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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_large_float,
> glob_disp_incr,
> djd_debug,
> glob_optimal_expect_sec,
> glob_hmax,
> glob_reached_optimal_h,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> min_in_hour,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_no_eqs,
> glob_relerr,
> glob_last_good_h,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_opt_iter,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_h,
> glob_iter,
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_max_minutes,
> glob_max_iter,
> glob_log10_relerr,
> glob_log10relerr,
> glob_small_float,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_initial_pass,
> centuries_in_millinium,
> years_in_century,
> days_in_year,
> glob_dump,
> glob_normmax,
> glob_start,
> glob_warned2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3,
> #END CONST
> array_m1,
> array_pole,
> array_y,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> 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 ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL,
glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic,
glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec,
glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt,
glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour,
glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr,
glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec,
glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned,
glob_log10_abserr, glob_not_yet_finished, glob_log10normmin,
glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec,
glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles,
glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter,
glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start,
glob_max_trunc_err, glob_initial_pass, centuries_in_millinium,
years_in_century, days_in_year, glob_dump, glob_normmax, glob_start,
glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec,
glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole,
array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0,
array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error,
array_norms, array_real_pole, array_y_set_initial, array_complex_pole,
array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher,
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
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_large_float,
> glob_disp_incr,
> djd_debug,
> glob_optimal_expect_sec,
> glob_hmax,
> glob_reached_optimal_h,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> min_in_hour,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_no_eqs,
> glob_relerr,
> glob_last_good_h,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_opt_iter,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_h,
> glob_iter,
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_max_minutes,
> glob_max_iter,
> glob_log10_relerr,
> glob_log10relerr,
> glob_small_float,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_initial_pass,
> centuries_in_millinium,
> years_in_century,
> days_in_year,
> glob_dump,
> glob_normmax,
> glob_start,
> glob_warned2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3,
> #END CONST
> array_m1,
> array_pole,
> array_y,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> 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 ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL,
glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic,
glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec,
glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt,
glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour,
glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr,
glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec,
glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned,
glob_log10_abserr, glob_not_yet_finished, glob_log10normmin,
glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec,
glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles,
glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter,
glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start,
glob_max_trunc_err, glob_initial_pass, centuries_in_millinium,
years_in_century, days_in_year, glob_dump, glob_normmax, glob_start,
glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec,
glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole,
array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0,
array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error,
array_norms, array_real_pole, array_y_set_initial, array_complex_pole,
array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher,
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
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_large_float,
> glob_disp_incr,
> djd_debug,
> glob_optimal_expect_sec,
> glob_hmax,
> glob_reached_optimal_h,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> min_in_hour,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_no_eqs,
> glob_relerr,
> glob_last_good_h,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_opt_iter,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_h,
> glob_iter,
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_max_minutes,
> glob_max_iter,
> glob_log10_relerr,
> glob_log10relerr,
> glob_small_float,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_initial_pass,
> centuries_in_millinium,
> years_in_century,
> days_in_year,
> glob_dump,
> glob_normmax,
> glob_start,
> glob_warned2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3,
> #END CONST
> array_m1,
> array_pole,
> array_y,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> 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 ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL,
glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic,
glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec,
glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt,
glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour,
glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr,
glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec,
glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned,
glob_log10_abserr, glob_not_yet_finished, glob_log10normmin,
glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec,
glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles,
glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter,
glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start,
glob_max_trunc_err, glob_initial_pass, centuries_in_millinium,
years_in_century, days_in_year, glob_dump, glob_normmax, glob_start,
glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec,
glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole,
array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0,
array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error,
array_norms, array_real_pole, array_y_set_initial, array_complex_pole,
array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher,
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
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_large_float,
> glob_disp_incr,
> djd_debug,
> glob_optimal_expect_sec,
> glob_hmax,
> glob_reached_optimal_h,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> min_in_hour,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_no_eqs,
> glob_relerr,
> glob_last_good_h,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_opt_iter,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_h,
> glob_iter,
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_max_minutes,
> glob_max_iter,
> glob_log10_relerr,
> glob_log10relerr,
> glob_small_float,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_initial_pass,
> centuries_in_millinium,
> years_in_century,
> days_in_year,
> glob_dump,
> glob_normmax,
> glob_start,
> glob_warned2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3,
> #END CONST
> array_m1,
> array_pole,
> array_y,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> 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 - 3 - 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 - 3 - 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 ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL,
glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic,
glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec,
glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt,
glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour,
glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr,
glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec,
glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned,
glob_log10_abserr, glob_not_yet_finished, glob_log10normmin,
glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec,
glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles,
glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter,
glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start,
glob_max_trunc_err, glob_initial_pass, centuries_in_millinium,
years_in_century, days_in_year, glob_dump, glob_normmax, glob_start,
glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec,
glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole,
array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0,
array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error,
array_norms, array_real_pole, array_y_set_initial, array_complex_pole,
array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher,
glob_last;
n := glob_max_terms;
m := n - 4;
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 - 4;
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
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_large_float,
> glob_disp_incr,
> djd_debug,
> glob_optimal_expect_sec,
> glob_hmax,
> glob_reached_optimal_h,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> min_in_hour,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_no_eqs,
> glob_relerr,
> glob_last_good_h,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_opt_iter,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_h,
> glob_iter,
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_max_minutes,
> glob_max_iter,
> glob_log10_relerr,
> glob_log10relerr,
> glob_small_float,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_initial_pass,
> centuries_in_millinium,
> years_in_century,
> days_in_year,
> glob_dump,
> glob_normmax,
> glob_start,
> glob_warned2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3,
> #END CONST
> array_m1,
> array_pole,
> array_y,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> 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 ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL,
glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic,
glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec,
glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt,
glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour,
glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr,
glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec,
glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned,
glob_log10_abserr, glob_not_yet_finished, glob_log10normmin,
glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec,
glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles,
glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter,
glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start,
glob_max_trunc_err, glob_initial_pass, centuries_in_millinium,
years_in_century, days_in_year, glob_dump, glob_normmax, glob_start,
glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec,
glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole,
array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0,
array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error,
array_norms, array_real_pole, array_y_set_initial, array_complex_pole,
array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher,
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
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_large_float,
> glob_disp_incr,
> djd_debug,
> glob_optimal_expect_sec,
> glob_hmax,
> glob_reached_optimal_h,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> min_in_hour,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_no_eqs,
> glob_relerr,
> glob_last_good_h,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_opt_iter,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_h,
> glob_iter,
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_max_minutes,
> glob_max_iter,
> glob_log10_relerr,
> glob_log10relerr,
> glob_small_float,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_initial_pass,
> centuries_in_millinium,
> years_in_century,
> days_in_year,
> glob_dump,
> glob_normmax,
> glob_start,
> glob_warned2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3,
> #END CONST
> array_m1,
> array_pole,
> array_y,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin $eq_no = 1 iii = 1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (3)) * factorial_3(0,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,2] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := -att(1,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (3)) * factorial_3(1,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,3] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := -att(2,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (3)) * factorial_3(2,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,4] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := -att(3,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,7] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (3)) * factorial_3(3,6);
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,5] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := -att(4,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,8] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (3)) * factorial_3(4,7);
> array_y[8] := temporary;
> array_y_higher[1,8] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,7] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,6] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 3;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL,
glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic,
glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec,
glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt,
glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour,
glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr,
glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec,
glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned,
glob_log10_abserr, glob_not_yet_finished, glob_log10normmin,
glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec,
glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles,
glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter,
glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start,
glob_max_trunc_err, glob_initial_pass, centuries_in_millinium,
years_in_century, days_in_year, glob_dump, glob_normmax, glob_start,
glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec,
glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole,
array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0,
array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error,
array_norms, array_real_pole, array_y_set_initial, array_complex_pole,
array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher,
glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 4] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h^3*factorial_3(0, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 2] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 5] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h^3*factorial_3(1, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 3] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 6] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h^3*factorial_3(2, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 4] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 7] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h^3*factorial_3(3, 6);
array_y[7] := temporary;
array_y_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 8] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h^3*factorial_3(4, 7);
array_y[8] := temporary;
array_y_higher[1, 8] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 7] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 3;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> 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)
> 1.0 - sin(x);
> end;
exact_soln_y := proc(x) 1.0 - sin(x) end proc
> exact_soln_yp := proc(x)
> -cos(x);
> end;
exact_soln_yp := proc(x) -cos(x) end proc
> exact_soln_ypp := proc(x)
> sin(x);
> end;
exact_soln_ypp := proc(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
> ALWAYS,
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_large_float,
> glob_disp_incr,
> djd_debug,
> glob_optimal_expect_sec,
> glob_hmax,
> glob_reached_optimal_h,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_not_yet_start_msg,
> glob_clock_sec,
> min_in_hour,
> glob_display_flag,
> MAX_UNCHANGED,
> glob_no_eqs,
> glob_relerr,
> glob_last_good_h,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_max_opt_iter,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_log10_abserr,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_subiter_method,
> glob_max_sec,
> glob_h,
> glob_iter,
> glob_orig_start_sec,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_hmin,
> hours_in_day,
> djd_debug2,
> glob_max_minutes,
> glob_max_iter,
> glob_log10_relerr,
> glob_log10relerr,
> glob_small_float,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_initial_pass,
> centuries_in_millinium,
> years_in_century,
> days_in_year,
> glob_dump,
> glob_normmax,
> glob_start,
> glob_warned2,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_3,
> #END CONST
> array_m1,
> array_pole,
> array_y,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> INFO := 2;
> glob_max_terms := 30;
> glob_iolevel := 5;
> DEBUGL := 3;
> glob_current_iter := 0;
> glob_unchanged_h_cnt := 0;
> glob_dump_analytic := false;
> glob_large_float := 9.0e100;
> glob_disp_incr := 0.1;
> djd_debug := true;
> glob_optimal_expect_sec := 0.1;
> glob_hmax := 1.0;
> glob_reached_optimal_h := false;
> glob_curr_iter_when_opt := 0;
> glob_smallish_float := 0.1e-100;
> glob_not_yet_start_msg := true;
> glob_clock_sec := 0.0;
> min_in_hour := 60.0;
> glob_display_flag := true;
> MAX_UNCHANGED := 10;
> glob_no_eqs := 0;
> glob_relerr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_almost_1 := 0.9990;
> sec_in_min := 60.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_opt_iter := 10;
> glob_percent_done := 0.0;
> glob_log10abserr := 0.0;
> glob_warned := false;
> glob_log10_abserr := 0.1e-10;
> glob_not_yet_finished := true;
> glob_log10normmin := 0.1;
> glob_subiter_method := 3;
> glob_max_sec := 10000.0;
> glob_h := 0.1;
> glob_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_hours := 0.0;
> glob_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_hmin := 0.00000000001;
> hours_in_day := 24.0;
> djd_debug2 := true;
> glob_max_minutes := 0.0;
> glob_max_iter := 1000;
> glob_log10_relerr := 0.1e-10;
> glob_log10relerr := 0.0;
> glob_small_float := 0.1e-50;
> glob_optimal_start := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_initial_pass := true;
> centuries_in_millinium := 10.0;
> years_in_century := 100.0;
> days_in_year := 365.0;
> glob_dump := false;
> glob_normmax := 0.0;
> glob_start := 0;
> glob_warned2 := false;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> glob_clock_start_sec := 0.0;
> glob_html_log := 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/h3sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 3 ) = sin(x);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 50;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);");
> omniout_str(ALWAYS,"array_y_init[2 + 1] := exact_soln_ypp(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 20;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"1.0 - sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"-cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_ypp := proc(x)");
> omniout_str(ALWAYS,"sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 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 := 50;
> 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_m1:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= 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_y_init:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work := Array(1..(4+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work2 := Array(1..(4+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := Array(1..(4+ 1) ,(1..max_terms+ 1),[]);
> 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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_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_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_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_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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 <=4 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 <=4 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=4 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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> 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_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_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3[1] := 3;
> 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 := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> array_y_init[2 + 1] := exact_soln_ypp(x_start);
> glob_h := 0.00001;
> glob_look_poles := true;
> glob_max_iter := 20;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := true;
> array_y_set_initial[1,3] := true;
> 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 := 3;
> #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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[4,iii] := array_y_higher[4,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 := 4;
> 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 := 3;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> 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 := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> 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 := 2;
> calc_term := 3;
> #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 := 3;
> #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 := 2;
> calc_term := 2;
> #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 := 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 := 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 := 4;
> #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 := 4;
> #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 := 3;
> #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 := 3;
> #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 , 3 ) = sin(x);");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-15T20:35:44-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"h3sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 3 ) = sin(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"h3sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"h3sin 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 ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL,
glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic,
glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec,
glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt,
glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour,
glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr,
glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec,
glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned,
glob_log10_abserr, glob_not_yet_finished, glob_log10normmin,
glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec,
glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles,
glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter,
glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start,
glob_max_trunc_err, glob_initial_pass, centuries_in_millinium,
years_in_century, days_in_year, glob_dump, glob_normmax, glob_start,
glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec,
glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole,
array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0,
array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error,
array_norms, array_real_pole, array_y_set_initial, array_complex_pole,
array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
ALWAYS := 1;
DEBUGMASSIVE := 4;
INFO := 2;
glob_max_terms := 30;
glob_iolevel := 5;
DEBUGL := 3;
glob_current_iter := 0;
glob_unchanged_h_cnt := 0;
glob_dump_analytic := false;
glob_large_float := 0.90*10^101;
glob_disp_incr := 0.1;
djd_debug := true;
glob_optimal_expect_sec := 0.1;
glob_hmax := 1.0;
glob_reached_optimal_h := false;
glob_curr_iter_when_opt := 0;
glob_smallish_float := 0.1*10^(-100);
glob_not_yet_start_msg := true;
glob_clock_sec := 0.;
min_in_hour := 60.0;
glob_display_flag := true;
MAX_UNCHANGED := 10;
glob_no_eqs := 0;
glob_relerr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_almost_1 := 0.9990;
sec_in_min := 60.0;
glob_optimal_clock_start_sec := 0.;
glob_max_opt_iter := 10;
glob_percent_done := 0.;
glob_log10abserr := 0.;
glob_warned := false;
glob_log10_abserr := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_log10normmin := 0.1;
glob_subiter_method := 3;
glob_max_sec := 10000.0;
glob_h := 0.1;
glob_iter := 0;
glob_orig_start_sec := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_hours := 0.;
glob_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_hmin := 0.1*10^(-10);
hours_in_day := 24.0;
djd_debug2 := true;
glob_max_minutes := 0.;
glob_max_iter := 1000;
glob_log10_relerr := 0.1*10^(-10);
glob_log10relerr := 0.;
glob_small_float := 0.1*10^(-50);
glob_optimal_start := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_initial_pass := true;
centuries_in_millinium := 10.0;
years_in_century := 100.0;
days_in_year := 365.0;
glob_dump := false;
glob_normmax := 0.;
glob_start := 0;
glob_warned2 := false;
glob_hmin_init := 0.001;
glob_optimal_done := false;
glob_clock_start_sec := 0.;
glob_html_log := 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/h3sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 3 ) = sin(x);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 50;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);");
omniout_str(ALWAYS, "array_y_init[2 + 1] := exact_soln_ypp(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 20;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "1.0 - sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "-cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_ypp := proc(x)");
omniout_str(ALWAYS, "sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*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 := 50;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_m1 := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_1st_rel_error := 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_y_init := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work := Array(1 .. 5, 1 .. max_terms + 1, []);
array_y_higher_work2 := Array(1 .. 5, 1 .. max_terms + 1, []);
array_y_higher := Array(1 .. 5, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_m1[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_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_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_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[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_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_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_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 4 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 <= 4 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 4 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_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_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3[term] := 0.; term := term + 1
end do;
array_const_3[1] := 3;
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 := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
array_y_init[3] := exact_soln_ypp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 20;
glob_h := 0.001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := true;
array_y_set_initial[1, 3] := true;
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 := 3;
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 := 3;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[4, iii] := array_y_higher[4, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
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 := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
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 := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
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 := 2;
calc_term := 3;
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 := 3;
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 := 2;
calc_term := 2;
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 := 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 := 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 := 4;
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 := 4;
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 := 3;
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 := 3;
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 , 3 ) = sin(x);");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-15T20:35:44-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "h3sin");
logitem_str(html_log_file, "diff ( y , x , 3 ) = sin(x);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"h3sin diffeq.mxt");
logitem_str(html_log_file,
"h3sin 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/h3sinpostode.ode#################
diff ( y , x , 3 ) = sin(x);
!
#BEGIN FIRST INPUT BLOCK
Digits := 50;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
array_y_init[2 + 1] := exact_soln_ypp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 20;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
1.0 - sin(x);
end;
exact_soln_yp := proc(x)
-cos(x);
end;
exact_soln_ypp := proc(x)
sin(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y[1] (analytic) = 0.90016658335317184769318580158938
y[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 0.89917162927043200487024788047681
y[1] (numeric) = 0.89917162912128250578920005293013
absolute error = 1.4914949908104782754667892027830e-10
relative error = 1.6587433836415016344597758481299e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 0.89817677601605448925135770391935
y[1] (numeric) = 0.89817677482322362141267466335016
absolute error = 1.1928308678386830405691827902844e-09
relative error = 1.3280580167409736581902396005394e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 0.89718202458489247230959578949541
y[1] (numeric) = 0.89718202056032099192052280805893
absolute error = 4.0245714803890729814364824662768e-09
relative error = 4.4857914783247678103432358210238e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 0.89618737597169730231102924533054
y[1] (numeric) = 0.89618736643489521701242741680904
absolute error = 9.5368020852986018285215035988518e-09
relative error = 1.0641526918361529952906784249708e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 0.89519283117111750956344639997322
y[1] (numeric) = 0.8951928125502615964102500009297
absolute error = 1.8620855913153196399043516484442e-08
relative error = 2.0800943958401506314468054662802e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 0.89419839117769781176790938198128
y[1] (numeric) = 0.89419835901073002654273954107322
absolute error = 3.2166967785225169840908058414351e-08
relative error = 3.5972965398494943843835194925487e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 0.89320405698587811947411929758354
y[1] (numeric) = 0.89320400592160489623564475095712
absolute error = 5.1064273223238474546626418920854e-08
relative error = 5.7169773047779404848022174120001e-06 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.39
NO POLE
x[1] = 0.108
y[1] (analytic) = 0.89220982958999254164058855096841
y[1] (numeric) = 0.89220975338918498140733402698083
absolute error = 7.6200807560233254523987587774421e-08
relative error = 8.5406823633909849669194384551780e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 0.89121570998426839130061474694456
y[1] (numeric) = 0.89121560152076333877002838808836
absolute error = 1.0846350505253058635885620044196e-07
relative error = 1.2170286479178555796032226737770e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 0.89022169916282519133505050991655
y[1] (numeric) = 0.89022155042462719853675370463503
absolute error = 1.4873819799279829680528151527235e-07
relative error = 1.6707995113203084459296886219799e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 0.88922779811967368035286344632307
y[1] (numeric) = 0.88922760021005785613411950929715
absolute error = 1.9790961582421874393702592112083e-07
relative error = 2.2256346038968943199875432040614e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 0.88823400784871481868048036989479
y[1] (numeric) = 0.88823375098733056292103267723679
absolute error = 2.5686138425575944769265800453477e-07
relative error = 2.8918210965359526696478769872527e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 0.8872403293437387944609098003048
y[1] (numeric) = 0.8872400028677144159134552567989
absolute error = 3.2647602437854745454350590396253e-07
relative error = 3.6796797167688551673023316146110e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 0.88624676359842402986363663600634
y[1] (numeric) = 0.88624635596347224651531672597369
absolute error = 4.0763495178334831991003264756513e-07
relative error = 4.5995649126912444682500306741857e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 0.8852533116063361874062827912803
y[1] (numeric) = 0.88525281038786050825569194370279
absolute error = 5.0121847567915059084757751483960e-07
relative error = 5.6618650177050987161249485336933e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 0.88425997436092717638902747574917
y[1] (numeric) = 0.88425936625512916353235705884188
absolute error = 6.0810579801285667041690728502190e-07
relative error = 6.8770024160863687810780632521528e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 0.88326675285553415944278068185407
y[1] (numeric) = 0.88326602368052156936183663321442
absolute error = 7.2917501259008094404863964262624e-07
relative error = 8.2554337093829655450382491278473e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 0.88227364808337855919210333203896
y[1] (numeric) = 0.88227278278027436213605622869985
absolute error = 8.6530310419705604710333910887668e-07
relative error = 9.8076498836479050711420872885981e-05 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=0.87
NO POLE
x[1] = 0.119
y[1] (analytic) = 0.88128066103756506503386742263883
y[1] (numeric) = 0.88127964367161734138571570169406
absolute error = 1.0173659477236481517209447644601e-06
relative error = 0.00011544176477512450233001595288051 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 0.88028779271108064003264938572903
y[1] (numeric) = 0.8802866064727733525504994415592
absolute error = 1.1862383072874821499441698321158e-06
