677070357520244195946779242631e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 0.93250615240918766140254430325241
y[1] (numeric) = 0.93250615240918766140257949273588
absolute error = 3.518948347e-23
relative error = 3.7736462519937032170767064201056e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.3MB, time=11.99
NO POLE
x[1] = 0.0701
y[1] (analytic) = 0.93241339693151992158639252044128
y[1] (numeric) = 0.93241339693151992158642776181775
absolute error = 3.524137647e-23
relative error = 3.7795871000970038839818408655760e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0702
y[1] (analytic) = 0.93232065212971820355848649916111
y[1] (numeric) = 0.93232065212971820355852179243506
absolute error = 3.529327395e-23
relative error = 3.7855295674700423830043525520184e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0703
y[1] (analytic) = 0.93222791800470995533607054634294
y[1] (numeric) = 0.93222791800470995533610589151877
absolute error = 3.534517583e-23
relative error = 3.7914736458065851750970221699910e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0704
y[1] (analytic) = 0.93213519455742251816845435983592
y[1] (numeric) = 0.93213519455742251816848975691823
absolute error = 3.539708231e-23
relative error = 3.7974193568355202985406341352702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0705
y[1] (analytic) = 0.93204248178878312652773961592249
y[1] (numeric) = 0.9320424817887831265277750649158
absolute error = 3.544899331e-23
relative error = 3.8033666922526984359132974631048e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0706
y[1] (analytic) = 0.93194977969971890809954762460473
y[1] (numeric) = 0.93194977969971890809958312551356
absolute error = 3.550090883e-23
relative error = 3.8093156523346842396127214155108e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0707
y[1] (analytic) = 0.93185708829115688377374805275606
y[1] (numeric) = 0.93185708829115688377378360558481
absolute error = 3.555282875e-23
relative error = 3.8152662244805063663506980376952e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0708
y[1] (analytic) = 0.93176440756402396763518871522983
y[1] (numeric) = 0.93176440756402396763522431998312
absolute error = 3.560475329e-23
relative error = 3.8212184325739555948276533788270e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0709
y[1] (analytic) = 0.93167173751924696695442643401933
y[1] (numeric) = 0.93167173751924696695446209070157
absolute error = 3.565668224e-23
relative error = 3.8271722543545961563436814769040e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 0.93157907815775258217845896555912
y[1] (numeric) = 0.9315790781577525821784946741749
absolute error = 3.570861578e-23
relative error = 3.8331277094174008553889005367452e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0711
y[1] (analytic) = 0.93148642948046740692145799626341
y[1] (numeric) = 0.93148642948046740692149375681725
absolute error = 3.576055384e-23
relative error = 3.8390847905261804793768791573263e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0712
y[1] (analytic) = 0.93139379148831792795550320639192
y[1] (numeric) = 0.93139379148831792795553901888818
absolute error = 3.581249626e-23
relative error = 3.8450434807787937407103497862756e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0713
y[1] (analytic) = 0.9313011641822305252013174023363
y[1] (numeric) = 0.93130116418223052520135326677958
absolute error = 3.586444328e-23
relative error = 3.8510038062169001582401350221404e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0714
y[1] (analytic) = 0.93120854756313147171900271742135
y[1] (numeric) = 0.93120854756313147171903863381617
absolute error = 3.591639482e-23
relative error = 3.8569657585284397051717353836839e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0715
y[1] (analytic) = 0.93111594163194693369877788131138
y[1] (numeric) = 0.9311159416319469336988138496622
absolute error = 3.596835082e-23
relative error = 3.8629293315458699185072998145879e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.3MB, time=12.38
NO POLE
x[1] = 0.0716
y[1] (analytic) = 0.93102334638960297045171655811561
y[1] (numeric) = 0.93102334638960297045175257842696
absolute error = 3.602031135e-23
relative error = 3.8688945330621893960052899623278e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0717
y[1] (analytic) = 0.9309307618370255344004867532854
y[1] (numeric) = 0.9309307618370255344005228255618
absolute error = 3.607227640e-23
relative error = 3.8748613622798120187049466734867e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0718
y[1] (analytic) = 0.93083818797514047107009128939515
y[1] (numeric) = 0.93083818797514047107012741364112
absolute error = 3.612424597e-23
relative error = 3.8808298194749994519662864838126e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0719
y[1] (analytic) = 0.93074562480487351907860935090012
y[1] (numeric) = 0.93074562480487351907864552712009
absolute error = 3.617621997e-23
relative error = 3.8867998952543210564181867101857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 0.9306530723271503101279390979631
y[1] (numeric) = 0.93065307232715031012797532616157
absolute error = 3.622819847e-23
relative error = 3.8927715974127022111728457142274e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0721
y[1] (analytic) = 0.93056053054289636899454134944336
y[1] (numeric) = 0.93056053054289636899457762962481
absolute error = 3.628018145e-23
relative error = 3.8987449240764440515040969254915e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0722
y[1] (analytic) = 0.93046799945303711352018433513963
y[1] (numeric) = 0.93046799945303711352022066730861
absolute error = 3.633216898e-23
relative error = 3.9047198830435188078736842938456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0723
y[1] (analytic) = 0.93037547905849785460268951738026
y[1] (numeric) = 0.93037547905849785460272590154129
absolute error = 3.638416103e-23
relative error = 3.9106964713665165786498018438693e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0724
y[1] (analytic) = 0.93028296936020379618667848205265
y[1] (numeric) = 0.93028296936020379618671491821024
absolute error = 3.643615759e-23
relative error = 3.9166746882466026408200301678070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0725
y[1] (analytic) = 0.93019047035908003525432089916478
y[1] (numeric) = 0.93019047035908003525435738732337
absolute error = 3.648815859e-23
relative error = 3.9226545264341969385662348398680e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0726
y[1] (analytic) = 0.93009798205605156181608355303103
y[1] (numeric) = 0.93009798205605156181612009319514
absolute error = 3.654016411e-23
relative error = 3.9286359948040332558041727110327e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0727
y[1] (analytic) = 0.93000550445204325890148044217551
y[1] (numeric) = 0.93000550445204325890151703434962
absolute error = 3.659217411e-23
relative error = 3.9346190893310906301074951427713e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0728
y[1] (analytic) = 0.92991303754797990254982394904445
y[1] (numeric) = 0.92991303754797990254986059323303
absolute error = 3.664418858e-23
relative error = 3.9406038092147194067557233467697e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0729
y[1] (analytic) = 0.9298205813447861618009770796207
y[1] (numeric) = 0.92982058134478616180101377582832
absolute error = 3.669620762e-23
relative error = 3.9465901654840551702536143862004e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 0.92972813584338659868610677303319
y[1] (numeric) = 0.92972813584338659868614352126427
absolute error = 3.674823108e-23
relative error = 3.9525781422829035549612267922342e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0731
y[1] (analytic) = 0.92963570104470566821843828125243
y[1] (numeric) = 0.92963570104470566821847508151151
absolute error = 3.680025908e-23
relative error = 3.9585677527922624213239636620648e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.3MB, time=13.03
NO POLE
x[1] = 0.0732
y[1] (analytic) = 0.92954327694966771838401061896648
y[1] (numeric) = 0.92954327694966771838404747125798
absolute error = 3.685229150e-23
relative error = 3.9645589843791052444833829620097e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0733
y[1] (analytic) = 0.92945086355919699013243308372769
y[1] (numeric) = 0.92945086355919699013246998805623
absolute error = 3.690432854e-23
relative error = 3.9705518588341763166184625597056e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0734
y[1] (analytic) = 0.92935846087421761736764284646505
y[1] (numeric) = 0.92935846087421761736767980283503
absolute error = 3.695636998e-23
relative error = 3.9765463527642855073750726289235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0735
y[1] (analytic) = 0.92926606889565362693866361245177
y[1] (numeric) = 0.92926606889565362693870062086771
absolute error = 3.700841594e-23
relative error = 3.9825424793548163688341635092133e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0736
y[1] (analytic) = 0.92917368762442893863036535282326
y[1] (numeric) = 0.92917368762442893863040241328962
absolute error = 3.706046636e-23
relative error = 3.9885402324242098947673276923731e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0737
y[1] (analytic) = 0.92908131706146736515422510673585
y[1] (numeric) = 0.92908131706146736515426221925712
