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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
> INFO,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> min_in_hour,
> djd_debug,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_smallish_float,
> glob_abserr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_hmin_init,
> glob_h,
> glob_log10abserr,
> glob_log10_relerr,
> days_in_year,
> hours_in_day,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> sec_in_min,
> glob_max_minutes,
> glob_max_iter,
> glob_relerr,
> glob_large_float,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_look_poles,
> glob_clock_start_sec,
> glob_almost_1,
> centuries_in_millinium,
> djd_debug2,
> glob_display_flag,
> glob_html_log,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_warned,
> glob_hmin,
> years_in_century,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_optimal_done,
> glob_initial_pass,
> glob_normmax,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_disp_incr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_type_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_log,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_1st_rel_error,
> array_y,
> array_x,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work2,
> array_poles,
> 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 INFO, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_unchanged_h_cnt, glob_max_rel_trunc_err, min_in_hour, djd_debug,
glob_dump, glob_percent_done, glob_log10relerr, glob_smallish_float,
glob_abserr, glob_log10_abserr, glob_dump_analytic, glob_hmax,
glob_not_yet_start_msg, glob_not_yet_finished, MAX_UNCHANGED,
glob_clock_sec, glob_optimal_expect_sec, glob_hmin_init, glob_h,
glob_log10abserr, glob_log10_relerr, days_in_year, hours_in_day,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, sec_in_min,
glob_max_minutes, glob_max_iter, glob_relerr, glob_large_float,
glob_reached_optimal_h, glob_subiter_method, glob_current_iter, glob_start,
glob_small_float, glob_optimal_clock_start_sec, glob_max_hours,
glob_look_poles, glob_clock_start_sec, glob_almost_1,
centuries_in_millinium, djd_debug2, glob_display_flag, glob_html_log,
glob_iter, glob_curr_iter_when_opt, glob_warned2, glob_warned, glob_hmin,
years_in_century, glob_no_eqs, glob_max_trunc_err, glob_last_good_h,
glob_optimal_done, glob_initial_pass, glob_normmax, glob_orig_start_sec,
glob_optimal_start, glob_disp_incr, array_const_0D0, array_const_1,
array_type_pole, array_norms, array_tmp0, array_tmp1, array_log,
array_last_rel_error, array_pole, array_m1, array_1st_rel_error, array_y,
array_x, array_y_init, array_y_higher_work, array_real_pole,
array_y_set_initial, array_complex_pole, array_y_higher_work2, array_poles,
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
> INFO,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> min_in_hour,
> djd_debug,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_smallish_float,
> glob_abserr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_hmin_init,
> glob_h,
> glob_log10abserr,
> glob_log10_relerr,
> days_in_year,
> hours_in_day,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> sec_in_min,
> glob_max_minutes,
> glob_max_iter,
> glob_relerr,
> glob_large_float,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_look_poles,
> glob_clock_start_sec,
> glob_almost_1,
> centuries_in_millinium,
> djd_debug2,
> glob_display_flag,
> glob_html_log,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_warned,
> glob_hmin,
> years_in_century,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_optimal_done,
> glob_initial_pass,
> glob_normmax,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_disp_incr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_type_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_log,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_1st_rel_error,
> array_y,
> array_x,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work2,
> array_poles,
> 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 INFO, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_unchanged_h_cnt, glob_max_rel_trunc_err, min_in_hour, djd_debug,
glob_dump, glob_percent_done, glob_log10relerr, glob_smallish_float,
glob_abserr, glob_log10_abserr, glob_dump_analytic, glob_hmax,
glob_not_yet_start_msg, glob_not_yet_finished, MAX_UNCHANGED,
glob_clock_sec, glob_optimal_expect_sec, glob_hmin_init, glob_h,
glob_log10abserr, glob_log10_relerr, days_in_year, hours_in_day,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, sec_in_min,
glob_max_minutes, glob_max_iter, glob_relerr, glob_large_float,
glob_reached_optimal_h, glob_subiter_method, glob_current_iter, glob_start,
glob_small_float, glob_optimal_clock_start_sec, glob_max_hours,
glob_look_poles, glob_clock_start_sec, glob_almost_1,
centuries_in_millinium, djd_debug2, glob_display_flag, glob_html_log,
glob_iter, glob_curr_iter_when_opt, glob_warned2, glob_warned, glob_hmin,
years_in_century, glob_no_eqs, glob_max_trunc_err, glob_last_good_h,
glob_optimal_done, glob_initial_pass, glob_normmax, glob_orig_start_sec,
glob_optimal_start, glob_disp_incr, array_const_0D0, array_const_1,
array_type_pole, array_norms, array_tmp0, array_tmp1, array_log,
array_last_rel_error, array_pole, array_m1, array_1st_rel_error, array_y,
array_x, array_y_init, array_y_higher_work, array_real_pole,
array_y_set_initial, array_complex_pole, array_y_higher_work2, array_poles,
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
> INFO,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> min_in_hour,
> djd_debug,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_smallish_float,
> glob_abserr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_hmin_init,
> glob_h,
> glob_log10abserr,
> glob_log10_relerr,
> days_in_year,
> hours_in_day,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> sec_in_min,
> glob_max_minutes,
> glob_max_iter,
> glob_relerr,
> glob_large_float,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_look_poles,
> glob_clock_start_sec,
> glob_almost_1,
> centuries_in_millinium,
> djd_debug2,
> glob_display_flag,
> glob_html_log,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_warned,
> glob_hmin,
> years_in_century,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_optimal_done,
> glob_initial_pass,
> glob_normmax,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_disp_incr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_type_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_log,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_1st_rel_error,
> array_y,
> array_x,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work2,
> array_poles,
> 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 INFO, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_unchanged_h_cnt, glob_max_rel_trunc_err, min_in_hour, djd_debug,
glob_dump, glob_percent_done, glob_log10relerr, glob_smallish_float,
glob_abserr, glob_log10_abserr, glob_dump_analytic, glob_hmax,
glob_not_yet_start_msg, glob_not_yet_finished, MAX_UNCHANGED,
glob_clock_sec, glob_optimal_expect_sec, glob_hmin_init, glob_h,
glob_log10abserr, glob_log10_relerr, days_in_year, hours_in_day,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, sec_in_min,
glob_max_minutes, glob_max_iter, glob_relerr, glob_large_float,
glob_reached_optimal_h, glob_subiter_method, glob_current_iter, glob_start,
glob_small_float, glob_optimal_clock_start_sec, glob_max_hours,
glob_look_poles, glob_clock_start_sec, glob_almost_1,
centuries_in_millinium, djd_debug2, glob_display_flag, glob_html_log,
glob_iter, glob_curr_iter_when_opt, glob_warned2, glob_warned, glob_hmin,
years_in_century, glob_no_eqs, glob_max_trunc_err, glob_last_good_h,
glob_optimal_done, glob_initial_pass, glob_normmax, glob_orig_start_sec,
glob_optimal_start, glob_disp_incr, array_const_0D0, array_const_1,
array_type_pole, array_norms, array_tmp0, array_tmp1, array_log,
array_last_rel_error, array_pole, array_m1, array_1st_rel_error, array_y,
array_x, array_y_init, array_y_higher_work, array_real_pole,
array_y_set_initial, array_complex_pole, array_y_higher_work2, array_poles,
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
> INFO,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> min_in_hour,
> djd_debug,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_smallish_float,
> glob_abserr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_hmin_init,
> glob_h,
> glob_log10abserr,
> glob_log10_relerr,
> days_in_year,
> hours_in_day,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> sec_in_min,
> glob_max_minutes,
> glob_max_iter,
> glob_relerr,
> glob_large_float,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_look_poles,
> glob_clock_start_sec,
> glob_almost_1,
> centuries_in_millinium,
> djd_debug2,
> glob_display_flag,
> glob_html_log,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_warned,
> glob_hmin,
> years_in_century,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_optimal_done,
> glob_initial_pass,
> glob_normmax,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_disp_incr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_type_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_log,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_1st_rel_error,
> array_y,
> array_x,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work2,
> array_poles,
> 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 - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_unchanged_h_cnt, glob_max_rel_trunc_err, min_in_hour, djd_debug,
glob_dump, glob_percent_done, glob_log10relerr, glob_smallish_float,
glob_abserr, glob_log10_abserr, glob_dump_analytic, glob_hmax,
glob_not_yet_start_msg, glob_not_yet_finished, MAX_UNCHANGED,
glob_clock_sec, glob_optimal_expect_sec, glob_hmin_init, glob_h,
glob_log10abserr, glob_log10_relerr, days_in_year, hours_in_day,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, sec_in_min,
glob_max_minutes, glob_max_iter, glob_relerr, glob_large_float,
glob_reached_optimal_h, glob_subiter_method, glob_current_iter, glob_start,
glob_small_float, glob_optimal_clock_start_sec, glob_max_hours,
glob_look_poles, glob_clock_start_sec, glob_almost_1,
centuries_in_millinium, djd_debug2, glob_display_flag, glob_html_log,
glob_iter, glob_curr_iter_when_opt, glob_warned2, glob_warned, glob_hmin,
years_in_century, glob_no_eqs, glob_max_trunc_err, glob_last_good_h,
glob_optimal_done, glob_initial_pass, glob_normmax, glob_orig_start_sec,
glob_optimal_start, glob_disp_incr, array_const_0D0, array_const_1,
array_type_pole, array_norms, array_tmp0, array_tmp1, array_log,
array_last_rel_error, array_pole, array_m1, array_1st_rel_error, array_y,
array_x, array_y_init, array_y_higher_work, array_real_pole,
array_y_set_initial, array_complex_pole, array_y_higher_work2, array_poles,
array_y_higher, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> min_in_hour,
> djd_debug,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_smallish_float,
> glob_abserr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_hmin_init,
> glob_h,
> glob_log10abserr,
> glob_log10_relerr,
> days_in_year,
> hours_in_day,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> sec_in_min,
> glob_max_minutes,
> glob_max_iter,
> glob_relerr,
> glob_large_float,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_look_poles,
> glob_clock_start_sec,
> glob_almost_1,
> centuries_in_millinium,
> djd_debug2,
> glob_display_flag,
> glob_html_log,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_warned,
> glob_hmin,
> years_in_century,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_optimal_done,
> glob_initial_pass,
> glob_normmax,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_disp_incr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_type_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_log,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_1st_rel_error,
> array_y,
> array_x,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work2,
> array_poles,
> 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 INFO, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_unchanged_h_cnt, glob_max_rel_trunc_err, min_in_hour, djd_debug,
glob_dump, glob_percent_done, glob_log10relerr, glob_smallish_float,
glob_abserr, glob_log10_abserr, glob_dump_analytic, glob_hmax,
glob_not_yet_start_msg, glob_not_yet_finished, MAX_UNCHANGED,
glob_clock_sec, glob_optimal_expect_sec, glob_hmin_init, glob_h,
glob_log10abserr, glob_log10_relerr, days_in_year, hours_in_day,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, sec_in_min,
glob_max_minutes, glob_max_iter, glob_relerr, glob_large_float,
glob_reached_optimal_h, glob_subiter_method, glob_current_iter, glob_start,
glob_small_float, glob_optimal_clock_start_sec, glob_max_hours,
glob_look_poles, glob_clock_start_sec, glob_almost_1,