relative error = 0.00013475573751104118335540216083295 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 0.87929504409679352793384977345972
y[1] (numeric) = 0.87929367130295816875624078284271
absolute error = 1.3727938353591776089906170060962e-06
relative error = 0.00015612436855814455434355237695312 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 0.87830241618745226029553225167281
y[1] (numeric) = 0.87830083828238037159915881409145
absolute error = 1.5779050718886963734375813593823e-06
relative error = 0.00017965396004921509456657297399525 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 0.8773099099756846637399747708799
y[1] (numeric) = 0.87730810753224123093728679901406
absolute error = 1.8024434434328026879718658394873e-06
relative error = 0.00020545116645071965845507233186869 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 0.87631752645399686732592566296706
y[1] (numeric) = 0.87631547917473458368921241855317
absolute error = 2.0472792622836367132444138913777e-06
relative error = 0.00023362299628627941292044200270432 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 0.87532526661477231004255729128789
y[1] (numeric) = 0.87532295333304671164025103511716
absolute error = 2.3132817255984023062561707340094e-06
relative error = 0.00026427681386883463189418168170973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 0.87433313145027074842610976010826
y[1] (numeric) = 0.87433053013135621825617417278788
absolute error = 2.6013189145301699355873203786005e-06
relative error = 0.00029752034104155694738960860780396 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 0.87334112195262726430021706667654
y[1] (numeric) = 0.87333820969483390450461639976581
absolute error = 2.9122577933597956006669107263168e-06
relative error = 0.00033346165892755998165522948279821 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 0.87234923911385127264090795551028
y[1] (numeric) = 0.87234599214964264368428479163515
absolute error = 3.2469642086289566231638751356562e-06
relative error = 0.00037220920968845961256657876141135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 0.87135748392582552956727360981603
y[1] (numeric) = 0.87135387762293725526209614622921
absolute error = 3.6063028882743051774635868214963e-06
relative error = 0.00041387179829183545431245269659524 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.2MB, time=1.33
x[1] = 0.13
y[1] (analytic) = 0.87036585738030514045879418929169
y[1] (numeric) = 0.87036186624286437771836811294823
absolute error = 3.9911374407627404260763434553806e-06
relative error = 0.00045855859428764546769035784588317 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 0.86937436046891656820031609690237
y[1] (numeric) = 0.86936995813856234040019139132787
absolute error = 4.4023303542278001247055744979050e-06
relative error = 0.00050637913359364594895296382240452 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 0.86838299418315664155567172956986
y[1] (numeric) = 0.86837815344016103438311114547563
absolute error = 4.8407429956071725605840942276343e-06
relative error = 0.00055744332028986948316087623426748 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 0.86739175951439156367093333907315
y[1] (numeric) = 0.8673864522787817823412467726829
absolute error = 5.3072356097813296865663902562932e-06
relative error = 0.00061186142842221378741575710587192 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 0.86640065745385592070829249982374
y[1] (numeric) = 0.86639485478653720742598015608208
absolute error = 5.8026673187132823123437416573716e-06
relative error = 0.00066974410381519471119050494276943 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 0.86540968899265169061155654955344
y[1] (numeric) = 0.86540336109653110115334352264964
absolute error = 6.3278961205894582130269038059637e-06
relative error = 0.00073120236589391700525881298973287 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 0.86441885512174725200425323733583
y[1] (numeric) = 0.86441197134285829030023901915607
absolute error = 6.8837788889617040142181797536654e-06
relative error = 0.00079634760951531681747406128195179 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 0.86342815683197639322133468075391
y[1] (numeric) = 0.86342068566060450280962310983234
absolute error = 7.4711713718904117115709215666191e-06
relative error = 0.00086529160680873022287643756589638 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 0.86243759511403732147547160042766
y[1] (numeric) = 0.862429504185846232704789890557
absolute error = 8.0909281910887706817098706610834e-06
relative error = 0.00093814650902584244733685995166274 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 0.86144717095849167215892866552446
y[1] (numeric) = 0.86143842705565060401288840526956
absolute error = 8.7439028410681460402602549038575e-06
relative error = 0.001015024848400072798196291763882 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 0.86045688535576351828201164829463
y[1] (numeric) = 0.8604474544080752336978100410814
absolute error = 9.4309476882845842016072132299942e-06
relative error = 0.0010960395400154506721491651499126 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 0.85946673929613838004907694910232
y[1] (numeric) = 0.85945658638216809360258306918542
absolute error = 1.0152913970286446493879916893845e-05
relative error = 0.0011813038836850383699698019444704 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=15.2MB, alloc=4.2MB, time=1.82
x[1] = 0.142
y[1] (analytic) = 0.85847673376976223457309391585971
y[1] (numeric) = 0.85846582311796737140141238915837
absolute error = 1.0910651794863171681526701338784e-05
relative error = 0.0012709315658389568096110456939156 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 0.85748686976664052572975024321969
y[1] (numeric) = 0.85747516475650133056150352460452
absolute error = 1.1705010139195168246718615174026e-05
relative error = 0.001365036661422070593735077050093 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 0.85649714827663717415209059733904
y[1] (numeric) = 0.85648461143978816931481090830503
absolute error = 1.2536836849004837279689034012681e-05
relative error = 0.0014637336358013892548880288034626 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 0.85550757028947358736667847149108
y[1] (numeric) = 0.855494163310835878639851485113
absolute error = 1.3406978637708726826986378083340e-05
relative error = 0.0015671373466832418713231745034765 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 0.85451813679472767007227113628341
y[1] (numeric) = 0.8545038205136420992537256507687
absolute error = 1.4316281085570818545485514708684e-05
relative error = 0.0016753630460402826189329404097724 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 0.85352884878183283456199740572324
y[1] (numeric) = 0.85351358319319397761448853460216
absolute error = 1.5265588638856947508871121080246e-05
relative error = 0.0017885263820483851998887671987545 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 0.85253970724007701129002779687021
y[1] (numeric) = 0.85252345149546802093401562373983
absolute error = 1.6255744608990356012173130380978e-05
relative error = 0.001906743401033484466431088104948 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 0.85155071315860165958372651632402
y[1] (numeric) = 0.85153342556742995120150771593767
absolute error = 1.7287591171708382218800386349642e-05
relative error = 0.0020301305494284239388207382819854 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 0.85056186752640077850227456131236
y[1] (numeric) = 0.85054350555703455821778117752338
absolute error = 1.8361969366220284493383788977435e-05
relative error = 0.0021588046757398682997794936739808 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 0.8495731713323199178427530766738
y[1] (numeric) = 0.84955369161322555164049047214549
absolute error = 1.9479719094366202262604528312404e-05
relative error = 0.002292883032525340333832869118451 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 0.84858462556505518929467596156972
y[1] (numeric) = 0.84856398388593541204043091509426
absolute error = 2.0641679119777254245046475456807e-05
relative error = 0.0024324832783804421688446839736244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 0.84759623121315227774396057131025
y[1] (numeric) = 0.84757438252608524096907059687934
absolute error = 2.1848687067036774889974430913244e-05
relative error = 0.0025777234799363210687223169208616 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=2.29
NO POLE
x[1] = 0.154
y[1] (analytic) = 0.84660798926500545272732521024132
y[1] (numeric) = 0.84658488768558461003746140851972
absolute error = 2.3101579420842689863801721604318e-05
relative error = 0.0027287221138674404207962975630234 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 0.84561990070885658003810196121268
y[1] (numeric) = 0.84559549951733140900668008962238
absolute error = 2.4401191525171031421871590296221e-05
relative error = 0.0028855980689097169587603907994244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 0.84463196653279413348445324573189
y[1] (numeric) = 0.84460621817521169288995120879595
absolute error = 2.5748357582440594502036935937768e-05
relative error = 0.0030484706478890856623212842246008 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 0.84364418772475220680098035650535
y[1] (numeric) = 0.84361704381409952806660497426362
absolute error = 2.7143910652678734375382241723192e-05
relative error = 0.0032174595697605541778732480342387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 0.84265656527250952571471205067536
y[1] (numeric) = 0.84262797658985683740802376070472
absolute error = 2.8588682652688306688289970639867e-05
relative error = 0.0033926849716578090106057575598154 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 0.84166910016368846016646113768246
y[1] (numeric) = 0.84163901665933324441573222636544
absolute error = 3.0083504355215750728911317012946e-05
relative error = 0.0035742674109534361474943062386326 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 0.84068179338575403668853684031401
y[1] (numeric) = 0.84065016418036591637178688233576
absolute error = 3.1629205388120316749957978249730e-05
relative error = 0.0037623278673298191826399482760331 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 0.83969464592601295093980055114447
y[1] (numeric) = 0.83966141931177940650162196358971
absolute error = 3.3226614233544438178587554760976e-05
relative error = 0.0039569877448607784314351551426362 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 0.83870765877161258039905244922922
y[1] (numeric) = 0.83867278221338549514950943893018
absolute error = 3.4876558227085249543010299038071e-05
relative error = 0.0041583688741040149380662128937871 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 0.83772083290953999721773628358307
y[1] (numeric) = 0.83768425304598302996679198436483
absolute error = 3.6579863556967250944299218239175e-05
relative error = 0.004366593514204423701939699392563 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 0.8367341693266209812329494706565
y[1] (numeric) = 0.83669583197135776511304873166697
absolute error = 3.8337355263216119900738989529584e-05
relative error = 0.0045817843550083408727668418591275 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=22.8MB, alloc=4.3MB, time=2.77
x[1] = 0.165
y[1] (analytic) = 0.83574766900951903314174549271711
y[1] (numeric) = 0.83570751915228219947035459094213
absolute error = 4.0149857236833671390901774978400e-05
relative error = 0.0048040645191887900912792564180205 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 0.83476133294473438783771542275181
y[1] (numeric) = 0.83471931475251541387079493292763
absolute error = 4.2018192218973966920489824182373e-05
relative error = 0.005033557564381793582907415769873 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 0.83377516211860302791083523922592
y[1] (numeric) = 0.83373121893680290733739840349681
absolute error = 4.3943181800120573436835729116706e-05
relative error = 0.0052703874853338140452540967086652 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 0.83278915751729569731156543076966
y[1] (numeric) = 0.83274323187087643233865162942151
absolute error = 4.5925646419264972913801348150858e-05
relative error = 0.0055146787160603938068641605247796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 0.83180332012681691518018922661023
y[1] (numeric) = 0.83175535372145382905676056086437
absolute error = 4.7966405363086123428665745864510e-05
relative error = 0.0057665561320160581746546696503306 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 0.83081765093300398984237562332915
y[1] (numeric) = 0.83076758465623885866982418232574
absolute error = 5.0066276765131172551441003405884e-05
relative error = 0.0060261450522755503304511172342387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 0.8298321509215260329719532122995
y[1] (numeric) = 0.8297799248439210356480873098577
absolute error = 5.2226077604997323865902441802696e-05
relative error = 0.0062935712417264655834022395210653 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 0.82884682107788297392188064494727
y[1] (numeric) = 0.82879237445417545906444017827826
absolute error = 5.4446623707514857440466669017747e-05
relative error = 0.0065689609132733532346435157128022 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 0.82786166238740457422439940478408
y[1] (numeric) = 0.82780493365766264291933350787229
absolute error = 5.6728729741931305065896911789474e-05
relative error = 0.0068524407300533547634742852222943 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 0.82687667583524944226135438597639
y[1] (numeric) = 0.82681760262602834548027872564982
absolute error = 5.9073209221096781075660326566736e-05
relative error = 0.0071441378076634475005319058709758 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 0.82589186240640404810566760804859
y[1] (numeric) = 0.8258303815319033976361040016473
absolute error = 6.1480874500650469563606401291426e-05
relative error = 0.0074441797163993634130152479804364 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 0.82490722308568173853495022516409
y[1] (numeric) = 0.82484327054890353026613774600153
absolute error = 6.3952536778208268812479162557783e-05
relative error = 0.0077526944835062530899560113290254 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.3MB, time=3.24
NO POLE
x[1] = 0.177
y[1] (analytic) = 0.82392275885772175221823781629032
y[1] (numeric) = 0.82385626985162920062449219759838
absolute error = 6.6489006092551593745618691939893e-05
relative error = 0.0080698105954411654818870432047438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 0.82293847070698823507683376943031
y[1] (numeric) = 0.82286937961566541773962071999812
absolute error = 6.9091091322817337213049432186081e-05
relative error = 0.008395657000147414419039442869298 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 0.82195435961776925582024539899536
y[1] (numeric) = 0.82188260001758156682932340506568
absolute error = 7.1759600187688990921993929688646e-05
relative error = 0.0087303631093409034054424174652522 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 0.82097042657417582165819726030079
y[1] (numeric) = 0.82089593123493123273137656928548
absolute error = 7.4495339244588926820691015308635e-05
relative error = 0.0090740588008084806630295060590958 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 0.81998667256014089418970594908918
y[1] (numeric) = 0.81990937344625202234996271211675
absolute error = 7.7299113888871839743236972427565e-05
relative error = 0.0094268744207183968801000562276987 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 0.81900309855941840547020049692454
y[1] (numeric) = 0.81892292683106538611807848994437
absolute error = 8.0171728353019352122006980171833e-05
relative error = 0.0097889407859429386022741125960563 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 0.81801970555558227425767229525488
y[1] (numeric) = 0.81793659156987643847609924320261
absolute error = 8.3113985705835781573052052272098e-05
relative error = 0.010160389186393310691440799720747 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 0.81703649453202542243883830191132
y[1] (numeric) = 0.81695036784417377736667959809218
absolute error = 8.6126687851645072158703819141320e-05
relative error = 0.010541351387366841769163745224828 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 0.81605346647195879163630110379855
y[1] (numeric) = 0.81596425583642930274617064797491
absolute error = 8.9210635529488890130455823644288e-05
relative error = 0.010931959631906587055601239897519 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 0.81507062235841035999768922853466
y[1] (numeric) = 0.81497825573009803411273520301381
absolute error = 9.2366628312325884954025520851990e-05
relative error = 0.011332346643173403513253072999173 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 0.81408796317422415916776091581804
y[1] (numeric) = 0.81399236770961792705134357992805
absolute error = 9.5595464606232116417335889990580e-05
relative error = 0.011742645626830572706789975777157 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.3MB, time=3.71
x[1] = 0.188
y[1] (analytic) = 0.81310548990205929144445437633573
y[1] (numeric) = 0.81300659196040968879583338685175
absolute error = 9.8897941649602648620989483972250e-05
relative error = 0.012162990273441047295885278283789 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 0.81212320352438894711986738208099
y[1] (numeric) = 0.81202092866887659280821774122149
absolute error = 0.00010227485551235431164964085950014
relative error = 0.012593514760877397587381922133656 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 0.81114110502349942200714884701869
y[1] (numeric) = 0.81103537802240429237542734136876
absolute error = 0.0001057270010951296317215056499383
relative error = 0.01303435375674453508632182956213 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 0.81015919538148913515428487112495
y[1] (numeric) = 0.81004994020936063322367279505985
absolute error = 0.00010925517212850193061207606509855
relative error = 0.013485642420815290502369530890036 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 0.80917747558026764674576153393323
y[1] (numeric) = 0.80906461541909546515061459060524
absolute error = 0.0001128601611721815951469433279869
relative error = 0.013947516407478924189008893795914 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 0.80819594660155467619308653584224
y[1] (numeric) = 0.8080794038419404526755290783527
absolute error = 0.00011654275961422351755745748954305
relative error = 0.014420111868202647517612048473969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 0.8072146094268791204151515965821
y[1] (numeric) = 0.80709430566920888470765981238243
absolute error = 0.00012030375767023570749178419966638
relative error = 0.014903565454006234217104709556278 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 0.80623346503757807230941733039465
y[1] (numeric) = 0.80610932109319548323294458403713
absolute error = 0.00012414394438258907647274635752269
relative error = 0.015398014317949801242513884914406 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 0.80525251441479583941490212666118
y[1] (numeric) = 0.80512445030717621101930946054374
absolute error = 0.00012806410761962839559266611743886
relative error = 0.015903596117634839272214541687939 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 0.80427175853948296276795637290694
y[1] (numeric) = 0.80413969350540807834072212341715
absolute error = 0.00013206503407488442723424948978976
relative error = 0.016420449017718573474223564629428 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 0.80329119839239523595180316432647
y[1] (numeric) = 0.80315505088312894872019778257613
absolute error = 0.00013614750926628723160538175033714
relative error = 0.016948711692441735726454972309308 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 0.8023108349540927243408264502072
y[1] (numeric) = 0.80217052263655734369195192314953
absolute error = 0.0001403123175353806488745270576674
relative error = 0.017488523328169830024482824544232 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.3MB, time=4.18
x[1] = 0.2
y[1] (analytic) = 0.80133066920493878454058737288161
y[1] (numeric) = 0.80118610896289224658289512280374
absolute error = 0.00014456024204653795769225007786874
relative error = 0.018040023625947973363090824494456 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 0.80035070212509908402454935910971
y[1] (numeric) = 0.80020181006031290531366615808015
absolute error = 0.00014889206478617871088320102956421
relative error = 0.018603352804069394934753852179438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 0.79937093469454062096849232708521
y[1] (numeric) = 0.79921762612797863421940059869315
absolute error = 0.00015330856656198674909172839205209
relative error = 0.019178651600657677049230422556995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 0.79839136789303074428359617456935
y[1] (numeric) = 0.79823355736602861489043306900358
absolute error = 0.0001578105270021293931631055657752
relative error = 0.019766061276262821743680502462109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 0.79741200270013617384917351498742
y[1] (numeric) = 0.79724960397558169603313233594859
absolute error = 0.00016239872455447781604117903882526
relative error = 0.020365723616471227622194712968277 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 0.79643284009522202094603142867336
y[1] (numeric) = 0.79626576615873619235106936257649
absolute error = 0.00016707393648582859496206609686514
relative error = 0.020977780934529662037363461116833 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 0.79545388105745080889144179581925
y[1] (numeric) = 0.79528204411856968244671944600135
absolute error = 0.00017183693888112644472234981790059
relative error = 0.021602376073983314304563072065004 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 0.79447512656578149387669957607767
y[1] (numeric) = 0.79429843805913880574390053805873
absolute error = 0.00017668850664268813279903801893431
relative error = 0.022239652411328016222025927746263 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 0.79349657759896848600824819717701
y[1] (numeric) = 0.79331494818547905843115082620714
absolute error = 0.00018162941348942757709737096986951
relative error = 0.022889753858676716756528675970184 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 0.79251823513556067055335101134286
y[1] (numeric) = 0.79233157470360458842624963128058
absolute error = 0.00018666043195608212710138006228032
relative error = 0.023552824866440298345712789068458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 0.79154010015390042939128757377236
y[1] (numeric) = 0.79134831782050798936208665755434
absolute error = 0.00019178233339244002920091621801355
relative error = 0.024229010426022822863681481070055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 0.79056217363212266267105329188374
y[1] (numeric) = 0.79036517774416009359408560923752
absolute error = 0.00019699588796256907696768264621566
relative error = 0.024918456072531295896632920235793 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=4.66
NO POLE
x[1] = 0.212
y[1] (analytic) = 0.78958445654815381067654078755991
y[1] (numeric) = 0.78938215468350976422938916595143
absolute error = 0.00020230186464404644715162160847304
relative error = 0.025621307887500038579928811957317 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 0.7886069498797108759001811071231
y[1] (numeric) = 0.78839924884848368617801328799161
absolute error = 0.00020770103122718972216781913149838
relative error = 0.026337712501629756857197120158966 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 0.78762965460430044532602270531804
y[1] (numeric) = 0.78741646044998615622617980020166
absolute error = 0.00021319415431428909984290511637714
relative error = 0.027067817097541398635865623564935 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 0.78665257169921771292322592014294
y[1] (numeric) = 0.78643378969989887213203718110895
absolute error = 0.00021878199931884079118873903399133
relative error = 0.027811769412544889931957185400108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 0.78567570214154550235095044495269
y[1] (numeric) = 0.78545123681108072074398046158364
absolute error = 0.00022446533046478160696998336905147
relative error = 0.028569717741422841720086412225696 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 0.78469904690815328987561309286506
y[1] (numeric) = 0.78446880199736756514178211468369
absolute error = 0.00023024491078572473383097818137881
relative error = 0.029341810939229319832419495996272 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 0.78372260697569622750149293613085
y[1] (numeric) = 0.78348648547357203080074679553697
absolute error = 0.00023612150212419670074614059387799
relative error = 0.030128198424103770882933528132544 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 0.78274638332061416631566068978145
y[1] (numeric) = 0.78250428745548329077910376708823
absolute error = 0.00024209586513087553655692269321444
relative error = 0.030929030180100197830677852645669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 0.78177037691913068004820899454299
y[1] (numeric) = 0.78152220815986684992885182430024
absolute error = 0.00024816875926383011935717024275171
relative error = 0.031744456760031679437937849910448 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 0.78079458874725208884876003870549
y[1] (numeric) = 0.78054024780446432813027250594649
absolute error = 0.00025434094278776071848753275900268
relative error = 0.032574629288330328526271035397732 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 0.77981901978076648328022674235797
y[1] (numeric) = 0.77955840660799324255032835946407
absolute error = 0.00026061317277324072989838289389618
relative error = 0.033419699463922784585367002922478 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=41.9MB, alloc=4.3MB, time=5.13
x[1] = 0.223
y[1] (analytic) = 0.778843670995242748530803510147
y[1] (numeric) = 0.77857668479014678892516400045025
absolute error = 0.000266986205095959605639509696751
relative error = 0.034279819563121336946617390218507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 0.77786854336602958884516234048672
y[1] (numeric) = 0.77759508257159362186692868428354
absolute error = 0.0002734607944359669782336562031749
relative error = 0.035155142442530775395210916062699 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 0.7768936378682545521758298599428
y[1] (numeric) = 0.77661360017397763419514008302844
absolute error = 0.00028003769427691798068977691436123
relative error = 0.036045821541971065761533226179754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 0.77591895547682305505572063133211
y[1] (numeric) = 0.77563223781991773529280993624147
absolute error = 0.0002867176569053197629106950906359
relative error = 0.03695201088741594870469376015032 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 0.77494449716641740769280186292349
y[1] (numeric) = 0.77465099573300762848755321953469
absolute error = 0.00029350143340977920524864338880686
relative error = 0.037873865093947560578164464547572 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 0.7739702639114958392878644239937
y[1] (numeric) = 0.77366987413781558745790344976861
absolute error = 0.00030038977368025182996097422508518
relative error = 0.038811539368727175949840663942059 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 0.77299625668629152357637484888623
y[1] (numeric) = 0.77268887325988423166505772054095
absolute error = 0.00030738342640729191131712834527641
relative error = 0.039765189513982172036365884790136 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 0.77202247646481160459538278763993
y[1] (numeric) = 0.77170799332573030081027603620715
absolute error = 0.00031448313908130378510675143278303
relative error = 0.04073497193000931600434342306539 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 0.77104892422083622267645813619863
y[1] (numeric) = 0.77072723456284442831816048701472
absolute error = 0.00032168965799179435829764918391035
relative error = 0.04172104361819447678913186612453 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 0.77007560092791754066563185318355
y[1] (numeric) = 0.76974659719969091384604078205332
absolute error = 0.00032900372822662681959107113023007
relative error = 0.042723562184048863785333933744108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 0.76910250755937877037131424320659
y[1] (numeric) = 0.76876608146570749481969363061606
absolute error = 0.00033642609367127555162061259052678
relative error = 0.043742685840261895471882607186908 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 0.7681296450883131992411642587249
y[1] (numeric) = 0.76778568759130511699562443623357
absolute error = 0.0003439574970080822455398224913348
relative error = 0.044778573409770801748850690837637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=4.3MB, time=5.61
x[1] = 0.235
y[1] (analytic) = 0.7671570144875832172688831434866
y[1] (numeric) = 0.76680541580786770405014074108013
absolute error = 0.00035159867971551321874240240646726
relative error = 0.045831384328847064482805232302173 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 0.76618461672981934413190551069257
y[1] (numeric) = 0.76582526634775192619544783165912
absolute error = 0.00035935038206741793645767903344791
relative error = 0.046901278650199801482742563504089 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 0.76521245278741925656096071810253
y[1] (numeric) = 0.76484523944428696782299788965294
absolute error = 0.00036721334313228873796282844958354
relative error = 0.047988417046096199859419486647143 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 0.76424052363254681594247717044265
y[1] (numeric) = 0.76386533533177429417432504456888
absolute error = 0.00037518830077252176815212587376328
relative error = 0.04909296081149910545728810830108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 0.76326883023713109615480194662958
y[1] (numeric) = 0.76288555424548741703959965732644
absolute error = 0.00038327599164367911520228930314576
relative error = 0.050215071867221875790293243807765 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 0.76229737357286541163920791551018
y[1] (numeric) = 0.76190589642167165948413613621228
absolute error = 0.00039147715119375215507177929790223
relative error = 0.051354912763100604660549826568141 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 0.76132615461120634570666026902879
y[1] (numeric) = 0.76092636209754391960308955867546
absolute error = 0.00039979251366242610357071035332775
relative error = 0.05251264668118382739243145308784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 0.76035517432337277908131416597463
y[1] (numeric) = 0.7599469515112924333045773442465
absolute error = 0.00040822281208034577673682172812179
relative error = 0.053688437438939816373918606444266 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 0.75938443368034491868171494273065
y[1] (numeric) = 0.75896766490207653612146319543897
absolute error = 0.00041676877826838256025174729168078
relative error = 0.054882449492481577362225204962003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 0.7584139336528633266406721097428
y[1] (numeric) = 0.75798850251002642405204149482976
absolute error = 0.00042543114283690258863061491304688
relative error = 0.056094847939809657781794345994754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 0.7574436752114279495647781137546
y[1] (numeric) = 0.75700946457624291342986131761367
absolute error = 0.00043421063518503613491679614092848
relative error = 0.057325798524072879019778337703155 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 0.75647365932629714803454260620757
y[1] (numeric) = 0.75603055134279719982293018978841
absolute error = 0.00044310798349994821161241641915869
relative error = 0.058575467636847105507144674240175 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=6.09
NO POLE
x[1] = 0.247
y[1] (analytic) = 0.75550388696748672634611271759229
y[1] (numeric) = 0.75505176305273061596253869274599
absolute error = 0.00045212391475611038357402484629816
relative error = 0.059844022321432164162629314782498 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 0.75453435910476896249554959594889
y[1] (numeric) = 0.75407309995005438870194798542586
absolute error = 0.00046125915471457379360161052303033
relative error = 0.061131630276167028571942745284413 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 0.75356507670767163840663122515975
y[1] (numeric) = 0.75309456227974939500518328532199
absolute error = 0.00047051442792224340144793983775162
relative error = 0.062438459857763383075974577182125 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 0.75259604074547707040315129515061
y[1] (numeric) = 0.75211615028776591696617731953007
absolute error = 0.00047989045771115343697397562053897
relative error = 0.063764680084657682749291090349043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 0.75162725218722113992668365162059
y[1] (numeric) = 0.7511378642210233958585087266709
absolute error = 0.000489387966197744068174924949697
relative error = 0.065110460640381826064029861272466 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 0.75065871200169232450078160745575
y[1] (numeric) = 0.75015970432741018521598135993119
absolute error = 0.00049900767428213928480024752455898
relative error = 0.0664759718769525578544196214453 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 0.74969042115743072894258115154618
y[1] (numeric) = 0.74918167085578330294429141062182
absolute error = 0.00050875030164742599828974092435716
relative error = 0.067861384818279721023645446844777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 0.7487223806227271168227768433228
y[1] (numeric) = 0.7482037640559681824640302405658
absolute error = 0.00051861656675893435874660275700199
relative error = 0.069266871163593476267693465266491 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 0.74775459136562194217493893295701
y[1] (numeric) = 0.74722598417875842288527178029227
absolute error = 0.00052860718686351928966715266473462
relative error = 0.070692603290890609930200163991446 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 0.7467870543539043814551399978256
y[1] (numeric) = 0.74624833147591553821399431842854
absolute error = 0.00053872287798884324114567939705858
relative error = 0.072138754260400050948254272235184 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 0.74581977055511136575285913553355
y[1] (numeric) = 0.74527080620016870559058747584722
absolute error = 0.00054896435494266016227165968633283
relative error = 0.073605497818067718701609779242737 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.3MB, time=6.56
x[1] = 0.258
y[1] (analytic) = 0.74485274093652661325413150250981
y[1] (numeric) = 0.74429340860521451256069612604067
absolute error = 0.00055933233131210069343537646913858
relative error = 0.07509300839906082443692314479574 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 0.74388596646517966195791073494597
y[1] (numeric) = 0.74331613894571670337865399085773
absolute error = 0.00056982751946295857925674408823423
relative error = 0.076601461131291749804482901384735 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 0.74291944810784490264661153563478
y[1] (numeric) = 0.74233899747730592434376060814797
absolute error = 0.00058045063053897830285092748680755