absolute error = 3.711252127e-23
relative error = 3.9945396154753009362608480160717e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0738
y[1] (analytic) = 0.92898895720769261213908885425976
y[1] (numeric) = 0.92898895720769261213912601884053
absolute error = 3.716458077e-23
relative error = 4.0005406395472548815279937953573e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0739
y[1] (analytic) = 0.92889660806402827812193446009864
y[1] (numeric) = 0.92889660806402827812197167674334
absolute error = 3.721664470e-23
relative error = 4.0065432876932929138955410739609e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 0.92880426963139785453863568822706
y[1] (numeric) = 0.92880426963139785453867295694015
absolute error = 3.726871309e-23
relative error = 4.0125475634161690930221172437357e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0741
y[1] (analytic) = 0.9287119419107247257147272875397
y[1] (numeric) = 0.92871194191072472571476460832562
absolute error = 3.732078592e-23
relative error = 4.0185534648360938841069358120453e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0742
y[1] (analytic) = 0.92861962490293216885617114860344
y[1] (numeric) = 0.92861962490293216885620852146681
absolute error = 3.737286337e-23
relative error = 4.0245610116097378500944033562315e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0743
y[1] (analytic) = 0.92852731860894335404012353160604
y[1] (numeric) = 0.92852731860894335404016095655127
absolute error = 3.742494523e-23
relative error = 4.0305701813994567632575627405937e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0744
y[1] (analytic) = 0.92843502302968134420570336559159
y[1] (numeric) = 0.92843502302968134420574084262316
absolute error = 3.747703157e-23
relative error = 4.0365809820168630696502294484694e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0745
y[1] (analytic) = 0.92834273816606909514476161907738
y[1] (numeric) = 0.92834273816606909514479914819975
absolute error = 3.752912237e-23
relative error = 4.0425934115818442154932096266044e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0746
y[1] (analytic) = 0.92825046401902945549265174214288
y[1] (numeric) = 0.92825046401902945549268932336061
absolute error = 3.758121773e-23
relative error = 4.0486074811409490489954782641273e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0747
y[1] (analytic) = 0.92815820058948516671900118008417
y[1] (numeric) = 0.92815820058948516671903881340176
absolute error = 3.763331759e-23
relative error = 4.0546231845065418547166137111428e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.3MB, time=13.73
NO POLE
x[1] = 0.0748
y[1] (analytic) = 0.92806594787835886311848395872526
y[1] (numeric) = 0.9280659478783588631185216441471
absolute error = 3.768542184e-23
relative error = 4.0606405101008413769705572336702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0749
y[1] (analytic) = 0.92797370588657307180159434147868
y[1] (numeric) = 0.92797370588657307180163207900934
absolute error = 3.773753066e-23
relative error = 4.0666594775922117480473284734860e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 0.92788147461505021268542155824885
y[1] (numeric) = 0.92788147461505021268545934789274
absolute error = 3.778964389e-23
relative error = 4.0726800700140902443948958855489e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0751
y[1] (analytic) = 0.92778925406471259848442560626829
y[1] (numeric) = 0.92778925406471259848446344802994
absolute error = 3.784176165e-23
relative error = 4.0787023005722984755388876751032e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0752
y[1] (analytic) = 0.92769704423648243470121412296116
y[1] (numeric) = 0.927697044236482434701252016845
absolute error = 3.789388384e-23
relative error = 4.0847261587631338975010854896046e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0753
y[1] (analytic) = 0.92760484513128181961732033092445
y[1] (numeric) = 0.92760484513128181961735827693504
absolute error = 3.794601059e-23
relative error = 4.0907516588736216428672268220214e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0754
y[1] (analytic) = 0.92751265675003274428398205512076
y[1] (numeric) = 0.92751265675003274428402005326258
absolute error = 3.799814182e-23
relative error = 4.0967787925551301151145233834940e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0755
y[1] (analytic) = 0.92742047909365709251292181237337
y[1] (numeric) = 0.92742047909365709251295986265085
absolute error = 3.805027748e-23
relative error = 4.1028075546903498701883327550767e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0756
y[1] (analytic) = 0.92732831216307664086712797325658
y[1] (numeric) = 0.92732831216307664086716607567425
absolute error = 3.810241767e-23
relative error = 4.1088379563353011357357156241762e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0757
y[1] (analytic) = 0.92723615595921305865163699647386
y[1] (numeric) = 0.92723615595921305865167515103613
absolute error = 3.815456227e-23
relative error = 4.1148699848238370039650925802629e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0758
y[1] (analytic) = 0.92714401048298790790431673581476
y[1] (numeric) = 0.92714401048298790790435494252613
absolute error = 3.820671137e-23
relative error = 4.1209036501348408294695349673880e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0759
y[1] (analytic) = 0.92705187573532264338665081978414
y[1] (numeric) = 0.92705187573532264338668907864916
absolute error = 3.825886502e-23
relative error = 4.1269389579362733464672074861184e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 0.92695975171713861257452410399521
y[1] (numeric) = 0.92695975171713861257456241501827
absolute error = 3.831102306e-23
relative error = 4.1329758912435060015347687747612e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0761
y[1] (analytic) = 0.9268676384293570556490091964178
y[1] (numeric) = 0.92686763842935705564904755960343
absolute error = 3.836318563e-23
relative error = 4.1390144654321018982792610721437e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0762
y[1] (analytic) = 0.92677553587289910548715405557591
y[1] (numeric) = 0.92677553587289910548719247092855
absolute error = 3.841535264e-23
relative error = 4.1450546710663715194324963611561e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=186.9MB, alloc=4.3MB, time=14.42
x[1] = 0.0763
y[1] (analytic) = 0.9266834440486857876527706617844
y[1] (numeric) = 0.92668344404868578765280912930861
absolute error = 3.846752421e-23
relative error = 4.1510965213681972246765562998026e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0764
y[1] (analytic) = 0.92659136295763802038722476151911
y[1] (numeric) = 0.92659136295763802038726328121925
absolute error = 3.851970014e-23
relative error = 4.1571399950293996855622406505369e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0765
y[1] (analytic) = 0.92649929260067661460022668501022
y[1] (numeric) = 0.9264992926006766146002652568908
absolute error = 3.857188058e-23
relative error = 4.1631851085097991235877344630053e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0766
y[1] (analytic) = 0.92640723297872227386062323715329
y[1] (numeric) = 0.92640723297872227386066186121881
absolute error = 3.862406552e-23
relative error = 4.1692318610045996626518350992903e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0767
y[1] (analytic) = 0.92631518409269559438719066182832
y[1] (numeric) = 0.92631518409269559438722933808328
absolute error = 3.867625496e-23
relative error = 4.1752802527880941172553508906720e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0768
y[1] (analytic) = 0.92622314594351706503942867971967
y[1] (numeric) = 0.92622314594351706503946740816857
absolute error = 3.872844890e-23
relative error = 4.1813302841345467806819835233230e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0769
y[1] (analytic) = 0.92613111853210706730835559972888
y[1] (numeric) = 0.92613111853210706730839438037607
absolute error = 3.878064719e-23
relative error = 4.1873819391217826207130349600768e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 0.92603910185938587530730450407165
y[1] (numeric) = 0.92603910185938587530734333692168
absolute error = 3.883285003e-23
relative error = 4.1934352396165407556129132840985e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0771
y[1] (analytic) = 0.92594709592627365576272050715282
y[1] (numeric) = 0.92594709592627365576275939221016
absolute error = 3.888505734e-23
relative error = 4.1994901772548062059361561164915e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0772
y[1] (analytic) = 0.92585510073369046800495908830917
y[1] (numeric) = 0.92585510073369046800499802557834
absolute error = 3.893726917e-23
relative error = 4.2055467577101756323628642907186e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0773
y[1] (analytic) = 0.92576311628255626395908549851388
y[1] (numeric) = 0.92576311628255626395912448799922
absolute error = 3.898948534e-23
relative error = 4.2116049618139945820851764690946e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0774
y[1] (analytic) = 0.92567114257379088813567524113288
y[1] (numeric) = 0.92567114257379088813571428283901
absolute error = 3.904170613e-23
relative error = 4.2176648200835263340484265621975e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0775
y[1] (analytic) = 0.92557917960831407762161562682775
y[1] (numeric) = 0.92557917960831407762165472075902