centuries_in_millinium, djd_debug2, glob_display_flag, glob_html_log,
glob_iter, glob_curr_iter_when_opt, glob_warned2, glob_warned, glob_hmin,
years_in_century, glob_no_eqs, glob_max_trunc_err, glob_last_good_h,
glob_optimal_done, glob_initial_pass, glob_normmax, glob_orig_start_sec,
glob_optimal_start, glob_disp_incr, array_const_0D0, array_const_1,
array_type_pole, array_norms, array_tmp0, array_tmp1, array_log,
array_last_rel_error, array_pole, array_m1, array_1st_rel_error, array_y,
array_x, array_y_init, array_y_higher_work, array_real_pole,
array_y_set_initial, array_complex_pole, array_y_higher_work2, array_poles,
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
> INFO,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> min_in_hour,
> djd_debug,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_smallish_float,
> glob_abserr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_hmin_init,
> glob_h,
> glob_log10abserr,
> glob_log10_relerr,
> days_in_year,
> hours_in_day,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> sec_in_min,
> glob_max_minutes,
> glob_max_iter,
> glob_relerr,
> glob_large_float,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_look_poles,
> glob_clock_start_sec,
> glob_almost_1,
> centuries_in_millinium,
> djd_debug2,
> glob_display_flag,
> glob_html_log,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_warned,
> glob_hmin,
> years_in_century,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_optimal_done,
> glob_initial_pass,
> glob_normmax,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_disp_incr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_type_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_log,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_1st_rel_error,
> array_y,
> array_x,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work2,
> array_poles,
> array_y_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre add $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_x[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre add $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D0[2] + array_x[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre add $eq_no = 1 i = 3
> array_tmp1[3] := array_const_0D0[3] + array_x[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add $eq_no = 1 i = 4
> array_tmp1[4] := array_const_0D0[4] + array_x[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add $eq_no = 1 i = 5
> array_tmp1[5] := array_const_0D0[5] + array_x[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit add $eq_no = 1
> array_tmp1[kkk] := array_const_0D0[kkk] + array_x[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp1[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 INFO, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_unchanged_h_cnt, glob_max_rel_trunc_err, min_in_hour, djd_debug,
glob_dump, glob_percent_done, glob_log10relerr, glob_smallish_float,
glob_abserr, glob_log10_abserr, glob_dump_analytic, glob_hmax,
glob_not_yet_start_msg, glob_not_yet_finished, MAX_UNCHANGED,
glob_clock_sec, glob_optimal_expect_sec, glob_hmin_init, glob_h,
glob_log10abserr, glob_log10_relerr, days_in_year, hours_in_day,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, sec_in_min,
glob_max_minutes, glob_max_iter, glob_relerr, glob_large_float,
glob_reached_optimal_h, glob_subiter_method, glob_current_iter, glob_start,
glob_small_float, glob_optimal_clock_start_sec, glob_max_hours,
glob_look_poles, glob_clock_start_sec, glob_almost_1,
centuries_in_millinium, djd_debug2, glob_display_flag, glob_html_log,
glob_iter, glob_curr_iter_when_opt, glob_warned2, glob_warned, glob_hmin,
years_in_century, glob_no_eqs, glob_max_trunc_err, glob_last_good_h,
glob_optimal_done, glob_initial_pass, glob_normmax, glob_orig_start_sec,
glob_optimal_start, glob_disp_incr, array_const_0D0, array_const_1,
array_type_pole, array_norms, array_tmp0, array_tmp1, array_log,
array_last_rel_error, array_pole, array_m1, array_1st_rel_error, array_y,
array_x, array_y_init, array_y_higher_work, array_real_pole,
array_y_set_initial, array_complex_pole, array_y_higher_work2, array_poles,
array_y_higher, glob_last;
array_tmp1[1] := array_const_0D0[1] + array_x[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp1[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D0[2] + array_x[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp1[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_const_0D0[3] + array_x[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp1[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_const_0D0[4] + array_x[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp1[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_const_0D0[5] + array_x[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp1[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_const_0D0[kkk] + array_x[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp1[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 + x*log(x)-x
> end;
exact_soln_y := proc(x) 2.0 + x*log(x) - 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
> INFO,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> min_in_hour,
> djd_debug,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_smallish_float,
> glob_abserr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> MAX_UNCHANGED,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_hmin_init,
> glob_h,
> glob_log10abserr,
> glob_log10_relerr,
> days_in_year,
> hours_in_day,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> sec_in_min,
> glob_max_minutes,
> glob_max_iter,
> glob_relerr,
> glob_large_float,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_current_iter,
> glob_start,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_look_poles,
> glob_clock_start_sec,
> glob_almost_1,
> centuries_in_millinium,
> djd_debug2,
> glob_display_flag,
> glob_html_log,
> glob_iter,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_warned,
> glob_hmin,
> years_in_century,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_last_good_h,
> glob_optimal_done,
> glob_initial_pass,
> glob_normmax,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_disp_incr,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_type_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_log,
> array_last_rel_error,
> array_pole,
> array_m1,
> array_1st_rel_error,
> array_y,
> array_x,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work2,
> array_poles,
> array_y_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> DEBUGL := 3;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_unchanged_h_cnt := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> min_in_hour := 60.0;
> djd_debug := true;
> glob_dump := false;
> glob_percent_done := 0.0;
> glob_log10relerr := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_abserr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_hmax := 1.0;
> glob_not_yet_start_msg := true;
> glob_not_yet_finished := true;
> MAX_UNCHANGED := 10;
> glob_clock_sec := 0.0;
> glob_optimal_expect_sec := 0.1;
> glob_hmin_init := 0.001;
> glob_h := 0.1;
> glob_log10abserr := 0.0;
> glob_log10_relerr := 0.1e-10;
> days_in_year := 365.0;
> hours_in_day := 24.0;
> glob_max_opt_iter := 10;
> glob_log10normmin := 0.1;
> glob_max_sec := 10000.0;
> sec_in_min := 60.0;
> glob_max_minutes := 0.0;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_reached_optimal_h := false;
> glob_subiter_method := 3;
> glob_current_iter := 0;
> glob_start := 0;
> glob_small_float := 0.1e-50;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_hours := 0.0;
> glob_look_poles := false;
> glob_clock_start_sec := 0.0;
> glob_almost_1 := 0.9990;
> centuries_in_millinium := 10.0;
> djd_debug2 := true;
> glob_display_flag := true;
> glob_html_log := true;
> glob_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_warned2 := false;
> glob_warned := false;
> glob_hmin := 0.00000000001;
> years_in_century := 100.0;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_optimal_done := false;
> glob_initial_pass := true;
> glob_normmax := 0.0;
> glob_orig_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_disp_incr := 0.1;
> #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/logpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = log ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 20.0;");
> omniout_str(ALWAYS,"x_end := 30.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 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,"2.0 + x*log(x)-x");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_log:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(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_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> 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_norms[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_log[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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_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 <=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 <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp1 := 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_log := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_log[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 20.0;
> x_end := 30.0 ;
> array_y_init[0 + 1] := exact_soln_y(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] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = log ( 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,"2012-06-15T20:51:05-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"log")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = log ( 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,"log diffeq.mxt")
> ;
> logitem_str(html_log_file,"log 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 INFO, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_unchanged_h_cnt, glob_max_rel_trunc_err, min_in_hour, djd_debug,
glob_dump, glob_percent_done, glob_log10relerr, glob_smallish_float,
glob_abserr, glob_log10_abserr, glob_dump_analytic, glob_hmax,
glob_not_yet_start_msg, glob_not_yet_finished, MAX_UNCHANGED,
glob_clock_sec, glob_optimal_expect_sec, glob_hmin_init, glob_h,
glob_log10abserr, glob_log10_relerr, days_in_year, hours_in_day,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, sec_in_min,
glob_max_minutes, glob_max_iter, glob_relerr, glob_large_float,
glob_reached_optimal_h, glob_subiter_method, glob_current_iter, glob_start,
glob_small_float, glob_optimal_clock_start_sec, glob_max_hours,
glob_look_poles, glob_clock_start_sec, glob_almost_1,
centuries_in_millinium, djd_debug2, glob_display_flag, glob_html_log,
glob_iter, glob_curr_iter_when_opt, glob_warned2, glob_warned, glob_hmin,
years_in_century, glob_no_eqs, glob_max_trunc_err, glob_last_good_h,
glob_optimal_done, glob_initial_pass, glob_normmax, glob_orig_start_sec,
glob_optimal_start, glob_disp_incr, array_const_0D0, array_const_1,
array_type_pole, array_norms, array_tmp0, array_tmp1, array_log,
array_last_rel_error, array_pole, array_m1, array_1st_rel_error, array_y,
array_x, array_y_init, array_y_higher_work, array_real_pole,
array_y_set_initial, array_complex_pole, array_y_higher_work2, array_poles,
array_y_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
DEBUGL := 3;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_iolevel := 5;
glob_unchanged_h_cnt := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
min_in_hour := 60.0;
djd_debug := true;
glob_dump := false;
glob_percent_done := 0.;
glob_log10relerr := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_abserr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_hmax := 1.0;
glob_not_yet_start_msg := true;
glob_not_yet_finished := true;
MAX_UNCHANGED := 10;
glob_clock_sec := 0.;
glob_optimal_expect_sec := 0.1;
glob_hmin_init := 0.001;
glob_h := 0.1;
glob_log10abserr := 0.;
glob_log10_relerr := 0.1*10^(-10);
days_in_year := 365.0;
hours_in_day := 24.0;
glob_max_opt_iter := 10;
glob_log10normmin := 0.1;
glob_max_sec := 10000.0;
sec_in_min := 60.0;
glob_max_minutes := 0.;
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_reached_optimal_h := false;
glob_subiter_method := 3;
glob_current_iter := 0;
glob_start := 0;
glob_small_float := 0.1*10^(-50);
glob_optimal_clock_start_sec := 0.;
glob_max_hours := 0.;
glob_look_poles := false;
glob_clock_start_sec := 0.;
glob_almost_1 := 0.9990;
centuries_in_millinium := 10.0;
djd_debug2 := true;
glob_display_flag := true;
glob_html_log := true;
glob_iter := 0;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_warned := false;
glob_hmin := 0.1*10^(-10);
years_in_century := 100.0;
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_optimal_done := false;
glob_initial_pass := true;
glob_normmax := 0.;
glob_orig_start_sec := 0.;
glob_optimal_start := 0.;
glob_disp_incr := 0.1;