relative error = 0.078131031838961626917512900760615 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 0.74195318683104061211179945608533
y[1] (numeric) = 0.74136198445657946816965633501529
absolute error = 0.00059120237446114394214312107004232
relative error = 0.079681897046123745223559218999444 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 0.74098718360102798663599464814456
y[1] (numeric) = 0.7403851001411010173870510172846
absolute error = 0.00060208345992696924894363085995839
relative error = 0.08125423398026691136377353853082 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 0.74002143938381017573155610324072
y[1] (numeric) = 0.73940834478940038678006292243144
absolute error = 0.00061309459440978895149318080928303
relative error = 0.082848220575918889089141551095316 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 0.73905595514513131613761264028424
y[1] (numeric) = 0.73843171866097326485642549961426
absolute error = 0.00062423648415805128118714066998918
relative error = 0.0844640354782700472029329994557 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 0.73809073185047556607600664521424
y[1] (numeric) = 0.73745522201628095435182049658092
absolute error = 0.00063550983419461172418614863331642
relative error = 0.086101858046817344405930379408248 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 0.73712577046506613976721630616662
y[1] (numeric) = 0.73647885511675011176859692909483
absolute error = 0.00064691534831602799861937707179833
relative error = 0.087761868359028780835386598710485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 0.73616107195386434220722182826113
y[1] (numeric) = 0.73550261822477248594913636413985
absolute error = 0.00065845372909185625808546412127824
relative error = 0.08944424721402844701022914306752 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 0.73519663728156860420628085106048
y[1] (numeric) = 0.73452651160370465568412594351715
absolute error = 0.00067012567786394852215490754333231
relative error = 0.09114917613630230182383120974457 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 0.73423246741261351769057802984597
y[1] (numeric) = 0.73355053551786776635600153953881
absolute error = 0.0006819318947457513345764903071586
relative error = 0.092876837379424812161771092256698 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=57.2MB, alloc=4.3MB, time=7.03
x[1] = 0.27
y[1] (analytic) = 0.73326856331116887126771347897946
y[1] (numeric) = 0.7325746902325472656178243993534
absolute error = 0.00069387307862160564988907962606131
relative error = 0.094627413929806587665462673440602 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 0.73230492594113868605699451178298
y[1] (numeric) = 0.73159897601399263810785559900459
absolute error = 0.0007059499271460479491389127783884
relative error = 0.096401089510463145113425636408722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 0.73134155626616025178549484656383
y[1] (numeric) = 0.73062339312941713920009359262643
absolute error = 0.0007181631367431125854012539373965
relative error = 0.098198048584804937850337955620528 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 0.73037845524960316315084518264563
y[1] (numeric) = 0.72964794184699752779104110621538
absolute error = 0.00073051340260563535980407643024832
relative error = 0.10001847636044878665994000663734 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 0.72941562385456835645171878353456
y[1] (numeric) = 0.72867262243587379812296858919014
absolute error = 0.00074300141869455832875019434442497
relative error = 0.10186255879305084945140446307207 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 0.72845306304388714648697543665472
y[1] (numeric) = 0.72769743516614891064394240045324
absolute error = 0.0007556278777382358430330362014889
relative error = 0.10373048259016126811001487594548 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 0.72749077378012026372442689042862
y[1] (numeric) = 0.72672238030888852190488686890403
absolute error = 0.00076839347123174181954002152459374
relative error = 0.10562243521510063185197491661543 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 0.72652875702555689174018659985692
y[1] (numeric) = 0.72574745813612071349395033131829
absolute error = 0.00078129888943617824623626853863699
relative error = 0.10753860489085839741996679781373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 0.72556701374221370492956634116763
y[1] (numeric) = 0.72477266892083572000844621320591
absolute error = 0.00079434482137798492112012796172342
relative error = 0.10947918060401340746075908829544 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 0.72460554489183390649048198455785
y[1] (numeric) = 0.72379801293698565606464118068297
absolute error = 0.00080753195484825042584080387488354
relative error = 0.11144435210867664943879936383474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 0.72364435143588626668033044154215
y[1] (numeric) = 0.72282349045948424234566335354714
absolute error = 0.00082086097640202433466708799500747
relative error = 0.11343430993045639846038489442865 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 0.72268343433556416134729952995054
y[1] (numeric) = 0.72184910176420653068780453162559
absolute error = 0.000834332571357630659494998324944
relative error = 0.11544924537044588841175450979455 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=7.50
NO POLE
x[1] = 0.282
y[1] (analytic) = 0.72172279455178461073707222518593
y[1] (numeric) = 0.72087484712798862820549134807002
absolute error = 0.00084794742379598253158087711591321
relative error = 0.11748935050923365685135722598673 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 0.72076243304518731857588649095688
y[1] (numeric) = 0.71990072682862742045520122460485
absolute error = 0.00086170621655989812068526635202495
relative error = 0.11955481821093671014169913357147 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 0.71980235077613371143091160634557
y[1] (numeric) = 0.71892674114488029363859996478955
absolute error = 0.00087560963125341779231164155602092
relative error = 0.12164584212725665635962109239562 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 0.71884254870470597834890162875478
y[1] (numeric) = 0.71795289035646485584517878213418
absolute error = 0.00088965834824112250372284662060286
relative error = 0.12376261670155895458568827828788 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 0.71788302779070611077408635400021
y[1] (numeric) = 0.7169791747440586573346695204081
absolute error = 0.0009038530466474534394168335921119
relative error = 0.12590533717297543024365159734618 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 0.71692378899365494274625985557732
y[1] (numeric) = 0.7160055945892989098595177837032
absolute error = 0.00091819440435603288674207187412211
relative error = 0.12807419958053020723974413069135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 0.71596483327279119138002640493412
y[1] (numeric) = 0.71503215017478220502769465375518
absolute error = 0.00093268309800898635233175117894534
relative error = 0.13026940076728920873897750331917 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 0.71500616158707049762616329342395
y[1] (numeric) = 0.71405884178406423170612863168759
absolute error = 0.00094731980300626592003466173635417
relative error = 0.1324911383845333795116784984627 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 0.71404777489516446731605979449563
y[1] (numeric) = 0.71308566970165949246504040072337
absolute error = 0.0009621051935049748510193937722559
relative error = 0.13473961089595578388833119134607 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 0.71308967415545971249019122160201
y[1] (numeric) = 0.71211263421304101906346396550517
absolute error = 0.00097703994241869342672725609683477
relative error = 0.1370150175818827344744409025309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 0.71213186032605689301158675327299
y[1] (numeric) = 0.71113973560464008697623868247992
absolute error = 0.00099212472141680603534807079306403
relative error = 0.13931755854351910789969064931466 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=64.8MB, alloc=4.4MB, time=7.97
x[1] = 0.293
y[1] (analytic) = 0.71117433436476975846524941180534
y[1] (numeric) = 0.71016697416384592896275765433162
absolute error = 0.0010073602009238295024917574737172
relative error = 0.14164743470721800500719651835851 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 0.71021709722912419034448629606947
y[1] (numeric) = 0.70919435017900544767775891969015
absolute error = 0.0010227470501187426667273763793214
relative error = 0.1440048478287749140292642524463 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 0.70926014987635724452510688202316
y[1] (numeric) = 0.70822186393942292732444682730102
absolute error = 0.001038285936934317200660054722142
relative error = 0.14639000049774653644578484925323 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 0.70830349326341619402844691665405
y[1] (numeric) = 0.70724951573535974435023194151054
absolute error = 0.0010539775280564496782149751435056
relative error = 0.14880309614179443638036237993684 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 0.70734712834695757207417514224732
y[1] (numeric) = 0.7062773058580340771853787833025
absolute error = 0.0010698224889234948887963589448132
relative error = 0.15124433903105367555752358726829 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 0.70639105608334621542383979809208
y[1] (numeric) = 0.70530523459962061502485166821438
absolute error = 0.0010858214837256003989881298777037
relative error = 0.1537139342825265970219979291492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 0.70543527742865430801611155600021
y[1] (numeric) = 0.70433330225325026565364985926296
absolute error = 0.0011019751754040423624616967372482
relative error = 0.15621208786450192200816118922304 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 0.70447979333866042489467925431497
y[1] (numeric) = 0.70336150911300986231592420951993
absolute error = 0.0011182842256505625787550447950463
relative error = 0.1587390066009993255443889687771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 0.70352460476884857642975450243418
y[1] (numeric) = 0.7023898554739418696281684251963
absolute error = 0.0011347492949067068015860772378859
relative error = 0.16129489817623965758335248970198 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 0.70256971267440725283414093426342
y[1] (numeric) = 0.70141834163204408853677903601993
absolute error = 0.001151371042363164297361898243485
relative error = 0.16387997113914097766529317125984 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 0.7016151180102284689748235944506
y[1] (numeric) = 0.70044696788426936032027911532161
absolute error = 0.0011681501259591086545444791289955
relative error = 0.16649443490784057234712020439005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 0.70066082173090680948103364573289
y[1] (numeric) = 0.69947573452852526963650174758122
absolute error = 0.0011850872023815398445318981516695
relative error = 0.16913849977424312586587347156656 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.4MB, time=8.45
x[1] = 0.305
y[1] (analytic) = 0.69970682479073847414974328925156
y[1] (numeric) = 0.69850464186367384661503019622594
absolute error = 0.0012021829270646275347130930256217
relative error = 0.17181237690859521575077011643277 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 0.69875312814372032364954549226047
y[1] (numeric) = 0.69753369018953126799519267921526
absolute error = 0.0012194379541890556543528130452097
relative error = 0.17451627836408630635379516617271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 0.69779973274354892552387281926885
y[1] (numeric) = 0.69656287980686755730991061439339
absolute error = 0.0012368529366813682139622048754616
relative error = 0.17725041708147641453469401216821 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 0.69684663954361960049450936332003
y[1] (numeric) = 0.69559221101740628411570015073558
absolute error = 0.0012544285262133163788092125844502
relative error = 0.18001500689375062301236728188655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 0.6958938494970254690663494738148
y[1] (numeric) = 0.69462168412382426226912775546199
absolute error = 0.0012721653732012067972217183528021
relative error = 0.1828102625308006181811475766563 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 0.69494136355655649843435667604104
y[1] (numeric) = 0.69365129942975124725002158053814
absolute error = 0.0012900641268052511843350955028964
relative error = 0.18563639962413343048734447317667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 0.69398918267469854969367587537158
y[1] (numeric) = 0.69268105723976963253174128532558
absolute error = 0.0013081254349289171619345900459977
relative error = 0.18849363471160755676887174522243 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 0.69303730780363242535385163593833
y[1] (numeric) = 0.69171095785941414499880994508748
absolute error = 0.0013263499442182803550416908508453
relative error = 0.19138218524219664527881250608469 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 0.69208573989523291715810501948532
y[1] (numeric) = 0.69074100159517153941221262769198
absolute error = 0.0013447383000613777458923917933375
relative error = 0.19430226958078092544252835730482 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 0.69113447990106785420862116504429
y[1] (numeric) = 0.68977118875448029192266717318913
absolute error = 0.0013632911465875622859539918551592
relative error = 0.19725410701296656573747302561979 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 0.69018352877239715139879948406602
y[1] (numeric) = 0.68880151964573029263217366296524
absolute error = 0.0013820091266668587666258211007738
relative error = 0.2002379177499331444353256726607 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 0.68923288746017185815341803867781
y[1] (numeric) = 0.68783199457826253720415001689943
absolute error = 0.0014008928819093209492680217783728
relative error = 0.20325392293330941930751129995868 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=8.92
NO POLE
x[1] = 0.317
y[1] (analytic) = 0.6882825569150332074776633628236
y[1] (numeric) = 0.68686261386236881752246210836117
absolute error = 0.0014199430526643899552012544624319
relative error = 0.20630234464007758376772361835104 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 0.68733253808731166531597667717754
y[1] (numeric) = 0.68589337780929141139965773799284
absolute error = 0.0014391602780202539163189391846978
relative error = 0.20938340588750619830880853300904 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 0.6863828319270259802216671389056
y[1] (numeric) = 0.68492428673122277133471475801759
absolute error = 0.0014585451958032088869523808880045
relative error = 0.21249733063811198748640410404363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 0.68543343938388223333824245658285
y[1] (numeric) = 0.68395534094130521232061458929832
absolute error = 0.0014780984425770210176278672845342
relative error = 0.21564434380465069410816654309376 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 0.68448436140727288869340688885654
y[1] (numeric) = 0.68298654075363059870205332354826
absolute error = 0.0014978206536422899913535653082741
relative error = 0.21882467125513718370534354791996 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 0.68353559894627584380667633277783
y[1] (numeric) = 0.6820178864832400300836035529561
absolute error = 0.0015177124630358137230727798217247
relative error = 0.22203853981789499379298910398502 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 0.68258715294965348061155989410811
y[1] (numeric) = 0.68104937844612352628864101903745
absolute error = 0.0015377745035299543229188750706601
relative error = 0.22528617728663552386635184368263 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 0.68163902436585171669325701733906
y[1] (numeric) = 0.68008101695921971136935112175988
absolute error = 0.0015580074066320053239058955791821
relative error = 0.22856781242556706353401721546587 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 0.68069121414299905684281893765035
y[1] (numeric) = 0.67911280234041549666813127890864
absolute error = 0.0015784118025835601746876587417156
relative error = 0.2318836749745338576533481683614 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 0.67974372322890564492872290056454
y[1] (numeric) = 0.67814473490854576293070607426431
absolute error = 0.0015989883203598819980168263002281
relative error = 0.23523399565418540881075693135637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 0.67879655257106231608680727764583
y[1] (numeric) = 0.67717681498339304147127308145075
absolute error = 0.0016197375876692746155341961950808
relative error = 0.23861900617117621897845993939852 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=76.2MB, alloc=4.4MB, time=9.39
x[1] = 0.328
y[1] (analytic) = 0.67784970311663964922951538822866
y[1] (numeric) = 0.67620904288568719438999819828086
absolute error = 0.001640660230952454839517189947806
relative error = 0.24203893922339617368072826520399 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 0.67690317581248701987539551785335
y[1] (numeric) = 0.67524141893710509384318027407834
absolute error = 0.0016617568753819260322152437750127
relative error = 0.24549402850523177351635736635396 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 0.67595697160513165329980430382978
y[1] (numeric) = 0.67427394346027030036640575978395
absolute error = 0.0016830281448613529333985440458273
relative error = 0.2489845087128584194102539399523 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 0.67501109144077767800776033714693
y[1] (numeric) = 0.67330661677875274025101505766489
absolute error = 0.0017044746620249377567452794820361
relative error = 0.25251061554956395950578667560045 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 0.67406553626530517952989450779567
y[1] (numeric) = 0.67233943921706838197420319413399
absolute error = 0.0017260970482367975556913136616849
relative error = 0.25607258573110370716098529994661 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 0.67312030702426925454244329747574
y[1] (numeric) = 0.67137241110067891168307838555117
absolute error = 0.0017478959235903428593649119245766
relative error = 0.25967065699108714107591321778205 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 0.67217540466289906531223089961467
y[1] (numeric) = 0.67040553275599140773300301292151
absolute error = 0.0017698719069076575792278866931614
relative error = 0.26330506808639650015569910954662 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 0.67123083012609689446758572163781
y[1] (numeric) = 0.66943880451035801428054246712181
absolute error = 0.001792025615738880187043254515998
relative error = 0.26697605880263748730390901789712 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 0.67028658435843720009613649849422
y[1] (numeric) = 0.66847222669207561393134827167966
absolute error = 0.0018143576663615861647882268145607
relative error = 0.27068386995962229794429087434423 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 0.66934266830416567117043291956346
y[1] (numeric) = 0.66750579963038549944330283519452
absolute error = 0.0018368686737801717271300843689396
relative error = 0.27442874341688519068554737375035 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 0.66839908290719828330233534324402
y[1] (numeric) = 0.66653952365547304448525413022882
absolute error = 0.0018595592517252388170812130152029
relative error = 0.27821092207923081917381107023134 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 0.66745582911112035482711784475499
y[1] (numeric) = 0.66557339909846737345166953990686
absolute error = 0.0018824300126529813754483048481348
relative error = 0.28203064990231554582102920347721 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=80.1MB, alloc=4.4MB, time=9.87
x[1] = 0.34
y[1] (analytic) = 0.66651290785918560321822851296921
y[1] (numeric) = 0.66460742629144103033353905754021
absolute error = 0.0019054815677445728846894554290036
relative error = 0.28588817189826195975463793340729 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 0.66557032009431520183365058143904
y[1] (numeric) = 0.66364160556740964664585896834881
absolute error = 0.0019287145269055551877916130902258
relative error = 0.2897837341413068230048404429298 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 0.66462806675909683699480764717492
y[1] (numeric) = 0.66267593726033160841202808576637
absolute error = 0.0019521294987652285827795614085432
relative error = 0.29371758377348267063062607174068 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 0.66368614879578376539895589819304
y[1] (numeric) = 0.66171042170510772220548955790614
absolute error = 0.0019757270906760431934663402869075
relative error = 0.29768996901033329218450481892798 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 0.66274456714629387186600593736127
y[1] (numeric) = 0.66074505923758088024895220251734
absolute error = 0.0019995079087129916170537348439298
relative error = 0.30170113914666332362891100431444 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 0.66180332275220872742071645564298
y[1] (numeric) = 0.65977985019453572457152627118318
absolute error = 0.0020234725576730028491901844597952
relative error = 0.30575134456232218054448068242843 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 0.66086241655477264771120167246664
y[1] (numeric) = 0.65881479491369831022410948559642
absolute error = 0.0020476216410743374870921868702265
relative error = 0.309840836728022565212059915607 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 0.65992184949489175176469412463536
y[1] (numeric) = 0.65784989373373576755336013049867
absolute error = 0.0020719557611559842113339941366931
relative error = 0.31396986821119378190648688706722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 0.65898162251313302108150404793491
y[1] (numeric) = 0.65688514699425596353459492928204
absolute error = 0.0020964755188770575469091186528758
relative error = 0.31813869268187009651104303403018 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 0.65804173654972335906811625740272
y[1] (numeric) = 0.65592055503580716216395036932702
absolute error = 0.0021211815139161969041658880756959
relative error = 0.32234756491861437834712119258919 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 0.65710219254454865081036509308237
y[1] (numeric) = 0.6549561181998776839101470848871
absolute error = 0.0021460743446709669002180081952726
relative error = 0.32659674081447726391424779592965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 0.65616299143715282318762765801042
y[1] (numeric) = 0.65399183682889556422619784572715
absolute error = 0.0021711546082572589614298122832727
relative error = 0.33088647738299208405125843462714 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=10.34
NO POLE
x[1] = 0.352
y[1] (analytic) = 0.65522413416673690532897523416392
y[1] (numeric) = 0.65302771126622821112140063977938
absolute error = 0.0021964229005086942075745943845379
relative error = 0.33521703276420579786029991851029 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 0.65428562167215808941222242013895
y[1] (numeric) = 0.65206374185618206179395927779505
absolute error = 0.0022218798159760276182631423438957
relative error = 0.33958866623074617858155710272706 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 0.65334745489192879180681319143277
y[1] (numeric) = 0.6510999289440022383245748873428
absolute error = 0.0022475259479265534822383040899677
relative error = 0.34400163819392549846832028220395 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 0.65240963476421571456148274036527
y[1] (numeric) = 0.6501362728758722024313526025334
absolute error = 0.0022733618883435121301301378318655
relative error = 0.34845621020988096158936145701457 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 0.65147216222683890723763360789966
y[1] (numeric) = 0.64917277399891340928636869453547
absolute error = 0.0022993882279254979512649133641811
relative error = 0.35295264498575213537871919231784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 0.65053503821727082908936427390812
y[1] (numeric) = 0.64820943266118496039424432628618
absolute error = 0.0023256055560858686951199476219432
relative error = 0.35749120638589563366204754965693 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 0.64959826367263541159108802577568
y[1] (numeric) = 0.64724624921168325553307305279421
absolute error = 0.0023520144609521560580149729814746
relative error = 0.3620721594381373058138115194842 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 0.64866183952970712131367957764527
y[1] (numeric) = 0.6462832240003416437580501260786
absolute error = 0.0023786155293654775556294515666679
relative error = 0.3666957703400621886409578803606 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 0.64772576672491002315008656407927
y[1] (numeric) = 0.64532035737803007346815260108492
absolute error = 0.0024054093468799496819339629943527
relative error = 0.37136230646534247954640628157206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 0.64679004619431684389134268244803
y[1] (numeric) = 0.64435764969655474153622017586957
absolute error = 0.0024323964977621023551225065784644
relative error = 0.37607203637010379149994193294685 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 0.64585467887364803615391890795416
y[1] (numeric) = 0.64339510130865774150278763594224
absolute error = 0.0024595775649902946511312720119144
relative error = 0.3808252297993299523350014517134 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=87.7MB, alloc=4.4MB, time=10.82
x[1] = 0.363
y[1] (analytic) = 0.64491966569827084265934885386328
y[1] (numeric) = 0.64243271256801671083402070890458
absolute error = 0.0024869531302541318253281449587046
relative error = 0.38562215769330661289758156439366 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 0.64398500760319836086706399723811
y[1] (numeric) = 0.64147048382924447724410807141992
absolute error = 0.0025145237739538836229559258181969
relative error = 0.39046309219410393059822245166263 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 0.64305070552308860796137413726246
y[1] (numeric) = 0.64050841544788870408246318609261
absolute error = 0.0025422900751999038789109511698462
relative error = 0.39534830665209859695988108907895 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 0.64211676039224358619352809909695
y[1] (numeric) = 0.63954650778043153478609058102554
absolute error = 0.0025702526118120514074375180714079
relative error = 0.4002780756325354798136741006092 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 0.64118317314460834857978934112779
y[1] (numeric) = 0.63858476118428923639747211965986
absolute error = 0.0025984119603191121823172214679371
relative error = 0.40525267492212915287109513706936 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 0.64024994471377006495646076745515
y[1] (numeric) = 0.63762317601781184214832974298106
absolute error = 0.0026267686959582228081310244740901
relative error = 0.41027238153570558749556097583642 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 0.63931707603295708839279269051843
y[1] (numeric) = 0.63666175264028279310962210029881
absolute error = 0.0026553233926742952831705902196134
relative error = 0.41533747372288428360817741279276 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 0.63838456803503802196270753087285
y[1] (numeric) = 0.63570049141191857890813341857409
absolute error = 0.0026840766231194430545741122987534
relative error = 0.42044823097480111879260624530425 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 0.63745242165252078587627448231464
y[1] (numeric) = 0.63473939269386837751001389367471
absolute error = 0.0027130289586524083662605886399255
relative error = 0.42560493403087219681202556865908 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 0.63652063781755168497186701080265
y[1] (numeric) = 0.633778456848213694071631819989
absolute error = 0.0027421809693379909002351908136495
relative error = 0.43080786488559897891757626850607 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 0.63558921746191447656993569494098
y[1] (numeric) = 0.63281768423796799885809860751521
absolute error = 0.0027715332239464777118370874257684
relative error = 0.43605730679541498351254874590258 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 0.6346581615170294386893285541723
y[1] (numeric) = 0.63185707522707636422982876787168
absolute error = 0.0028010862899530744594997863006205
relative error = 0.44135354428557434194005805273237 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=91.5MB, alloc=4.4MB, time=11.30
x[1] = 0.375
y[1] (analytic) = 0.63372747091395243862709064828374
y[1] (numeric) = 0.63089663018041510069749788263731
absolute error = 0.0028308407335373379295927656464275
relative error = 0.44669686315708250038425699133089 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 0.63279714658337400190267436834815
y[1] (numeric) = 0.62993634946379139204576249903417
absolute error = 0.0028607971195826098569118693139752
relative error = 0.45208755049366936011642136504731 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 0.63186718945561838156749147481296
y[1] (numeric) = 0.62897623344394292952610682920194
absolute error = 0.0028909560116754520413846456110121
relative error = 0.45752589466880515057768727165199 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 0.6309376004606426278807375731069
y[1] (numeric) = 0.62801628248853754511918206018694
absolute error = 0.0029213179721050827615555129199519
relative error = 0.46301218535275933207000673779022 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 0.63000838052803565835241935086267
y[1] (numeric) = 0.62705649696617284386700501227592
absolute error = 0.0029518835618628144854143385867504
relative error = 0.46854671351970282712619656227676 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 0.6290795305870173281545145336508
y[1] (numeric) = 0.62609687724637583527538381344528
absolute error = 0.002982653340641492879130720205518
relative error = 0.47412977145485388194896928471569 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 0.62815105156643750090119414798726
y[1] (numeric) = 0.62513742369960256378693918746942
absolute error = 0.0030136278668349371142549605178401
relative error = 0.47976165276166786164773991360305 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 0.6272229443947751197990363113152
y[1] (numeric) = 0.62417813669723773832509088263601
absolute error = 0.0030448076975373814739454286791876
relative error = 0.48544265236907128536098451943244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 0.62629521000013727916816039866944
y[1] (numeric) = 0.62321901661159436090937969705091
absolute error = 0.0030761933885429182587807016185235
relative error = 0.49117306653874040973117602387985 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 0.62536784931025829633521006481245
y[1] (numeric) = 0.62226006381591335434249648517991
absolute error = 0.0031077854943449419927135796325409
relative error = 0.49695319287242467159902943341735 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 0.6244408632524987838991132287812
y[1] (numeric) = 0.621301278684363188969390458567
absolute error = 0.0031395845681355949297227702141991
relative error = 0.50278333031931530320414627072031 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 0.62351425275384472237054675500772
y[1] (numeric) = 0.62034266159203950850883002159005
absolute error = 0.0031715911618052138617167334176674
relative error = 0.50866377918345943562035092624771 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=11.79
NO POLE
x[1] = 0.387
y[1] (analytic) = 0.62258801874090653318603319147135
y[1] (numeric) = 0.61938421291496475495779031066162
absolute error = 0.0032038058259417782282428808097316
relative error = 0.51459484113122000861625696387675 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 0.62166216213991815209759655070879
y[1] (numeric) = 0.61842593303008779256904253245631
absolute error = 0.0032362291098303595285540182524724
relative error = 0.52057681919878180761508797143386 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 0.62073668387673610293890374394874
y[1] (numeric) = 0.61746782231528353090232112354385
absolute error = 0.0032688615614525720365826204048927
relative error = 0.52661001779970395093270629936571 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 0.61981158487683857176881790215284
y[1] (numeric) = 0.6165098811493525469494456802294
absolute error = 0.0033017037274860248193722219234431
relative error = 0.53269474273251915299937699841819 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 0.61888686606532448139328944033205
y[1] (numeric) = 0.61555210991202070633377553344766
absolute error = 0.0033347561533037750595139068843911
relative error = 0.53883130118838009181921856269045 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 0.61796252836691256626651034317064
y[1] (numeric) = 0.61459450898393878358437576922465
absolute error = 0.0033680193829737826821345739459874
relative error = 0.54502000175875321149177393666492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 0.6170385727059404477722567707261
y[1] (numeric) = 0.61363707874668208148527442050938
absolute error = 0.0034014939592583662869823502167162
relative error = 0.5512611544431602932128840224777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 0.61611500000636370988634470278558
y[1] (numeric) = 0.61267981958275004950019148108671
absolute error = 0.0034351804236136603861532216988774
relative error = 0.55755507065696813078727315922042 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 0.61519181119175497522112295934603
y[1] (numeric) = 0.61172273187556590127312131681039
absolute error = 0.0034690793161890739480016425356387
relative error = 0.56390206323922664932317545982221 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 0.61426900718530298145292755264793
y[1] (numeric) = 0.6107658160094762312051509735421
absolute error = 0.0035031911758267502477765791058289
relative error = 0.57030244646055580844015841583484 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 0.61334658890981165813342094323165
y[1] (numeric) = 0.60980907236975063010789780494623
absolute error = 0.0035375165400610280255231382854141
relative error = 0.57675653603108163400525398622003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 0.61242455728769920388573938859978
y[1] (numeric) = 0.60885250134258129993395076667065
absolute error = 0.0035720559451179039517886219291259
relative error = 0.58326464910842172511980790527735 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=12.25
NO POLE
x[1] = 0.399
y[1] (analytic) = 0.6115029132409971639863711882616
y[1] (numeric) = 0.60789610331508266758470064644021
absolute error = 0.003606809925914496401670541821393
relative error = 0.58982710430572058581032789707312 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 0.61058165769134950833368824320429
y[1] (numeric) = 0.60693987867529099779594542220042
absolute error = 0.0036417790160585105377428210038742
relative error = 0.596444221699735133631275902402 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 0.60966079156001170980405296118265
y[1] (numeric) = 0.60598382781216400510165786267383
absolute error = 0.0036769637478477047023950985088172
relative error = 0.60311632283897074016643568204119 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 0.60874031576784982299642215164349