absolute error = 3.909393127e-23
relative error = 4.2237263036257731435894062856494e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0776
y[1] (analytic) = 0.92548722738704546207090840269345
y[1] (numeric) = 0.92548722738704546207094754885447
absolute error = 3.914616102e-23
relative error = 4.2297894408032485913732198757554e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0777
y[1] (analytic) = 0.92539528591090456369547345572698
y[1] (numeric) = 0.92539528591090456369551265412211
absolute error = 3.919839513e-23
relative error = 4.2358542048780171531000972789986e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0778
y[1] (analytic) = 0.925303355180810797255953590715
y[1] (numeric) = 0.9253033551808107972559928413487
absolute error = 3.925063370e-23
relative error = 4.2419206069268115354073310095621e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.3MB, time=15.09
NO POLE
x[1] = 0.0779
y[1] (analytic) = 0.92521143519768347005252038263549
y[1] (numeric) = 0.92521143519768347005255968551225
absolute error = 3.930287676e-23
relative error = 4.2479886504647911780645004433405e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 0.92511952596244178191568110366356
y[1] (numeric) = 0.92511952596244178191572045878795
absolute error = 3.935512439e-23
relative error = 4.2540583444130816573456294203114e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0781
y[1] (analytic) = 0.92502762747600482519708672487441
y[1] (numeric) = 0.92502762747600482519712613225076
absolute error = 3.940737635e-23
relative error = 4.2601296631026542566148644344255e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0782
y[1] (analytic) = 0.92493573973929158476034099273373
y[1] (numeric) = 0.92493573973929158476038045236658
absolute error = 3.945963285e-23
relative error = 4.2662026295061697222661323780149e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0783
y[1] (analytic) = 0.92484386275322093797181058047009
y[1] (numeric) = 0.92484386275322093797185009236385
absolute error = 3.951189376e-23
relative error = 4.2722772298423183324998489406420e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0784
y[1] (analytic) = 0.9247519965187116546914363144183
y[1] (numeric) = 0.92475199651871165469147587857753
absolute error = 3.956415923e-23
relative error = 4.2783534806025638323918559408580e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0785
y[1] (analytic) = 0.9246601410366823972635454754283
y[1] (numeric) = 0.92466014103668239726358509185737
absolute error = 3.961642907e-23
relative error = 4.2844313615145186481532693270643e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0786
y[1] (analytic) = 0.92456829630805172050766517542888
y[1] (numeric) = 0.9245682963080517205077048441323
absolute error = 3.966870342e-23
relative error = 4.2905108879899346441550817870025e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0787
y[1] (analytic) = 0.92447646233373807170933680924057
y[1] (numeric) = 0.92447646233373807170937653022278
absolute error = 3.972098221e-23
relative error = 4.2965920527309906278607859338295e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0788
y[1] (analytic) = 0.92438463911465979061093158172766
y[1] (numeric) = 0.92438463911465979061097135499308
absolute error = 3.977326542e-23
relative error = 4.3026748538458309476420414392542e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0789
y[1] (analytic) = 0.92429282665173510940246711038198
y[1] (numeric) = 0.92429282665173510940250693593518
absolute error = 3.982555320e-23
relative error = 4.3087593078341498250683294840171e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 0.92420102494588215271242510343087
y[1] (numeric) = 0.92420102494588215271246498127627
absolute error = 3.987784540e-23
relative error = 4.3148453987415888706232418626588e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0791
y[1] (analytic) = 0.92410923399801893759857011355952
y[1] (numeric) = 0.92410923399801893759861004370159
absolute error = 3.993014207e-23
relative error = 4.3209331322497747470483480742449e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0792
y[1] (analytic) = 0.92401745380906337353876936734122
y[1] (numeric) = 0.92401745380906337353880934978441
absolute error = 3.998244319e-23
relative error = 4.3270225064668389694796790515001e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0793
y[1] (analytic) = 0.92392568437993326242181367046627
y[1] (numeric) = 0.92392568437993326242185370521503
absolute error = 4.003474876e-23
relative error = 4.3331135216646992175940599102235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0794
y[1] (analytic) = 0.92383392571154629853823938886173
y[1] (numeric) = 0.92383392571154629853827947592052
absolute error = 4.008705879e-23
relative error = 4.3392061791976884856199976265901e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.3MB, time=15.76
NO POLE
x[1] = 0.0795
y[1] (analytic) = 0.92374217780482006857115150579363
y[1] (numeric) = 0.92374217780482006857119164516698
absolute error = 4.013937335e-23
relative error = 4.3453004869158583024818632856367e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0796
y[1] (analytic) = 0.9236504406606720515870477550439
y[1] (numeric) = 0.92365044066067205158708794673615
absolute error = 4.019169225e-23
relative error = 4.3513964245230630723694601616310e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0797
y[1] (analytic) = 0.92355871428001961902664383025245
y[1] (numeric) = 0.9235587142800196190266840742681
absolute error = 4.024401565e-23
relative error = 4.3574940096118417302027745364353e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0798
y[1] (analytic) = 0.92346699866378003469569967051808
y[1] (numeric) = 0.92346699866378003469573996686168
absolute error = 4.029634360e-23
relative error = 4.3635932478699514094936426098574e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0799
y[1] (analytic) = 0.92337529381287045475584682234873
y[1] (numeric) = 0.92337529381287045475588717102459
absolute error = 4.034867586e-23
relative error = 4.3696941135807548174777347605165e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 0.923283599728207927715416878052
y[1] (numeric) = 0.9232835997282079277154572790647
absolute error = 4.040101270e-23
relative error = 4.3757966362548916017392978455667e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0801
y[1] (analytic) = 0.92319191641070939442027099066038
y[1] (numeric) = 0.92319191641070939442031144401438
absolute error = 4.045335400e-23
relative error = 4.3819008031698494365069939231761e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0802
y[1] (analytic) = 0.92310024386129168804463046547981
y[1] (numeric) = 0.92310024386129168804467097117952
absolute error = 4.050569971e-23
relative error = 4.3880066091810641852766213091881e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0803
y[1] (analytic) = 0.92300858208087153408190842835512
y[1] (numeric) = 0.92300858208087153408194898640496
absolute error = 4.055804984e-23
relative error = 4.3941140556422705670891944617755e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0804
y[1] (analytic) = 0.92291693107036555033554257074355
y[1] (numeric) = 0.92291693107036555033558318114801
absolute error = 4.061040446e-23
relative error = 4.4002231504087293382011808033273e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0805
y[1] (analytic) = 0.92282529083069024690982897168814
y[1] (numeric) = 0.9228252908306902469098696344517
absolute error = 4.066276356e-23
relative error = 4.4063338926696530073759661615754e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0806
y[1] (analytic) = 0.92273366136276202620075699678241
y[1] (numeric) = 0.92273366136276202620079771190946
absolute error = 4.071512705e-23
relative error = 4.4124462729439021186037469385108e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0807
y[1] (analytic) = 0.9226420426674971828868452742178
y[1] (numeric) = 0.92264204266749718288688604171286
absolute error = 4.076749506e-23
relative error = 4.4185603055909991185968197164729e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0808
y[1] (analytic) = 0.92255043474581190391997874800655
y[1] (numeric) = 0.92255043474581190392001956787407
absolute error = 4.081986752e-23
relative error = 4.4246759832969998696767839161381e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0809
y[1] (analytic) = 0.92245883759862226851624680847025
y[1] (numeric) = 0.92245883759862226851628768071462
absolute error = 4.087224437e-23
relative error = 4.4307932998289748765557027746845e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=198.3MB, alloc=4.3MB, time=16.43
x[1] = 0.081
y[1] (analytic) = 0.92236725122684424814678250008644
y[1] (numeric) = 0.92236725122684424814682342471218
absolute error = 4.092462574e-23
relative error = 4.4369122695505501768086636800668e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0811
y[1] (analytic) = 0.92227567563139370652860280678532
y[1] (numeric) = 0.92227567563139370652864378379683
absolute error = 4.097701151e-23
relative error = 4.4430328797240553935704492659884e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0812
y[1] (analytic) = 0.92218411081318639961545001478674
y[1] (numeric) = 0.92218411081318639961549104418853
absolute error = 4.102940179e-23
relative error = 4.4491551425474112195462860288665e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0813