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/logpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = log ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 20.0;");
omniout_str(ALWAYS, "x_end := 30.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 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, "2.0 +\tx*log(x)-x");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_type_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_log := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_y_higher_work := Array(1 .. 3, 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_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
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_norms[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_log[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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_log := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_log[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 20.0;
x_end := 30.0;
array_y_init[1] := exact_soln_y(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] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = log ( 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, "2012-06-15T20:51:05-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "log");
logitem_str(html_log_file, "diff ( y , x , 1 ) = log ( 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,
"log diffeq.mxt");
logitem_str(html_log_file,
"log 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/logpostode.ode#################
diff ( y , x , 1 ) = log ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 20.0;
x_end := 30.0 ;
array_y_init[0 + 1] := exact_soln_y(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)
2.0 + x*log(x)-x
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 20
y[1] (analytic) = 41.91464547107981986870447152285
y[1] (numeric) = 41.91464547107981986870447152285
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.001
y[1] (analytic) = 41.917641228352957203447594256844
y[1] (numeric) = 41.93464597107981986870447152285
absolute error = 0.017004742726862665256877266006
relative error = 0.040567031513597459231837404918373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.002
y[1] (analytic) = 41.920637035623594684014675969956
y[1] (numeric) = 41.95464747107981986870447152285
absolute error = 0.034010435456225184689795552894
relative error = 0.081130531073093123883895838623257 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.003
y[1] (analytic) = 41.923632892889232685358847286516
y[1] (numeric) = 41.97464997107981986870447152285
absolute error = 0.051017078190587183345624236334
relative error = 0.12169049929649658676078889506449 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.004
y[1] (analytic) = 41.926628800147371832358255077728
y[1] (numeric) = 41.99465347107981986870447152285
absolute error = 0.068024670932448036346216445122
relative error = 0.16224693680167514461002091435777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.005
y[1] (analytic) = 41.929624757395512999778581205422
y[1] (numeric) = 42.01465797107981986870447152285
absolute error = 0.085033213684306868925890317428
relative error = 0.20279984420635383836598420656291 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.006
y[1] (analytic) = 41.932620764631157312235568760188
y[1] (numeric) = 42.03466347107981986870447152285
absolute error = 0.102042706448662556468902762662
relative error = 0.24334922212811549338050046847825 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.007
y[1] (analytic) = 41.935616821851806144157555792004
y[1] (numeric) = 42.05466997107981986870447152285
absolute error = 0.119053149228013724546915730846
relative error = 0.28389507118440075963991157739108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.008
y[1] (analytic) = 41.938612929054961119748016531504
y[1] (numeric) = 42.07467747107981986870447152285
absolute error = 0.136064542024858748956454991346
relative error = 0.32443739199250815196872494338528 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.009
y[1] (analytic) = 41.941609086238124112948110100007
y[1] (numeric) = 42.09468597107981986870447152285
absolute error = 0.153076884841695755756361422843
relative error = 0.36497618516959409021981859961167 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.01
y[1] (analytic) = 41.944605293398797247399236706435
y[1] (numeric) = 42.11469547107981986870447152285
absolute error = 0.170090177681022621305234816415
relative error = 0.40551145133267293945121120765445 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.011
y[1] (analytic) = 41.947601550534482896405601329236
y[1] (numeric) = 42.13470597107981986870447152285
absolute error = 0.187104420545336972298870193614
relative error = 0.44604319109861705008940215290252 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.012
y[1] (analytic) = 41.950597857642683682896784881476
y[1] (numeric) = 42.15471747107981986870447152285
absolute error = 0.204119613437136185807686641374
relative error = 0.48657140508415679807928690246668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.013
y[1] (analytic) = 41.95359421472090247939032285719
y[1] (numeric) = 42.17472997107981986870447152285
absolute error = 0.22113575635891738931414866566
relative error = 0.52709609390588062502065279610938 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.014
y[1] (analytic) = 41.956590621766642407954291457161
y[1] (numeric) = 42.19474347107981986870447152285
absolute error = 0.238152849313177460750180065689
relative error = 0.56761725818023507829126043821392 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.015
y[1] (analytic) = 41.95958707877740684016990119222
y[1] (numeric) = 42.21475797107981986870447152285
absolute error = 0.25517089230241302853457033063
relative error = 0.6081348985235248511565158567529 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.016
y[1] (analytic) = 41.962583585750699397094097962236
y[1] (numeric) = 42.23477347107981986870447152285
absolute error = 0.272189885329120471610373560614
relative error = 0.64864901555191282286573859278518 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.017
y[1] (analytic) = 41.965580142684023949222171608893
y[1] (numeric) = 42.25478997107981986870447152285
absolute error = 0.289209828395795919482299913957
relative error = 0.68915960988142009873503088193585 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.018
y[1] (analytic) = 41.968576749574884616450371940423
y[1] (numeric) = 42.27480747107981986870447152285
absolute error = 0.306230721504935252254099582427
relative error = 0.72966668212792605021675308689541 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.019
y[1] (analytic) = 41.971573406420785768038532226405
y[1] (numeric) = 42.29482597107981986870447152285
absolute error = 0.323252564659034100665939296445
relative error = 0.77017023290716835495561053787029 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.02
y[1] (analytic) = 41.974570113219232022572700160763
y[1] (numeric) = 42.31484547107981986870447152285
absolute error = 0.340275357860587846131771362087
relative error = 0.81067026283474303683135693561817 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.021
y[1] (analytic) = 41.977566869967728247927776291111
y[1] (numeric) = 42.33486597107981986870447152285
absolute error = 0.357299101112091620776695231739
relative error = 0.85116677252610450598811946942265 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.022
y[1] (analytic) = 41.980563676663779561230159912581
y[1] (numeric) = 42.35488747107981986870447152285
absolute error = 0.374323794416040307474311610269
relative error = 0.89165976259656559885035080014861 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.023
y[1] (analytic) = 41.983560533304891328820402424251
y[1] (numeric) = 42.37490997107981986870447152285
absolute error = 0.391349437774928539884069098599
relative error = 0.93214923366129761812541305632495 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.024
y[1] (analytic) = 41.986557439888569166215868146323
y[1] (numeric) = 42.39493347107981986870447152285
absolute error = 0.408376031191250702488603376527
relative error = 0.97263518633533037279279898888236 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.025
y[1] (analytic) = 41.989554396412318938073402596207
y[1] (numeric) = 42.41495797107981986870447152285
absolute error = 0.425403574667500930631068926643
relative error = 1.0131176212335522180799954279208 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.026
y[1] (analytic) = 41.992551402873646758152008221592
y[1] (numeric) = 42.43498347107981986870447152285
absolute error = 0.442432068206173110552463301258
relative error = 1.0535965389707100954249941828245 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.027
y[1] (analytic) = 41.995548459270058989275527588721
y[1] (numeric) = 42.45500997107981986870447152285
absolute error = 0.459461511809760879428943934129
relative error = 1.0940719401614095724254555244787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.028
y[1] (analytic) = 41.998545565599062243295334023925
y[1] (numeric) = 42.47503747107981986870447152285
absolute error = 0.476491905480757625409137498925
relative error = 1.134543825420114882774529386497 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.029
y[1] (analytic) = 42.001542721858163381053029706633
y[1] (numeric) = 42.49506597107981986870447152285
absolute error = 0.493523249221656487651441816217
relative error = 1.1750121953611489661833394197441 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.03
y[1] (analytic) = 42.004539928044869512343151211936
y[1] (numeric) = 42.51509547107981986870447152285
absolute error = 0.510555543034950356361320310914
relative error = 1.2154770505986935082901350325403 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.031
y[1] (analytic) = 42.007537184156687995875882500882
y[1] (numeric) = 42.53512597107981986870447152285
absolute error = 0.527588786923131872828589021968
relative error = 1.2559383917467889805561165464642 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.032
y[1] (analytic) = 42.010534490191126439239775356631
y[1] (numeric) = 42.55515747107981986870447152285
absolute error = 0.544622980888693429464696166219
relative error = 1.2963962194193346801479385955532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.033
y[1] (analytic) = 42.01353184614569269886447726461
y[1] (numeric) = 42.57518997107981986870447152285
absolute error = 0.56165812493412716983999425824
relative error = 1.3368505342300887698068968944479 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.034
y[1] (analytic) = 42.01652925201789487998346673482
y[1] (numeric) = 42.59522347107981986870447152285
absolute error = 0.57869421906192498872100478803
relative error = 1.3773013367926683177048034987659 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.035
y[1] (analytic) = 42.019526707805241336596796064411
y[1] (numeric) = 42.61525797107981986870447152285
absolute error = 0.595731263274578532107675458439
relative error = 1.4177486277205493372865556788515 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.036
y[1] (analytic) = 42.022524213505240671433841538716
y[1] (numeric) = 42.63529347107981986870447152285
absolute error = 0.612769257574579197270629984134
relative error = 1.4581924076270668270994035256395 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.037
y[1] (analytic) = 42.025521769115401735916061068829
y[1] (numeric) = 42.65532997107981986870447152285
absolute error = 0.629808201964418132788410454021
relative error = 1.4986326771254148106089214054029 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.038
y[1] (analytic) = 42.028519374633233630119759263922
y[1] (numeric) = 42.67536747107981986870447152285
absolute error = 0.646848096446586238584712258928
relative error = 1.5390694368286463760016883776615 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.039
y[1] (analytic) = 42.031517030056245702738859936423
y[1] (numeric) = 42.69540597107981986870447152285
absolute error = 0.663888941023574165965611586427
relative error = 1.5795026873496737159746826884854 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.04
y[1] (analytic) = 42.034514735381947551047686038187
y[1] (numeric) = 42.71544547107981986870447152285
absolute error = 0.680930735697872317656785484663
relative error = 1.619932429301268167511395449177 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.041
y[1] (analytic) = 42.037512490607849020863747025844
y[1] (numeric) = 42.73548597107981986870447152285
absolute error = 0.697973480471970847840724497006
relative error = 1.6603586632960602516446686079717 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.042
y[1] (analytic) = 42.040510295731460206510533653426
y[1] (numeric) = 42.75552747107981986870447152285
absolute error = 0.715017175348359662193937869424