y[1] (numeric) = 0.60502795111558046487630340652902
absolute error = 0.0037123646522693581201187451144693
relative error = 0.60984373075186816121842499510785 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 0.60782023123533956336636916560423
y[1] (numeric) = 0.60407224897633982345609727781206
absolute error = 0.0037479822589997399102718877921668
relative error = 0.6166267699550417173033430942546 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 0.60690053888256538675044514638653
y[1] (numeric) = 0.60311672178616180733959071635069
absolute error = 0.0037838170964035794108544300358304
relative error = 0.62346576646156908791968408002679 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 0.60598123962921956928179986676729
y[1] (numeric) = 0.60216136993768603146797712251258
absolute error = 0.0038198696915335378138227442547051
relative error = 0.63036104778933308593774171126939 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 0.60506233439460128769798223684934
y[1] (numeric) = 0.60120619382447160658550983597871
absolute error = 0.0038561405701296811124724008706236
relative error = 0.63731294296941578135802104745384 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 0.60414382409761570004184017477465
y[1] (numeric) = 0.60025119384099674568042418808151
absolute error = 0.0038926302566189543614159866931409
relative error = 0.64432178255454534661489877471517 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 0.60322570965677302675643913930379
y[1] (numeric) = 0.59929637038265836950675738675287
absolute error = 0.0039293392741146572496817525509129
relative error = 0.65138789862759599855518174313082 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 0.60230799199018763217491822926617
y[1] (numeric) = 0.5983417238457717111874607122292
absolute error = 0.0039662681444159209874575170369654
relative error = 0.65851162481014141520054918021336 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=102.9MB, alloc=4.4MB, time=12.73
x[1] = 0.41
y[1] (analytic) = 0.60139067201557710640620235994886
y[1] (numeric) = 0.59738725462756991989919942036849
absolute error = 0.0040034173880071865070029395803614
relative error = 0.66569329627106200840837789457957 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 0.6004737506502613476174886306349
y[1] (numeric) = 0.5964329631262036636392366687464
absolute error = 0.0040407875240576839782519618885062
relative error = 0.67293324973520643657739381145478 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 0.59955722881116164471442460072855
y[1] (numeric) = 0.59547884974074073107479869861428
absolute error = 0.0040783790704209136396259021142778
relative error = 0.68023182349210774460322230222382 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 0.59864110741479976041989579421255
y[1] (numeric) = 0.59452491487116563247531942332092
absolute error = 0.0041161925436341279445763708916236
relative error = 0.6875893574047545213744815748474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 0.59772538737729701475233935357361
y[1] (numeric) = 0.59357115891837919972796349092006
absolute error = 0.0041542284589178150243758626535529
relative error = 0.69500619291841746821283817928792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 0.5968100696143733689045003648061
y[1] (numeric) = 0.59261758228419818543682780540721
absolute error = 0.0041924873301751834676725593988884
relative error = 0.70248267306953177480068448905505 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 0.59589515504134650952354697466115
y[1] (numeric) = 0.59166418537135486110622240735111
absolute error = 0.0042309696699916484173245673100396
relative error = 0.71001914249463570230807065293589 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 0.59498064457313093339346001994986
y[1] (numeric) = 0.59071096858349661440843253060513
absolute error = 0.0042696759896343189850274893447343
relative error = 0.71761594743936577662649657724224 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 0.59406653912423703252061248643465
y[1] (numeric) = 0.58975793232518554553636456730323
absolute error = 0.0043086067990514869842479191314216
relative error = 0.72527343576750899784141443872355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 0.59315283960877017962345371165307
y[1] (numeric) = 0.58880507700189806264147958846083
absolute error = 0.0043477626068721169819741231922464
relative error = 0.73299195697011247532808334713907 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 0.59223954694042981402721284191366
y[1] (numeric) = 0.58785240302002447635741898221324
absolute error = 0.0043871439204053376697938597004167
relative error = 0.74077186217465090113703227779895 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 0.59132666203250852796453564868418
y[1] (numeric) = 0.58689991078686859340972768603241
absolute error = 0.0044267512456399345548079626517613
relative error = 0.748613504154252277646105412714 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.4MB, time=13.20
x[1] = 0.422
y[1] (analytic) = 0.59041418579789115328296840365935
y[1] (numeric) = 0.58594760071064730931208140316473
absolute error = 0.004466585087243843970887000494615
relative error = 0.75651723733698231879616866350626 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 0.58950211914905384856020210494802
y[1] (numeric) = 0.58499547320049020014942510702881
absolute error = 0.0045066459485636484107769979192103
relative error = 0.76448341781518794759733349767738 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 0.58859046299806318662798993905953
y[1] (numeric) = 0.58404352866643911344843105040073
absolute error = 0.004546934331624073179558888658795
relative error = 0.77251240335490031599229338290271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 0.58767921825657524250565045469569
y[1] (numeric) = 0.58309176751944775813568540889461
absolute error = 0.0045874507371274843699650458010796
relative error = 0.7806045534052977765933614001466 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 0.58676838583583468174406851476933
y[1] (numeric) = 0.58214019017138129358401360051768
absolute error = 0.0046281956644533881600549142516478
relative error = 0.7887602291082292392703401569645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 0.58585796664667384918110568257234
y[1] (numeric) = 0.58118879703501591774735523494037
absolute error = 0.0046691696116579314337504476319725
relative error = 0.79697979330779834905774549736661 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 0.58494796159951185810933128660698
y[1] (numeric) = 0.58023758852403845438460055757199
absolute error = 0.0047103730754734037247307290349858
relative error = 0.80526361056000892537244526877093 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 0.58403837160435367985698499627348
y[1] (numeric) = 0.5792865650530459393728011645714
absolute error = 0.004751806551307740484183831702077
relative error = 0.81361204714247210608676839582315 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 0.58312919757078923378308132737543
y[1] (numeric) = 0.57833572703754520611016867554717
absolute error = 0.0047934705332440276729126518282645
relative error = 0.82202547106417564358789579940769 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 0.58222044040799247768756608226273
y[1] (numeric) = 0.5773850748939524700092759609143
absolute error = 0.0048353655140400076782901213484235
relative error = 0.83050425207531580357217464691507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 0.58131210102472049863743431437966
y[1] (numeric) = 0.57643460903959291208087643067148
absolute error = 0.0048774919851275865565578837081847
relative error = 0.83904876167719232097321571028406 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 0.58040418032931260420971899102467
y[1] (numeric) = 0.57548432989270026160875780074491
absolute error = 0.0049198504366123426009611902797634
relative error = 0.84765937313216687110555828702708 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=13.67
NO POLE
x[1] = 0.434
y[1] (analytic) = 0.57949667922968941415225911125708
y[1] (numeric) = 0.57453423787241637791604766201021
absolute error = 0.0049624413572730362362114492468712
relative error = 0.8563364614736855178216396527742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 0.57858959863335195246315561810729
y[1] (numeric) = 0.57358433339879083122338908565198
absolute error = 0.0050052652345611212397665324553191
relative error = 0.8650804035163656042291112484615 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 0.5776829394473807398898230255586
y[1] (numeric) = 0.57263461689278048259940540665032
absolute error = 0.0050483225546002572904176189082728
relative error = 0.87389157786614755529853012783497 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 0.57677670257843488684854426117356
y[1] (numeric) = 0.57168508877624906300387423489486
absolute error = 0.0050916138021858238446700262786966
relative error = 0.88277036493051206550845348853876 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 0.57587088893275118676543580473445
y[1] (numeric) = 0.57073574947196675142403165071681
absolute error = 0.0051351394607844353414041540176441
relative error = 0.89171714692876314852631183104444 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 0.57496549941614320983972978185704
y[1] (numeric) = 0.56978659940360975210442844849998
absolute error = 0.0051789000125334577353013333570518
relative error = 0.90073230790237752980947148499135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 0.57406053493400039723027924922008
y[1] (numeric) = 0.56883763899575987087076119847918
absolute error = 0.0052228959382405263595180507408987
relative error = 0.90981623372542086693196260754062 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 0.57315599639128715566619248482993
y[1] (numeric) = 0.5678888686739040905481018028596
absolute error = 0.0052671277173830651180906819703285
relative error = 0.91896931211503128639879067534262 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 0.57225188469254195248250167261022
y[1] (numeric) = 0.56694028886443414547395012799229
absolute error = 0.0053115958281078070085515446179337
relative error = 0.92819193264197072970191807269904 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 0.57134820074187641108177094557285
y[1] (numeric) = 0.56599189999464609510653519951766
absolute error = 0.0053563007472303159752357460551934
relative error = 0.93748448674124460540025150871427 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 0.57044494544297440682254832588658
y[1] (numeric) = 0.56504370249273989672879135214021
absolute error = 0.0054012429502345100937569737463699
relative error = 0.94684736772279024807065837816267 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=114.4MB, alloc=4.4MB, time=14.14
x[1] = 0.445
y[1] (analytic) = 0.56954211969909116333556567331613
y[1] (numeric) = 0.56409569678781897724843663002279
absolute error = 0.0054464229112721860871290432933398
relative error = 0.95628097078223468907852237872365 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 0.56863972441305234926859032575643
y[1] (numeric) = 0.56314788330988980409458163768624
absolute error = 0.0054918411031625451740086880701889
relative error = 0.96578569301172224825500118233857 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 0.56773776048725317546083168693519
y[1] (numeric) = 0.56220026248986145521129794476993
absolute error = 0.0055374979973917202495337421652663
relative error = 0.975361933410812459744336154496 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 0.56683622882365749254780558680187
y[1] (numeric) = 0.56125283475954518814857605104875
absolute error = 0.0055833940641123043992295357531158
relative error = 0.98501009289744884949865944487546 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 0.56593513032379688899755880966357
y[1] (numeric) = 0.56030560055165400825110382071297
absolute error = 0.0056295297721428807464549889505965
relative error = 0.99473057431899908615012470428506 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 0.5650344658887697895791557537681
y[1] (numeric) = 0.55935856029980223594529719709618
absolute error = 0.0056759055889675536338585566719206
relative error = 1.0045237824633670312812357776443 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 0.56413423641924055426432875377253
y[1] (numeric) = 0.55841171443850507312501591078494
absolute error = 0.0057225219807354811393128429875957
relative error = 1.0143901240701772194443486834699 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 0.56323444281543857756319316437161
y[1] (numeric) = 0.55746506340317816863639779535791
absolute error = 0.0057693794122604089267953690136985
relative error = 1.0243300078420323026508659092812 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 0.56233508597715738829492786929617
y[1] (numeric) = 0.5565186076301371828622462258843
absolute error = 0.0058164783470202054326816434118678
relative error = 1.0343438444558439984600226609569 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 0.56143616680375374979432144492579
y[1] (numeric) = 0.55557234755659735140640609575758
absolute error = 0.0058638192471563983879153491682121
relative error = 1.0444320465742380852467806226503 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 0.56053768619414676055508377189468
y[1] (numeric) = 0.55462628362067304787856464745236
absolute error = 0.0059114025734737126765191244423197
relative error = 1.0545950288570339927185987721376 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 0.55963964504681695531082245130418
y[1] (numeric) = 0.5536804162613773457799143723671
absolute error = 0.0059592287854396095309080789370814
relative error = 1.0648332079727995402821500047133 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=118.2MB, alloc=4.4MB, time=14.62
x[1] = 0.457
y[1] (analytic) = 0.55874204425980540655458294449053
y[1] (numeric) = 0.55273474591862157949011609405313
absolute error = 0.0060072983411838270644668504374067
relative error = 1.0751470026104813804338083396025 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 0.55784488473071282649785091673299
y[1] (numeric) = 0.5517892730332149043560012478305
absolute error = 0.0060556116974979221418496689024902
relative error = 1.0855368334911117089623604037757 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 0.55694816735669866946991482582499
y[1] (numeric) = 0.55084399804686385588245326805161
absolute error = 0.0061041693098348135874615577733842
relative error = 1.0960031233795918084093173444073 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 0.5560518930344802347584863560711
y[1] (numeric) = 0.54989892140217190802590889209449
absolute error = 0.0061529716323083267325774639766126
relative error = 1.1065462970965529959318445500902 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 0.55515606266033176989247585701442
y[1] (numeric) = 0.54895404354263903059092108754768
absolute error = 0.0062020191176927393015547694667397
relative error = 1.1171667815302955514561164556172 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 0.55426067713008357436781950404435
y[1] (numeric) = 0.54800936491266124573022620598681
absolute error = 0.0062513122174223286375932980575416
relative error = 1.1278650056488062067952768702986 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 0.55336573733912110381725445498295
y[1] (numeric) = 0.54706488595753018354875886323892
absolute error = 0.0063008513815909202684955917440394
relative error = 1.1386414005118547812365810773333 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 0.55247124418238407462493783279988
y[1] (numeric) = 0.54612060712343263681205894208238
absolute error = 0.0063506370589514378128788907175018
relative error = 1.149496399283170553977158597416 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 0.55157719855436556898680491976248
y[1] (numeric) = 0.54517652885745011475951600893856
absolute error = 0.006400669696915454227288910823926
relative error = 1.1604304372426989687076140704402 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 0.55068360134911114041756150258825
y[1] (numeric) = 0.54423265160755839602289733127342
absolute error = 0.0064509497415527443946641713148259
relative error = 1.1714439517989392706078322009426 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 0.54979045346021791970520486153262
y[1] (numeric) = 0.5432889758226270806506065771439
absolute error = 0.0065014776375908390545982843887136
relative error = 1.1825373825013636810303301498787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 0.54889775578083372131396744881682
y[1] (numeric) = 0.54234550195241914123812117259301
absolute error = 0.0065522538284145800758462762238135
relative error = 1.1937111710529187202037712090377 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=15.09
NO POLE
x[1] = 0.469
y[1] (analytic) = 0.54800550920365615023657685337748
y[1] (numeric) = 0.54140223044759047316505718641885
absolute error = 0.0066032787560656770715196669586272
relative error = 1.2049657613226092933932862543079 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 0.54711371462093170929672519960359
y[1] (numeric) = 0.54045916175968944393931150521527
absolute error = 0.0066545528612422653574136943883198
relative error = 1.2163015993581661611055187084253 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 0.54622237292445490690264067751721
y[1] (numeric) = 0.53951629634115644164873195450434
absolute error = 0.0067060765832984652539087230128673
relative error = 1.2277191333987974191252941618881 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 0.54533148500556736525265345075175
y[1] (numeric) = 0.53857363464532342252076691425292
absolute error = 0.0067578503602439427318865364988321
relative error = 1.2392188138880246194180023149271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 0.54444105175515692899364773668793
y[1] (numeric) = 0.53763117712641345759054686908607
absolute error = 0.0068098746287434714031008676018599
relative error = 1.2508010934866041682276567932153 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 0.54355107406365677433329140022077
y[1] (numeric) = 0.5366889242395402784778512250779
absolute error = 0.0068621498241164958554401751428686
relative error = 1.2624664270855346430456633659973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 0.54266155282104451860693394885391
y[1] (numeric) = 0.53574687644070782227341461611515
absolute error = 0.0069146763803366963335193327387622
relative error = 1.2742152718191506755200803643987 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 0.54177248891684133030006336214914
y[1] (numeric) = 0.53480503418680977553502781348943
absolute error = 0.0069674547300315547650355486597059
relative error = 1.2860480870783040528201034289959 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 0.54088388324011103952721173299992
y[1] (numeric) = 0.53386339793562911739388924257904
absolute error = 0.0070204853044819221333224904208761
relative error = 1.2979653345236326954661625074468 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 0.53999573667945924896819924174937
y[1] (numeric) = 0.53292196814583766177166400023086
absolute error = 0.0070737685336215871965352415185109
relative error = 1.309967478098918175182900370006 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 0.53910805012303244526260552683451
y[1] (numeric) = 0.53198074527699559870870815574515
absolute error = 0.0071273048460368465538973710893617
relative error = 1.3220549840445324419309326732079 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 0.53822082445851711086335705741136
y[1] (numeric) = 0.53103972978955103480391700720071
absolute error = 0.00718109466896607605944005021065
relative error = 1.334228320910974434924199474718 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=15.57
NO POLE
x[1] = 0.481
y[1] (analytic) = 0.53733406057313883635031865429955
y[1] (numeric) = 0.53009892214483953276665685323385
absolute error = 0.007235138428299303583661801065698
relative error = 1.3464879595724972581434426851637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 0.5364477593536614332047768455809
y[1] (numeric) = 0.52915832280508365008124072830103
absolute error = 0.0072894365485777831235361172798787
relative error = 1.3588343732408266066134248117332 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 0.53556192168638604704570228229476
y[1] (numeric) = 0.52821793223339247678440943691098
absolute error = 0.0073439894529935702612928453837763
relative error = 1.3712680374789711355224891279913 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 0.53467654845715027132867797789364
y[1] (numeric) = 0.52727775089376117235628010930684
absolute error = 0.0073987975633890989723978685867962
relative error = 1.3837894302151254701285038407139 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 0.53379164055132726150837967245725
y[1] (numeric) = 0.52633777925107050172522538761097
absolute error = 0.0074538613002567597831542848462741
relative error = 1.3963990317566665603156928592104 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 0.53290719885382484966549415911054
y[1] (numeric) = 0.52539801777108637038714723751479
absolute error = 0.0075091810827384792783469215957543
relative error = 1.4090973248042440896428996177706 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 0.53202322424908465959896094565383
y[1] (numeric) = 0.52445846692045935863961026620095
absolute error = 0.0075647573286253009593506794528799
relative error = 1.4218847944659656547560306163688 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 0.53113971762108122238442215908945
y[1] (numeric) = 0.52351912716672425493130031232583
absolute error = 0.0076205904543569674531218467636234
relative error = 1.43476192827167743712636091094 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 0.53025667985332109239976513452147
y[1] (numeric) = 0.52257999897829958832727495856474
absolute error = 0.0076766808750215040724901759567274
relative error = 1.4477292161873410952226401864164 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 0.52937411182884196381864166281204
y[1] (numeric) = 0.52164108282448716009047350143047
absolute error = 0.0077330290043548037281681613815748
relative error = 1.4607871506295076114291073478116 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 0.52849201443021178757284740340174
y[1] (numeric) = 0.52070237917547157437995479681612
absolute error = 0.0077896352547402131928926065856213
relative error = 1.4739362264798888342842024921963 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.4MB, time=16.04
x[1] = 0.492
y[1] (analytic) = 0.52761038853952788878444449984064
y[1] (numeric) = 0.51976388850231976806633228298529
absolute error = 0.0078465000372081207181122168553443
relative error = 1.4871769411000274629365631443529 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 0.52672923503841608466850996583417
y[1] (numeric) = 0.51882561127698053966487636553542
absolute error = 0.0079036237614355450036336002987497
relative error = 1.500509794346066227096419042078 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 0.52584855480802980290739193898176
y[1] (numeric) = 0.51788754797228407738675523119258
absolute error = 0.0079610068357457255206367077891845
relative error = 1.5139352885836170222023757414832 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 0.52496834872904920049735542787856
y[1] (numeric) = 0.51694969906194148630888603915769
absolute error = 0.0080186496671077141884693887208739
relative error = 1.5274539287027307660264280676703 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 0.52408861768168028306849870586105
y[1] (numeric) = 0.51601206502054431466286932011345
absolute error = 0.0080765526611359684056293857476019
relative error = 1.5410662221329687495045032281354 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 0.52320936254565402467882103140682
y[1] (numeric) = 0.51507464632356407924348029391819
absolute error = 0.0081347162220899454353407374886247
relative error = 1.5547726788585762612065406649935 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 0.52233058420022548808332190104733
y[1] (numeric) = 0.51413744344735178993719169745571
absolute error = 0.0081931407528736981461302035916146
relative error = 1.5685738114337592715497191285264 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 0.52145228352417294547901156562125
y[1] (numeric) = 0.51320045686913747337120359407873
absolute error = 0.0082518266550354721078079715425201
relative error = 1.5824701349980649696115960296123 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 0.52057446139579699972671206478443
y[1] (numeric) = 0.51226368706702969568345651557637
absolute error = 0.0083107743287673040432555492080608
relative error = 1.596462167291866952217292323275 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 0.5196971186929197060505275579023
y[1] (numeric) = 0.5113271345200150844141051666128
absolute error = 0.008369984172904621636422391289501
relative error = 1.6105504286719558718571079621392 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 0.51882025629288369421586225178126
y[1] (numeric) = 0.51039079970795784951893080012354
absolute error = 0.0084294565849258446969314516577279
relative error = 1.6247354421272363569387659229231 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 0.51794387507255129118686374714781
y[1] (numeric) = 0.50945468311159930350517125021697
absolute error = 0.0084891919609519876816924969308439
relative error = 1.6390177332945310248925422444734 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.4MB, time=16.52
x[1] = 0.504
y[1] (analytic) = 0.51706797590830364426416914635909
y[1] (numeric) = 0.50851878521255738069024848671126
absolute error = 0.0085491906957462635739206596478384
relative error = 1.6533978304744924157285385177042 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 0.51619255967603984470383078452566
y[1] (numeric) = 0.50758310649332615558387443253889
absolute error = 0.0086094531827136891199563519867734
relative error = 1.6678762646476236807939928299199 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 0.51531762725117605181829796504763
y[1] (numeric) = 0.50664764743727536039401666187296
absolute error = 0.0086699798139006914242813031746743
relative error = 1.6824535694904088686955142779387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 0.51444317950864461756033059850955
y[1] (numeric) = 0.50571240852864990165720647296924
absolute error = 0.0087307709799947159031241255403035
relative error = 1.6971302813915536576371819102022 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.508
y[1] (analytic) = 0.51356921732289321159072016094739
y[1] (numeric) = 0.5047773902525693759936727053758
absolute error = 0.0087918270703238355970474555715813
relative error = 1.7119069394683373907812966161633 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 0.51269574156788394683069290369378
y[1] (numeric) = 0.50384259309502758498778554633583
absolute error = 0.0088531484728563618429073573579542
relative error = 1.7267840855830772786649476260405 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 0.51182275311709250549986976232543
y[1] (numeric) = 0.50290801754289204919429544589956
absolute error = 0.0089147355742004563055743164258646
relative error = 1.7417622643597056402031958884008 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 0.51095025284350726564065692667989
y[1] (numeric) = 0.5019736640839035212708531344659
absolute error = 0.0089765887596037443698037922139969
relative error = 1.7568420232004610613793351324757 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 0.51007824161962842812994054747852
y[1] (numeric) = 0.50103953320667549823729761019299
absolute error = 0.0090387084129529298926429372855301
relative error = 1.772023912302694358365126980206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 0.50920672031746714417895856778793
y[1] (numeric) = 0.50010562540069373286219983694935
absolute error = 0.0091010949167734113167587308385733
relative error = 1.7873084846757902395298868482292 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 0.50833568980854464332222217937555
y[1] (numeric) = 0.49917194115631574417715076622089
absolute error = 0.0091637486522288991450714131546611
relative error = 1.8026962961582055685875991941056 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.515
y[1] (analytic) = 0.5074651509638913618963589149652
y[1] (numeric) = 0.4982384809647703271192831686452
absolute error = 0.0092266699991210347770757463199963
relative error = 1.8181879054346251389966494686957 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=16.99
NO POLE
x[1] = 0.516
y[1] (analytic) = 0.50659510465404607200974889747675
y[1] (numeric) = 0.49730524531815706130251763261034
absolute error = 0.009289859335889010707231264866416
relative error = 1.8337838740532358776680705366246 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 0.50572555174905501100382527654134
y[1] (numeric) = 0.49637223470944581891802395863116
absolute error = 0.0093533170396091920858013179101809
relative error = 1.8494847664431204040562170749265 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 0.50485649311847101140690939091887
y[1] (numeric) = 0.49543944963247627176439004900086
absolute error = 0.0094170434859947396425193419180073
relative error = 1.8652911499317708788013155830873 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 0.50398792963135263138145070291028
y[1] (numeric) = 0.49450689058195739740799126250763
absolute error = 0.009481039049395233973459440402648
relative error = 1.8812035947627240842672125494419 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 0.50311986215626328566554105745225
y[1] (numeric) = 0.49357455805346698447405407380612
absolute error = 0.0095453041027963011914869836461322
relative error = 1.8972226741133186875706909370431 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 0.50225229156127037700957232430744
y[1] (numeric) = 0.49264245254345113706890874633857
absolute error = 0.0096098390178192399406635779688682
relative error = 1.9133489641125756450317870174952 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 0.50138521871394442810890598662047
y[1] (numeric) = 0.49171057454922377833392659651192
absolute error = 0.0096746441647206497749793901085588
relative error = 1.9295830438592027153884669781473 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 0.50051864448135821403342274309759
y[1] (numeric) = 0.49077892456896615313163829515196
absolute error = 0.0097397199123920609017844479456353
relative error = 1.9459254954397240576146768063572 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 0.49965256973008589515481969418814
y[1] (numeric) = 0.48984750310172632986453052007508
absolute error = 0.0098050666283595652902891741130554
relative error = 1.9623769039467358977590308535182 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 0.4987869953262021505725221848984
y[1] (numeric) = 0.48891631064741870142701914093921
absolute error = 0.009870684678783449145503043959191
relative error = 1.9789378574972892578831354551921 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 0.49792192213528131203907687825382
y[1] (numeric) = 0.4879853477068234852910979843593
absolute error = 0.009936574428457826747978893894519
relative error = 1.9956089472514007489246455279099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=141.1MB, alloc=4.4MB, time=17.47
x[1] = 0.527
y[1] (analytic) = 0.49705735102239649838589213394419
y[1] (numeric) = 0.4870546147815862227261630935969
absolute error = 0.010002736240810275659729040347295
relative error = 2.0123907674306924381415260446005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 0.49619328285211875045019126633951
y[1] (numeric) = 0.48612411237421727715351326295782
absolute error = 0.010069170477901473296678003381691
relative error = 2.029283915337161810711549077099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 0.49532971848851616650404375485096
y[1] (numeric) = 0.48519384098809133163602849235557
absolute error = 0.010135877500424834868015262495388
relative error = 2.0462889913720828540657236873378 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 0.49446665879515303818633897753392
y[1] (numeric) = 0.48426380112744688550352887232023
absolute error = 0.010202857667706152682810105213694
relative error = 2.0634065990550393026270641179844 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 0.49360410463508898693856653588713
y[1] (numeric) = 0.48333399329738575011431727405185
absolute error = 0.010270111337703236824249261835286
relative error = 2.0806373450430910898077961515945 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 0.49274205687087810094526673499584
y[1] (numeric) = 0.48240441800387254375341008293385
absolute error = 0.010337638867005557191856652061991
relative error = 2.0979818391500750633897378894788 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 0.49188051636456807258001427849642
y[1] (numeric) = 0.48147507575373418566796107723339
absolute error = 0.010405440610833886912053201263033
relative error = 2.1154406943660410297751364434215 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 0.491019483977699336357797732307
y[1] (numeric) = 0.48054596705465938924038441652278
absolute error = 0.010473516923039947117413315784218
relative error = 2.1330145268768242020496743539496 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 0.49015896057130420739465680467269
y[1] (numeric) = 0.47961709241519815429968356665672
absolute error = 0.01054186815610605309497323801597
relative error = 2.1507039560837551363466686332519 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 0.48929894700590602037543898281642
y[1] (numeric) = 0.47868845234476125857149384993404
absolute error = 0.010610494661144761803945132882384
relative error = 2.168509604623508250642672476163 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 0.48843944414151826903053655836697
y[1] (numeric) = 0.47776004735361974826734717035914
absolute error = 0.010679396787898520763189388007832
relative error = 2.1864320983880900298507679452577 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 0.48758045283764374612246456475538
y[1] (numeric) = 0.47683187795290442781366832469582
absolute error = 0.010748574884739318308796240059564
relative error = 2.2044720665449680309098322812786 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=144.9MB, alloc=4.4MB, time=17.94
x[1] = 0.539
y[1] (analytic) = 0.48672197395327368394313963993034
y[1] (numeric) = 0.4759039446546053487210131702748
absolute error = 0.010818029298668335222126469655533
relative error = 2.2226301415573418114970079434055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 0.48586400834688689532271931704176
y[1] (numeric) = 0.47497624797157129759405978027404
absolute error = 0.010887760375315597728659536767714
relative error = 2.2409069592045569160175562847921 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 0.485006556876448915150860734182
y[1] (numeric) = 0.47404878841750928328286457643814
absolute error = 0.010957768458939631867996157743868
relative error = 2.2593031586026630626522885265249 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.542
y[1] (analytic) = 0.48414962039941114241125724185424
y[1] (numeric) = 0.47312156650698402317589628793787
absolute error = 0.011028053892427119235360953916377
relative error = 2.2778193822251176854689195443841 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 0.48329319977270998273031087355997
y[1] (numeric) = 0.47219458275541742863536144329317
absolute error = 0.011098617017292554094949430266799