y[1] (analytic) = 0.92209255677313797558863415307089
y[1] (numeric) = 0.92209255677313797558867523486733
absolute error = 4.108179644e-23
relative error = 4.4552790431109982628757884653995e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0814
y[1] (analytic) = 0.92200101351216397484787651157226
y[1] (numeric) = 0.92200101351216397484791764576791
absolute error = 4.113419565e-23
relative error = 4.4614046022908537579731560062406e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0815
y[1] (analytic) = 0.92190948103117983000215423719071
y[1] (numeric) = 0.92190948103117983000219542378998
absolute error = 4.118659927e-23
relative error = 4.4675318040911905079097665254434e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0816
y[1] (analytic) = 0.92181795933110086586054600770885
y[1] (numeric) = 0.92181795933110086586058724671615
absolute error = 4.123900730e-23
relative error = 4.4736606487819219039776308481283e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0817
y[1] (analytic) = 0.92172644841284229942307878370902
y[1] (numeric) = 0.92172644841284229942312007512877
absolute error = 4.129141975e-23
relative error = 4.4797911377178500206922917745158e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0818
y[1] (analytic) = 0.92163494827731923987157563858055
y[1] (numeric) = 0.92163494827731923987161698241727
absolute error = 4.134383672e-23
relative error = 4.4859232820194305015744343290035e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0819
y[1] (analytic) = 0.92154345892544668856050466670949
y[1] (numeric) = 0.92154345892544668856054606296758
absolute error = 4.139625809e-23
relative error = 4.4920570689384034027032808090261e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 0.92145198035813953900782896994114
y[1] (numeric) = 0.92145198035813953900787041862506
absolute error = 4.144868392e-23
relative error = 4.4981925052556937473825326744364e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0821
y[1] (analytic) = 0.92136051257631257688585772240822
y[1] (numeric) = 0.9213605125763125768858992235225
absolute error = 4.150111428e-23
relative error = 4.5043295988401315398995545629127e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0822
y[1] (analytic) = 0.92126905558088048001209831381567
y[1] (numeric) = 0.92126905558088048001213986736463
absolute error = 4.155354896e-23
relative error = 4.5104683271706732763684689311769e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0823
y[1] (analytic) = 0.9211776093727578183401095712725
y[1] (numeric) = 0.9211776093727578183401511772607
absolute error = 4.160598820e-23
relative error = 4.5166087165677067477617113132013e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0824
y[1] (analytic) = 0.92108617395285905395035605976474
y[1] (numeric) = 0.9210861739528590539503977181965
absolute error = 4.165843176e-23
relative error = 4.5227507412495443110290698038297e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0825
y[1] (analytic) = 0.9209947493220985410410634613575
y[1] (numeric) = 0.92099474932209854104110517223732
absolute error = 4.171087982e-23
relative error = 4.5288944210269864572899924963960e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.3MB, time=17.12
NO POLE
x[1] = 0.0826
y[1] (analytic) = 0.92090333548139052591907503322094
y[1] (numeric) = 0.92090333548139052591911679655335
absolute error = 4.176333241e-23
relative error = 4.5350397594302064560814924138503e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0827
y[1] (analytic) = 0.92081193243164914699070914456946
y[1] (numeric) = 0.92081193243164914699075096035881
absolute error = 4.181578935e-23
relative error = 4.5411867371846791170476617880272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0828
y[1] (analytic) = 0.92072054017378843475261789260572
y[1] (numeric) = 0.92072054017378843475265976085645
absolute error = 4.186825073e-23
relative error = 4.5473353643329448311616379322963e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0829
y[1] (analytic) = 0.92062915870872231178264679756199
y[1] (numeric) = 0.92062915870872231178268871827859
absolute error = 4.192071660e-23
relative error = 4.5534856465765373095962449198547e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 0.92053778803736459273069557692949
y[1] (numeric) = 0.9205377880373645927307375501163
absolute error = 4.197318681e-23
relative error = 4.5596375678926838354582686239952e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0831
y[1] (analytic) = 0.92044642816062898430957999896644
y[1] (numeric) = 0.92044642816062898430962202462805
absolute error = 4.202566161e-23
relative error = 4.5657911557092832827949813127538e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0832
y[1] (analytic) = 0.92035507907942908528589481557835
y[1] (numeric) = 0.9203550790794290852859368937191
absolute error = 4.207814075e-23
relative error = 4.5719463831381262805104631066889e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0833
y[1] (analytic) = 0.92026374079467838647087777465884
y[1] (numeric) = 0.92026374079467838647091990528324
absolute error = 4.213062440e-23
relative error = 4.5781032689192777291846545322526e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0834
y[1] (analytic) = 0.92017241330729027071127471198553
y[1] (numeric) = 0.92017241330729027071131689509796
absolute error = 4.218311243e-23
relative error = 4.5842617991975172925698649878412e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0835
y[1] (analytic) = 0.92008109661817801288020572275975
y[1] (numeric) = 0.92008109661817801288024795836464
absolute error = 4.223560489e-23
relative error = 4.5904219796754764129210996087187e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0836
y[1] (analytic) = 0.91998979072825477986803241288316
y[1] (numeric) = 0.91998979072825477986807470098496
absolute error = 4.228810180e-23
relative error = 4.5965838127970049181377937612088e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0837
y[1] (analytic) = 0.91989849563843363057322623006168
y[1] (numeric) = 0.91989849563843363057326857066488
absolute error = 4.234060320e-23
relative error = 4.6027473031809355537852785410545e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0838
y[1] (analytic) = 0.9198072113496275158932378748285
y[1] (numeric) = 0.91980721134962751589328026793754
absolute error = 4.239310904e-23
relative error = 4.6089124456631351530612977234979e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0839
y[1] (analytic) = 0.91971593786274927871536779157713
y[1] (numeric) = 0.91971593786274927871541023719636
absolute error = 4.244561923e-23
relative error = 4.6150792307281109150499018225639e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 0.9196246751787116539076377396957
y[1] (numeric) = 0.91962467517871165390768023782964
absolute error = 4.249813394e-23
relative error = 4.6212476771288560569598385817762e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0841
y[1] (analytic) = 0.91953342329842726830966344489487
y[1] (numeric) = 0.91953342329842726830970599554795
absolute error = 4.255065308e-23
relative error = 4.6274177753504587445263343353660e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.3MB, time=17.77
NO POLE
x[1] = 0.0842
y[1] (analytic) = 0.91944218222280864072352833081904
y[1] (numeric) = 0.91944218222280864072357093399558
absolute error = 4.260317654e-23
relative error = 4.6335895136988572695068747190456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0843
y[1] (analytic) = 0.91935095195276818190465833103279
y[1] (numeric) = 0.91935095195276818190470098673732
absolute error = 4.265570453e-23
relative error = 4.6397629152823724253022029534541e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0844
y[1] (analytic) = 0.91925973248921819455269778147478
y[1] (numeric) = 0.91925973248921819455274048971178
absolute error = 4.270823700e-23
relative error = 4.6459379749347299941325119555841e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0845
y[1] (analytic) = 0.91916852383307087330238639346873
y[1] (numeric) = 0.91916852383307087330242915424257
absolute error = 4.276077384e-23
relative error = 4.6521146809598252093647312099359e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0846
y[1] (analytic) = 0.91907732598523830471443730738341
y[1] (numeric) = 0.9190773259852383047144801206985
absolute error = 4.281331509e-23
relative error = 4.6582930379774860231700262491981e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0847
y[1] (analytic) = 0.91898613894663246726641622703317
y[1] (numeric) = 0.91898613894663246726645909289404
absolute error = 4.286586087e-23
relative error = 4.6644730593144794087888687118337e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0848
y[1] (analytic) = 0.91889496271816523134362163491028
y[1] (numeric) = 0.91889496271816523134366455332127
absolute error = 4.291841099e-23
relative error = 4.6706547245665475410512545586810e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0849
y[1] (analytic) = 0.91880379730074835922996608833887
y[1] (numeric) = 0.91880379730074835923000905930449
absolute error = 4.297096562e-23
relative error = 4.6768380525025721343700339916866e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 0.91871264269529350509885859664413
y[1] (numeric) = 0.91871264269529350509890162016871
absolute error = 4.302352458e-23
relative error = 4.6830230238019566811643830945671e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0851