relative error = 1.7007813899465397132062623203728 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.043
y[1] (analytic) = 42.043508150750291450780320190462
y[1] (numeric) = 42.77556997107981986870447152285
absolute error = 0.732061820329528417924151332388
relative error = 1.7412006098650555605631568213085 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.044
y[1] (analytic) = 42.046506055661853344896974063652
y[1] (numeric) = 42.79561347107981986870447152285
absolute error = 0.749107415417966523807497459198
relative error = 1.7816163236638161053405939002694 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.045
y[1] (analytic) = 42.049504010463656728478772920297
y[1] (numeric) = 42.81565797107981986870447152285
absolute error = 0.766153960616163140225698602553
relative error = 1.8220285319548890021318630782076 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.046
y[1] (analytic) = 42.052502015153212689501229111614
y[1] (numeric) = 42.83570347107981986870447152285
absolute error = 0.783201455926607179203242411236
relative error = 1.8624372353502012881948375828794 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.047
y[1] (analytic) = 42.055500069728032564259921594093
y[1] (numeric) = 42.85574997107981986870447152285
absolute error = 0.800249901351787304444549928757
relative error = 1.9028424344615394231352652170318 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=3.8MB, alloc=2.7MB, time=0.19
x[1] = 20.048
y[1] (analytic) = 42.058498174185627937333335247056
y[1] (numeric) = 42.87579747107981986870447152285
absolute error = 0.817299296894191931371136275794
relative error = 1.9432441299005493285768192116103 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.049
y[1] (analytic) = 42.061496328523510641545707604541
y[1] (numeric) = 42.89584597107981986870447152285
absolute error = 0.834349642556309227158763918309
relative error = 1.9836423222787364278179141540441 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.05
y[1] (analytic) = 42.064494532739192757929882999696
y[1] (numeric) = 42.91589547107981986870447152285
absolute error = 0.851400938340627110774588523154
relative error = 2.0240370122074656854752920793035 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.051
y[1] (analytic) = 42.067492786830186615690174119807
y[1] (numeric) = 42.93594597107981986870447152285
absolute error = 0.868453184249633253014297403043
relative error = 2.0644282002979616471143838093588 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.052
y[1] (analytic) = 42.070491090794004792165230970119
y[1] (numeric) = 42.95599747107981986870447152285
absolute error = 0.885506380285815076539240552731
relative error = 2.1048158871613084788664506243807 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.053
y[1] (analytic) = 42.073489444628160112790917244624
y[1] (numeric) = 42.97604997107981986870447152285
absolute error = 0.902560526451659755913554278226
relative error = 2.1452000734084500070325113467717 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.054
y[1] (analytic) = 42.076487848330165651063194101937
y[1] (numeric) = 42.99610347107981986870447152285
absolute error = 0.919615622749654217641277420913
relative error = 2.185580759650189757674059917045 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.055
y[1] (analytic) = 42.07948630189753472850101134442
y[1] (numeric) = 43.01615797107981986870447152285
absolute error = 0.93667166918228514020346017843
relative error = 2.2259579464971909961905785382623 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.056
y[1] (analytic) = 42.082484805327780914609205998739
y[1] (numeric) = 43.03621347107981986870447152285
absolute error = 0.953728665752038954095265524111
relative error = 2.2663316345599767668838514634789 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.057
y[1] (analytic) = 42.085483358618418026841408295976
y[1] (numeric) = 43.05626997107981986870447152285
absolute error = 0.970786612461401841863063226874
relative error = 2.3067018244489299325090844985916 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.058
y[1] (analytic) = 42.088481961766960130562955049448
y[1] (numeric) = 43.07632747107981986870447152285
absolute error = 0.987845509312859738141516473402
relative error = 2.3470685167742932138128352907111 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.059
y[1] (analytic) = 42.091480614770921539013810428426
y[1] (numeric) = 43.09638597107981986870447152285
absolute error = 1.004905356308898329690661094424
relative error = 2.3874317121461692290577594698769 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.06
y[1] (analytic) = 42.094479317627816813271494125867
y[1] (numeric) = 43.11644547107981986870447152285
absolute error = 1.021966153452003055432977396983
relative error = 2.4277914111745205335341777099281 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.061
y[1] (analytic) = 42.097478070335160762214016918347
y[1] (numeric) = 43.13650597107981986870447152285
absolute error = 1.039027900744659106490454604503
relative error = 2.4681476144691696590584687719605 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.062
y[1] (analytic) = 42.100476872890468442482823616343
y[1] (numeric) = 43.15656747107981986870447152285
absolute error = 1.056090598189351426221647906507
relative error = 2.5085003226397991534582935917 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.063
y[1] (analytic) = 42.103475725291255158445743403008
y[1] (numeric) = 43.17662997107981986870447152285
absolute error = 1.073154245788564710258728119842
relative error = 2.5488495362959516200446554699322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.064
y[1] (analytic) = 42.106474627535036462159947559627
y[1] (numeric) = 43.19669347107981986870447152285
absolute error = 1.090218843544783406544523963223
relative error = 2.5891952560470297570708014228281 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.065
y[1] (analytic) = 42.109473579619328153334914575877
y[1] (numeric) = 43.21675797107981986870447152285
absolute error = 1.107284391460491715369556946973
relative error = 2.6295374825022963971779697469647 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.066
y[1] (analytic) = 42.112472581541646279295402643092
y[1] (numeric) = 43.23682347107981986870447152285
absolute error = 1.124350889538173589409068879758
relative error = 2.6698762162708745468279888514585 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.067
y[1] (analytic) = 42.115471633299507134944429528655
y[1] (numeric) = 43.25688997107981986870447152285
absolute error = 1.141418337780312733760041994195
relative error = 2.7102114579617474257227324076253 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.068
y[1] (analytic) = 42.118470734890427262726259829701
y[1] (numeric) = 43.27695747107981986870447152285
absolute error = 1.158486736189392605978211693149
relative error = 2.7505432081837585062104358642402 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.069
y[1] (analytic) = 42.121469886311923452589399604287
y[1] (numeric) = 43.29702597107981986870447152285
absolute error = 1.175556084767896416115071918563
relative error = 2.7908714675456115526788793743462 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.07
y[1] (analytic) = 42.124469087561512741949598378184
y[1] (numeric) = 43.31709547107981986870447152285
absolute error = 1.192626383518307126754873144666
relative error = 2.8311962366558706609354421773721 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.071
y[1] (analytic) = 42.127468338636712415652858525468
y[1] (numeric) = 43.33716597107981986870447152285
absolute error = 1.209697632443107453051612997382
relative error = 2.8715175161229602975740334780796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.072
y[1] (analytic) = 42.130467639535040005938452021055
y[1] (numeric) = 43.35723747107981986870447152285
absolute error = 1.226769831544779862766019501795
relative error = 2.9118353065551653393289048617473 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.073
y[1] (analytic) = 42.133466990254013292401944563366
y[1] (numeric) = 43.37730997107981986870447152285
absolute error = 1.243842980825806576302526959484
relative error = 2.9521496085606311124153492827136 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.074
y[1] (analytic) = 42.136466390791150301958227065253
y[1] (numeric) = 43.39738347107981986870447152285
absolute error = 1.260917080288669566746244457597
relative error = 2.9924604227473634318572916613489 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.075
y[1] (analytic) = 42.139465841143969308804554511395
y[1] (numeric) = 43.41745797107981986870447152285
absolute error = 1.277992129935850559899917011455
relative error = 3.0327677497232286408017761221508 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.076
y[1] (analytic) = 42.142465341309988834383592180283
y[1] (numeric) = 43.43753347107981986870447152285
absolute error = 1.295068129769831034320879342567
relative error = 3.0730715900959536498203549036945 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.077
y[1] (analytic) = 42.145464891286727647346469229003
y[1] (numeric) = 43.45760997107981986870447152285
absolute error = 1.312145079793092221358002293847
relative error = 3.1133719444731259761973839687645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.078
y[1] (analytic) = 42.148464491071704763515839638942
y[1] (numeric) = 43.47768747107981986870447152285
absolute error = 1.329222980008115105188631883908
relative error = 3.1536688134621937832052303410219 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.079
y[1] (analytic) = 42.151464140662439445848950520623
y[1] (numeric) = 43.49776597107981986870447152285
absolute error = 1.346301830417380422855521002227
relative error = 3.1939621976704659193663961921779 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.08
y[1] (analytic) = 42.154463840056451204400717775803
y[1] (numeric) = 43.51784547107981986870447152285
absolute error = 1.363381631023368664303753747047
relative error = 3.234252097705111957702564701645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.081
y[1] (analytic) = 42.15746358925125979628680911502
y[1] (numeric) = 43.53792597107981986870447152285
absolute error = 1.38046238182856007241766240783
relative error = 3.2745385141731622349705727083281 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.082
y[1] (analytic) = 42.160463388244385225646734428771
y[1] (numeric) = 43.55800747107981986870447152285
absolute error = 1.397544082835434643057737094079
relative error = 3.3148214476815078908853151720535 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.083
y[1] (analytic) = 42.163463237033347743606943510441
y[1] (numeric) = 43.57808997107981986870447152285
absolute error = 1.414626734046472125097528012409
relative error = 3.3551008988369009073295864601062 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.084
y[1] (analytic) = 42.166463135615667848243931129221
y[1] (numeric) = 43.59817347107981986870447152285
absolute error = 1.431710335464152020460540393629
relative error = 3.3953768682459541475508634718829 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.085
y[1] (analytic) = 42.169463083988866284547349451119
y[1] (numeric) = 43.61825797107981986870447152285
absolute error = 1.448794887090953584157122071731
relative error = 3.4356493565151413953450356128222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.086
y[1] (analytic) = 42.172463082150464044383127806284
y[1] (numeric) = 43.63834347107981986870447152285
absolute error = 1.465880388929355824321343716566
relative error = 3.4759183642507973942270866263159 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.087
y[1] (analytic) = 42.175463130097982366456599800793
y[1] (numeric) = 43.65842997107981986870447152285
absolute error = 1.482966840981837502247871722057
relative error = 3.5161838920591178865887332903043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.088
y[1] (analytic) = 42.178463227828942736275637771063
y[1] (numeric) = 43.67851747107981986870447152285
absolute error = 1.500054243250877132428833751787
relative error = 3.5564459405461596528430259830581 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.089
y[1] (analytic) = 42.181463375340866886113794579089
y[1] (numeric) = 43.69860597107981986870447152285
absolute error = 1.517142595738952982590676943761
relative error = 3.5967045103178405505559161203835 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.09
y[1] (analytic) = 42.18446357263127679497345274665
y[1] (numeric) = 43.71869547107981986870447152285
absolute error = 1.5342318984485430737310187762
relative error = 3.6369596019799395535647954644639 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.091
y[1] (analytic) = 42.187463819697694688548980926689
y[1] (numeric) = 43.73878597107981986870447152285
absolute error = 1.551322151382125180155490596161