relative error = 2.2964562759236359959310667517327 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 0.48243729585276599144079813076171
y[1] (numeric) = 0.47126783767908808957533595999111
absolute error = 0.011169458173677901865462170770605
relative error = 2.3152144889491887385683177224681 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 0.4815819094954830171613860184838
y[1] (numeric) = 0.47034133179513075818321825362436
absolute error = 0.011240577700352258978167764859436
relative error = 2.3340946739731488261039288384041 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 0.48072704155624734589285475196364
y[1] (numeric) = 0.46941506562153583178502014505404
absolute error = 0.011311975934711514107834606909604
relative error = 2.3530974871085880499744190347403 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 0.47987269288992684563188303805971
y[1] (numeric) = 0.46848903967714883485501270026288
absolute error = 0.011383653212778010776870337796823
relative error = 2.3722235879317250729187268744043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 0.47901886435087011150325131755937
y[1] (numeric) = 0.46756325448166990017024499320978
absolute error = 0.011455609869200211333006324349591
relative error = 2.3914736395035259211648584472447 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 0.47816555679290561141131783611242
y[1] (numeric) = 0.46663771055565324911045463712366
absolute error = 0.011527846237252362300863198988756
relative error = 2.4108483083914582047002343985102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 0.47731277106934083221162189224271
y[1] (numeric) = 0.46571240842050667110388978428287
absolute error = 0.011600362648834161107732107959836
relative error = 2.4303482646914003051794270490924 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=18.41
NO POLE
x[1] = 0.551
y[1] (analytic) = 0.47646050803296142640346809076379
y[1] (numeric) = 0.46478734859849100221956314841472
absolute error = 0.01167315943447042418390494234907
relative error = 2.4499741820497067822008574335642 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 0.47560876853603035934434490894292
y[1] (numeric) = 0.46386253161271960290645945741761
absolute error = 0.011746236923310756437885451525308
relative error = 2.4697267376854312599735057377564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 0.47475755343028705698703036092402
y[1] (numeric) = 0.46293795798715783488021859715493
absolute error = 0.011819595443129222106811763769097
relative error = 2.4896066124127080677970000663081 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 0.47390686356694655414023702323283
y[1] (numeric) = 0.46201362824662253715781755959384
absolute error = 0.011893235320324016982419463638985
relative error = 2.5096144906632939192948253134553 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 0.47305669979669864325364816064811
y[1] (numeric) = 0.46108954291678150124077516056342
absolute error = 0.01196715687991714201287300008469
relative error = 2.5297510605092709269720885373937 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 0.47220706296970702372819616733216
y[1] (numeric) = 0.46016570252415294544740434388367
absolute error = 0.012041360445554078280791823448485
relative error = 2.5500170136859122604175570202758 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 0.47135795393560845175243401287092
y[1] (numeric) = 0.45924210759610498839463773956931
absolute error = 0.012115846339503463357796273301611
relative error = 2.5704130456147117683358326768898 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 0.47050937354351189066584985678171
y[1] (numeric) = 0.45831875866085512162995299423888
absolute error = 0.012190614882656769035896862542837
relative error = 2.5909398554265788965808395708689 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 0.46966132264199766184997446810299
y[1] (numeric) = 0.45739565624746968141392524175995
absolute error = 0.01226566639452798043604922634304
relative error = 2.6115981459852002464675934937276 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 0.46881380207911659614813055888797
y[1] (numeric) = 0.45647280088586331965393493153386
absolute error = 0.01234100119325327649419562735411
relative error = 2.6323886239105691298668231174709 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.561
y[1] (analytic) = 0.46796681270238918581467261178217
y[1] (numeric) = 0.45555019310679847398956008066813
absolute error = 0.012416619595590711825112531114043
relative error = 2.6533119996026844899377663818507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 0.46712035535880473699456525237423
y[1] (numeric) = 0.45462783344188483703018286460008
absolute error = 0.012492521916919899964382387774153
relative error = 2.6743689872654205688297349438475 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=18.88
NO POLE
x[1] = 0.563
y[1] (analytic) = 0.46627443089482052273414768667114
y[1] (numeric) = 0.45370572242357882474534130852094
absolute error = 0.012568708471241697988806378150206
relative error = 2.695560304930568716284201517143 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 0.46542904015636093652393119286274
y[1] (numeric) = 0.45278386058518304400835768920429
absolute error = 0.012645179571177892515573503658453
relative error = 2.7168866744820527457976141907191 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 0.46458418398881664637427612450758
y[1] (numeric) = 0.45186224846084575929377610356626
absolute error = 0.012721935527970887080500020941316
relative error = 2.7383488216803192578622895924861 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.566
y[1] (analytic) = 0.46373986323704374942479434939252
y[1] (numeric) = 0.4509408865855603585291425064753
absolute error = 0.012798976651483390895651842917223
relative error = 2.7599474761869043627900113567716 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 0.4628960787453629270883225145933
y[1] (numeric) = 0.45001977549516481810166136598703
absolute error = 0.012876303250198108986661148606274
relative error = 2.7816833715891782487418073337821 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 0.46205283135755860073031099369233
y[1] (numeric) = 0.44909891572634116702026392930304
absolute error = 0.01295391563121743371004706438929
relative error = 2.8035572454252690538392614104231 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 0.46121012191687808788447283669442
y[1] (numeric) = 0.44817830781661495023362393734057
absolute error = 0.013031814100263137650848899353858
relative error = 2.8255698392091675146191144854685 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 0.46036795126603075900553650692117
y[1] (numeric) = 0.44725795230435469110465746985261
absolute error = 0.013109998961676067900879037068561
relative error = 2.8477218984560138766153228054427 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 0.45952632024718719475994565206105
y[1] (numeric) = 0.44633784972877135304204444655405
absolute error = 0.013188470518415841717901205507003
relative error = 2.8700141727075685665126874610333 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 0.45868522970197834385534861860512
y[1] (numeric) = 0.4454180006299178002893101526871
absolute error = 0.013267229072060543566038465918013
relative error = 2.8924474155578681391151817396051 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 0.45784468047149468140971988010875
y[1] (numeric) = 0.44449840554868825787200599989997
absolute error = 0.013346274922806423537713880208782
relative error = 2.9150223846790680263117372740249 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=156.4MB, alloc=4.4MB, time=19.36
x[1] = 0.574
y[1] (analytic) = 0.45700467339628536786095501008776
y[1] (numeric) = 0.44357906502681777070352957521262
absolute error = 0.013425608369467597157425434875145
relative error = 2.9377398418474736293040784883394 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 0.45616520931635740841778028988382
y[1] (numeric) = 0.44265997960688166185012487220476
absolute error = 0.013505229709475746567655417679055
relative error = 2.9606005529697613095868098533048 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 0.45532628907117481305281750051966
y[1] (numeric) = 0.44174114983229498995560443938067
absolute error = 0.013585139238879823097213061138985
relative error = 2.9836052881093908485409734882549 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 0.45448791349965775703864390540909
y[1] (numeric) = 0.44082257624731200582633602094328
absolute error = 0.013665337252345751212307884465811
relative error = 3.00675482151321096002033691822 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 0.45365008344018174202768688779204
y[1] (numeric) = 0.43990425939702560817703710494585
absolute error = 0.013745824043156133850649782846187
relative error = 3.0300499316382594549763934936118 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 0.45281279973057675767679216292994
y[1] (numeric) = 0.4389861998273667985379216329812
absolute error = 0.01382659990320995913887052994874
relative error = 3.0534914011787596719851324841658 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 0.45197606320812644381730394042354
y[1] (numeric) = 0.43806839808510413532374396421637
absolute error = 0.013907665123022308493559976207167
relative error = 3.077080017093314802507754019758 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 0.45113987470956725317149486650297
y[1] (numeric) = 0.43715085471784318706528602468328
absolute error = 0.013989019991724066106208841819696
relative error = 3.100816570632301754840378460738 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.582
y[1] (analytic) = 0.45030423507108761461618302979055
y[1] (numeric) = 0.43623357027402598480383441029265
absolute error = 0.014070664797061629812348619497908
relative error = 3.1247018573654662159861640493678 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 0.44946914512832709699437276684941
y[1] (numeric) = 0.43531654530293047364919504904848
absolute error = 0.014152599825396623345177717800933
relative error = 3.1487366772097205861188557281457 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 0.44863460571637557347575545580759
y[1] (numeric) = 0.4343997803546699635017938644027
absolute error = 0.014234825361705609973961591404894
relative error = 3.1729218344571464759014182962471 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 0.4478006176697723864669059374871
y[1] (numeric) = 0.4334832759801925789394127176035
absolute error = 0.014317341689579807527493219883595
relative error = 3.1972581378032034726788569650422 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=160.2MB, alloc=4.4MB, time=19.85
x[1] = 0.586
y[1] (analytic) = 0.44696718182250551307200965377196
y[1] (numeric) = 0.43256703273128070826911074225571
absolute error = 0.014400149091224804802898911516241
relative error = 3.2217464003751458974824183790206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.587
y[1] (analytic) = 0.44613429900801073110495504241853
y[1] (numeric) = 0.43165105116055045174488201912578
absolute error = 0.014483247847460279360073023292747
relative error = 3.2463874397606492908649382547769 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 0.44530197005917078565362517614627
y[1] (numeric) = 0.43073533182145106895160137348788
absolute error = 0.014566638237719716702023802658395
relative error = 3.2711820780366483818360236770433 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 0.44447019580831455619722208164774
y[1] (numeric) = 0.42981987526826442535581091101913
absolute error = 0.014650320540050130841411170628605
relative error = 3.2961311417983883105829175540255 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 0.44363897708721622427745662112423
y[1] (numeric) = 0.42890468205610443802390074141149
absolute error = 0.01473429503111178625355587971274
relative error = 3.3212354621886908922502019177903 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 0.44280831472709444172443626508772
y[1] (numeric) = 0.4279897527409165205082381714731
absolute error = 0.014818561986177921216198093614628
relative error = 3.3464958749274377258108914817894 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 0.44197820955861149943808253047211
y[1] (numeric) = 0.42707508787947702690180048154395
absolute error = 0.014903121679134472536282048928154
relative error = 3.3719132203412719689949089561314 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 0.44114866241187249672590930256691
y[1] (numeric) = 0.42616068802939269506186723054658
absolute error = 0.014987974382479801664042072020329
relative error = 3.3974883433935206173504032101209 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 0.44031967411642451119799270292604
y[1] (numeric) = 0.42524655374910008900332886593304
absolute error = 0.015073120367324422194663836992998
relative error = 3.4232220937143391428008792445201 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 0.43949124550125576921996260821254
y[1] (numeric) = 0.42433268559786504046216924517333
absolute error = 0.01515855990339072875779336303921
relative error = 3.44911532563108036452868885351 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 0.43866337739479481692484536691856
y[1] (numeric) = 0.4234190841357820896296805052559
absolute error = 0.015244293259012727295164861662668
relative error = 3.4751688981988894426651418921319 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 0.43783607062490969178458670204891
y[1] (numeric) = 0.42250574992377392505796954593898
absolute error = 0.015330320701135766726617156109935
relative error = 3.5013836752315269031014249469224 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=20.34
NO POLE
x[1] = 0.598
y[1] (analytic) = 0.43700932601890709474208322817614
y[1] (numeric) = 0.42159268352359082273731622119952
absolute error = 0.015416642495316272004767006976614
relative error = 3.5277605253324216197547676636495 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 0.43618314440353156290455045076672
y[1] (numeric) = 0.4206798854978100843459441614748
absolute error = 0.015503258905721478558606289291926
relative error = 3.5543003219259556988330140958893 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 0.43535752660496464279905455434134
y[1] (numeric) = 0.41976735640983547467276597687895
absolute error = 0.015590170195129168126288577462389
relative error = 3.5810039432889832280401009885017 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 0.43453247344882406419103472386862
y[1] (numeric) = 0.41885509682389665821366541860263
absolute error = 0.015677376624927405977369305265992
relative error = 3.6078722725825848722571077565053 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 0.43370798576016291446664218080111
y[1] (numeric) = 0.41794310730504863494187990216631
absolute error = 0.015764878455114279524762278634805
relative error = 3.6349061978840603160207423534393 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 0.43288406436346881357972155134577
y[1] (numeric) = 0.41703138841917117525304762209803
absolute error = 0.015852675944297638326673929247741
relative error = 3.6621066122191605721056093424247 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 0.43206071008266308956425961991864
y[1] (numeric) = 0.41611994073296825408548431294111
absolute error = 0.015940769349694835478775306977528
relative error = 3.6894744135945621947006455709009 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 0.4312379237410999546131259552665
y[1] (numeric) = 0.41520876481396748421625553626813
absolute error = 0.016029158927132470396870418998376
relative error = 3.7170105050305854550560077571609 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 0.43041570616156568172392933044603
y[1] (numeric) = 0.41429786123051954873361119758149
absolute error = 0.016117844931046132990318132864539
relative error = 3.7447157945941585570667868301912 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 0.42959405816627778191281329073545
y[1] (numeric) = 0.41338723055179763268634982061887
absolute error = 0.016206827614480149226463470116572
relative error = 3.7725911954320299900565671811115 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 0.42877298057688418199701365561464
y[1] (numeric) = 0.41247687334779685391068092965188
absolute error = 0.016296107229087328086332725962764
relative error = 3.8006376258042311360294359921275 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=167.8MB, alloc=4.4MB, time=20.80
x[1] = 0.609
y[1] (analytic) = 0.42795247421446240294700017218763
y[1] (numeric) = 0.41156679018933369303515471286807
absolute error = 0.016385684025128709911845459319564
relative error = 3.8288560091177912688759995708832 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 0.42713253989951873880902396783728
y[1] (numeric) = 0.41065698164804542266422896185926
absolute error = 0.016475558251473316144795005978017
relative error = 3.8572472739607071034497317658344 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 0.42631317845198743619889187949639
y[1] (numeric) = 0.40974744829638953574104410360153
absolute error = 0.016565730155597900457847775894865
relative error = 3.8858123541361690730770466889003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 0.42549439069122987436778816569248
y[1] (numeric) = 0.40883819070764317308997796210424
absolute error = 0.016656199983586701277810203588246
relative error = 3.9145521886970465349303681520317 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.613
y[1] (analytic) = 0.42467617743603374584096353547619
y[1] (numeric) = 0.40792920945590255013955270712573
absolute error = 0.016746967980131195701410828350452
relative error = 3.943467721980634123780707301284 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 0.42385853950461223763011085547598
y[1] (numeric) = 0.40702050511608238282626726700085
absolute error = 0.016838034388529854803843588475133
relative error = 3.9725599036436614959574360488535 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 0.4230414777146032130202463226353
y[1] (numeric) = 0.40611207826391531267992930170003
absolute error = 0.016929399450687900340317020935271
relative error = 4.0018296886975687268806679232564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 0.42222499288306839393191431568267
y[1] (numeric) = 0.40520392947595133109106165074022
absolute error = 0.017021063407117062840852664942449
relative error = 4.0312780375440496472985739124801 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 0.42140908582649254385953356306188
y[1] (numeric) = 0.40429605932955720276095898849302
absolute error = 0.017113026496935341098574574568862
relative error = 4.0609059160108654253607464219741 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 0.42059375736078265138670168890796
y[1] (numeric) = 0.40338846840291588833497123678548
absolute error = 0.017205288957866763051730452122489
relative error = 4.0907142953879307238920913545854 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 0.41977900830126711427927462169634
y[1] (numeric) = 0.40248115727502596621959110146195
absolute error = 0.017297851026241148059683520234398
relative error = 4.1207041524636747847024228470139 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 0.41896483946269492415703677241779
y[1] (numeric) = 0.40157412652570105358392391577131
absolute error = 0.017390712936993870573112856646477
relative error = 4.1508764695616798144777387061129 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=171.6MB, alloc=4.4MB, time=21.27
x[1] = 0.621
y[1] (analytic) = 0.41815125165923485174477731054103
y[1] (numeric) = 0.40066737673556922654611878906145
absolute error = 0.017483874923665625198658521479577
relative error = 4.1812322345775990697528839363804 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 0.41733824570447463270358728661891
y[1] (numeric) = 0.39976090848607243954534087430156
absolute error = 0.017577337218402193158246412317352
relative error = 4.2117724410163570616648178052967 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 0.41652582241142015404319177017304
y[1] (numeric) = 0.39885472235946594389986538241156
absolute error = 0.017671100051954210143326387761485
relative error = 4.2424980880296343246338760322192 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 0.41571398259249464111613059045704
y[1] (numeric) = 0.39794881893881770555187478525621
absolute error = 0.017765163653676935564255805200831
relative error = 4.2734101804536392168201903000907 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 0.41490272705953784519460068584992
y[1] (numeric) = 0.39704319880800782199954146245822
absolute error = 0.017859528251530023195059223391704
relative error = 4.3045097288471692441567562956551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 0.41409205662380523163077248496947
y[1] (numeric) = 0.39613786255172793841697885989896
absolute error = 0.017954194072077293213793625070503
relative error = 4.3357977495299644239725308503293 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 0.4132819720959671686013921591217
y[1] (numeric) = 0.39523281075548066296264503990726
absolute error = 0.018049161340486505638747119214444
relative error = 4.3672752646213552286914290250132 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 0.41247247428610811643748100141646
y[1] (numeric) = 0.39432804400557898127678331468362
absolute error = 0.018144430280529135160697686732832
relative error = 4.3989433020792076748292628169347 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 0.4116635640037258175399426027822
y[1] (numeric) = 0.39342356288914567016848546547085
absolute error = 0.018240001114580147371457137311345
relative error = 4.4308028957391681475136338831879 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 0.41085524205773048688188790920538
y[1] (numeric) = 0.39251936799411271049296386035864
absolute error = 0.01833587406361777638892404884674
relative error = 4.4628550853542105760247228041066 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 0.41004750925644400309848765780185
y[1] (numeric) = 0.39161545990922069921961959340134
absolute error = 0.018432049347223303878868064400508
relative error = 4.4951009166344886014010072534971 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
y[1] (analytic) = 0.40924036640759910016516110180038
y[1] (numeric) = 0.39071183922401826069149457693163
absolute error = 0.018528527183580839473666524868755
relative error = 4.5275414412874954029764326485777 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=21.75
NO POLE
x[1] = 0.633
y[1] (analytic) = 0.40843381431833855966490934618239
y[1] (numeric) = 0.389808506528861457076696327569
absolute error = 0.018625307789477102588213018613395
relative error = 4.5601777170585338768177349880629 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 0.40762785379521440364560102657702
y[1] (numeric) = 0.38890546241491319801238499444911
absolute error = 0.018722391380301205633216032127908
relative error = 4.5930108077714998854158027283249 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 0.40682248564418708806801747405878
y[1] (numeric) = 0.38800270747414264944191298563783
absolute error = 0.018819778170044438626104488420956
relative error = 4.6260417833699813246565318752121 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 0.40601771067062469684546391773531
y[1] (numeric) = 0.38710024229932464164570835554094
absolute error = 0.01891746837130005519975556219437
relative error = 4.6592717199586757810579888720933 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 0.40521352967930213647575268544688
y[1] (numeric) = 0.38619806748403907646649392237703
absolute error = 0.019015462195263060009258763069851
relative error = 4.6927016998451295795153065551301 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 0.40440994347440033126636377052741
y[1] (numeric) = 0.38529618362267033372943489044482
absolute error = 0.019113759851729997536928880082597
relative error = 4.7263328115818010493461015829015 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 0.40360695285950541915358753939926
y[1] (numeric) = 0.38439459131040667685780855698795
absolute error = 0.019212361549098742295778982411304
relative error = 4.7601661500084508642808650664034 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 0.40280455863760794811645376079207
y[1] (numeric) = 0.38349329114323965768479048793801
absolute error = 0.01931126749436829043166327285406
relative error = 4.7942028162948623401983355852993 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 0.40200276161110207318625054258986
y[1] (numeric) = 0.38259228371796352046195235069994
absolute error = 0.019410477893138552724298191889913
relative error = 4.8284439179838946028689562084261 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 0.40120156258178475405243616672017
y[1] (numeric) = 0.38169156963217460506506739543241
absolute error = 0.01950999294961014898736877128776
relative error = 4.8628905690348715667438329073018 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 0.40040096235085495326574621610695
y[1] (numeric) = 0.38079114948427074939782037896789
absolute error = 0.019609812866584203867925837139061
relative error = 4.8975438898673096949158874341317 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 0.3996009617189128350392977905129
y[1] (numeric) = 0.37989102387345069099401952761272
absolute error = 0.019709937845462144045278262900176
relative error = 4.9324050074049875397879187931764 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.4MB, time=22.23
NO POLE
x[1] = 0.645
y[1] (analytic) = 0.39880156148595896464849201010053
y[1] (numeric) = 0.37899119339971346781890893656538
absolute error = 0.019810368086245496829583073535151
relative error = 4.9674750551203600937128889108038 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 0.3980027624513935084305154067426
y[1] (numeric) = 0.37809165866385781827018060459052
absolute error = 0.01991110378753569016033480215208
relative error = 5.0027551730793210089288153345971 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 0.39720456541401543438424020351384
y[1] (numeric) = 0.37719242026748158037928610288682
absolute error = 0.020012145146533854004954100627018
relative error = 5.0382465079863157764981230939588 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 0.39640697117202171337132288239725
y[1] (numeric) = 0.37629347881298109021364867678697
absolute error = 0.020113492359040623157674205610279
relative error = 5.0739502132298089846831672859337 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 0.39560998052300652091929983903959
y[1] (numeric) = 0.37539483490355057948037737802737
absolute error = 0.020215145619455941438922461012216
relative error = 5.1098674489281088082499280223523 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 0.39481359426396043962747832139406
y[1] (numeric) = 0.3744964891431815723320856238234
absolute error = 0.020317105120778867295392697570662
relative error = 5.1459993819755519115946938066108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 0.39401781319126966217642024629276
y[1] (numeric) = 0.37359844213666228137541737688133
absolute error = 0.020419371054607380801002869411431
relative error = 5.1823471860890519803380358847355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 0.39322263810071519494181588439859
y[1] (numeric) = 0.37270069448957700288288493777042
absolute error = 0.02052194361113819205893094662817
relative error = 5.2189120418550151281307370559277 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 0.39242806978747206221354379959662
y[1] (numeric) = 0.37180324680830551120862313776691
absolute error = 0.020624822979166551004920661829704
relative error = 5.2556951367766254578718317706005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 0.39163410904610851102071282369871
y[1] (numeric) = 0.37090609970002245240866551636543
absolute error = 0.020728009346086058612047307333273
relative error = 5.2926976653215040893538543392154 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 0.39084075667058521656348124135303
y[1] (numeric) = 0.3700092537726967370663488631309
absolute error = 0.020831502897888479497132378222135
relative error = 5.3299208289697449985291500917285 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=183.1MB, alloc=4.4MB, time=22.72
x[1] = 0.656
y[1] (analytic) = 0.39004801345425448825244775327319
y[1] (numeric) = 0.36911270963509093232345329843592
absolute error = 0.02093530381916355592899445483727
relative error = 5.3673658362623310471381096712907 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 0.38925588018985947635640817832977
y[1] (numeric) = 0.36821646789676065311768586189296
absolute error = 0.021039412293098823238722316436811
relative error = 5.4050339028499336153599273919989 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 0.38846435766953337925927124668149
y[1] (numeric) = 0.36732052916805395262711637094679
absolute error = 0.0211438285014794266321548757347
relative error = 5.442926251542099284443508427133 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.659
y[1] (analytic) = 0.38767344668479865132692622696415
y[1] (numeric) = 0.36642489406011071192217510514079
absolute error = 0.02124855262468793940475112182337
relative error = 5.4810441123568270509550646801992 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 0.3868831480265662113848545206037
y[1] (numeric) = 0.36552956318486202882582266400834
absolute error = 0.021353584841704182559031856595363
relative error = 5.5193887225705395893444150262433 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 0.38609346248513465180727674557586
y[1] (numeric) = 0.36463453715502960598250313836874
absolute error = 0.021458925330105045824773607207115
relative error = 5.55796132676845211498877392072 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 0.38530439085018944821862622039934
y[1] (numeric) = 0.36373981658412513813649252602326
absolute error = 0.02156457426606431008213369437608
relative error = 5.5967631768953424357256680064626 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 0.38451593391080216980813914682333
y[1] (numeric) = 0.362845402086449698620255113452
absolute error = 0.021670531824352471187884033371326
relative error = 5.6357955323067258161404221898771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 0.38372809245542969025835117655314
y[1] (numeric) = 0.36195129427709312505342133510402
absolute error = 0.021776798178336565204929841449121
relative error = 5.6750596598204383155333285504693 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 0.38294086727191339928828943345192
y[1] (numeric) = 0.36105749377193340425300141125167
absolute error = 0.021883373499979995035288022200242
relative error = 5.7145568337686322975621431399145 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.666
y[1] (analytic) = 0.38215425914747841481214844796039
y[1] (numeric) = 0.36016400118763605635544985414422
absolute error = 0.021990257959842358456698593816168
relative error = 5.7542883360501878470420038215334 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 0.38136826886873279571423784499337
y[1] (numeric) = 0.35927081714165351815119672034497
absolute error = 0.022097451727079277563041124648402
relative error = 5.7942554561835438672923512284369 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=186.9MB, alloc=4.4MB, time=23.19
x[1] = 0.668
y[1] (analytic) = 0.38058289722166675524098901029949
y[1] (numeric) = 0.35837794225222452563226227466922
absolute error = 0.022204954969442229608726735630275
relative error = 5.8344594913599526697541579208542 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 0.37979814499165187501080734321209
y[1] (numeric) = 0.35748537713837349575357251805696
absolute error = 0.022312767853278379257234825155128
relative error = 5.8749017464971619063659909548548 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 0.37901401296344031964255608587341
y[1] (numeric) = 0.35659312241990990740859381801323
absolute error = 0.022420890543530412233962267860177
relative error = 5.9155835342935277343894842191461 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 0.37823050192116405200345710038291
y[1] (numeric) = 0.35570117871742768161990566592992
absolute error = 0.022529323203736370383551434452988
relative error = 5.9565061752825631430190847981086 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 0.37744761264833404907719334590347
y[1] (numeric) = 0.35480954665230456094533137066466
absolute error = 0.022638065996029488131861975238808
relative error = 5.9976709978879254112029409312316 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 0.37666534592783951845299718755764
y[1] (numeric) = 0.35391822684670148810024728219431
absolute error = 0.02274711908113803035274990536333
relative error = 6.0390793384788467066470704892516 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 0.37588370254194711543650804796045
y[1] (numeric) = 0.35302721992356198379669192298214
absolute error = 0.022856482618385131639816124978307
relative error = 6.0807325414260118769791159589001 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 0.3751026832723001607831822904657
y[1] (numeric) = 0.35213652650661152379989718789761
absolute error = 0.02296615676568863698328510256809
relative error = 6.1226319591578875255167585588746 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 0.37432228889991785905503760065086
y[1] (numeric) = 0.35124614722035691520286455610572
absolute error = 0.023076141679560943852173044545141
relative error = 6.164778952217506506025011407337 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 0.37354252020519451760151350923091
y[1] (numeric) = 0.35035608269008567191961004029774
absolute error = 0.023186437515108845681903468933172
relative error = 6.2071748893197120132619991375872 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 0.37276337796789876616522907547561
y[1] (numeric) = 0.34946633354186538939770237996629
absolute error = 0.023297044426033376767526695509328
relative error = 6.2498211474088654890103980804565 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 0.3719848629671727771134181253074
y[1] (numeric) = 0.34857690040254311855071976613445
absolute error = 0.023407962564629658562698359172952
relative error = 6.2927191117170226066774768912134 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.4MB, time=23.67
NO POLE
x[1] = 0.68
y[1] (analytic) = 0.37120697598153148629582181257975
y[1] (numeric) = 0.3476877838997447389112511650301
absolute error = 0.023519192081786747384570647549659
relative error = 6.3358701758225816414267440002122 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 0.37042971778886181452981764557857
y[1] (numeric) = 0.34679898466187433100506908765182
absolute error = 0.02363073312698748352474855792675
relative error = 6.3792757417094085771847603350918 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 0.36965308916642188971356349355254
y[1] (numeric) = 0.34591050331811354794710143100138
absolute error = 0.023742585848308341766462062551157
relative error = 6.4229372198264433467539825691797 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.683
y[1] (analytic) = 0.36887709089084026956793446006375
y[1] (numeric) = 0.34502234049842098625983079495846
absolute error = 0.023854750392419283308103665105294
relative error = 6.4668560291477916466629184589267 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 0.36810172373811516500802988115697
y[1] (numeric) = 0.34413449683353155591475045634606
absolute error = 0.02396722690458360909327942481091
relative error = 6.5110335972333068143048432630127 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.685
y[1] (analytic) = 0.36732698848361366414502707677567
y[1] (numeric) = 0.34324697295495584959750695867796