y[1] (analytic) = 0.91862149890271221500408807942509
y[1] (numeric) = 0.91862149890271221500413115551313
absolute error = 4.307608804e-23
relative error = 4.6892096572368624925182746139136e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0852
y[1] (analytic) = 0.91853036592391592687070790602491
y[1] (numeric) = 0.91853036592391592687075103468087
absolute error = 4.312865596e-23
relative error = 4.6953979487241524695568491485166e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0853
y[1] (analytic) = 0.9184392437598159704859215162878
y[1] (numeric) = 0.918439243759815970485964697516
absolute error = 4.318122820e-23
relative error = 4.7015878832908911750763267597396e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0854
y[1] (analytic) = 0.91834813241132356748996912269415
y[1] (numeric) = 0.91834813241132356749001235649915
absolute error = 4.323380500e-23
relative error = 4.7077794873367035348993002435332e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0855
y[1] (analytic) = 0.91825703187934983136701549396656
y[1] (numeric) = 0.91825703187934983136705878035266
absolute error = 4.328638610e-23
relative error = 4.7139727328205656530666155155968e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0856
y[1] (analytic) = 0.91816594216480576743603882023484
y[1] (numeric) = 0.91816594216480576743608215920653
absolute error = 4.333897169e-23
relative error = 4.7201676407009324133126319846080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0857
y[1] (analytic) = 0.91807486326860227284172065985446
y[1] (numeric) = 0.91807486326860227284176405141625
absolute error = 4.339156179e-23
relative error = 4.7263642134274270288953786424341e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.3MB, time=18.45
NO POLE
x[1] = 0.0858
y[1] (analytic) = 0.91798379519165013654533696796735
y[1] (numeric) = 0.91798379519165013654538041212356
absolute error = 4.344415621e-23
relative error = 4.7325624305742823749640449569485e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0859
y[1] (analytic) = 0.9178927379348600393156502068962
y[1] (numeric) = 0.91789273793486003931569370365128
absolute error = 4.349675508e-23
relative error = 4.7387623065699456381824485031960e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 0.9178016914991425537198025384649
y[1] (numeric) = 0.91780169149914255371984608782327
absolute error = 4.354935837e-23
relative error = 4.7449638384154890736469304382886e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0861
y[1] (analytic) = 0.91771065588540814411421009833446
y[1] (numeric) = 0.91771065588540814411425370030062
absolute error = 4.360196616e-23
relative error = 4.7511670350970023477368790460919e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0862
y[1] (analytic) = 0.91761963109456716663545835244682
y[1] (numeric) = 0.91761963109456716663550200702506
absolute error = 4.365457824e-23
relative error = 4.7573718740004907558963860196410e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0863
y[1] (analytic) = 0.91752861712752986919119853566585
y[1] (numeric) = 0.91752861712752986919124224286068
absolute error = 4.370719483e-23
relative error = 4.7635783793678682311847655984370e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0864
y[1] (analytic) = 0.91743761398520639145104517270919
y[1] (numeric) = 0.91743761398520639145108893252502
absolute error = 4.375981583e-23
relative error = 4.7697865405707710115134623521062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0865
y[1] (analytic) = 0.91734662166850676483747468145922
y[1] (numeric) = 0.9173466216685067648375184939005
absolute error = 4.381244128e-23
relative error = 4.7759963622378831687055452647304e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0866
y[1] (analytic) = 0.91725564017834091251672505874617
y[1] (numeric) = 0.91725564017834091251676892381725
absolute error = 4.386507108e-23
relative error = 4.7822078337366633047759428053943e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0867
y[1] (analytic) = 0.91716466951561864938969664869292
y[1] (numeric) = 0.9171646695156186493897405663983
absolute error = 4.391770538e-23
relative error = 4.7884209716881286078725610751506e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0868
y[1] (analytic) = 0.9170737096812496820828539937141
y[1] (numeric) = 0.91707370968124968208289796405817
absolute error = 4.397034407e-23
relative error = 4.7946357643687023523871840384437e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0869
y[1] (analytic) = 0.91698276067614360893912876825862
y[1] (numeric) = 0.9169827606761436089391727912458
absolute error = 4.402298718e-23
relative error = 4.8008522153174771324510285434857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 0.91689182250120992000882379538807
y[1] (numeric) = 0.91689182250120992000886787102281
absolute error = 4.407563474e-23
relative error = 4.8070703280748082246379060961053e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0871
y[1] (analytic) = 0.91680089515735799704051814628137
y[1] (numeric) = 0.91680089515735799704056227456805
absolute error = 4.412828668e-23
relative error = 4.8132900952748200703191826149168e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0872
y[1] (analytic) = 0.91670997864549711347197332275631
y[1] (numeric) = 0.9167099786454971134720175036994
absolute error = 4.418094309e-23
relative error = 4.8195115270022938715903416206180e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=213.6MB, alloc=4.3MB, time=19.13
x[1] = 0.0873
y[1] (analytic) = 0.91661907296653643442104052289982
y[1] (numeric) = 0.91661907296653643442108475650372
absolute error = 4.423360390e-23
relative error = 4.8257346158904182946076486838704e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0874
y[1] (analytic) = 0.91652817812138501667656898989681
y[1] (numeric) = 0.91652817812138501667661327616591
absolute error = 4.428626910e-23
relative error = 4.8319593611157610610532256888008e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0875
y[1] (analytic) = 0.91643729411095180868931544414926
y[1] (numeric) = 0.91643729411095180868935978308802
absolute error = 4.433893876e-23
relative error = 4.8381857705838786368495488969727e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0876
y[1] (analytic) = 0.91634642093614565056285459877642
y[1] (numeric) = 0.91634642093614565056289899038922
absolute error = 4.439161280e-23
relative error = 4.8444138358339666542894524414321e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0877
y[1] (analytic) = 0.9162555585978752740444907585864
y[1] (numeric) = 0.91625555859787527404453520287765
absolute error = 4.444429125e-23
relative error = 4.8506435604071065859001935645262e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0878
y[1] (analytic) = 0.91616470709704930251617050261087
y[1] (numeric) = 0.91616470709704930251621499958495
absolute error = 4.449697408e-23
relative error = 4.8568749412966021125488500294720e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0879
y[1] (analytic) = 0.91607386643457625098539645029295
y[1] (numeric) = 0.91607386643457625098544099995436
absolute error = 4.454966141e-23
relative error = 4.8631079918686478070062127401437e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 0.91598303661136452607614211142017
y[1] (numeric) = 0.91598303661136452607618671377327
absolute error = 4.460235310e-23
relative error = 4.8693426971097929914928553366915e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0881
y[1] (analytic) = 0.91589221762832242601976781989179
y[1] (numeric) = 0.91589221762832242601981247494103
absolute error = 4.465504924e-23
relative error = 4.8755790671126145537500572946980e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0882
y[1] (analytic) = 0.91580140948635814064593775141316
y[1] (numeric) = 0.91580140948635814064598245916296
absolute error = 4.470774980e-23
relative error = 4.8818170988702732087846218428663e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0883
y[1] (analytic) = 0.91571061218637975137353802520642
y[1] (numeric) = 0.91571061218637975137358278566124
absolute error = 4.476045482e-23
relative error = 4.8880567970189311178058936734501e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0884
y[1] (analytic) = 0.91561982572929523120159588982948
y[1] (numeric) = 0.91561982572929523120164070299363
absolute error = 4.481316415e-23
relative error = 4.8942981454454764590181293400822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0885
y[1] (analytic) = 0.91552905011601244470019999319285
y[1] (numeric) = 0.91552905011601244470024485907077
absolute error = 4.486587792e-23
relative error = 4.9005411586136739624321884116037e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0886
y[1] (analytic) = 0.91543828534743914800142173686667
y[1] (numeric) = 0.91543828534743914800146665546285
absolute error = 4.491859618e-23
relative error = 4.9067858422538997345319313559494e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0887
y[1] (analytic) = 0.91534753142448298879023771476767
y[1] (numeric) = 0.91534753142448298879028268608645
absolute error = 4.497131878e-23
relative error = 4.9130321802490352881120860248267e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0888
y[1] (analytic) = 0.91525678834805150629545323631659
y[1] (numeric) = 0.91525678834805150629549826036237
absolute error = 4.502404578e-23
relative error = 4.9192801794198079453780225763513e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.3MB, time=19.81