relative error = 3.6772112161380967910840123022249 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.092
y[1] (analytic) = 42.190464116537643039189897709994
y[1] (numeric) = 43.75887747107981986870447152285
absolute error = 1.568413354542176829514573812856
relative error = 3.7174593533978135867973694891371 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.093
y[1] (analytic) = 42.193464463148644565864042765421
y[1] (numeric) = 43.77896997107981986870447152285
absolute error = 1.585505507931175302840428757429
relative error = 3.7577040143644524979376093519262 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.094
y[1] (analytic) = 42.19646485952822223412075531176
y[1] (numeric) = 43.79906347107981986870447152285
absolute error = 1.60259861155159763458371621109
relative error = 3.7979451996432373543528904418372 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.095
y[1] (analytic) = 42.199465305673899256054059919484
y[1] (numeric) = 43.81915797107981986870447152285
absolute error = 1.619692665405920612650411603366
relative error = 3.8381829098392532975602611275955 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.096
y[1] (analytic) = 42.202465801583199090265859640518
y[1] (numeric) = 43.83925347107981986870447152285
absolute error = 1.636787669496620778438611882332
relative error = 3.878417145557446819786135015298 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.097
y[1] (analytic) = 42.20546634725364544182913646421
y[1] (numeric) = 43.85934997107981986870447152285
absolute error = 1.65388362382617442687533505864
relative error = 3.9186479074026258029937731801936 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.098
y[1] (analytic) = 42.208466942682762262251159097698
y[1] (numeric) = 43.87944747107981986870447152285
absolute error = 1.670980528397057606453312425152
relative error = 3.9588751959794595578977781931256 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.099
y[1] (analytic) = 42.211467587868073749436698068846
y[1] (numeric) = 43.89954597107981986870447152285
absolute error = 1.688078383211746119267773454004
relative error = 3.999099011892478862965604922295 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.1
y[1] (analytic) = 42.214468282807104347651248149898
y[1] (numeric) = 43.91964547107981986870447152285
absolute error = 1.705177188272715521053223372952
relative error = 4.0393193557460760034060930889112 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.101
y[1] (analytic) = 42.217469027497378747484258100075
y[1] (numeric) = 43.93974597107981986870447152285
absolute error = 1.722276943582441121220213422775
relative error = 4.0795362281445048101450265529454 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.102
y[1] (analytic) = 42.220469821936421885812367725263
y[1] (numeric) = 43.95984747107981986870447152285
absolute error = 1.739377649143397982892103797587
relative error = 4.1197496296918806987877243032402 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.103
y[1] (analytic) = 42.223470666121758945762652252989
y[1] (numeric) = 43.97994997107981986870447152285
absolute error = 1.756479304958060922941819269861
relative error = 4.1599595609921807085686681239488 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.104
y[1] (analytic) = 42.22647156005091535667587402084
y[1] (numeric) = 44.00005347107981986870447152285
absolute error = 1.77358191102890451202859750201
relative error = 4.2001660226492435412881719072301 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.105
y[1] (analytic) = 42.229472503721416794069741476544
y[1] (numeric) = 44.02015797107981986870447152285
absolute error = 1.790685467358403074634730046306
relative error = 4.2403690152667696002360975798108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.106
y[1] (analytic) = 42.23247349713078917960217548786
y[1] (numeric) = 44.04026347107981986870447152285
absolute error = 1.80778997394903068910229603499
relative error = 4.2805685394483210291026226090552 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.107
y[1] (analytic) = 42.235474540276558681034582960486
y[1] (numeric) = 44.06036997107981986870447152285
absolute error = 1.824895430803261187669888562364
relative error = 4.3207645957973217508760640518746 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.108
y[1] (analytic) = 42.23847563315625171219513776214
y[1] (numeric) = 44.08047747107981986870447152285
absolute error = 1.84200183792356815650933376071
relative error = 4.3609571849170575067277641077961 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.109
y[1] (analytic) = 42.241476775767394932942068951029
y[1] (numeric) = 44.10058597107981986870447152285
absolute error = 1.859109195312424935762402571821
relative error = 4.4011463074106758948840421352083 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.11
y[1] (analytic) = 42.244477968107515249126956306861
y[1] (numeric) = 44.12069547107981986870447152285
absolute error = 1.876217502972304619577515215989
relative error = 4.4413319638811864094852180878059 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.111
y[1] (analytic) = 42.2474792101741398125580331626
y[1] (numeric) = 44.14080597107981986870447152285
absolute error = 1.89332676090568005614643836025
relative error = 4.4815141549314604794317123259936 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.112
y[1] (analytic) = 42.250480501964796020963496535155
y[1] (numeric) = 44.16091747107981986870447152285
absolute error = 1.910436969115023847740974987695
relative error = 4.521692881164231507217226755888 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.113
y[1] (analytic) = 42.253481843477011517954824553161
y[1] (numeric) = 44.18102997107981986870447152285
absolute error = 1.927548127602808350749646969689
relative error = 4.5618681431820949077490122464917 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.114
y[1] (analytic) = 42.256483234708314192990101180073
y[1] (numeric) = 44.20114347107981986870447152285
absolute error = 1.944660236371505675714370342777
relative error = 4.6020399415875081471552272733138 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.115
y[1] (analytic) = 42.259484675656232181337348230726
y[1] (numeric) = 44.22125797107981986870447152285
absolute error = 1.961773295423587687367123292124
relative error = 4.6422082769827907815793927347373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.116
y[1] (analytic) = 42.26248616631829386403786467959
y[1] (numeric) = 44.24137347107981986870447152285
absolute error = 1.97888730476152600466660684326
relative error = 4.6823731499701244959619478851029 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=7.6MB, alloc=3.5MB, time=0.41
x[1] = 20.117
y[1] (analytic) = 42.265487706692027867869573258854
y[1] (numeric) = 44.26148997107981986870447152285
absolute error = 1.996002264387792000834898263996
relative error = 4.7225345611515531428089123265742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.118
y[1] (analytic) = 42.26848929677496306531037434457
y[1] (numeric) = 44.28160747107981986870447152285
absolute error = 2.01311817430485680339409717828
relative error = 4.7626925111289827809476589994667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.119
y[1] (analytic) = 42.271490936564628574501507129031
y[1] (numeric) = 44.30172597107981986870447152285
absolute error = 2.030235034515191294202964393819
relative error = 4.8028470005041817142698031087289 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.12
y[1] (analytic) = 42.274492626058553759210918077566
y[1] (numeric) = 44.32184547107981986870447152285
absolute error = 2.047352845021266109493553445284
relative error = 4.8429980298787805304612119221011 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.121
y[1] (analytic) = 42.277494365254268228796636667961
y[1] (numeric) = 44.34196597107981986870447152285
absolute error = 2.064471605825551639907834854889
relative error = 4.8831455998542721397191403732771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.122
y[1] (analytic) = 42.280496154149301838170158410659
y[1] (numeric) = 44.36208747107981986870447152285
absolute error = 2.081591316930518030534313112191
relative error = 4.9232897110320118134564974013968 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.123
y[1] (analytic) = 42.283497992741184687759835147987
y[1] (numeric) = 44.38220997107981986870447152285
absolute error = 2.098711978338635180944636374863
relative error = 4.9634303640132172229932479558289 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.124
y[1] (analytic) = 42.286499881027447123474272630535
y[1] (numeric) = 44.40233347107981986870447152285
absolute error = 2.115833590052372745230198892315
relative error = 5.0035675593989684782349555933716 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.125
y[1] (analytic) = 42.289501819005619736665735368936
y[1] (numeric) = 44.42245797107981986870447152285
absolute error = 2.132956152074200132038736153914
relative error = 5.0437012977902081663384705925621 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.126
y[1] (analytic) = 42.292503806673233364093558759213
y[1] (numeric) = 44.44258347107981986870447152285
absolute error = 2.150079664406586504610912763637
relative error = 5.083831579787741390364768507857 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.127
y[1] (analytic) = 42.295505844027819087887568479867
y[1] (numeric) = 44.46270997107981986870447152285
absolute error = 2.167204127052000780816903042983
relative error = 5.1239584059922358079189440842978 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.128
y[1] (analytic) = 42.298507931066908235511507158962
y[1] (numeric) = 44.48283747107981986870447152285
absolute error = 2.184329540012911633192964363888
relative error = 5.1640817770042216697773654509412 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.129
y[1] (analytic) = 42.301510067788032379726468309311
y[1] (numeric) = 44.50296597107981986870447152285
absolute error = 2.201455903291787488978003213539
relative error = 5.204201693424091858501993509583 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.13
y[1] (analytic) = 42.304512254188723338554337530053
y[1] (numeric) = 44.52309547107981986870447152285
absolute error = 2.218583216891096530150133992797
relative error = 5.244318155852101927041871432715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.131
y[1] (analytic) = 42.307514490266513175241240972742
y[1] (numeric) = 44.54322597107981986870447152285
absolute error = 2.235711480813306693463230550108
relative error = 5.2844311648883701373217891829486 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.132
y[1] (analytic) = 42.310516776018934198221001070175
y[1] (numeric) = 44.56335747107981986870447152285
absolute error = 2.252840695060885670483470452675
relative error = 5.3245407211328774988181279637478 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.133
y[1] (analytic) = 42.31351911144351896107859952617
y[1] (numeric) = 44.58348997107981986870447152285
absolute error = 2.26997085963630090762587199668
relative error = 5.3646468251854678071218895092329 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.134
y[1] (analytic) = 42.316521496537800262513647564441
y[1] (numeric) = 44.60362347107981986870447152285
absolute error = 2.287101974542019606190823958409
relative error = 5.4047494776458476824889151188477 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.135
y[1] (analytic) = 42.319523931299311146303863434841
y[1] (numeric) = 44.62375797107981986870447152285
absolute error = 2.304234039780508722400608088009
relative error = 5.4448486791135866083772993402569 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.136
y[1] (analytic) = 42.32252641572558490126855717508
y[1] (numeric) = 44.64389347107981986870447152285
absolute error = 2.32136705535423496743591434777
relative error = 5.4849444301881169699720032021232 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.137
y[1] (analytic) = 42.325528949814155061232122626214
y[1] (numeric) = 44.66402997107981986870447152285
absolute error = 2.338501021265664807472348896636
relative error = 5.5250367314687340926966718958258 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.138
y[1] (analytic) = 42.328531533562555404987536700021
y[1] (numeric) = 44.68416747107981986870447152285
absolute error = 2.355635937517264463716934822829
relative error = 5.5651255835545962807126618035082 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.139
y[1] (analytic) = 42.331534166968319956259865896509
y[1] (numeric) = 44.70430597107981986870447152285
absolute error = 2.372771804111499912444605626341
relative error = 5.6052109870447248554052817674062 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.14
y[1] (analytic) = 42.334536850028982983669780069749
y[1] (numeric) = 44.72444547107981986870447152285
absolute error = 2.389908621050836885034691453101
relative error = 5.6452929425380041938572534934178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.141