absolute error = 0.024080015528657814547520118097708
relative error = 6.5554713602896663013623745504977 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 0.36655288590207095691915785350657
y[1] (numeric) = 0.34235976949497951119736005239312
absolute error = 0.024193116407091445721797801113449
relative error = 6.6001707632319473244939511172799 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 0.36577941676758956036458312561155
y[1] (numeric) = 0.34147288708666260352159149606454
absolute error = 0.024306529680926956842991629547011
relative error = 6.6451332597457063217764202273652 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 0.36500658185363854450694038940761
y[1] (numeric) = 0.34058632636383897523549500412093
absolute error = 0.02442025548979956927144538528669
relative error = 6.6903603123495668914623080902499 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 0.36423438193305275889433815338313
y[1] (numeric) = 0.33970008796111562702858040103866
absolute error = 0.024534293971937131865757752344475
relative error = 6.7358533924583209382278269840601 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 0.36346281777803205976257079299128
y[1] (numeric) = 0.33881417251387207700762581574689
absolute error = 0.024648645264159982754944977244391
relative error = 6.7816139804465478012652492272654 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 0.36269189016014053783532666484154
y[1] (numeric) = 0.33792858065825972531721252314083
absolute error = 0.024763309501880812518114141700711
relative error = 6.8276435657127561883180400803837 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.4MB, time=24.14
NO POLE
x[1] = 0.692
y[1] (analytic) = 0.36192159985030574676016168001679
y[1] (numeric) = 0.33704331303120121798837781211541
absolute error = 0.024878286819104528771783867901381
relative error = 6.8739436467440537900762731495708 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 0.36115194761881793218100990047802
y[1] (numeric) = 0.33615837027038981001602203141336
absolute error = 0.024993577348428122164987869064662
relative error = 6.9205157311813495002506366883691 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 0.36038293423532926144800208598196
y[1] (numeric) = 0.3352737530142887276657067358277
absolute error = 0.025109181221040533782295350154268
relative error = 6.9673613358850932181331617529393 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 0.35961456046885305396536248162878
y[1] (numeric) = 0.33438946190213053001048162590722
absolute error = 0.025225098566722523954880855721555
relative error = 7.0144819870015582625391500463563 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 0.35884682708776301217815349807899
y[1] (numeric) = 0.33350549757391646969837874428501
absolute error = 0.025341329513846542479774753793972
relative error = 7.0618792200296714787152407926825 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 0.35807973485979245319863729763077
y[1] (numeric) = 0.33262186067041585295121316108228
absolute error = 0.025457874189376600247424136548494
relative error = 7.1095545798883961731008276883822 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 0.35731328455203354107302265973213
y[1] (numeric) = 0.33173855183316539879533014953372
absolute error = 0.025574732718868142277692510198412
relative error = 7.1575096209846730647519213184256 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 0.35654747693093651968936485911696
y[1] (numeric) = 0.33085557170446859752493962103373
absolute error = 0.025691905226467922164425238083231
relative error = 7.2057459072819244967859602895027 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 0.35578231276230894632738564860128
y[1] (numeric) = 0.32997292092739506839867935621552
absolute error = 0.025809391834913877928706292385763
relative error = 7.2542650123691272063910267094235 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 0.35501779281131492585097979665585
y[1] (numeric) = 0.32909060014577991657004933544654
absolute error = 0.025927192665535009280930461209314
relative error = 7.3030685195304590077715512694977 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 0.35425391784247434554417398718465
y[1] (numeric) = 0.32820861000422308925236023825211
absolute error = 0.026045307838251256291813748932535
relative error = 7.3521580218155247988831462443369 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=198.3MB, alloc=4.4MB, time=24.61
x[1] = 0.703
y[1] (analytic) = 0.35349068861966211059130324548666
y[1] (numeric) = 0.32732695114808873111883994666523
absolute error = 0.026163737471573379472463298821423
relative error = 7.4015351221101673599500425429461 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 0.35272810590610738020216941016085
y[1] (numeric) = 0.32644562422350453893854265234229
absolute error = 0.026282481682602841263626757818561
relative error = 7.4512014332078684695682077524549 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 0.35196617046439280438294552573213
y[1] (numeric) = 0.32556462987736111544870593148179
absolute error = 0.026401540587031688934239594250345
relative error = 7.501158577881745922684182801934 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 0.35120488305645376135358938503038
y[1] (numeric) = 0.32468396875731132246420191513524
absolute error = 0.026520914299142438889387469895136
relative error = 7.55140818895715209391271279197 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 0.35044424444357759561252880384534
y[1] (numeric) = 0.32380364151176963322472944540503
absolute error = 0.026640602931807962387799358440313
relative error = 7.6019519093848797495242023305363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 0.3496842553864028566493805631088
y[1] (numeric) = 0.32292364878991148398039487028321
absolute error = 0.026760606596491372668985692825594
relative error = 7.6527913923149808720048611806547 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.709
y[1] (analytic) = 0.34892491664491853830646430582142
y[1] (numeric) = 0.32204399124167262481632989149636
absolute error = 0.026880925403245913490134414325057
relative error = 7.7039283011712043223772119910822 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 0.34816622897846331878987202714716
y[1] (numeric) = 0.32116466951774846971699564068462
absolute error = 0.027001559460714849072876386462547
relative error = 7.7553643097260582274756261349668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 0.3474081931457248013308531465424
y[1] (numeric) = 0.32028568426959344587082291955654
absolute error = 0.027122508876131355460030226985856
relative error = 7.807101102176503042110083917533 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 0.34665080990473875549827450047127
y[1] (numeric) = 0.31940703614942034221583929932545
absolute error = 0.027243773755318413282435201145816
relative error = 7.8591403732202812995309012167756 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 0.34589408001288835916291394318423
y[1] (numeric) = 0.31852872581019965722693453374578
absolute error = 0.027365354202688701935979409438456
relative error = 7.9114838281328901278373394806035 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 0.34513800422690344111434559120292
y[1] (numeric) = 0.3176507539056589459454164984297
absolute error = 0.027487250321244495168929092773227
relative error = 7.964133182845202674963569363459 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=202.1MB, alloc=4.4MB, time=25.09
x[1] = 0.715
y[1] (analytic) = 0.344382583302859724331174094563
y[1] (numeric) = 0.31677312109028216625151062683371
absolute error = 0.027609462212577558079663467729291
relative error = 8.0170901640217446506362776248154 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 0.34362781799617806990537466451765
y[1] (numeric) = 0.31589582801930902438045657036121
absolute error = 0.027731989976869045524918094156444
relative error = 8.0703565091396322602393198635283 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 0.34287370906162372162149493329869
y[1] (numeric) = 0.31501887534873431968285656642984
absolute error = 0.027854833712889401938638366868851
relative error = 8.1239339665681778728523981624233 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 0.3421202572533055511914740666705
y[1] (numeric) = 0.31414226373530728862993075410075
absolute error = 0.027977993517998262561543312569746
relative error = 8.177824295649169833863097194828 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 0.34136746332467530414583389439473
y[1] (numeric) = 0.31326599383653094806433543195966
absolute error = 0.028101469488144356081498462435069
relative error = 8.2320292667778329014952059417776 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 0.34061532802852684638199616735183
y[1] (numeric) = 0.31239006631066143769720100737677
absolute error = 0.028225261717865408684795159975063
relative error = 8.2865506614844758563616950030718 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 0.3398638521169954113704793929394
y[1] (numeric) = 0.31151448181670736185204714005289
absolute error = 0.028349370300288049518432252886514
relative error = 8.3413902725168329037487729475458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 0.33911303634155684801972804248768
y[1] (numeric) = 0.31063924101442913045623333588161
absolute error = 0.028473795327127717563494706606076
relative error = 8.3965499039231055597790242365782 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 0.33836288145302686920032626580041
y[1] (numeric) = 0.30976434456433829928060399962212
absolute error = 0.028598536888688569919722266178295
relative error = 8.4520313711357117848978069518898 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 0.33761338820156030092934758854468
y[1] (numeric) = 0.30888979312769690942798770668263
absolute error = 0.028723595073863391501359881862043
relative error = 8.5078365010557492012890902433026 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 0.33686455733665033221559140807746
y[1] (numeric) = 0.30801558736651682607121120546006
absolute error = 0.028848969970133506144380202617393
relative error = 8.563967132138179304866129315391 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 0.33611638960712776556645644240991
y[1] (numeric) = 0.30714172794355907644128941216686
absolute error = 0.028974661663568689125167030243051
relative error = 8.6204251144777396574103634721649 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.4MB, time=25.57
NO POLE
x[1] = 0.727
y[1] (analytic) = 0.33536888576116026815720062537343
y[1] (numeric) = 0.30626821552233318706645340989985
absolute error = 0.029100670238827081090747215473582
relative error = 8.6772123098955911202603996987639 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 0.33462204654625162366333627866526
y[1] (numeric) = 0.30539505076709652026267921286787
absolute error = 0.029226995779155103400657065797385
relative error = 8.7343305920267072676937984052244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 0.33387587270924098475690872831604
y[1] (numeric) = 0.30452223434285360987638080519411
absolute error = 0.029353638366387374880527923121928
relative error = 8.7917818464080131958096683030604 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 0.33313036499630212626740586923847
y[1] (numeric) = 0.30364976691535549627993171154472
absolute error = 0.029480598080946629987474157693752
relative error = 8.8495679705672810213220366974359 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 0.33238552415294269900804551688526
y[1] (numeric) = 0.30277764915109906062068010400685
absolute error = 0.029607875001843638387365412878414
relative error = 8.9076908741127894442249989878819 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 0.33164135092400348426818671966681
y[1] (numeric) = 0.30190588171732635832412319614538
absolute error = 0.029735469206677125944063523521429
relative error = 8.9661524788237548288033553326166 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 0.33089784605365764897261053965515
y[1] (numeric) = 0.30103446528202395185190742100845
absolute error = 0.029863380771633697120703118646709
relative error = 9.0249547187415413389495837249105 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 0.33015501028541000150841514223148
y[1] (numeric) = 0.30016340051392224271532163502606
absolute error = 0.029991609771487758793093507205427
relative error = 9.0840995402616577462225325101822 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 0.32941284436209624822026936771989
y[1] (numeric) = 0.29929268808249480274495133425282
absolute error = 0.030120156279601445475318033467073
relative error = 9.1435889022265486125582847702389 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 0.32867134902588225057476828969201
y[1] (numeric) = 0.29842232865795770461716261324489
absolute error = 0.030249020367924545957605676447118
relative error = 9.2034247760191876340325858696897 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 0.32793052501826328299463359552502
y[1] (numeric) = 0.29755232291126885163808534003145
absolute error = 0.030378202106994431356548255493565
relative error = 9.2636091456574810175905613728361 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 0.32719037308006329136350095495073
y[1] (numeric) = 0.29668267151412730678576576314154
absolute error = 0.030507701565935984577735191809193
relative error = 9.3241440078894888492169098397563 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.4MB, time=26.05
NO POLE
x[1] = 0.739
y[1] (analytic) = 0.32645089395143415220203587174673
y[1] (numeric) = 0.29581337513897262101115950847788
absolute error = 0.030637518812461531190876363268857
relative error = 9.3850313722894724996322579090012 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 0.32571208837185493251611884239183
y[1] (numeric) = 0.29494443445898416079863666498862
absolute error = 0.030767653912870771717482177403212
relative error = 9.4462732613547762022830408037502 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 0.32497395708013115031783997343909
y[1] (numeric) = 0.29407585014808043498667139857592
absolute error = 0.030898106932050715331168574863172
relative error = 9.5078717106035510281574534182957 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 0.32423650081439403582004253655019
y[1] (numeric) = 0.29320762288091842084938927349564
absolute error = 0.03102887793347561497065326305455
relative error = 9.5698287686733295728232484003026 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 0.32349972031209979330515426658597
y[1] (numeric) = 0.29233975333289288943964619964471
absolute error = 0.031159966979206903865508066941253
relative error = 9.6321464974204597630591938937096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 0.32276361631002886366904453386027
y[1] (numeric) = 0.29147224218013573019431366260088
absolute error = 0.031291374129893133474730871259388
relative error = 9.6948269720204062835558167767539 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 0.32202818954428518764064484663867
y[1] (numeric) = 0.29060509009951527480244563107351
absolute error = 0.031423099444769912838199215565161
relative error = 9.7578722810689282184078388561361 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 0.32129344075029546967806946419994
y[1] (numeric) = 0.289738297768635620337003273542
absolute error = 0.031555142981659849341066190657931
relative error = 9.8212845266841415975258781948714 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 0.32055937066280844254197222427846
y[1] (numeric) = 0.28887186586583595165081435230089
absolute error = 0.03168750479697249089115787197757
relative error = 9.8850658246094756346741768359446 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 0.31982598001589413254687501146943
y[1] (numeric) = 0.28800579507018986303744489889555
absolute error = 0.031820184945704269509430112573889
relative error = 9.949218304317531541610201168982 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 0.3190932695429431254912026152071
y[1] (numeric) = 0.28714008606150467915766151002046
absolute error = 0.031953183481438446333541105186639
relative error = 10.013744109114852901777047531033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=213.6MB, alloc=4.4MB, time=26.52
x[1] = 0.75
y[1] (analytic) = 0.31836123997666583326675804722011
y[1] (numeric) = 0.28627473952032077523216333736118
absolute error = 0.032086500456345058034594709858926
relative error = 10.078645396247616687197016453689 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.751
y[1] (analytic) = 0.31762989204909176114837170892742
y[1] (numeric) = 0.28540975612791089650126357859116
absolute error = 0.032220135921180864647108130336266
relative error = 10.143924337008254103651078844401 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 0.3168992264915687757644571190647
y[1] (numeric) = 0.28454513656627947695220100978546
absolute error = 0.032354089925289298812256109279239
relative error = 10.209583116843010551921076220144 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 0.31616924403476237374920523092425
y[1] (numeric) = 0.28368088151816195731476283188292
absolute error = 0.032488362516600416434442399041331
relative error = 10.275623935460454096836454049946 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 0.31543994540865495107714868695348
y[1] (numeric) = 0.2828169916670241023259008355171
absolute error = 0.032622953741630848751247851436376
relative error = 10.342049006940941941122454714796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 0.31471133134254507308082667608652
y[1] (numeric) = 0.28195346769706131726402361954301
absolute error = 0.032757863645483755816803056543508
relative error = 10.408860559847054507609584283784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 0.31398340256504674515228037608347
y[1] (numeric) = 0.28109031029319796375364832891035
absolute error = 0.032893092271848781398632047173121
relative error = 10.476060837335006841252666416191 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 0.31325615980408868412910827932099
y[1] (numeric) = 0.28022752014108667484109610717463
absolute error = 0.033028639663002009288012172146356
relative error = 10.543652097267047151640024079687 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 0.31252960378691359036581001591817
y[1] (numeric) = 0.27936509792710766934191618789354
absolute error = 0.033164505859805921023893828024625
relative error = 10.611636612324852427267672223129 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 0.31180373524007742049114660279324
y[1] (numeric) = 0.27850304433836806546072427742735
absolute error = 0.033300690901709355030422325365888
relative error = 10.68001667012393116482852316369 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 0.31107855488944866085224436123027
y[1] (numeric) = 0.27764136006270119368414160924783
absolute error = 0.033437194826747467168102751982441
relative error = 10.748794573329043370141441085802 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 0.31035406346020760164616905879138
y[1] (numeric) = 0.27678004578866590894752177675934
absolute error = 0.033574017671541692698647282032041
relative error = 10.817972639770648102138755796576 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=217.4MB, alloc=4.4MB, time=27.00
x[1] = 0.762
y[1] (analytic) = 0.30963026167684561173969614393974
y[1] (numeric) = 0.27591910220554590207615317784784
absolute error = 0.033711159471299709663542966091904
relative error = 10.887553202562388947563069668708 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 0.30890715026316441417800225354293
y[1] (numeric) = 0.2750585300033490105016256298982
absolute error = 0.033848620259815403676376623644724
relative error = 10.957538610219627931714668963221 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 0.30818472994227536238300248450447
y[1] (numeric) = 0.27419832987280652825405043885557
absolute error = 0.033986400069468834128952045648896
relative error = 11.027931226779038489759682151995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 0.30746300143659871704205723112624
y[1] (numeric) = 0.27333850250537251523082393005332
absolute error = 0.03412449893122620181123330107292
relative error = 11.098733431919268243776716234307 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 0.30674196546786292368777169943441
y[1] (numeric) = 0.27247904859322310574262517198644
absolute error = 0.034262916874639817945146527447972
relative error = 11.1699476210826824529067571493 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 0.30602162275710389096961051860939
y[1] (numeric) = 0.2716199688292558163373393469751
absolute error = 0.034401653927848074632271171634292
relative error = 11.241576205598199127698664024978 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 0.30530197402466426961804917784491
y[1] (numeric) = 0.27076126390708885290259894473724
absolute error = 0.034540710117575416715450233107667
relative error = 11.313621612805226925031958073874 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 0.30458301999019273210198332442474
y[1] (numeric) = 0.26990293452106041704763567627132
absolute error = 0.034680085469132315054347648153424
relative error = 11.386086286178717066871466629564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
y[1] (analytic) = 0.30386476137264325298011626554779
y[1] (numeric) = 0.26904498136622801176513672613946
absolute error = 0.034819780006415241214979539408332
relative error = 11.45897268545534065458671985679 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 0.30314719889027438994704432245398
y[1] (numeric) = 0.26818740513836774637379968123694
absolute error = 0.034959793751906643573244641217041
relative error = 11.532283286760802880675133722674 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 0.30243033326064856557475899070575
y[1] (numeric) = 0.2673302065339736407422811934351
absolute error = 0.035100126726674924832477797270651
relative error = 11.606020582738305771484607931016 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 0.30171416520063134975028416506311
y[1] (numeric) = 0.26647338625025692879523515209108
absolute error = 0.035240778950374420955049012972035
relative error = 11.680187082678171227961225677875 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.4MB, time=27.47
NO POLE
x[1] = 0.774
y[1] (analytic) = 0.30099869542639074281016599125526
y[1] (numeric) = 0.26561694498514536130213686032815
absolute error = 0.03538175044124538150802913092711
relative error = 11.754785312648636266574616859729 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 0.30028392465339645937253221009913
y[1] (numeric) = 0.26476088343728250794959042620439
absolute error = 0.03552304121611395142294178389474
relative error = 11.829817815627832499420946679055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.776
y[1] (analytic) = 0.29956985359641921286743716184588
y[1] (numeric) = 0.26390520230602705869781729640408
absolute error = 0.035664651290392154169619865441798
relative error = 11.905287151636962031095487574792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 0.29885648296953000076620792035069
y[1] (numeric) = 0.26304990229145212442202457590516
absolute error = 0.035806580678077876344183344445526
relative error = 11.981195897874682090287761352056 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 0.29814381348609939051050632766018
y[1] (numeric) = 0.2621949840943445368393524921961
absolute error = 0.035948829391754853671153835464071
relative error = 12.057546648852710856207110824941 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 0.29743184585879680614182099989582
y[1] (numeric) = 0.26134044841620414772210107703634
absolute error = 0.036091397442592658419719922859478
relative error = 12.134342016532667083920466155038 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 0.29672058079958981563210267488208
y[1] (numeric) = 0.26048629595924312739793685247531
absolute error = 0.036234284840346688234165822406772
relative error = 12.211584630464156278502585996404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 0.2960100190197434189162555708243
y[1] (numeric) = 0.25963252742638526253778102086479
absolute error = 0.036377491593358156378474549959508
relative error = 12.289277137924116315588145265532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 0.29530016122981933662719672348589
y[1] (numeric) = 0.25877914352126525323208137091804
absolute error = 0.036521017708554083395115352567846
relative error = 12.367422204057435555501076165025 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 0.29459100813967529953419456674599
y[1] (numeric) = 0.257926144948228009356170823485
absolute error = 0.036664863191447290178023743260991
relative error = 12.446022512018856649646318554309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 0.29388256045846433868519731813999
y[1] (numeric) = 0.25707353241232794622541625162658
absolute error = 0.036809028046136392459781066513411
relative error = 12.525080763116179391309783408859 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
memory used=225.0MB, alloc=4.4MB, time=27.96
y[1] (analytic) = 0.29317481889463407625386102699527
y[1] (numeric) = 0.25622130661932827954086191978048
absolute error = 0.036953512275305796712999107214786
relative error = 12.604599676954776118451481314145 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 0.292467784155926017091986438075
y[1] (numeric) = 0.25536946827570031962607259631624
absolute error = 0.037098315880225697465913841758759
relative error = 12.684581991583433333522444910099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 0.29176145694937484098807311823418
y[1] (numeric) = 0.25451801808862276495588210257768
absolute error = 0.037243438860752076032191015656502
relative error = 12.765030463641533364816741096562 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 0.29105583798130769563269858747478
y[1] (numeric) = 0.25366695676598099497775376960537
absolute error = 0.037388881215326700654944817869408
relative error = 12.84594786850759005541442698666 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 0.29035092795734349029142948896187
y[1] (numeric) = 0.25281628501636636222645998111961
absolute error = 0.037534642940977128064969507842264
relative error = 12.92733700044915262940910198219 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 0.2896467275823921901859711250308
y[1] (numeric) = 0.25196600354907548373278868802541
absolute error = 0.037680724033316706453182437005393
relative error = 13.009200672774092050874550952207 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 0.28894323756065411158426097797705
y[1] (numeric) = 0.25111611307410953172698548567405
absolute error = 0.037827124486544579857275492302998
relative error = 13.091541717983284358939127056995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 0.28824045859561921760021112547646
y[1] (numeric) = 0.25026661430217352363764055037983
absolute error = 0.037973844293445693962570575096626
relative error = 13.174362987924705632434724515663 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.793
y[1] (analytic) = 0.2875383913900664147038037508348
y[1] (numeric) = 0.24941750794467561138673043624604
absolute error = 0.038120883445390803317073314588763
relative error = 13.257667353948953409900657238476 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 0.28683703664606284994224323791253
y[1] (numeric) = 0.2485687947137263699815254371991
absolute error = 0.038268241932336479960717800713437
relative error = 13.341457707066209565283190904213 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 0.28613639506496320887286762951401
y[1] (numeric) = 0.24772047532213808540407392226418
absolute error = 0.038415919742825123468793707249832
relative error = 13.425736958104659816511070639771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 0.28543646734740901420852151627135
y[1] (numeric) = 0.24687255048342404179897575453875
absolute error = 0.038563916863984972409545761732604
relative error = 13.510508037870385223278843909555 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=228.8MB, alloc=4.4MB, time=28.45
x[1] = 0.797
y[1] (analytic) = 0.28473725419332792517609171059139
y[1] (numeric) = 0.24602502091179780796015760603098
absolute error = 0.038712233281530117215934104560409
relative error = 13.595773897308741211866310092314 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 0.28403875630193303758890634707191
y[1] (numeric) = 0.24517788732217252311736368152857
absolute error = 0.038860868979760514471542665543333
relative error = 13.681537507667239848697766319752 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 0.28334097437172218463369733692953
y[1] (numeric) = 0.24433115043016018202307606494747
absolute error = 0.039009823941562002610621271982061
relative error = 13.767801860659951270633124371483 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 0.28264390910047723837282538941861
y[1] (numeric) = 0.24348481095207091934057960118066
absolute error = 0.039159098148406319032245788237959
relative error = 13.854569968633440368719244741715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 0.28194756118526341196246609795798
y[1] (numeric) = 0.2426388696049122933338869253226
absolute error = 0.039308691580351118628579172635385
relative error = 13.941844864734255013349317626923 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 0.28125193132242856258745487272111
y[1] (numeric) = 0.24179332710638856886023994928443
absolute error = 0.039458604216039993727214923436688
relative error = 14.029629603077982302516719301054 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 0.28055702020760249511348778478693
y[1] (numeric) = 0.2409481841748999996659048132388
absolute error = 0.039608836032702495447582971548134
relative error = 14.117927258919889511143954967791 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 0.27986282853569626645737466959218
y[1] (numeric) = 0.24010344152954210998597800603955
absolute error = 0.039759387006154156471396663552628
relative error = 14.206740928827166618354110250564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 0.27916935700090149067604011937443
y[1] (numeric) = 0.23925909989010497544892205475026
absolute error = 0.039910257110796515227118064624162
relative error = 14.296073730852787491069303109186 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 0.27847660629668964477496727554668
y[1] (numeric) = 0.238415159977072503286549878686
absolute error = 0.040061446319617141488417396860686
relative error = 14.385928804711007006506181860143 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 0.27778457711581137523677861250211
y[1] (numeric) = 0.237571622511621711850177597924
absolute error = 0.040212954604189663386601014578111
relative error = 14.47630931195451160303138463506 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 0.27709327015029580527064718421017
y[1] (numeric) = 0.23672848821562200943366628007046
absolute error = 0.040364781934673795836980904139711
relative error = 14.567218436153240958479508756161 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=232.7MB, alloc=4.4MB, time=28.94
x[1] = 0.809
y[1] (analytic) = 0.2764026860914498427832310841352
y[1] (numeric) = 0.2358857578116344724040738021814
absolute error = 0.040516928279815370379157281953797
relative error = 14.65865938307489870746260965728 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 0.27571282562985748907182314748546
y[1] (numeric) = 0.23504343202291112264063869712591
absolute error = 0.040669393606946366431184450359544
relative error = 14.75063538086717032445427024439 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 0.27502368945537914824040720258509
y[1] (numeric) = 0.23420151157339420428281854534735
absolute error = 0.040822177881984943957588657237738
relative error = 14.843149680241666517554213661687 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 0.27433527825715093733931145525542
y[1] (numeric) = 0.23335999718771545978810616392414
absolute error = 0.040975281069435477551205291331283
relative error = 14.93620555465961069887329577464 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 0.27364759272358399722914886649459
y[1] (numeric) = 0.23251888959119540530034753505347
absolute error = 0.041128703132388591928801331441124
relative error = 15.029806300519289321466199943353 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 0.27296063354236380416973365945774
y[1] (numeric) = 0.23167818950984260532928610557963
absolute error = 0.041282444032521198840447553878103
relative error = 15.123955237345284099723640273482 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 0.27227440140044948213466236676389
y[1] (numeric) = 0.23083789767035294674205877796229
absolute error = 0.041436503730096535392603588801598
relative error = 15.218655707979505360161429555273 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 0.2715888969840731158522471034912
y[1] (numeric) = 0.2299980148001089120673696011281
absolute error = 0.041590882183964203784877502363096
relative error = 15.313911078774046002655160265891 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 0.27090412097873906457348802486997
y[1] (numeric) = 0.22915854162717885211306785697155
absolute error = 0.041745579351560212460420167898424
relative error = 15.40972473978587578841197599897 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 0.27022007406922327656777120064388
y[1] (numeric) = 0.22831947888031625789785792486618
absolute error = 0.041900595188907018669913275777699
relative error = 15.506100104973395910391202639159 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 0.26953675693957260434697741034436
y[1] (numeric) = 0.22748082728895903189786899241583
absolute error = 0.04205592965061357244910841792853
relative error = 15.603040612394874044530433858137 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 0.26885417027310412061868663531228
y[1] (numeric) = 0.22664258758322875860881336581522
absolute error = 0.042211582689875362009873269497055
relative error = 15.700549724408780326050751591238 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.4MB, time=29.42
NO POLE
x[1] = 0.821
y[1] (analytic) = 0.26817231475240443496916229420547
y[1] (numeric) = 0.22580476049392997442446281760106
absolute error = 0.042367554258474460544699476604412
relative error = 15.79863092787604494435260698299 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 0.2674911910593290112767985389509
y[1] (numeric) = 0.22496734675254943683217309325624
absolute error = 0.042523844306779574444625445694662
relative error = 15.897287734364258302621772664166 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 0.26681079987500148585671319763723
y[1] (numeric) = 0.22413034709125539292618738108184
absolute error = 0.042680452783746092930525816555387
relative error = 15.99652368035383494429278254424 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 0.26613114187981298633716821969816
y[1] (numeric) = 0.22329376224289684723945023197254
absolute error = 0.042837379636916139097717987725622
relative error = 16.096342327446162708016291561999 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 0.26545221775342145126849874690922
y[1] (numeric) = 0.22245759294100282889466409722035
absolute error = 0.042994624812418622373834649688867
relative error = 16.196747262573758835798531862662 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 0.26477402817475095046523120121228
y[1] (numeric) = 0.22162183991978165807532133322929
absolute error = 0.043152188254969292389909867982992
relative error = 16.297742098212455025578070849713 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.827
y[1] (analytic) = 0.26409657382199100608207004719305