NO POLE
x[1] = 0.0889
y[1] (analytic) = 0.91516605611905213128062693415794
y[1] (numeric) = 0.91516605611905213128067201093511
absolute error = 4.507677717e-23
relative error = 4.9255298389406230064413530988852e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 0.91507533473839218603499645653182
y[1] (numeric) = 0.91507533473839218603504158604485
absolute error = 4.512951303e-23
relative error = 4.9317811678206718250878636510387e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0891
y[1] (analytic) = 0.91498462420697888436440524438928
y[1] (numeric) = 0.91498462420697888436445042664265
absolute error = 4.518225337e-23
relative error = 4.9380341674221742955471169315213e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0892
y[1] (analytic) = 0.91489392452571933158223039334157
y[1] (numeric) = 0.91489392452571933158227562833956
absolute error = 4.523499799e-23
relative error = 4.9442888161542668507457282186592e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0893
y[1] (analytic) = 0.91480323569552052450031160053334
y[1] (numeric) = 0.91480323569552052450035688828042
absolute error = 4.528774708e-23
relative error = 4.9505451350494997441804040100062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0894
y[1] (analytic) = 0.91471255771728935141988119653248
y[1] (numeric) = 0.91471255771728935141992653703301
absolute error = 4.534050053e-23
relative error = 4.9568031123514333808641394266223e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0895
y[1] (analytic) = 0.91462189059193259212249526232484
y[1] (numeric) = 0.9146218905919325921225406555833
absolute error = 4.539325846e-23
relative error = 4.9630627614458269687277463913744e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0896
y[1] (analytic) = 0.91453123432035691786096583150671
y[1] (numeric) = 0.91453123432035691786101127752742
absolute error = 4.544602071e-23
relative error = 4.9693240651068268037415674134968e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0897
y[1] (analytic) = 0.9144405889034688913502941777637
y[1] (numeric) = 0.91444058890346889135033967655112
absolute error = 4.549878742e-23
relative error = 4.9755870389085484186102211149143e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0898
y[1] (analytic) = 0.91434995434217496675860518772879
y[1] (numeric) = 0.9143499543421749667586507392873
absolute error = 4.555155851e-23
relative error = 4.9818516743703309345012887881718e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0899
y[1] (analytic) = 0.91425933063738148969808281930825
y[1] (numeric) = 0.91425933063738148969812842364232
absolute error = 4.560433407e-23
relative error = 4.9881179816022943185020989370902e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 0.91416871778999469721590664556776
y[1] (numeric) = 0.91416871778999469721595230268171
absolute error = 4.565711395e-23
relative error = 4.9943859444650648530373427210583e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0901
y[1] (analytic) = 0.91407811580092071778518948426765
y[1] (numeric) = 0.91407811580092071778523519416593
absolute error = 4.570989828e-23
relative error = 5.0006555774446818973633278301088e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0902
y[1] (analytic) = 0.9139875246710655712959161131397
y[1] (numeric) = 0.91398752467106557129596187582678
absolute error = 4.576268708e-23
relative error = 5.0069268829976105350255611942971e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0903
y[1] (analytic) = 0.91389694440133516904588307099489
y[1] (numeric) = 0.91389694440133516904592888647512
absolute error = 4.581548023e-23
relative error = 5.0131998482621324877052239023540e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0904
y[1] (analytic) = 0.91380637499263531373163954475271
y[1] (numeric) = 0.91380637499263531373168541303044
absolute error = 4.586827773e-23
relative error = 5.0194744735031716699606025775043e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.3MB, time=20.48
NO POLE
x[1] = 0.0905
y[1] (analytic) = 0.91371581644587169943942934248328
y[1] (numeric) = 0.91371581644587169943947526356294
absolute error = 4.592107966e-23
relative error = 5.0257507677410718741769832033052e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0906
y[1] (analytic) = 0.91362526876194991163613395255254
y[1] (numeric) = 0.9136252687619499116361799264386
absolute error = 4.597388606e-23
relative error = 5.0320287356214475337198655423376e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0907
y[1] (analytic) = 0.91353473194177542716021668896121
y[1] (numeric) = 0.91353473194177542716026271565794
absolute error = 4.602669673e-23
relative error = 5.0383083555200322168323042873473e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0908
y[1] (analytic) = 0.91344420598625361421266792296709
y[1] (numeric) = 0.91344420598625361421271400247894
absolute error = 4.607951185e-23
relative error = 5.0445896474046329168264553858566e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0909
y[1] (analytic) = 0.9133536908962897323479514010832
y[1] (numeric) = 0.91335369089628973234799753341465
absolute error = 4.613233145e-23
relative error = 5.0508726148278382013569786632649e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 0.91326318667278893246495164954075
y[1] (numeric) = 0.91326318667278893246499783469612
absolute error = 4.618515537e-23
relative error = 5.0571572405389836647049260068194e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0911
y[1] (analytic) = 0.91317269331665625679792246530733
y[1] (numeric) = 0.9131726933166562567979687032911
absolute error = 4.623798377e-23
relative error = 5.0634435423230827176961584088905e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0912
y[1] (analytic) = 0.91308221082879663890743649375248
y[1] (numeric) = 0.91308221082879663890748278456902
absolute error = 4.629081654e-23
relative error = 5.0697315084018815410645142693568e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0913
y[1] (analytic) = 0.91299173921011490367133589304917
y[1] (numeric) = 0.91299173921011490367138223670283
absolute error = 4.634365366e-23
relative error = 5.0760211368500151432335075702008e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0914
y[1] (analytic) = 0.91290127846151576727568408540296
y[1] (numeric) = 0.9129012784615157672757304818981
absolute error = 4.639649514e-23
relative error = 5.0823124290274382547010259702013e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0915
y[1] (analytic) = 0.9128108285839038372057185951988
y[1] (numeric) = 0.91281082858390383720576504453994
absolute error = 4.644934114e-23
relative error = 5.0886054027272601320651750522617e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0916
y[1] (analytic) = 0.91272038957818361223680497415671
y[1] (numeric) = 0.91272038957818361223685147634816
absolute error = 4.650219145e-23
relative error = 5.0949000352113447677743066476208e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0917
y[1] (analytic) = 0.91262996144525948242539181358494
y[1] (numeric) = 0.91262996144525948242543836863115
absolute error = 4.655504621e-23
relative error = 5.1011963420831019122916742354991e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0918
y[1] (analytic) = 0.91253954418603572909996684382366
y[1] (numeric) = 0.91253954418603572910001345172892
absolute error = 4.660790526e-23
relative error = 5.1074943060766948778880456416207e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0919
y[1] (analytic) = 0.91244913780141652485201412096696
y[1] (numeric) = 0.91244913780141652485206078173577
absolute error = 4.666076881e-23
relative error = 5.1137939504695054836853619488387e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=225.0MB, alloc=4.3MB, time=21.16
x[1] = 0.092
y[1] (analytic) = 0.91235874229230593352697230095623
y[1] (numeric) = 0.91235874229230593352701901459298
absolute error = 4.671363675e-23
relative error = 5.1200952634740751727933585725389e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0921
y[1] (analytic) = 0.9122683576596079102151940011329
y[1] (numeric) = 0.91226835765960791021524076764197
absolute error = 4.676650907e-23
relative error = 5.1263982442598161575530159682490e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0922
y[1] (analytic) = 0.91217798390422630124290624934255
y[1] (numeric) = 0.91217798390422630124295306872829
absolute error = 4.681938574e-23
relative error = 5.1327028898031131832027069876302e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0923
y[1] (analytic) = 0.91208762102706484416317202068
y[1] (numeric) = 0.91208762102706484416321889294689
absolute error = 4.687226689e-23
relative error = 5.1390092146211833264790824700060e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0924
y[1] (analytic) = 0.91199726902902716774685286196666
y[1] (numeric) = 0.91199726902902716774689978711902
absolute error = 4.692515236e-23
relative error = 5.1453172014385122182674834171989e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0925
y[1] (analytic) = 0.91190692791101679197357260404891
y[1] (numeric) = 0.91190692791101679197361958209113
absolute error = 4.697804222e-23
relative error = 5.1516268581944672805438417167586e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0926
y[1] (analytic) = 0.91181659767393712802268216200973
y[1] (numeric) = 0.91181659767393712802272919294619
absolute error = 4.703093646e-23