y[1] (analytic) = 42.337539582742079000697073440221
y[1] (numeric) = 44.74458597107981986870447152285
absolute error = 2.407046388337740868007398082629
relative error = 5.6853714506331817673093959797734 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.142
y[1] (analytic) = 42.340542365105142765644192851891
y[1] (numeric) = 44.76472747107981986870447152285
absolute error = 2.424185105974677103060278670959
relative error = 5.725446511928868179608538859474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.143
y[1] (analytic) = 42.343545197115709281599773272204
y[1] (numeric) = 44.78486997107981986870447152285
absolute error = 2.441324773964110587104698250646
relative error = 5.7655181270235372056426695431348 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.144
y[1] (analytic) = 42.346548078771313796402180533205
y[1] (numeric) = 44.80501347107981986870447152285
absolute error = 2.458465392308506072302290989645
relative error = 5.8055862965155258297633190466899 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.145
y[1] (analytic) = 42.349551010069491802603061311994
y[1] (numeric) = 44.82515797107981986870447152285
absolute error = 2.475606961010328066101410210856
relative error = 5.8456510210030342841951913863169 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.146
y[1] (analytic) = 42.352553991007779037430900348701
y[1] (numeric) = 44.84530347107981986870447152285
absolute error = 2.492749480072040831273571174149
relative error = 5.8857123010841260874330414208777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.147
y[1] (analytic) = 42.355557021583711482754584900216
y[1] (numeric) = 44.86544997107981986870447152285
absolute error = 2.509892949496108385949886622634
relative error = 5.9257701373567280826258060199439 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.148
y[1] (analytic) = 42.358560101794825365046976427835
y[1] (numeric) = 44.88559747107981986870447152285
absolute error = 2.527037369284994503657495095015
relative error = 5.965824530418630475947993433544 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.149
y[1] (analytic) = 42.36156323163865715534848951707
y[1] (numeric) = 44.90574597107981986870447152285
absolute error = 2.54418273944116271335598200578
relative error = 6.0058754808674868749583357374503 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.15
y[1] (analytic) = 42.364566411112743569230678027797
y[1] (numeric) = 44.92589547107981986870447152285
absolute error = 2.561329059967076299473793495053
relative error = 6.0459229893008143269457092258989 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.151
y[1] (analytic) = 42.367569640214621566759828472968
y[1] (numeric) = 44.94604597107981986870447152285
absolute error = 2.578476330865198301944643049882
relative error = 6.0859670563159933572623276213982 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.152
y[1] (analytic) = 42.370572918941828352460560624081
y[1] (numeric) = 44.96619747107981986870447152285
absolute error = 2.595624552137991516243910898769
relative error = 6.1260076825102680076442129692611 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.153
y[1] (analytic) = 42.373576247291901375279435341614
y[1] (numeric) = 44.98634997107981986870447152285
absolute error = 2.612773723787918493425036181236
relative error = 6.1660448684807458745189490823571 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.154
y[1] (analytic) = 42.376579625262378328548569628652
y[1] (numeric) = 45.00650347107981986870447152285
absolute error = 2.629923845817441540155901894198
relative error = 6.2060786148243981473007223994234 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.155
y[1] (analytic) = 42.379583052850797149949258905876
y[1] (numeric) = 45.02665797107981986870447152285
absolute error = 2.647074918229022718755212616974
relative error = 6.2461089221380596466726551183203 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.156
y[1] (analytic) = 42.382586530054696021475606506165
y[1] (numeric) = 45.04681347107981986870447152285
absolute error = 2.664226941025123847228865016685
relative error = 6.2861357910184288628564354633121 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.157
y[1] (analytic) = 42.385590056871613369398160386993
y[1] (numeric) = 45.06696997107981986870447152285
absolute error = 2.681379914208206499306311135857
relative error = 6.3261592220620679938692499435243 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.158
y[1] (analytic) = 42.38859363329908786422755705883
y[1] (numeric) = 45.08712747107981986870447152285
absolute error = 2.69853383778073200447691446402
relative error = 6.3661792158654029837680224575649 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.159
y[1] (analytic) = 42.391597259334658420678172727782
y[1] (numeric) = 45.10728597107981986870447152285
absolute error = 2.715688711745161448026298795068
relative error = 6.4061957730247235608809650971326 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.16
y[1] (analytic) = 42.394600934975864197631781650642
y[1] (numeric) = 45.12744547107981986870447152285
absolute error = 2.732844536103955671072689872208
relative error = 6.4462088941361832760264455004948 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.161
y[1] (analytic) = 42.397604660220244598101221700606
y[1] (numeric) = 45.14760597107981986870447152285
absolute error = 2.750001310859575270603249822244
relative error = 6.48621857979579954071917560442 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.162
y[1] (analytic) = 42.400608435065339269194067141834
y[1] (numeric) = 45.16776747107981986870447152285
absolute error = 2.767159036014480599510404381016
relative error = 6.5262248305994536653637266412369 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.163
y[1] (analytic) = 42.403612259508688102076308611076
y[1] (numeric) = 45.18792997107981986870447152285
absolute error = 2.784317711571131766628162911774
relative error = 6.5662276471428908974353752254989 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.164
y[1] (analytic) = 42.406616133547831231936040304584
y[1] (numeric) = 45.20809347107981986870447152285
absolute error = 2.801477337531988636768431218266
relative error = 6.6062270300217204596482853726385 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.165
y[1] (analytic) = 42.409620057180309037947154368522
y[1] (numeric) = 45.22825797107981986870447152285
absolute error = 2.818637913899510830757317154328
relative error = 6.646222979831415588111031289927 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.166
y[1] (analytic) = 42.412624030403662143233042491073
y[1] (numeric) = 45.24842347107981986870447152285
absolute error = 2.835799440676157725471429031777
relative error = 6.6862154971673135704694657779933 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.167
y[1] (analytic) = 42.415628053215431414830304694474
y[1] (numeric) = 45.26858997107981986870447152285
absolute error = 2.852961917864388453874166828376
relative error = 6.7262045826246157840369390789908 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.168
y[1] (analytic) = 42.418632125613157963652465325186
y[1] (numeric) = 45.28875747107981986870447152285
absolute error = 2.870125345466661905052006197664
relative error = 6.7661902367983877339118730054681 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.169
y[1] (analytic) = 42.421636247594383144453696240429
y[1] (numeric) = 45.30892597107981986870447152285
absolute error = 2.887289723485436724250775282421
relative error = 6.8061724602835590910826951818564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.17
y[1] (analytic) = 42.424640419156648555792547189264
y[1] (numeric) = 45.32909547107981986870447152285
absolute error = 2.904455051923171312911924333586
relative error = 6.8461512536749237305201382285192 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.171
y[1] (analytic) = 42.427644640297496039995683386475
y[1] (numeric) = 45.34926597107981986870447152285
absolute error = 2.921621330782323828708788136375
relative error = 6.8861266175671397692569087160458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.172
y[1] (analytic) = 42.430648911014467683121630277452
y[1] (numeric) = 45.36943747107981986870447152285
absolute error = 2.938788560065352185582841245398
relative error = 6.9260985525547296044547307155164 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.173
y[1] (analytic) = 42.433653231305105814924525492287
y[1] (numeric) = 45.38960997107981986870447152285
absolute error = 2.955956739774714053779946030563
relative error = 6.9660670592320799514587687683542 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.174
y[1] (analytic) = 42.436657601166953008817877987315
y[1] (numeric) = 45.40978347107981986870447152285
absolute error = 2.973125869912866859886593535535
relative error = 7.0060321381934418818394350972487 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.175
y[1] (analytic) = 42.439662020597552081838334372308
y[1] (numeric) = 45.42995797107981986870447152285
absolute error = 2.990295950482267786866137150542
relative error = 7.04599379003293086142158587761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.176
y[1] (analytic) = 42.442666489594446094609452421547
y[1] (numeric) = 45.45013347107981986870447152285
absolute error = 3.007466981485373774095019101303
relative error = 7.0859520153445267883011113868944 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.177
y[1] (analytic) = 42.445671008155178351305481766979
y[1] (numeric) = 45.47030997107981986870447152285
absolute error = 3.024638962924641517398989755871
relative error = 7.1259068147220740308489248471019 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.178
y[1] (analytic) = 42.448675576277292399615151771715
y[1] (numeric) = 45.49048747107981986870447152285
absolute error = 3.041811894802527469089319751135
relative error = 7.1658581887592814657023547735502 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.179
y[1] (analytic) = 42.451680193958332030705466582028
y[1] (numeric) = 45.51066597107981986870447152285
absolute error = 3.058985777121487837999004940822
relative error = 7.2058061380497225157439456411902 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.18
y[1] (analytic) = 42.454684861195841279185507356143
y[1] (numeric) = 45.53084547107981986870447152285
absolute error = 3.076160609883978589518964166707
relative error = 7.2457506631868351880676716773217 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.181
y[1] (analytic) = 42.457689577987364423070241667983
y[1] (numeric) = 45.55102597107981986870447152285
absolute error = 3.093336393092455445634229854867
relative error = 7.2856917647639221119325685878093 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.182
y[1] (analytic) = 42.460694344330445983744340084135
y[1] (numeric) = 45.57120747107981986870447152285
absolute error = 3.110513126749373884960131438715
relative error = 7.3256294433741505767037880215774 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.183
y[1] (analytic) = 42.463699160222630725925999912216
y[1] (numeric) = 45.59138997107981986870447152285
absolute error = 3.127690810857189142778471610634
relative error = 7.3655636996105525697810795762966 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.184
y[1] (analytic) = 42.466704025661463657630776118918
y[1] (numeric) = 45.61157347107981986870447152285
absolute error = 3.144869445418356211073695403932
relative error = 7.4054945340660248145147051458527 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.185
y[1] (analytic) = 42.469708940644490030135419415899
y[1] (numeric) = 45.63175797107981986870447152285
absolute error = 3.162049030435329838569052106951
relative error = 7.4454219473333288081087904084028 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.186
y[1] (analytic) = 42.472713905169255337941721511781
y[1] (numeric) = 45.65194347107981986870447152285
absolute error = 3.179229565910564530762750011069
memory used=11.4MB, alloc=3.6MB, time=0.64
relative error = 7.4853459400050908595121182515105 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.187
y[1] (analytic) = 42.475718919233305318740367528479
y[1] (numeric) = 45.67212997107981986870447152285
absolute error = 3.196411051846514549964103994371
relative error = 7.525266512673802127296368928879 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.188
y[1] (analytic) = 42.478723982834185953374795580053
y[1] (numeric) = 45.69231747107981986870447152285
absolute error = 3.213593488245633915329675942797
relative error = 7.5651836659318186575218117412134 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.189
y[1] (analytic) = 42.481729095969443465805063512354
y[1] (numeric) = 45.71250597107981986870447152285
absolute error = 3.230776875110376402899408010496
relative error = 7.6050974003713614215904530314728 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.19