y[1] (numeric) = 0.22078650391412021181744520204758
absolute error = 0.043310069907870794264624845145467
relative error = 16.399330472595633689730802833617 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 0.26341985537259591442443215316827
y[1] (numeric) = 0.21995158565958318912277407591554
absolute error = 0.043468269713012725301658077252737
relative error = 16.501516049930537954902812135563 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 0.26274387350328406849420694029164
y[1] (numeric) = 0.2191170858924123753941237325833
absolute error = 0.043626787610871693100083207708336
relative error = 16.604302520616678216217599658881 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 0.26206862889003728127141977386192
y[1] (numeric) = 0.21828300534952590619366330597522
absolute error = 0.043785623540511375077756467886703
relative error = 16.707693601466358340345236513367 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 0.26139412220810010973247531511345
y[1] (numeric) = 0.21744934476851753032484113386321
absolute error = 0.043944777439582579407634181250243
relative error = 16.811693035927344897213283861647 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=240.3MB, alloc=4.4MB, time=29.90
x[1] = 0.832
y[1] (analytic) = 0.26072035413197917960565681518938
y[1] (numeric) = 0.21661610488765587223869742056219
absolute error = 0.044104249244323307366959394627187
relative error = 16.916304594307703089340717795473 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 0.26004732533544251086455659574197
y[1] (numeric) = 0.21578328644588369376530130827314
absolute error = 0.044264038889558817099255287468832
relative error = 17.021532074002823340945491802683 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 0.25937503649151884396011222267346
y[1] (numeric) = 0.21495089018281715517105062557541
absolute error = 0.044424146308701688789061597098053
relative error = 17.127379299724662806173594210969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 0.25870348827249696679192214092496
y[1] (numeric) = 0.21411891683874507554257325570686
absolute error = 0.044584571433751891249348885218097
relative error = 17.233850123733226357083334955834 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.836
y[1] (analytic) = 0.2580326813499250424195137989418
y[1] (numeric) = 0.21328736715462819249796974066885
absolute error = 0.04474531419529684992154405827295
relative error = 17.340948426070311917454947821714 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 0.25736261639460993751423655149115
y[1] (numeric) = 0.21245624187209842122613740985175
absolute error = 0.044906374522511516288099141639407
relative error = 17.44867811479554531814526316532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 0.25669329407661655155245088888304
y[1] (numeric) = 0.21162554173345811285491699379517
absolute error = 0.045067752343158438697533895087865
relative error = 17.557043126224730163634071996842 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 0.25602471506526714675068479934958
y[1] (numeric) = 0.21079526748167931214880335487445
absolute error = 0.045229447583587834601881444475131
relative error = 17.666047425170538517677801412715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 0.25535688002914067874342732937035
y[1] (numeric) = 0.20996541986040301453696263714074
absolute error = 0.045391460168737664206464692229616
relative error = 17.775695005185568538663265209547 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 0.25468978963607212800422866409446
y[1] (numeric) = 0.20913599961393842247229880723579
absolute error = 0.045553790022133705531929856858665
relative error = 17.885989888807795522406648040781 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 0.25402344455315183201077530670349
y[1] (numeric) = 0.20830700748726220112231322725278
absolute error = 0.045716437065889630888462079450712
relative error = 17.996936127808443141838746858321 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 0.25335784544672481815460819158468
y[1] (numeric) = 0.20747844422601773339250156862163
absolute error = 0.045879401220707084762106622963054
relative error = 18.108537803442302009326183981613 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=244.1MB, alloc=4.4MB, time=30.37
x[1] = 0.844
y[1] (analytic) = 0.25269299298239013739615082154036
y[1] (numeric) = 0.20665031057651437428303304355985
absolute error = 0.046042682405875763113117777980512
relative error = 18.220799026700523028370330977322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 0.2520288878250001986657137739502
y[1] (numeric) = 0.20582260728572670457945759734751
absolute error = 0.046206280539273494086256176602695
relative error = 18.333723938565913347172726113326 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 0.25136553063866010401114117482621
y[1] (numeric) = 0.20499533510129378387818737065693
absolute error = 0.046370195537366320132953804169277
relative error = 18.447316710270763077130711682642 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 0.25070292208672698449276399305858
y[1] (numeric) = 0.20416849477151840294749940639347
absolute error = 0.046534427315208581545264586665109
relative error = 18.561581543557231294803960545927 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 0.25004106283180933682632425984381
y[1] (numeric) = 0.20334208704536633542480723998225
absolute error = 0.046698975786443001401517019861563
relative error = 18.676522670940320206346843812264 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 0.24937995353576636077453357031556
y[1] (numeric) = 0.20251611267246558885094967576704
absolute error = 0.046863840863300771923583894548521
relative error = 18.79214435597346671890981658964 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 0.24871959485970729728792847576453
y[1] (numeric) = 0.20169057240310565504224571517001
absolute error = 0.047029022456601642245682760594523
relative error = 18.908450893516781034153054976444 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 0.24805998746399076739568462553681
y[1] (numeric) = 0.20086546698823675980106526449493
absolute error = 0.047194520475754007594619361041886
relative error = 19.025446610007962254866662973317 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 0.2474011320082241118470507677415
y[1] (numeric) = 0.20004079717946911196566591174067
absolute error = 0.047360334828754999881384856000821
relative error = 19.143135863735921376834413908965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.853
y[1] (analytic) = 0.24674302915126273150406296727849
y[1] (numeric) = 0.19921656372907215180004672252564
absolute error = 0.047526465422190579704016244752848
relative error = 19.26152304511714242459408584467 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 0.24608567955120942848619864841736
y[1] (numeric) = 0.19839276738997379872457066520658
absolute error = 0.047692912161235629761627983210777
relative error = 19.38061257697481288172026500458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 0.24542908386541374806762931721824
y[1] (numeric) = 0.19756940891575969838810793450684
absolute error = 0.047859674949654049679521382711404
relative error = 19.500408914820754963769703810403 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=247.9MB, alloc=4.4MB, time=30.85
x[1] = 0.856
y[1] (analytic) = 0.24477324275047132132773006648732
y[1] (numeric) = 0.19674648906067246908245310144788
absolute error = 0.048026753689798852245276965039439
relative error = 19.620916547140189685171042078965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 0.24411815686222320855550321270245
y[1] (numeric) = 0.19592400857961094749976967510413
absolute error = 0.04819414828261226105573353759832
relative error = 19.742139995679366080197502415741 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 0.24346382685575524340857266043075
y[1] (numeric) = 0.19510196822812943383381631867377
absolute error = 0.048361858627625809574756341756979
relative error = 19.864083815736088352822111206962 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 0.24281025338539737782740483518898
y[1] (numeric) = 0.19428036876243693622570961857631
absolute error = 0.04852988462296044160169521661267
relative error = 19.986752596453174150810645966375 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 0.24215743710472302770541127047135
y[1] (numeric) = 0.19345921093939641455497896075129
absolute error = 0.048698226165326613150432309720062
relative error = 20.11015096111487758594998078717 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 0.24150537866654841931558717878744
y[1] (numeric) = 0.19263849551652402357666972304006
absolute error = 0.04886688315002439573891745574738
relative error = 20.234283567446311054932476939934 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 0.24085407872293193649433958001736
y[1] (numeric) = 0.19181822325198835540525164648454
absolute error = 0.049035855470943581089087933532819
relative error = 20.359155107915900354215826893619 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 0.24020353792517346858315780320164
y[1] (numeric) = 0.19099839490460968134608990157143
absolute error = 0.049205143020563787237067901630209
relative error = 20.484770310040908027249217435495 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 0.2395537569238137591287784200408
y[1] (numeric) = 0.19017901123385919307523701788748
absolute error = 0.049374745689954566053541402153318
relative error = 20.611133936696060333899400075215 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 0.23890473636863375534249590988562
y[1] (numeric) = 0.18936007299985824316830449733084
absolute error = 0.049544663368775512174191412554772
relative error = 20.738250786425313689824502978507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 0.23825647690865395831926959685314
y[1] (numeric) = 0.18854158096337758497917358194354
absolute error = 0.049714895945276373340096014909603
relative error = 20.866125693756796888031167602412 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 0.23760897919213377401727663990728
y[1] (numeric) = 0.18772353588583661186930529759083
absolute error = 0.049885443306297162147971342316456
relative error = 20.994763529520965886015577190802 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.4MB, time=31.32
NO POLE
x[1] = 0.868
y[1] (analytic) = 0.23696224386657086499856009629705
y[1] (numeric) = 0.18690593852930259578841054411423
absolute error = 0.05005630533726826921014955218282
relative error = 21.124169201172008419836681059655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 0.23631627157870050293142031765021
y[1] (numeric) = 0.18608878965648992520724165122447
absolute error = 0.050227481922210577724178666425739
relative error = 21.254347653112536191307744711581 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 0.23567106297449492185519717627715
y[1] (numeric) = 0.18527209003075934240326746727943
absolute error = 0.050398972943735579451929708997713
relative error = 21.385303867021602866329460629106 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 0.23502661869916267220808985684866
y[1] (numeric) = 0.18445584041611718009999469520835
absolute error = 0.050570778283045492108095161640314
relative error = 21.517042862186086621335314928611 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
y[1] (analytic) = 0.23438293939714797561866018557423
y[1] (numeric) = 0.18364004157721459746069883619739
absolute error = 0.050742897819933378157961349376841
relative error = 21.649569695835476480990720550999 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 0.2337400257121300804616647053235
y[1] (numeric) = 0.18282469427934681543732874734196
absolute error = 0.05091533143278326502433595798154
relative error = 21.782889463480102203796556846027 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 0.23309787828702261817885994080533
y[1] (numeric) = 0.18200979928845235147534946429747
absolute error = 0.051088078998570266703510476507867
relative error = 21.917007299252847993212152483192 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.875
y[1] (analytic) = 0.23245649776397296036542453294546
y[1] (numeric) = 0.18119535737111225357528858402195
absolute error = 0.051261140392860706790135948923513
relative error = 22.051928376254390840451401027244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 0.231815884784361576622641155987
y[1] (numeric) = 0.18038136929454933371175214600033
absolute error = 0.05143451548981224291088900998667
relative error = 22.187657906902004841339665214471 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.877
y[1] (analytic) = 0.23117603998880139317748036457849
y[1] (numeric) = 0.17956783582662740061067659287061
absolute error = 0.051608204162173992566803771707883
relative error = 22.324201143281973373671576530817 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 0.23053696401713715226972775121205
y[1] (numeric) = 0.17875475773585049188558403313597
absolute error = 0.051782206281286660384143718076077
relative error = 22.461563377505651573506091184631 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=255.5MB, alloc=4.4MB, time=31.79
x[1] = 0.879
y[1] (analytic) = 0.22989865750844477230729502683122
y[1] (numeric) = 0.17794213579136210553360866964373
absolute error = 0.051956521717082666773686357187492
relative error = 22.599749942069222108902733218418 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 0.22926112110103070879035486924401
y[1] (numeric) = 0.17712997076294443079206289774044
absolute error = 0.052131150338086277998291971503563
relative error = 22.738766210217187817871584238226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 0.22862435543243131600493861515303
y[1] (numeric) = 0.17631826342101757835631221647317
absolute error = 0.052306092011413737648626398679861
relative error = 22.878617596309645353911286033194 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 0.22798836113941220948663510215197
y[1] (numeric) = 0.17550701453663880995972873489772
absolute error = 0.052481346602773399526906367254256
relative error = 23.019309556193384567578444472992 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 0.22735313885796762925502819693626
y[1] (numeric) = 0.17469622488150176731649369347621
absolute error = 0.052656913976465861938534503460047
relative error = 23.160847587576858946205060168937 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 0.2267186892233198038195097752374
y[1] (numeric) = 0.17388589522793570042802005769717
absolute error = 0.052832793995384103391489717540236
relative error = 23.303237230409073036297070547848 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 0.22608501286991831495710414761512
y[1] (numeric) = 0.17307602634890469525376687743124
absolute error = 0.053008986521013619703337270183875
relative error = 23.44648406726243338444832966319 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 0.22545211043143946326293915322968
y[1] (numeric) = 0.17226661901800690074721774114384
absolute error = 0.053185491413432562515721412085841
relative error = 23.590593723719610152934436957509 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 0.22481998254078563447399837107075
y[1] (numeric) = 0.1714576740094737552577962889218
absolute error = 0.053362308531311879216202082148947
relative error = 23.735571868764457195656363104987 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 0.22418862983008466656678812483747
y[1] (numeric) = 0.17064919209816921229949238233413
absolute error = 0.053539437731915454267295742503338
relative error = 23.881424215177039018934015766092 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 0.22355805293068921762955218375027
y[1] (numeric) = 0.16984117405958896568697316243613
absolute error = 0.05371687887110025194257902131414
relative error = 24.028156519932813699956593143768 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 0.22292825247317613450966628702682
y[1] (numeric) = 0.16903362066985967403995385974124
absolute error = 0.053894631803316460469712427285579
relative error = 24.175774584606021493634338892792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=259.4MB, alloc=4.4MB, time=32.26
x[1] = 0.891
y[1] (analytic) = 0.22229922908734582223684384457509
y[1] (numeric) = 0.16822653270573818465660385172519
absolute error = 0.054072696381607637580239992849903
relative error = 24.324284255777329526322438072303 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 0.22167098340222161422278339064533
y[1] (numeric) = 0.16741991094461075675676409439177
absolute error = 0.054251072457610857466019296253563
relative error = 24.473691425445783652562382951852 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 0.22104351604604914323788759074086
y[1] (numeric) = 0.16661375616449228409575268461796
absolute error = 0.054429759881556859142134906122901
relative error = 24.624002031445119238772148838572 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 0.22041682764629571316568282501642
y[1] (numeric) = 0.16580806914402551694953593940817
absolute error = 0.054608758502270196216146885608244
relative error = 24.775222057864483335879824932465 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 0.219790918829649671535567593692
y[1] (numeric) = 0.1650028506624802834720430068216
absolute error = 0.0547880681671693880635245868704
relative error = 24.927357535473621411404783165407 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 0.21916579022201978283451721168161
y[1] (numeric) = 0.16419810149975271042540265119328
absolute error = 0.054967688722267072409114560488339
relative error = 25.0804145421525825306179046151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 0.2185414424485346025983714806799
y[1] (numeric) = 0.16339382243636444328388148234702
absolute error = 0.055147620012170159314489998332885
relative error = 25.234399203325997606332768708084 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 0.21791787613354185228333124736692
y[1] (numeric) = 0.16259001425346186571230352479713
absolute error = 0.05532786188007998657102772256979
relative error = 25.389317692401986077771140060543 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 0.21729509190060779491828897618233
y[1] (numeric) = 0.16178667773281531841973164845416
absolute error = 0.055508414167792476498557327728168
relative error = 25.545176231215747130989862460142 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 0.21667309037251661153861768428645
y[1] (numeric) = 0.16098381365681831738919200708826
absolute error = 0.055689276715698294149425677198196
relative error = 25.701981090477892336736958703954 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 0.2160518721712697784020418048673
y[1] (numeric) = 0.16018142280848677148422325476051
absolute error = 0.055870449362783006917818550106784
relative error = 25.859738590227577356510240703397 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 0.21543143791808544498721276287073
y[1] (numeric) = 0.15937950597145819943303293360787
absolute error = 0.056051931946627245554179829262857
relative error = 26.018455100290491154213355968126 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.4MB, time=32.74
NO POLE
x[1] = 0.903
y[1] (analytic) = 0.21481178823339781277561126452646
y[1] (numeric) = 0.15857806392999094619104404875997
absolute error = 0.05623372430340686658456721576649
relative error = 26.178137040741761949336697982013 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 0.21419292373685651481739751871573
y[1] (numeric) = 0.15777709746896339868261546777603
absolute error = 0.0564158262678931161347820509397
relative error = 26.338790882373839958232284940284 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 0.2135748450473259960818298242788
y[1] (numeric) = 0.15697660737387320092272040281605
absolute error = 0.056598237673452795159109421462747
relative error = 26.500423147169417793004461265249 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 0.21295755278288489459287117279202
y[1] (numeric) = 0.15617659443083646851936785380243
absolute error = 0.056780958352048426073503318989586
relative error = 26.663040408779450223007669173371 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 0.21234104756082542335060273115629
y[1] (numeric) = 0.15537705942658700255755251008508
absolute error = 0.056963988134238420793050221071209
relative error = 26.826649293006335852137888117626 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 0.21172532999765275303906228253193
y[1] (numeric) = 0.15457800314847550286551922659463
absolute error = 0.057147326849177250173543055937301
relative error = 26.991256478292324126238781775481 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 0.21111040070908439552112491773005
y[1] (numeric) = 0.1537794263844687806641288081537
absolute error = 0.057330974324615614856996109576356
relative error = 27.156868696213211959234153312178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 0.21049626031004958812104248212845
y[1] (numeric) = 0.15298132992314897060011245251486
absolute error = 0.05751493038690061752093002961359
relative error = 27.323492731977395154265989275859 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 0.20988290941468867869525749552114
y[1] (numeric) = 0.15218371455371274216400281880514
absolute error = 0.057699194860975936531254676715999
relative error = 27.491135424930340697387220229263 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 0.20927034863635251149210647403642
y[1] (numeric) = 0.15138658106597051049353030338024
absolute error = 0.05788376757038200099857617065618
relative error = 27.659803669064546916459522292803 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 0.2086585785876018138010267943691
y[1] (numeric) = 0.15058993025034564656327371962663
absolute error = 0.058068648337256167237753074742464
relative error = 27.829504413535059427072421180697 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 0.20804759988020658339188045106857
y[1] (numeric) = 0.1497937628978736867613551919947
absolute error = 0.05825383698233289663052525907387
relative error = 28.000244663180611730768328815754 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.4MB, time=33.21
NO POLE
x[1] = 0.915
y[1] (analytic) = 0.20743741312514547674500726750837
y[1] (numeric) = 0.14899807980020154185396968750252
absolute error = 0.058439333324943934891037580005848
relative error = 28.172031479050460288871014445922 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 0.20682801893260519807261933043264
y[1] (numeric) = 0.14820288174958670533854022011457
absolute error = 0.058625137183018492734079110318072
relative error = 28.344871978936984868018929645867 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 0.20621941791197988913214762663437
y[1] (numeric) = 0.14740816953889646118629037477428
absolute error = 0.058811248373083427945857251860091
relative error = 28.518773337914125941350871471793 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 0.20561161067187051983215106836788
y[1] (numeric) = 0.14661394396160709097502640845195
absolute error = 0.058997666710263428857124659915928
relative error = 28.693742788881731932435433054035 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 0.20500459782008427963139730153571
y[1] (numeric) = 0.14582020581180308041292179535975
absolute error = 0.059184392008281199218475506175957
relative error = 28.869787623115890107738053034995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.92
y[1] (analytic) = 0.20439837996363396973172389751838
y[1] (numeric) = 0.14502695588417632525409769248314
absolute error = 0.059371424079457644477626205035237
relative error = 29.046915190825315957945571119099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 0.20379295770873739606528773573527
y[1] (numeric) = 0.1442341949740253366067934097822
absolute error = 0.059558762734712059458494325953065
relative error = 29.225132901713876959088300330922 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 0.20318833166081676307680958963652
y[1] (numeric) = 0.14344192387725444563492157682601
absolute error = 0.059746407783562317441888012810505
relative error = 29.404448225549327671389047783084 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 0.20258450242449806830142013383096
y[1] (numeric) = 0.14265014339037300765380330423875
absolute error = 0.059934359034125060647616829592212
relative error = 29.584868692738334217407703643868 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 0.20198147060361049773871279445357
y[1] (numeric) = 0.14185885431049460562087924415598
absolute error = 0.060122616293115892117833550297585
relative error = 29.766401894907867281624663718269 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 0.20137923680118582202360806866915
y[1] (numeric) = 0.1410680574353362530221930589137
absolute error = 0.060311179365849569001415009755453
relative error = 29.949055485493043891407494324033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=270.8MB, alloc=4.4MB, time=33.71
x[1] = 0.926
y[1] (analytic) = 0.20077780161945779339463314239777
y[1] (numeric) = 0.14027775356321759615544441142023
absolute error = 0.06050004805624019723918873097754
relative error = 30.132837180331499374629385750323 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 0.20017716565986154346021983793189
y[1] (numeric) = 0.13948794349306011581040919409157
absolute error = 0.060689222166801427649810643840317
relative error = 30.317754758264372042357137313483 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 0.19957732952303298176362312509717
y[1] (numeric) = 0.13869862802438632834752531586332
absolute error = 0.060878701498646653416097809233856
relative error = 30.503816061743984316308418974538 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 0.19897829380880819514706163098832
y[1] (numeric) = 0.13790980795731898617544296862691
absolute error = 0.061068485851489208971618662361418
relative error = 30.691028997448305210506404896882 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 0.19838005911622284791568078408935
y[1] (numeric) = 0.13712148409258027762833889547323
absolute error = 0.061258575023642570287341888616112
relative error = 30.879401536902280285054031940629 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 0.19778262604351158280193842876516
y[1] (numeric) = 0.13633365723149102624379478336273
absolute error = 0.061448968812020556558143645402434
relative error = 31.068941717106116417535596119691 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 0.19718599518810742273101194568898
y[1] (numeric) = 0.1355463281759698894420405022767
absolute error = 0.061639667012137533288971443412272
relative error = 31.259657641170609984561817795531 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 0.19659016714664117338782511274851
y[1] (numeric) = 0.13475949772853255660736351154008
absolute error = 0.061830669418108616780461601208425
relative error = 31.451557478959608312743823615795 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 0.19599514251494082658629213935434
y[1] (numeric) = 0.13397316669229094657248635183912
absolute error = 0.062021975822649880013805787515212
relative error = 31.644649467739695545256067310583 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 0.19540092188803096444137550485671
y[1] (numeric) = 0.13318733587095240450671473848992
absolute error = 0.062213586017078559934660766366792
relative error = 31.83894191283719537747894744917 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 0.19480750586013216434455342896323
y[1] (numeric) = 0.1324020060688188982086593677425
absolute error = 0.062405499791313266135894061220733
relative error = 32.034443188302584443356365723994 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 0.19421489502466040474329199864048
y[1] (numeric) = 0.13161717809078621380433514333195
absolute error = 0.062597716933874190938956855308529
relative error = 32.2311617375824114834261123687 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=274.6MB, alloc=4.4MB, time=34.19
x[1] = 0.938
y[1] (analytic) = 0.19362308997422647172511617197774
y[1] (numeric) = 0.13083285274234315085144212511004
absolute error = 0.062790237231883320873674046867705
relative error = 32.429106074198818796353135556306 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 0.19303209130063536640687307489267
y[1] (numeric) = 0.13004903082957071685063309540962
absolute error = 0.062983060471064649556239979483049
relative error = 32.62828478243676386859592435804 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 0.19244189959488571312978020136585
y[1] (numeric) = 0.12926571315914132116457323180685
absolute error = 0.063176186435744391965206969559002
relative error = 32.828706518039040491950138407847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 0.19185251544716916846085032210711
y[1] (numeric) = 0.12848290053831796834559796715459
absolute error = 0.063369614908851200115252354952518
relative error = 33.030380008909200116534383847768 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 0.19126393944686983100128410017909
y[1] (numeric) = 0.12770059377495345087277570916175
absolute error = 0.063563345671916380128508391017336
relative error = 33.233314055822475647711354195777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 0.19067617218256365200242060513652
y[1] (numeric) = 0.12691879367748954129918268238869
absolute error = 0.063757378505074110703237922747838
relative error = 33.437517533144811379881831473563 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.944
y[1] (analytic) = 0.19008921424201784678983510968148
y[1] (numeric) = 0.12613750105495618381019774531644
absolute error = 0.063951713187061662979637364365039
relative error = 33.642999389560104268465558498481 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 0.18950306621219030699617274468771
y[1] (numeric) = 0.12535671671697068519362562412766
absolute error = 0.064146349495219621802547120560051
relative error = 33.849768648805763274116069818004 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 0.18891772867922901360330577971155
y[1] (numeric) = 0.12457644147373690522245759300852
absolute error = 0.064341287205492108380848186703035
relative error = 34.057834410416695070738737734663 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 0.18833320222847145079440148678306
y[1] (numeric) = 0.12379667613604444645107921814347
absolute error = 0.06453652609242700434332226863959
relative error = 34.267205850477825991633464030851 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 0.18774948744444402061648673536087
y[1] (numeric) = 0.12301742151526784342573536912772
absolute error = 0.06473206592917617719075136623315
relative error = 34.477892222385271696515097606745 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 0.18716658491086145845409465583714
y[1] (numeric) = 0.12223867842336575131006328726458
absolute error = 0.064927906487495707144031368572566
relative error = 34.689902857616267676733991028843 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.4MB, time=34.67
NO POLE
x[1] = 0.95
y[1] (analytic) = 0.18658449521062624931457789789744
y[1] (numeric) = 0.12146044767288013392650508514724
absolute error = 0.065124047537746115388072812750206
relative error = 34.903247166507975377193254291055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 0.18600321892582804492567219837358
y[1] (numeric) = 0.12068273007693545121441163604475
absolute error = 0.065320488848892593711260562328823
relative error = 35.117934639045280401714461152317 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 0.1854227566377430816458931609772
y[1] (numeric) = 0.11990552644923784610565039492055
absolute error = 0.065517230188505235540242766056643
relative error = 35.333974845657700984425353949165 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 0.18484310892683359918834833746895
y[1] (numeric) = 0.11912883760407433081853027540796
absolute error = 0.065714271322759268369818062060988
relative error = 35.551377438025526653626517947667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 0.18426427637274726015854588640262
y[1] (numeric) = 0.11835266435631197257085728875005
absolute error = 0.065911612016435287587688597652571
relative error = 35.770152149895308787043798162324 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 0.18368625955431657040678027158725
y[1] (numeric) = 0.1175770075213970787129352315803
absolute error = 0.066109252032919491693845040006958
relative error = 35.990308797904826558904059169708 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 0.18310905904955830019567464783323
y[1] (numeric) = 0.11680186791535438128132628947547
absolute error = 0.066307191134203918914348358357762
relative error = 36.211857282417653610408508580295 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 0.18253267543567290618345876639169
y[1] (numeric) = 0.11602724635478622097418700245217
absolute error = 0.066505429080886685209271763939523
relative error = 36.434807588367452636455317680136 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 0.18195710928904395422356041676126
y[1] (numeric) = 0.1152531436568717305489956170031
absolute error = 0.066703965632172223674564799758157
relative error = 36.659169786112126973427332441083 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 0.18138236118523754298108760522243
y[1] (numeric) = 0.11447956063936601764348742687759
absolute error = 0.066902800545871525337600178344839
relative error = 36.884954032297960196067708347141 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 0.18080843169900172836677785356957
y[1] (numeric) = 0.11370649812059934702061528160302
absolute error = 0.067101933578402381346162571966552
relative error = 37.112170570733876686483767460061 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 0.18023532140426594878899018404309
y[1] (numeric) = 0.11293395691947632223835301771841
absolute error = 0.067301364484789626550637166324682
relative error = 37.340829733275958125725956631909 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.4MB, time=35.13
NO POLE
x[1] = 0.962
y[1] (analytic) = 0.17966303087414045122431453842204
y[1] (numeric) = 0.11216193785547506674516014284862
absolute error = 0.067501093018665384479154395573423
relative error = 37.570941940722352878774660800247 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 0.17909156068091571810737256061982
y[1] (numeric) = 0.11139044174864640440192667708617
absolute error = 0.06770111893226931370544588353365
relative error = 37.802517703718717297734709390071 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 0.1785209113960618950403828529345
y[1] (numeric) = 0.11061946941961303943121762966763
absolute error = 0.067901441976448855609165223266866
relative error = 38.035567623674330056199609961355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 0.17795108359022821932306299634073
y[1] (numeric) = 0.10984902168956873579463716163164
absolute error = 0.068102061900659483528425834709083
relative error = 38.27010239368902275073100163893 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 0.17738207783324244930343980487371
y[1] (numeric) = 0.10907909938027749599913305702616
absolute error = 0.068302978452964953304306747847543
relative error = 38.506132799491072163842203957281 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 0.17681389469411029455013846324732
y[1] (numeric) = 0.10830970331407273933306269629194
absolute error = 0.068504191380037555217075766955374
relative error = 38.743669720386201777429490160584 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 0.1762465347410148468467203753698
y[1] (numeric) = 0.10754083431385647953284229568779
absolute error = 0.068705700427158367313878079682012