relative error = 5.1579381840577244435896231144659e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0927
y[1] (analytic) = 0.91172627831869147826422542338249
y[1] (numeric) = 0.9117262783186914782642725072177
absolute error = 4.708383521e-23
relative error = 5.1642511935519721336792833702147e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0928
y[1] (analytic) = 0.9116359698461830362499062244586
y[1] (numeric) = 0.91163596984618303624995336119676
absolute error = 4.713673816e-23
relative error = 5.1705658529416305725292909331483e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0929
y[1] (analytic) = 0.91154567225731488670405641477685
y[1] (numeric) = 0.91154567225731488670410360442257
absolute error = 4.718964572e-23
relative error = 5.1768822074643245536753224271736e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 0.9114553855529900055146050098891
y[1] (numeric) = 0.91145538555299000551465225244665
absolute error = 4.724255755e-23
relative error = 5.1832002200894803882358063408071e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0931
y[1] (analytic) = 0.91136510973411125972404843248735
y[1] (numeric) = 0.91136510973411125972409572796105
absolute error = 4.729547370e-23
relative error = 5.1895198965646544313448234214066e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0932
y[1] (analytic) = 0.91127484480158140752042184198659
y[1] (numeric) = 0.91127484480158140752046919038093
absolute error = 4.734839434e-23
relative error = 5.1958412558079022895937918417634e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0933
y[1] (analytic) = 0.91118459075630309822827155265235
y[1] (numeric) = 0.91118459075630309822831895397173
absolute error = 4.740131938e-23
relative error = 5.2021642882103471825989105357044e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0934
y[1] (analytic) = 0.91109434759917887229962854036252
y[1] (numeric) = 0.91109434759917887229967599461122
absolute error = 4.745424870e-23
relative error = 5.2084889808664167313282856856640e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0935
y[1] (analytic) = 0.91100411533111116130498303809423
y[1] (numeric) = 0.9110041153311111613050305452767
absolute error = 4.750718247e-23
relative error = 5.2148153526982876829014271282805e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.3MB, time=21.84
NO POLE
x[1] = 0.0936
y[1] (analytic) = 0.91091389395300228792426022022696
y[1] (numeric) = 0.91091389395300228792430778034765
absolute error = 4.756012069e-23
relative error = 5.2211434039729135961626543162308e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0937
y[1] (analytic) = 0.91082368346575446593779697575077
y[1] (numeric) = 0.91082368346575446593784458881398
absolute error = 4.761306321e-23
relative error = 5.2274731184885989064627259218773e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0938
y[1] (analytic) = 0.91073348387026980021731977047007
y[1] (numeric) = 0.91073348387026980021736743648017
absolute error = 4.766601010e-23
relative error = 5.2338045041934381144950923663904e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0939
y[1] (analytic) = 0.91064329516745028671692359829411
y[1] (numeric) = 0.91064329516745028671697131725553
absolute error = 4.771896142e-23
relative error = 5.2401375679404057565835987891835e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 0.91055311735819781246405202170364
y[1] (numeric) = 0.91055311735819781246409979362078
absolute error = 4.777191714e-23
relative error = 5.2464723067009446046259513529874e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0941
y[1] (analytic) = 0.91046295044341415555047830148388
y[1] (numeric) = 0.91046295044341415555052612636112
absolute error = 4.782487724e-23
relative error = 5.2528087185434951063070123449688e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0942
y[1] (analytic) = 0.91037279442400098512328761581429
y[1] (numeric) = 0.910372794424000985123335493656
absolute error = 4.787784171e-23
relative error = 5.2591468026340389240313559185384e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0943
y[1] (analytic) = 0.91028264930085986137586036880532
y[1] (numeric) = 0.91028264930085986137590829961581
absolute error = 4.793081049e-23
relative error = 5.2654865526452833066080809856803e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0944
y[1] (analytic) = 0.91019251507489223553885658857178
y[1] (numeric) = 0.91019251507489223553890457235555
absolute error = 4.798378377e-23
relative error = 5.2718279897140013467085061474907e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0945
y[1] (analytic) = 0.91010239174699944987120141493443
y[1] (numeric) = 0.91010239174699944987124945169579
absolute error = 4.803676136e-23
relative error = 5.2781710932316505660404086040005e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0946
y[1] (analytic) = 0.91001227931808273765107167683755
y[1] (numeric) = 0.91001227931808273765111976658088
absolute error = 4.808974333e-23
relative error = 5.2845158711524229054312566792883e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0947
y[1] (analytic) = 0.90992217778904322316688355957503
y[1] (numeric) = 0.90992217778904322316693170230474
absolute error = 4.814272971e-23
relative error = 5.2908623270375362399174324387511e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0948
y[1] (analytic) = 0.9098320871607819217082813619137
y[1] (numeric) = 0.90983208716078192170832955763416
absolute error = 4.819572046e-23
relative error = 5.2972104567557467590935910481128e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0949
y[1] (analytic) = 0.90974200743419973955712734320423
y[1] (numeric) = 0.90974200743419973955717559191991
absolute error = 4.824871568e-23
relative error = 5.3035602715630075454587803353873e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 0.90965193861019747397849266057046
y[1] (numeric) = 0.90965193861019747397854096228559
absolute error = 4.830171513e-23
relative error = 5.3099117453426513404989689164086e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0951
y[1] (analytic) = 0.90956188068967581321164939626543
y[1] (numeric) = 0.90956188068967581321169775098444
absolute error = 4.835471901e-23
relative error = 5.3162649003424601321328083509905e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.3MB, time=22.52
NO POLE
x[1] = 0.0952
y[1] (analytic) = 0.90947183367353533646106367528682
y[1] (numeric) = 0.90947183367353533646111208301414
absolute error = 4.840772732e-23
relative error = 5.3226197368280975939814389994207e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0953
y[1] (analytic) = 0.90938179756267651388738987333971
y[1] (numeric) = 0.90938179756267651388743833407962
absolute error = 4.846073991e-23
relative error = 5.3289762385704650601142779041257e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0954
y[1] (analytic) = 0.90929177235799970659846591523711
y[1] (numeric) = 0.90929177235799970659851442899404
absolute error = 4.851375693e-23
relative error = 5.3353344223266015016821036716308e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0955
y[1] (analytic) = 0.90920175806040516664030966382959
y[1] (numeric) = 0.90920175806040516664035823060792
absolute error = 4.856677833e-23
relative error = 5.3416942828627197470752008685911e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0956
y[1] (analytic) = 0.90911175467079303698811639955227
y[1] (numeric) = 0.90911175467079303698816501935645
absolute error = 4.861980418e-23
relative error = 5.3480558281425117170559524578996e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0957
y[1] (analytic) = 0.90902176219006335153725739068076
y[1] (numeric) = 0.90902176219006335153730606351505
absolute error = 4.867283429e-23
relative error = 5.3544190375305021269579427300033e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0958
y[1] (analytic) = 0.90893178061911603509427955438429
y[1] (numeric) = 0.90893178061911603509432828025314
absolute error = 4.872586885e-23
relative error = 5.3607839321902164174579439015260e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0959
y[1] (analytic) = 0.90884180995885090336790620866845
y[1] (numeric) = 0.90884180995885090336795498757618
absolute error = 4.877890773e-23
relative error = 5.3671504980837681691653680626946e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 0.90875185021016766296003891529494
y[1] (numeric) = 0.90875185021016766296008774724595
absolute error = 4.883195101e-23
relative error = 5.3735187442761851033849462732543e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0961
y[1] (analytic) = 0.90866190137396591135676041377039
y[1] (numeric) = 0.90866190137396591135680929876902
absolute error = 4.888499863e-23
relative error = 5.3798886644286685379681483638231e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0962
y[1] (analytic) = 0.90857196345114513691933864649276
y[1] (numeric) = 0.9085719634511451369193875845434
absolute error = 4.893805064e-23
relative error = 5.3862602643066753707170818489416e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0963
y[1] (analytic) = 0.90848203644260471887523187514634
y[1] (numeric) = 0.90848203644260471887528086625338
absolute error = 4.899110704e-23
relative error = 5.3926335441741139130060586027807e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0964
y[1] (analytic) = 0.90839212034924392730909488843467
y[1] (numeric) = 0.90839212034924392730914393260245
absolute error = 4.904416778e-23