y[1] (analytic) = 42.484734258636624323071722801665
y[1] (numeric) = 45.73269547107981986870447152285
absolute error = 3.247961212443195545632748721185
relative error = 7.6450077165845163540866452828858 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.191
y[1] (analytic) = 42.487739470833275235259699610563
y[1] (numeric) = 45.75288597107981986870447152285
absolute error = 3.265146500246544633444771912287
relative error = 7.684914615163234390605162105974 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.192
y[1] (analytic) = 42.490744732556943155462182999233
y[1] (numeric) = 45.77307747107981986870447152285
absolute error = 3.282332738522876713242288523617
relative error = 7.7248180966993315055667438987484 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.193
y[1] (analytic) = 42.493750043805175279744520290482
y[1] (numeric) = 45.79326997107981986870447152285
absolute error = 3.299519927274644588959951232368
relative error = 7.7647181617844887500211189621391 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.194
y[1] (analytic) = 42.496755404575519047108119586638
y[1] (numeric) = 45.81346347107981986870447152285
absolute error = 3.316708066504300821596351936212
relative error = 7.8046148110102522894375048508143 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.195
y[1] (analytic) = 42.499760814865522139454359436618
y[1] (numeric) = 45.83365797107981986870447152285
absolute error = 3.333897156214297729250112086232
relative error = 7.8445080449680334414825947372318 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.196
y[1] (analytic) = 42.502766274672732481548505651334
y[1] (numeric) = 45.85385347107981986870447152285
absolute error = 3.351087196407087387155965871516
relative error = 7.884397864249108713786033564998 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.197
y[1] (analytic) = 42.505771783994698240983635265732
y[1] (numeric) = 45.87404997107981986870447152285
absolute error = 3.368278187085121627720836257118
relative error = 7.9242842694446198416933887652282 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.198
y[1] (analytic) = 42.508777342828967828144567645637
y[1] (numeric) = 45.89424747107981986870447152285
absolute error = 3.385470128250852040559903877213
relative error = 7.9641672611455738260066203078549 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.199
y[1] (analytic) = 42.511782951173089896171802737674
y[1] (numeric) = 45.91444597107981986870447152285
absolute error = 3.402663019906729972532668785176
relative error = 8.0040468399428429707120548575244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.2
y[1] (analytic) = 42.514788609024613340925466460473
y[1] (numeric) = 45.93464547107981986870447152285
absolute error = 3.419856862055206527779005062377
relative error = 8.0439230064271649206958688018252 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.201
y[1] (analytic) = 42.517794316381087300949263235416
y[1] (numeric) = 45.95484597107981986870447152285
absolute error = 3.437051654698732567755208287434
relative error = 8.0837957611891426994470849174058 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.202
y[1] (analytic) = 42.520800073240061157434435655126
y[1] (numeric) = 45.97504747107981986870447152285
absolute error = 3.454247397839758711270035867724
relative error = 8.1236651048192447467480874376348 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.203
y[1] (analytic) = 42.523805879599084534183731287956
y[1] (numeric) = 45.99524997107981986870447152285
absolute error = 3.471444091480735334520740234894
relative error = 8.1635310379078049563526602832533 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.204
y[1] (analytic) = 42.526811735455707297575376616712
y[1] (numeric) = 46.01545347107981986870447152285
absolute error = 3.488641735624112571129094906138
relative error = 8.2033935610450227136515532154775 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.205
y[1] (analytic) = 42.529817640807479556527058109824
y[1] (numeric) = 46.03565797107981986870447152285
absolute error = 3.505840330272340312177413413026
relative error = 8.2432526748209629333255806690102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.206
y[1] (analytic) = 42.532823595651951662459910423223
y[1] (numeric) = 46.05586347107981986870447152285
absolute error = 3.523039875427868206244561099627
relative error = 8.2831083798255560969862580202543 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.207
y[1] (analytic) = 42.535829599986674209262511731143
y[1] (numeric) = 46.07606997107981986870447152285
absolute error = 3.540240371093145659441959791707
relative error = 8.3229606766485982908039800440733 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.208
y[1] (analytic) = 42.538835653809198033254886184101
y[1] (numeric) = 46.09627747107981986870447152285
absolute error = 3.557441817270621835449585338749
relative error = 8.3628095658797512431237463103072 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.209
y[1] (analytic) = 42.541841757117074213152513492263
y[1] (numeric) = 46.11648597107981986870447152285
absolute error = 3.574644213962745655551958030587
relative error = 8.4026550481085423620684382693172 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.21
y[1] (analytic) = 42.544847909907854070030345632473
y[1] (numeric) = 46.13669547107981986870447152285
absolute error = 3.591847561171965798674125890377
relative error = 8.4424971239243647731296527736136 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.211
y[1] (analytic) = 42.547854112179089167286830677142
y[1] (numeric) = 46.15690597107981986870447152285
absolute error = 3.609051858900730701417640845708
relative error = 8.482335793916477356746096780776 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.212
y[1] (analytic) = 42.550860363928331310607943743268
y[1] (numeric) = 46.17711747107981986870447152285
absolute error = 3.626257107151488558096527779582
relative error = 8.5221710586740047858695479806415 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.213
y[1] (analytic) = 42.553866665153132547931225059802
y[1] (numeric) = 46.19732997107981986870447152285
absolute error = 3.643463305926687320773246463048
relative error = 8.5620029187859375635183860878379 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.214
y[1] (analytic) = 42.556873015851045169409825151615
y[1] (numeric) = 46.21754347107981986870447152285
absolute error = 3.660670455228774699294646371235
relative error = 8.60183137484113206031869953859 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.215
y[1] (analytic) = 42.559879416019621707376557138299
y[1] (numeric) = 46.23775797107981986870447152285
absolute error = 3.677878555060198161327914384551
relative error = 8.6416564274283105520329723287454 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.216
y[1] (analytic) = 42.562885865656414936307956146035
y[1] (numeric) = 46.25797347107981986870447152285
absolute error = 3.695087605423404932396515376815
relative error = 8.6814780771360612570763557279206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.217
y[1] (analytic) = 42.565892364758977872788345830788
y[1] (numeric) = 46.27818997107981986870447152285
absolute error = 3.712297606320841995916125692062
relative error = 8.7212963245528383740205296025636 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.218
y[1] (analytic) = 42.568898913324863775473912011051
y[1] (numeric) = 46.29840747107981986870447152285
absolute error = 3.729508557754956093230559511799
relative error = 8.7611111702669621190851580787837 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.219
y[1] (analytic) = 42.571905511351626145056783408385
y[1] (numeric) = 46.31862597107981986870447152285
absolute error = 3.746720459728193723647688114465
relative error = 8.8009226148666187636169442736988 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.22
y[1] (analytic) = 42.574912158836818724229119494013
y[1] (numeric) = 46.33884547107981986870447152285
absolute error = 3.763933312243001144475352028837
relative error = 8.8407306589398606715562888219855 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.221
y[1] (analytic) = 42.577918855777995497647205439685
y[1] (numeric) = 46.35906597107981986870447152285
absolute error = 3.781147115301824371057266083165
relative error = 8.8805353030746063368915569223842 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.222
y[1] (analytic) = 42.580925602172710691895554171068
y[1] (numeric) = 46.37928747107981986870447152285
absolute error = 3.798361868907109176808917351782
relative error = 8.9203365478586404211009586267844 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.223
y[1] (analytic) = 42.583932398018518775451015521919
y[1] (numeric) = 46.39950997107981986870447152285
absolute error = 3.815577573061301093253456000931
relative error = 8.9601343938796137905820470924679 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.224
y[1] (analytic) = 42.586939243312974458646892487271
y[1] (numeric) = 46.41973347107981986870447152285
absolute error = 3.832794227766845410057579035579
relative error = 8.9999288417250435540688395161278 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.225
y[1] (analytic) = 42.589946138053632693637064573862
y[1] (numeric) = 46.43995797107981986870447152285
absolute error = 3.850011833026187175067406948988
relative error = 9.0397198919823131000365654662491 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.226
y[1] (analytic) = 42.592953082238048674360118246089
y[1] (numeric) = 46.46018347107981986870447152285
absolute error = 3.867230388841771194344353276761
relative error = 9.0795075452386721340940473282705 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.227
y[1] (analytic) = 42.595960075863777836503484465712
y[1] (numeric) = 46.48040997107981986870447152285
absolute error = 3.884449895216042032200987057138
relative error = 9.1192918020812367163637175750661 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.228
y[1] (analytic) = 42.598967118928375857467583323542
y[1] (numeric) = 46.50063747107981986870447152285
absolute error = 3.901670352151444011236888199308
relative error = 9.1590726630969892988492775732278 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.229
y[1] (analytic) = 42.601974211429398656329975761382
y[1] (numeric) = 46.52086597107981986870447152285
absolute error = 3.918891759650421212374495761468
relative error = 9.1988501288727787627910026335178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.23
y[1] (analytic) = 42.604981353364402393809522382473
y[1] (numeric) = 46.54109547107981986870447152285
absolute error = 3.936114117715417474894949140377
relative error = 9.2386241999953204560086980118711 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.231
y[1] (analytic) = 42.607988544730943472230549348653
y[1] (numeric) = 46.56132597107981986870447152285
absolute error = 3.953337426348876396473922174197
relative error = 9.2783948770511962302323105654178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.232
y[1] (analytic) = 42.610995785526578535487021362529
y[1] (numeric) = 46.58155747107981986870447152285
absolute error = 3.970561685553241333217450160321
relative error = 9.318162160626854478420200765732 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.233
y[1] (analytic) = 42.614003075748864469006721732875
y[1] (numeric) = 46.60178997107981986870447152285
absolute error = 3.987786895330955399697749789975
relative error = 9.3579260513086101720650797697134 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.234
y[1] (analytic) = 42.617010415395358399715439521527
y[1] (numeric) = 46.62202347107981986870447152285
absolute error = 4.005013055684461468989032001323
relative error = 9.397686549682644898487616246335 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.235
y[1] (analytic) = 42.620017804463617696001163769997
y[1] (numeric) = 46.64225797107981986870447152285
absolute error = 4.022240166616202172703307752853
relative error = 9.4374436563350068981177176555943 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.236
y[1] (analytic) = 42.6230252429511999676782848041
y[1] (numeric) = 46.66249347107981986870447152285
absolute error = 4.03946822812861990102618671875
relative error = 9.477197371851611101763490673798 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.237
y[1] (analytic) = 42.626032730855663065951802614801
y[1] (numeric) = 46.68272997107981986870447152285
absolute error = 4.056697240224156802752668908049
relative error = 9.5169476968182391678678854575135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.238
y[1] (analytic) = 42.629040268174565083381542313569
y[1] (numeric) = 46.70296747107981986870447152285
absolute error = 4.073927202905254785322929209281
relative error = 9.5566946318205395197530284362965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.239
y[1] (analytic) = 42.63204785490546435384637666045