relative error = 38.982724130217842356925343900132 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 0.17567999854131601200863872937179
y[1] (numeric) = 0.1067724932030985018810017460399
absolute error = 0.068907505338217510127636983331894
relative error = 39.223307098338803695232315274424 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 0.17511428666154994252337996214366
y[1] (numeric) = 0.10600468080583553973646795269174
absolute error = 0.069109605855714402786912009451914
relative error = 39.465429790594511912425661800222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 0.17454939966742847101435848319357
y[1] (numeric) = 0.1052373979466704504979001463027
absolute error = 0.069312001720758020516458336890868
relative error = 39.709103470317969052993159978809 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 0.17398533812383854452913119388423
y[1] (numeric) = 0.1044706454507713910009012010913
absolute error = 0.069514692673067153528229992792931
relative error = 39.954339499336594107730957989879 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=286.1MB, alloc=4.4MB, time=35.61
x[1] = 0.973
y[1] (analytic) = 0.17342210259484165965249751378665
y[1] (numeric) = 0.10370442414387099234992956324311
absolute error = 0.069717678450970667302567950543536
relative error = 40.201149338991107013069312107609 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 0.17285969364367329844504980100387
y[1] (numeric) = 0.10293873485226553418573695750261
absolute error = 0.069920958791407764259312843501252
relative error = 40.449544551166619647310577955472 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 0.17229811183274236520773822786723
y[1] (numeric) = 0.10217357840281411838915760444248
absolute error = 0.070124533429928246818580623424747
relative error = 40.699536799336100351788175181666 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 0.17173735772363062407301334739332
y[1] (numeric) = 0.10140895562293784222207524455221
absolute error = 0.070328402100692781850938102841108
relative error = 40.951137849616381056079200321645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 0.17117743187709213742310875931219
y[1] (numeric) = 0.10064486734061897090639482811018
absolute error = 0.070532564536473166516713931202008
relative error = 41.204359571836878680920586580419 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 0.17061833485305270513602545733743
y[1] (numeric) = 0.099881314384400109641846291798537
absolute error = 0.070737020468652595494179165538891
relative error = 41.459213940621205131201079476224 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 0.17006006721060930465977861164691
y[1] (numeric) = 0.099118297583383375063448404188019
absolute error = 0.070941769627225929596330207458887
relative error = 41.715713036481842875157270038261 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 0.16950262950802953191546671228085
y[1] (numeric) = 0.098355817767229566139461222559958
absolute error = 0.071146811740799965776005489720896
relative error = 41.973869046928065835536903659626 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 0.16894602230275104302972217034147
y[1] (numeric) = 0.097593875766157334510656263043824
absolute error = 0.071352146536593708519065907297651
relative error = 42.233694267587288094869384437657 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 0.168390246151380996897101644497
y[1] (numeric) = 0.096832472410942354271734044731043
absolute error = 0.07155777374043864262536759976596
relative error = 42.495201103340025740982248818754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 0.1678353016096954985729735303534
y[1] (numeric) = 0.096071608532916491195719226278346
absolute error = 0.071763693076779007377254304075056
relative error = 42.758402069468660051421914726077 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 0.16728118923263904349745921975985
y[1] (numeric) = 0.095311284963966971402164110536276
absolute error = 0.07196990426867207209529510922357
relative error = 43.02330979282019313739425177553 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=289.9MB, alloc=4.4MB, time=36.09
x[1] = 0.985
y[1] (analytic) = 0.16672790957432396255098390606041
y[1] (numeric) = 0.094551502536535549469991848930091
absolute error = 0.07217640703778841308099205713032
relative error = 43.289937012983190140171408997919 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 0.16617546318802986794199187969491
y[1] (numeric) = 0.093792262083617675995811232680511
absolute error = 0.072383201104412191946180647014398
relative error = 43.558296583479105096571161639385 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 0.16562385062620309992738042638742
y[1] (numeric) = 0.093033564438761664598535512480165
absolute error = 0.072590286187441435328844913907252
relative error = 43.828401472968190666078852902669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 0.16507307244045617436620560744248
y[1] (numeric) = 0.092275410436067858371138241937491
absolute error = 0.072797662004388315995067365504986
relative error = 44.100264766470195041445080214722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 0.16452312918156723110721236839716
y[1] (numeric) = 0.091517800910187795780379692962793
absolute error = 0.073005328271379435326832675434363
relative error = 44.373899666600052548170548953859 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 0.16397402139947948321074058845289
y[1] (numeric) = 0.090760736696323376015337943300518
absolute error = 0.073213284703156107195402645152371
relative error = 44.64931949481877767722006503512 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 0.16342574964330066700555784873517
y[1] (numeric) = 0.090004218630226023785579287607129
absolute error = 0.073421531013074643219978561128037
relative error = 44.926537692699775590649148830874 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.992
y[1] (analytic) = 0.16287831446130249298116886250245
y[1] (numeric) = 0.089248247548195853569803173834546
absolute error = 0.073630066913106639411365688667905
relative error = 45.205567823210785492660014382712 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 0.16233171640092009751615067494915
y[1] (numeric) = 0.088492824287080833315797416204579
absolute error = 0.07383889211383926420035325874457
relative error = 45.486423572011676670032058005586 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 0.16178595600875149544306190422175
y[1] (numeric) = 0.087737949684275947592539984749456
absolute error = 0.074048006324475547850521919472289
relative error = 45.769118748768320477022040324905 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 0.16124103383055703345047345869323
y[1] (numeric) = 0.086983624577722360195284219246906
absolute error = 0.074257409252834673255189239446327
relative error = 46.053667288482765071850964425227 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 0.16069695041125884432266732841958
y[1] (numeric) = 0.086229849805906576204464862394804
absolute error = 0.074467100605352268118202466024778
relative error = 46.340083252839943305962564563342 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.4MB, time=36.57
NO POLE
x[1] = 0.997
y[1] (analytic) = 0.16015370629494030201754921103397
y[1] (numeric) = 0.085476626207859603499262853249529
absolute error = 0.074677080087080698518286357784436
relative error = 46.628380831571147824551365731108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 0.15961130202484547758331989412072
y[1] (numeric) = 0.084723954623156113726667367293348
absolute error = 0.074887347401689363856652526827369
relative error = 46.918574343834511158640786135546 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 0.15906973814337859591444947735228
y[1] (numeric) = 0.083971835891913602726874133998877
absolute error = 0.075097902251464993187575343353408
relative error = 47.210678239612732376493933631973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 0.1585290151921034933474976783697
y[1] (numeric) = 0.083220270854791550415859606422339
absolute error = 0.075308744337311942931638071947362
relative error = 47.504707101128295716638256518268 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.001
y[1] (analytic) = 0.15798913371174307609732262654106
y[1] (numeric) = 0.082469260352990580125971100181439
absolute error = 0.075519873358752495971351526359617
relative error = 47.800675644276430547583781345176 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.002
y[1] (analytic) = 0.15745009424217877953421970834405
y[1] (numeric) = 0.081718805228251617405373561157651
absolute error = 0.075731289013927162128846147186398
relative error = 48.098598720076065991744729537216 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.003
y[1] (analytic) = 0.15691189732245002830253118718872
y[1] (numeric) = 0.080968906322855048277194162406065
absolute error = 0.075942990999594980025337024782653
relative error = 48.398491316139037614495603934759 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.004
y[1] (analytic) = 0.15637454349075369728126647902573
y[1] (numeric) = 0.080219564479619876959206471058045
absolute error = 0.076154979011133820322060007967687
relative error = 48.700368558157807715094111958892 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.005
y[1] (analytic) = 0.15583803328444357338727212307505
y[1] (numeric) = 0.079470780541902883044896465462334
absolute error = 0.076367252742540690342375657612718
relative error = 49.004245711411964965802932683949 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.006
y[1] (analytic) = 0.15530236724002981822148964446015
y[1] (numeric) = 0.078722555353597778146753221428371
absolute error = 0.076579811886432040074736423031776
relative error = 49.310138182293773430389068505769 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.007
y[1] (analytic) = 0.1547675458931784315588386624451
y[1] (numeric) = 0.077974889759134362002627624210835
absolute error = 0.076792656134044069556211038234269
relative error = 49.618061519853045354753118879175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=297.5MB, alloc=4.4MB, time=37.03
x[1] = 1.008
y[1] (analytic) = 0.15423356977871071568226175434684
y[1] (numeric) = 0.077227784603477678046002999806395
absolute error = 0.077005785175233037636258754540449
relative error = 49.928031417361616562252808280691 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.009
y[1] (analytic) = 0.15370043943060274056146674103291
y[1] (numeric) = 0.076481240732127168441022095221652
absolute error = 0.077219198698475572120444645811257
relative error = 50.240063713897707805879530880629 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.01
y[1] (analytic) = 0.15316815538198480987690121521799
y[1] (numeric) = 0.075735258991115828583115372614898
absolute error = 0.077432896390868981293785842603096
relative error = 50.55417439595046003040083919522 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.011
y[1] (analytic) = 0.15263671816514092788949328854018
y[1] (numeric) = 0.074989840227009361066076116612911
absolute error = 0.077646877938131566823417171927265
relative error = 50.870379599044936181507039991616 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.012
y[1] (analytic) = 0.15210612831150826715669168763168
y[1] (numeric) = 0.074244985286905329116428387657209
absolute error = 0.077861143024602938040263299974472
relative error = 51.188695609387886967542539079666 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.013
y[1] (analytic) = 0.15157638635167663709533748309973
y[1] (numeric) = 0.073500695018432309495934386941233
absolute error = 0.078075691333244327599403096158492
relative error = 51.509138865534582834244119406766 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.014
y[1] (analytic) = 0.15104749281538795339189888850143
y[1] (numeric) = 0.072756970269749044873088330360528
absolute error = 0.078290522545638908518810558140901
relative error = 51.831725960077019355767254224816 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.015
y[1] (analytic) = 0.15051944823153570826059971903376
y[1] (numeric) = 0.072013811889543595664444459911385
absolute error = 0.078505636341992112596155259122376
relative error = 52.156473641353808277913505618132 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.016
y[1] (analytic) = 0.14999225312816444154997125176595
y[1] (numeric) = 0.071271220727032491346627351139285
absolute error = 0.078721032401131950203343900626665
relative error = 52.483398815182071573670921543446 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.017
y[1] (analytic) = 0.14946590803246921269835638081839
y[1] (numeric) = 0.070529197631959881239873204556082
absolute error = 0.078936710400509331458483176262304
relative error = 52.812518546611661088778133984582 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.018
y[1] (analytic) = 0.14894041347079507353889411193989
y[1] (numeric) = 0.069787743454596684763951337413885
absolute error = 0.079152670016198388774942774526002
relative error = 53.143850061702031667894643646503 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.019
y[1] (analytic) = 0.14841576996863654195451159145488
y[1] (numeric) = 0.069046859045739741167315619843335
absolute error = 0.079368910922896800787195971611545
relative error = 53.477410749322101062018623185294 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.4MB, time=37.51
NO POLE
x[1] = 1.02
y[1] (analytic) = 0.14789197805063707638345001454462
y[1] (numeric) = 0.068306545256710958730336126133973
absolute error = 0.079585432793926117653113888410652
relative error = 53.813218162973435426995528574796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.021
y[1] (analytic) = 0.14736903824058855117584990729276
y[1] (numeric) = 0.067566802939356463443461797854155
absolute error = 0.079802235301232087732388109438601
relative error = 54.15129002263710483330489924835 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.022
y[1] (analytic) = 0.14684695106143073280192042586617
y[1] (numeric) = 0.066827632946045747161165440576916
absolute error = 0.080019318115384985640754985289256
relative error = 54.491644216644558920841973451949 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.023
y[1] (analytic) = 0.1463257170352507569122164646183
y[1] (numeric) = 0.06608903612967081523252290019578
absolute error = 0.080236680905579941679693564422515
relative error = 54.834298803572878651213216158589 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.024
y[1] (analytic) = 0.14580533668328260625054651279403
y[1] (numeric) = 0.065351013343645333609278788180324
absolute error = 0.080454323339637272641267724613707
relative error = 55.179272014164766036274749430723 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.025
y[1] (analytic) = 0.14528581052590658942003334688506
y[1] (numeric) = 0.064613565441903775432251647634696
absolute error = 0.080672245084002813987781699250367
relative error = 55.526582253273639757441416829728 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.026
y[1] (analytic) = 0.14476713908264882050284879253134
y[1] (numeric) = 0.063876693278900567096931973682789
absolute error = 0.080890445803748253405916818848551
relative error = 55.876248101834210737911596377866 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.027
y[1] (analytic) = 0.14424932287218069953414293619066
y[1] (numeric) = 0.063140397709609233799127022510912
absolute error = 0.081108925162571465735015913679749
relative error = 56.228288318858917991668219917233 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.028
y[1] (analytic) = 0.1437323624123183938306873126038
y[1] (numeric) = 0.062404679589521544561506863351919
absolute error = 0.081327682822796849269180449251883
relative error = 56.582721843460611451259799827507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.029
y[1] (analytic) = 0.14321625822002232017475073936883
y[1] (numeric) = 0.061669539774646656741906646793519
absolute error = 0.081546718445375663432844092575312
relative error = 56.939567796901874973318590279753 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.03
y[1] (analytic) = 0.14270101081139662785372561470558
y[1] (numeric) = 0.060934979121510260024240581037194
absolute error = 0.081766031689886367829485033668386
relative error = 57.298845484671389338971502517552 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=305.1MB, alloc=4.4MB, time=37.98
x[1] = 1.031
y[1] (analytic) = 0.14218662070168868255602163874092
y[1] (numeric) = 0.060200998487153719892883625122417
absolute error = 0.081985622214534962663138013618507
relative error = 57.660574398587741808232723186119 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.032
y[1] (analytic) = 0.14167308840528855112374306237812
y[1] (numeric) = 0.059467598729133220591377424663103
absolute error = 0.082205489676155330532365637715018
relative error = 58.024774218931095655680632786934 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.033
y[1] (analytic) = 0.14116041443572848716266471103004
y[1] (numeric) = 0.058734780705518907566317531318935
absolute error = 0.082425633730209579596347179711101
relative error = 58.391464816603140111818236093621 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.034
y[1] (analytic) = 0.14064859930568241751002117319736
y[1] (numeric) = 0.058002545274894029397279462042885
absolute error = 0.082646054030788388112741711154474
relative error = 58.760666255315748263157105082912 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.035
y[1] (analytic) = 0.14013764352696542956062268605983
y[1] (numeric) = 0.057270893296354079213641668107356
absolute error = 0.082866750230611350346981017952469
relative error = 59.13239879380877772697099273635 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.036
y[1] (analytic) = 0.13962754761053325945181039192184
y[1] (numeric) = 0.056539825629505935599163997014442
absolute error = 0.0830877219810273238526463949074
relative error = 59.506682888097456316619452309823 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.037
y[1] (analytic) = 0.1391183120664817811077627805146
y[1] (numeric) = 0.05580934313446700298518074264024
absolute error = 0.083308968932014778122582037874364
relative error = 59.883539193749802453189599952711 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.038
y[1] (analytic) = 0.13860993740404649614366427280568
y[1] (numeric) = 0.055079446671864351533267890348536
absolute error = 0.083530490732182144610396382457143
relative error = 60.262988568194537761855701492385 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.039
y[1] (analytic) = 0.13810242413160202463024604210498
y[1] (numeric) = 0.054350137102833856508244674334943
absolute error = 0.083752287028768168122001367770034
relative error = 60.645052073059957119787749014382 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.04
y[1] (analytic) = 0.13759577275666159671920830788383
y[1] (numeric) = 0.053621415289019337142370074128215
absolute error = 0.083974357467642259576838233755619
relative error = 61.02975097654422939969553906777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.041
y[1] (analytic) = 0.13708998378587654513003247684256
y[1] (numeric) = 0.052893282092571694991595385980471
absolute error = 0.084196701693304850138437090862091
relative error = 61.417106755817610282287279555981 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=309.0MB, alloc=4.4MB, time=38.47
x[1] = 1.042
y[1] (analytic) = 0.13658505772503579849869064437203
y[1] (numeric) = 0.052165738376148051784734512821976
absolute error = 0.084419319348887746713956131550057
relative error = 61.807141099457056795235847747672 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.043
y[1] (analytic) = 0.13608099507906537558875910765756
y[1] (numeric) = 0.05143878500291088676641412353831
absolute error = 0.084642210076154488822344984119249
relative error = 62.199875909913741678938772980715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.044
y[1] (analytic) = 0.13557779635202788036544167926943
y[1] (numeric) = 0.050712422836527173534666338547911
absolute error = 0.084865373515500706830775340721515
relative error = 62.595333306013974283761772738105 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.045
y[1] (analytic) = 0.13507546204712199793300772717468
y[1] (numeric) = 0.049986652741167516374027104015354
absolute error = 0.085088809305954481558980623159323
relative error = 62.993535625494043472978707081835 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.046
y[1] (analytic) = 0.13457399266668199133614900369011
y[1] (numeric) = 0.049261475581505286085003921530027
absolute error = 0.085312517085176705251145082160079
relative error = 63.394505427569506943750046420231 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.047
y[1] (analytic) = 0.1340733887121771992257584619777
y[1] (numeric) = 0.048536892222715755310777103710461
absolute error = 0.085536496489461443914981358267235
relative error = 63.798265495539460488784676394782 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.048
y[1] (analytic) = 0.13357365068421153438963339426183
y[1] (numeric) = 0.047812903530475233361999228961003
absolute error = 0.085760747153736301027634165300826
relative error = 64.204838839426330007455799183834 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.049
y[1] (analytic) = 0.13307477908252298314860436102333
y[1] (numeric) = 0.047089510370960200540557970509273
absolute error = 0.08598526871156278260804639051406
relative error = 64.614248698651738540825007629847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.05
y[1] (analytic) = 0.13257677440598310561859051499973
y[1] (numeric) = 0.046366713610846441963167975889446
absolute error = 0.086210060795136663655422539110283
relative error = 65.026518544749010254090069254214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.051
y[1] (analytic) = 0.1320796371525965368390810578947
y[1] (numeric) = 0.045644514117308180885657973207286
absolute error = 0.086435123035288355953423084687415
relative error = 65.441672084112883126321087844574 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.052
y[1] (analytic) = 0.13158336781950048876854170127377
y[1] (numeric) = 0.044922912758017211528819779827619
absolute error = 0.086660455061483277239721921446147
relative error = 65.85973326078701213498703821927 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.053
y[1] (analytic) = 0.13108796690296425314724413619817
y[1] (numeric) = 0.044201910401142031406686387562951
absolute error = 0.086886056501822221740557748635222
relative error = 66.280726259289854945794020461636 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.4MB, time=38.95
NO POLE
x[1] = 1.054
y[1] (analytic) = 0.13059343489838870522801564872615
y[1] (numeric) = 0.043481507915346973158106796012865
absolute error = 0.087111926983041732069908852713289
relative error = 66.704675507479542540947436722349 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.055
y[1] (analytic) = 0.13009977230030580837540515049052
y[1] (numeric) = 0.042761706169791335882485762406986
absolute error = 0.087338066130514472492919388083536
relative error = 67.131605679458347845400221942957 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.056
y[1] (analytic) = 0.12960697960237811953376102514534
y[1] (numeric) = 0.042042506034128515980557132139411
absolute error = 0.087564473568249603553203893005933
relative error = 67.561541698517376245346397216046 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.057
y[1] (analytic) = 0.12911505729739829556471532256259
y[1] (numeric) = 0.041323908378505137501059909148805
absolute error = 0.087791148918893158063655413413782
relative error = 67.994508740122112940654829477923 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.058
y[1] (analytic) = 0.12862400587728860045456796325345
y[1] (numeric) = 0.040605914073560181994186719395657
absolute error = 0.088018091803728418460381243857789
relative error = 68.430532234939473337709201903773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.059
y[1] (analytic) = 0.12813382583310041339206374558905
y[1] (numeric) = 0.039888523990424117872674813915698
absolute error = 0.088245301842676295519388931673355
relative error = 68.869637871907014175932314346722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.06
y[1] (analytic) = 0.12764451765501373771705407800258
y[1] (numeric) = 0.039171739000718029281410250285927
absolute error = 0.088472778654295708435643827716654
relative error = 69.311851601344974794942666909892 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.061
y[1] (analytic) = 0.12715608183233671074053448747008
y[1] (numeric) = 0.038455559976552744476416382826481
absolute error = 0.088700521855783966264118104643601
relative error = 69.757199638111829894749644543757 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.062
y[1] (analytic) = 0.12666851885350511443654808419172
y[1] (numeric) = 0.037739987790527963714098282477213
absolute error = 0.088928531062977150722449801714504
relative error = 70.205708464804047323688347274672 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.063
y[1] (analytic) = 0.12618182920608188700644429052911
y[1] (numeric) = 0.037025023315731386651615197031882
absolute error = 0.08915680589035050035482909349723
relative error = 70.657404835000756853094060684596 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.064
y[1] (analytic) = 0.12569601337675663531598126989944
y[1] (numeric) = 0.03631066742573783925925365128479
absolute error = 0.089385345951018796056727618614651
relative error = 71.112315776554048569310522063254 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=316.6MB, alloc=4.4MB, time=39.42
x[1] = 1.065
y[1] (analytic) = 0.12521107185134514820575961848314
y[1] (numeric) = 0.035596920994608400245674274643989
absolute error = 0.089614150856736747960085343839149
relative error = 71.570468594925632437932804474598 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.066
y[1] (analytic) = 0.12472700511478891067547400927103
y[1] (numeric) = 0.034883784896889526996905930891454
absolute error = 0.089843220217899383678568078379578
relative error = 72.03189087657060377775168710655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.067
y[1] (analytic) = 0.12424381365115461894246860415874
y[1] (numeric) = 0.034171260007612181029961211023237
absolute error = 0.090072553643542437912507393135502
relative error = 72.49661049236907282837161866559 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.068
y[1] (analytic) = 0.1237614979436336963750811754925
y[1] (numeric) = 0.033459347202290952961947835481235
absolute error = 0.090302150741342743413133340011269
relative error = 72.964655601106430311735019530583 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.069
y[1] (analytic) = 0.12328005847454181030126000368204
y[1] (numeric) = 0.032748047356923186995550996592264
absolute error = 0.090532011117618623305709007089775
relative error = 73.436054653003034879757864053617 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.07
y[1] (analytic) = 0.12279949572531838969293674222318
y[1] (numeric) = 0.032037361347988104921762155659108
absolute error = 0.090762134377330284771174586564071
relative error = 73.910836393294122614064993129209 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.071
y[1] (analytic) = 0.1223198101765261437266375657173
y[1] (numeric) = 0.031327290052445929640730291901778
absolute error = 0.090992520124080214085907273815523
relative error = 74.389029865860753305655540567221 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.072
y[1] (analytic) = 0.12184100230785058122081404023625
y[1] (numeric) = 0.03061783434773700820161208232467
absolute error = 0.091223167960113573019201957911584
relative error = 74.870664416912623098627542795 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.073
y[1] (analytic) = 0.12136307259809953095037427866185
y[1] (numeric) = 0.02990899511178093436229797258637
absolute error = 0.091454077486318596588076306075483
relative error = 75.355769698723588239399754244987 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.074
y[1] (analytic) = 0.12088602152520266283889406642884
y[1] (numeric) = 0.029200773222975670669891579072919
absolute error = 0.091685248302226992169002487355923
relative error = 75.844375673420760137900693585329 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.075
y[1] (analytic) = 0.12040984956621101002898676542027
y[1] (numeric) = 0.028493169560196670062820341621968
absolute error = 0.091916680006014339966166423798301
relative error = 76.336512616828047726826249037736 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=320.4MB, alloc=4.4MB, time=39.89
x[1] = 1.076
y[1] (analytic) = 0.11993455719729649183130992560556
y[1] (numeric) = 0.027786185002795996995455824713972
absolute error = 0.092148372194500494835854100891591
relative error = 76.832211122365039206341809562245 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.077
y[1] (analytic) = 0.11946014489375143755268565537494
y[1] (numeric) = 0.027079820430601448086122542436891
absolute error = 0.092380324463149989466563112938045
relative error = 77.33150210500213169173912333655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.078
y[1] (analytic) = 0.11898661312998811120381092241007
y[1] (numeric) = 0.026374076723915672289374659142285
absolute error = 0.092612536406072438914436263267784
relative error = 77.834416805272834047944969279335 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.079
y[1] (analytic) = 0.11851396237953823708703307734115
y[1] (numeric) = 0.025668954763515290593420393442777
absolute error = 0.092845007616022946493612683898373
relative error = 78.340986793344185304992805846892 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.08
y[1] (analytic) = 0.11804219311505252626466501237524
y[1] (numeric) = 0.024964455430650015243574428053143
absolute error = 0.0930777376844025110210905843221
relative error = 78.851243973146248510370702039668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.081
y[1] (analytic) = 0.11757130580830020390831348654134
y[1] (numeric) = 0.024260579607041768492619101949202
absolute error = 0.093310726201258435415694384592134
relative error = 79.365220586561657695501221584818 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.082
y[1] (analytic) = 0.11710130093016853752969326818436
y[1] (numeric) = 0.023557328174883800878955634409876
absolute error = 0.093543972755284736650737633774485
relative error = 79.882949217676213822640095225484 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.083
y[1] (analytic) = 0.11663217895066236609339886385476
y[1] (numeric) = 0.022854702016839809033427102717738
absolute error = 0.093777476933822557059971761137017
relative error = 80.404462797091544143550722044306 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.084
y[1] (analytic) = 0.11616394033890363001210472078256
y[1] (numeric) = 0.022152702016043053015695366621534
absolute error = 0.094011238322860576996409354161024
relative error = 80.929794606300858350978118357048 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.085
y[1] (analytic) = 0.11569658556313090202466390769669
y[1] (numeric) = 0.021451329056095473181054603110207
absolute error = 0.094245256507035428843609304586484
relative error = 81.458978282128854246978867741891 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.086
y[1] (analytic) = 0.11523011509069891895757439585166
y[1] (numeric) = 0.020750584021066806578564584611294
absolute error = 0.094479531069632112379009811240363
relative error = 81.992047821236845397551292625925 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.087
y[1] (analytic) = 0.11476452938807811437028117875633
y[1] (numeric) = 0.020050467795493702881387302406791
absolute error = 0.094714061592584411488893876349544
relative error = 82.529037584694203399965128548361 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.4MB, time=40.37
NO POLE
x[1] = 1.088
y[1] (analytic) = 0.11429982892085415208478158526382
y[1] (numeric) = 0.019350981264378839850211004856169
absolute error = 0.094948847656475312234570580407651
relative error = 83.069982302617227967155457250785 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.089
y[1] (analytic) = 0.11383601415372746060000025637812
y[1] (numeric) = 0.018652125313190038330646186928822
absolute error = 0.095183888840537422269354069449303
relative error = 83.614917078876579042201171159435 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.09
y[1] (analytic) = 0.11337308555051276839139937136395
y[1] (numeric) = 0.017953900827859376785478533576177
absolute error = 0.095419184722653391605920837787773
relative error = 84.163877395874426605176464093316 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.091
y[1] (analytic) = 0.1129110435741386400962888235106
y[1] (numeric) = 0.017256308694782305362664284616758
absolute error = 0.095654734879356334733624538893837
relative error = 84.716899119392495734717092413851 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.092
y[1] (analytic) = 0.11244988868664701358530016020116
y[1] (numeric) = 0.016559349800816759499953953064993
absolute error = 0.095890538885830254085346207136168
relative error = 85.274018503512206847910219184555 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.093
y[1] (analytic) = 0.11198962134919273792048721577454
y[1] (numeric) = 0.01586302503328227306703079220619
absolute error = 0.096126596315910464853456423568354
relative error = 85.835272195608133875289818070507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.094
y[1] (analytic) = 0.11153024202204311220051547904107
y[1] (numeric) = 0.015167335279959091046050869205313
absolute error = 0.096362906742084021154464609835762
relative error = 86.400697241416026443761856781732 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.095
y[1] (analytic) = 0.11107175116457742529340135022401
y[1] (numeric) = 0.014472281429087281751472064635525
absolute error = 0.096599469735490143541929285588486
relative error = 86.970331090176665950435925966032 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.096
y[1] (analytic) = 0.11061414923528649645726155454927
y[1] (numeric) = 0.013777864369365848590059778023537
absolute error = 0.096836284865920647867201776525729
relative error = 87.544211599856849726129548679825 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.097
y[1] (analytic) = 0.11015743669177221684953209169568
y[1] (numeric) = 0.01308408498995184136195757933202
absolute error = 0.097073351701820375487574512363658
relative error = 88.122377042448822320558696182943 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.098
y[1] (analytic) = 0.10970161399074709192511521184868
y[1] (numeric) = 0.012390944180459467103711505234385
absolute error = 0.09731066981028762482140370661429
relative error = 88.704866109349498304055440931551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=328.0MB, alloc=4.4MB, time=40.85
x[1] = 1.099
y[1] (analytic) = 0.10924668158803378472391202017221
y[1] (numeric) = 0.011698442830959200474137157083529
absolute error = 0.097548238757074584249774863088679
relative error = 89.291717916820846885493743859309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.1
y[1] (analytic) = 0.1087926399385646600481974221283
y[1] (numeric) = 0.011006581831976893683919214633312
absolute error = 0.097786058106587766364278207494984
relative error = 89.882972011532835105708408686432 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 3 ) = sin(x);
Iterations = 1000
Total Elapsed Time = 40 Seconds
Elapsed Time(since restart) = 40 Seconds
Expected Time Remaining = 2 Minutes 38 Seconds
Optimized Time Remaining = 2 Minutes 38 Seconds
Time to Timeout = 14 Minutes 19 Seconds
Percent Done = 20.43 %
> quit
memory used=328.6MB, alloc=4.4MB, time=40.92