relative error = 5.3990084987906203637116348651501e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0965
y[1] (analytic) = 0.90830221517196192315378630124133
y[1] (numeric) = 0.90830221517196192315383539847422
absolute error = 4.909723289e-23
relative error = 5.4053851317212515851481558825207e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0966
y[1] (analytic) = 0.90821232091165775818137694530895
y[1] (numeric) = 0.90821232091165775818142609561134
absolute error = 4.915030239e-23
relative error = 5.4117634454312664130455829935397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0967
y[1] (analytic) = 0.90812243756923037499415935152598
y[1] (numeric) = 0.90812243756923037499420855490228
absolute error = 4.920337630e-23
relative error = 5.4181434423867540413144120711320e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.3MB, time=23.20
NO POLE
x[1] = 0.0968
y[1] (analytic) = 0.90803256514557860701565832391146
y[1] (numeric) = 0.90803256514557860701570758036591
absolute error = 4.925645445e-23
relative error = 5.4245251041302744374803845605665e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0969
y[1] (analytic) = 0.90794270364160117848164260538658
y[1] (numeric) = 0.90794270364160117848169191492373
absolute error = 4.930953715e-23
relative error = 5.4309084650637064799332355829278e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 0.90785285305819670443113763542556
y[1] (numeric) = 0.90785285305819670443118699804966
absolute error = 4.936262410e-23
relative error = 5.4372934924108978238974756777413e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0971
y[1] (analytic) = 0.90776301339626369069743939967189
y[1] (numeric) = 0.90776301339626369069748881538729
absolute error = 4.941571540e-23
relative error = 5.4436801974469378319813860785550e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0972
y[1] (analytic) = 0.9076731846567005338991293716133
y[1] (numeric) = 0.90767318465670053389917884042442
absolute error = 4.946881112e-23
relative error = 5.4500685881460799533520151542385e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0973
y[1] (analytic) = 0.90758336684040552143109054640352
y[1] (numeric) = 0.9075833668404055214311400683147
absolute error = 4.952191118e-23
relative error = 5.4564586559581811662161702282328e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0974
y[1] (analytic) = 0.90749355994827683145552456692072
y[1] (numeric) = 0.90749355994827683145557414193631
absolute error = 4.957501559e-23
relative error = 5.4628504022469932812401188275002e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0975
y[1] (analytic) = 0.90740376398121253289296994215299
y[1] (numeric) = 0.90740376398121253289301957027742
absolute error = 4.962812443e-23
relative error = 5.4692438360909788320768814421201e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0976
y[1] (analytic) = 0.90731397894011058541332135800071
y[1] (numeric) = 0.90731397894011058541337103923829
absolute error = 4.968123758e-23
relative error = 5.4756389445289620197462630094070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0977
y[1] (analytic) = 0.90722420482586883942685008058466
y[1] (numeric) = 0.90722420482586883942689981493981
absolute error = 4.973435515e-23
relative error = 5.4820357399465474421511703236348e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0978
y[1] (analytic) = 0.90713444163938503607522545215121
y[1] (numeric) = 0.90713444163938503607527523962825
absolute error = 4.978747704e-23
relative error = 5.4884342115842752944595635506793e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0979
y[1] (analytic) = 0.90704468938155680722253747966274
y[1] (numeric) = 0.90704468938155680722258732026608
absolute error = 4.984060334e-23
relative error = 5.4948343696254292733189211459982e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 0.90695494805328167544632051616457
y[1] (numeric) = 0.90695494805328167544637040989852
absolute error = 4.989373395e-23
relative error = 5.5012362033079562823685008074348e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0981
y[1] (analytic) = 0.90686521765545705402857803501672
y[1] (numeric) = 0.90686521765545705402862798188571
absolute error = 4.994686899e-23
relative error = 5.5076397261247904830200147291345e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0982
y[1] (analytic) = 0.90677549818898024694680849708178
y[1] (numeric) = 0.9067754981889802469468584970901
absolute error = 5.000000832e-23
relative error = 5.5140449229010314841947432617658e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=240.3MB, alloc=4.3MB, time=23.89
x[1] = 0.0983
y[1] (analytic) = 0.90668578965474844886503231095699
y[1] (numeric) = 0.90668578965474844886508236410901
absolute error = 5.005315202e-23
relative error = 5.5204518027198204439212030101318e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0984
y[1] (analytic) = 0.90659609205365874512481988634174
y[1] (numeric) = 0.90659609205365874512486999264184
absolute error = 5.010630010e-23
relative error = 5.5268603669465581682978908360336e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0985
y[1] (analytic) = 0.90650640538660811173632078062939
y[1] (numeric) = 0.90650640538660811173637094008189
absolute error = 5.015945250e-23
relative error = 5.5332706092250861680799796757400e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0986
y[1] (analytic) = 0.90641672965449341536929393881304
y[1] (numeric) = 0.90641672965449341536934415142231
absolute error = 5.021260927e-23
relative error = 5.5396825353322823076324148574788e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0987
y[1] (analytic) = 0.90632706485821141334413902679558
y[1] (numeric) = 0.90632706485821141334418929256599
absolute error = 5.026577041e-23
relative error = 5.5460961455303920929827606222732e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0988
y[1] (analytic) = 0.90623741099865875362292885819312
y[1] (numeric) = 0.90623741099865875362297917712905
absolute error = 5.031893593e-23
relative error = 5.5525114411850817819020004629042e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0989
y[1] (analytic) = 0.90614776807673197480044291472169
y[1] (numeric) = 0.90614776807673197480049328682756
absolute error = 5.037210587e-23
relative error = 5.5589284269731296673282012022263e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 0.90605813609332750609520196025718
y[1] (numeric) = 0.90605813609332750609525238553725
absolute error = 5.042528007e-23
relative error = 5.5653470854993790773224095127090e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0991
y[1] (analytic) = 0.90596851504934166734050374865708
y[1] (numeric) = 0.90596851504934166734055422711573
absolute error = 5.047845865e-23
relative error = 5.5717674302677943559187297733125e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0992
y[1] (analytic) = 0.90587890494567066897545982543548
y[1] (numeric) = 0.90587890494567066897551035707702
absolute error = 5.053164154e-23
relative error = 5.5781894538134313894348040582234e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0993
y[1] (analytic) = 0.90578930578321061203603342337902
y[1] (numeric) = 0.90578930578321061203608400820788
absolute error = 5.058482886e-23
relative error = 5.5846131696444259754406093132626e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0994
y[1] (analytic) = 0.90569971756285748814607845219513
y[1] (numeric) = 0.90569971756285748814612909021566
absolute error = 5.063802053e-23
relative error = 5.5910385691917380546304110944819e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0995
y[1] (analytic) = 0.90561014028550717950837958228074
y[1] (numeric) = 0.90561014028550717950843027349721
absolute error = 5.069121647e-23
relative error = 5.5974656438827897527957989131628e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0996
y[1] (analytic) = 0.90552057395205545889569342270164
y[1] (numeric) = 0.90552057395205545889574416711852
absolute error = 5.074441688e-23
relative error = 5.6038944160629045477382185153410e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0997
y[1] (analytic) = 0.90543101856339798964179079347296
y[1] (numeric) = 0.9054310185633979896418415910946
absolute error = 5.079762164e-23
relative error = 5.6103248727438165206074241300020e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0998
y[1] (analytic) = 0.90534147412043032563250009222861
y[1] (numeric) = 0.90534147412043032563255094305924
absolute error = 5.085083063e-23
relative error = 5.6167570009319733488528305570492e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.3MB, time=24.57
NO POLE
x[1] = 0.0999
y[1] (analytic) = 0.90525194062404791129675175537007
y[1] (numeric) = 0.9052519406240479112968026594142
absolute error = 5.090404413e-23
relative error = 5.6231908318151292849841608529319e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 0.90516241807514608159762381378548
y[1] (numeric) = 0.90516241807514608159767477104737
absolute error = 5.095726189e-23
relative error = 5.6296263380402031227919349525528e-21 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = sin ( x ) - cos ( x );
Iterations = 1000
Total Elapsed Time = 24 Seconds
Elapsed Time(since restart) = 24 Seconds
Expected Time Remaining = 40 Minutes 32 Seconds
Optimized Time Remaining = 40 Minutes 31 Seconds
Time to Timeout = 14 Minutes 35 Seconds
Percent Done = 1.001 %
> quit
memory used=244.6MB, alloc=4.3MB, time=24.64