y[1] (numeric) = 46.72320597107981986870447152285
absolute error = 4.0911581161743555148580948624
relative error = 9.5964381774440273828522483224747 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.24
y[1] (analytic) = 42.635055491045919452508455663169
y[1] (numeric) = 46.74344547107981986870447152285
absolute error = 4.108389980033900416196015859681
relative error = 9.6361783342740848219298000240031 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.241
y[1] (analytic) = 42.638063176593489195777443245457
y[1] (numeric) = 46.76368597107981986870447152285
absolute error = 4.125622794486330672927028277393
relative error = 9.6759151028959607782882911446784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.242
y[1] (analytic) = 42.64107091154573264127476098288
y[1] (numeric) = 46.78392747107981986870447152285
absolute error = 4.14285655953408722742971053997
relative error = 9.7156484838947711069638157537772 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.243
y[1] (analytic) = 42.64407869590020908779783890445
y[1] (numeric) = 46.80416997107981986870447152285
absolute error = 4.1600912751796107809066326184
relative error = 9.7553784778554986139088001051625 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.244
y[1] (analytic) = 42.647086529654478075284373358213
y[1] (numeric) = 46.82441347107981986870447152285
absolute error = 4.177326941425341793420098164637
relative error = 9.7951050853629930931625649841041 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.245
y[1] (analytic) = 42.650094412806099384776591939136
y[1] (numeric) = 46.84465797107981986870447152285
absolute error = 4.194563558273720483927879583714
relative error = 9.834828307001971364009609357722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.246
y[1] (analytic) = 42.653102345352633038385525477495
y[1] (numeric) = 46.86490347107981986870447152285
absolute error = 4.211801125727186830318946045355
relative error = 9.874548143357017308125620003257 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.247
y[1] (analytic) = 42.656110327291639299255287086055
y[1] (numeric) = 46.88514997107981986870447152285
absolute error = 4.229039643788180569449184436795
relative error = 9.9142645950125819067112117861343 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.248
y[1] (analytic) = 42.659118358620678671527358264282
y[1] (numeric) = 46.90539747107981986870447152285
absolute error = 4.246279112459141197177113258568
relative error = 9.9539776625529832776134032579047 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.249
y[1] (analytic) = 42.662126439337311900304882057843
y[1] (numeric) = 46.92564597107981986870447152285
absolute error = 4.263519531742507968399589465007
relative error = 9.9936873465624067124348322421017 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.25
y[1] (analytic) = 42.665134569439099971616963271669
y[1] (numeric) = 46.94589547107981986870447152285
absolute error = 4.280760901640719897087508251181
relative error = 10.033393647624904713630716073992 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.251
y[1] (analytic) = 42.668142748923604112382975734818
y[1] (numeric) = 46.96614597107981986870447152285
absolute error = 4.298003222156215756321495788032
relative error = 10.073096566324397031593561158288 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.252
y[1] (analytic) = 42.67115097778838579037687661541
y[1] (numeric) = 46.98639747107981986870447152285
absolute error = 4.31524649329143407832759490744
relative error = 10.112796103244670701725626506805 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.253
y[1] (analytic) = 42.674159256031006714191527783899
y[1] (numeric) = 47.00664997107981986870447152285
absolute error = 4.332490715048813154512943738951
relative error = 10.152492258969380081499145916032 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.254
y[1] (analytic) = 42.677167583649028833203024222904
y[1] (numeric) = 47.02690347107981986870447152285
absolute error = 4.349735887430791035501447299946
relative error = 10.192185034082046887504313442729 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.255
y[1] (analytic) = 42.680175960640014337535029481931
y[1] (numeric) = 47.04715797107981986870447152285
absolute error = 4.366982010439805531169442040919
relative error = 10.231874429166060232485036833346 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.256
y[1] (analytic) = 42.683184387001525658023118175169
y[1] (numeric) = 47.06741347107981986870447152285
memory used=15.2MB, alloc=3.6MB, time=0.87
absolute error = 4.384229084078294210681353347681
relative error = 10.271560444804676662362463561454 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.257
y[1] (analytic) = 42.686192862731125466179125520677
y[1] (numeric) = 47.08766997107981986870447152285
absolute error = 4.401477108348694402525346002173
relative error = 10.311243081581020193246284125031 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.258
y[1] (analytic) = 42.689201387826376674155503919194
y[1] (numeric) = 47.10792747107981986870447152285
absolute error = 4.418726083253443194548967603656
relative error = 10.350922340078082348433817253669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.259
y[1] (analytic) = 42.692209962284842434709686570841
y[1] (numeric) = 47.12818597107981986870447152285
absolute error = 4.435976008794977433994784952009
relative error = 10.390598220878722195396881673651 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.26
y[1] (analytic) = 42.695218586104086141168458128
y[1] (numeric) = 47.14844547107981986870447152285
absolute error = 4.45322688497573372753601339485
relative error = 10.430270724565666382756459076847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.261
y[1] (analytic) = 42.698227259281671427392332382597
y[1] (numeric) = 47.16870597107981986870447152285
absolute error = 4.470478711798148441312139140253
relative error = 10.469939851721509177245152937488 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.262
y[1] (analytic) = 42.701235981815162167739936986073
y[1] (numeric) = 47.18896747107981986870447152285
absolute error = 4.487731489264657700964534536777
relative error = 10.50960560292871250065744781877 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.263
y[1] (analytic) = 42.704244753702122477032405200318
y[1] (numeric) = 47.20922997107981986870447152285
absolute error = 4.504985217377697391672066322532
relative error = 10.549267978769605966787773809231 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.264
y[1] (analytic) = 42.707253574940116710517774677805
y[1] (numeric) = 47.22949347107981986870447152285
absolute error = 4.522239896139703158186696845045
relative error = 10.588926979826386918356380726988 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.265
y[1] (analytic) = 42.710262445526709463835393269212
y[1] (numeric) = 47.24975797107981986870447152285
absolute error = 4.539495525553110404869078253638
relative error = 10.628582606681120463923026727754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.266
y[1] (analytic) = 42.713271365459465572980331856797
y[1] (numeric) = 47.27002347107981986870447152285
absolute error = 4.556752105620354295724139666053
relative error = 10.668234859915739514788485950668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.267
y[1] (analytic) = 42.716280334735950114267804211777
y[1] (numeric) = 47.29028997107981986870447152285
absolute error = 4.574009636343869754436667311073
relative error = 10.707883740112044821883879833961 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.268
y[1] (analytic) = 42.719289353353728404297593873997
y[1] (numeric) = 47.31055747107981986870447152285
absolute error = 4.591268117726091464406877648853
relative error = 10.747529247851705012647836730453 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.269
y[1] (analytic) = 42.722298421310365999918488052135
y[1] (numeric) = 47.33082597107981986870447152285
absolute error = 4.608527549769453868785983470715
relative error = 10.787171383716256627891484450955 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.27
y[1] (analytic) = 42.725307538603428698192718542745
y[1] (numeric) = 47.35109547107981986870447152285
absolute error = 4.625787932476391170511752980105
relative error = 10.826810148287104158651280361522 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.271
y[1] (analytic) = 42.728316705230482536360409666357
y[1] (numeric) = 47.37136597107981986870447152285
absolute error = 4.643049265849337332344061856493
relative error = 10.866445542145520083029683658754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.272
y[1] (analytic) = 42.731325921189093791804033218965
y[1] (numeric) = 47.39163747107981986870447152285
absolute error = 4.660311549890726076900438303885
relative error = 10.906077565872644903023674445017 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.273
y[1] (analytic) = 42.734335186476828982012870437107
y[1] (numeric) = 47.41190997107981986870447152285
absolute error = 4.677574784602990886691601085743
relative error = 10.94570622004948718134112422386 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.274
y[1] (analytic) = 42.73734450109125486454748097486
y[1] (numeric) = 47.43218347107981986870447152285
absolute error = 4.69483896998856500415699054799
relative error = 10.985331505256923578205022433552 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.275
y[1] (analytic) = 42.740353865029938437004178890999
y[1] (numeric) = 47.45245797107981986870447152285
absolute error = 4.712104106049881431700292631851
relative error = 11.024953422075698888145563634914 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.276
y[1] (analytic) = 42.743363278290446936979515644585
y[1] (numeric) = 47.47273347107981986870447152285
absolute error = 4.729370192789372931724955878265
relative error = 11.06457197108642607678009996757 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.277
y[1] (analytic) = 42.746372740870347842034770097262
y[1] (numeric) = 47.49300997107981986870447152285
absolute error = 4.746637230209472026669701425588
relative error = 11.104187152869586317580963486741 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.278
y[1] (analytic) = 42.749382252767208869660445520543
y[1] (numeric) = 47.51328747107981986870447152285
absolute error = 4.763905218312610999044026002307
relative error = 11.143798968005529028631162990698 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.279
y[1] (analytic) = 42.75239181397859797724077360634
y[1] (numeric) = 47.53356597107981986870447152285
absolute error = 4.78117415710122189146369791651
relative error = 11.183407417074471909367959947106 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.28
y[1] (analytic) = 42.755401424502083362018225479024
y[1] (numeric) = 47.55384547107981986870447152285
absolute error = 4.798444046577736506686246043826
relative error = 11.223012500656500977314328124406 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.281
y[1] (analytic) = 42.758411084335233461058029707288
y[1] (numeric) = 47.57412597107981986870447152285
absolute error = 4.815714886744586407646441815562
relative error = 11.262614219331570604798301532447 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.282
y[1] (analytic) = 42.761420793475616951212697314086
y[1] (numeric) = 47.59440747107981986870447152285
absolute error = 4.832986677604202917491774208764
relative error = 11.302212573679503555660215274606 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.283
y[1] (analytic) = 42.764430551920802749086553782904
y[1] (numeric) = 47.61468997107981986870447152285
absolute error = 4.850259419159017119617917739946
relative error = 11.341807564279991021947843911704 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.284
y[1] (analytic) = 42.767440359668360011000278058687
y[1] (numeric) = 47.63497347107981986870447152285
absolute error = 4.867533111411459857704193464163
relative error = 11.381399191712592660599441935844 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.285
y[1] (analytic) = 42.770450216715858132955448541641
y[1] (numeric) = 47.65525797107981986870447152285
absolute error = 4.884807754363961735749022981209
relative error = 11.420987456556736630114690950659 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.286
y[1] (analytic) = 42.773460123060866750599096072219
y[1] (numeric) = 47.67554347107981986870447152285
absolute error = 4.902083348018953118105375450631
relative error = 11.460572359391719627213558152165 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.287
y[1] (analytic) = 42.776470078700955739188263905564
y[1] (numeric) = 47.69582997107981986870447152285
absolute error = 4.919359892378864129516207617286
relative error = 11.500153900796706923483070702623 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.288
y[1] (analytic) = 42.779480083633695213554574673682
y[1] (numeric) = 47.71611747107981986870447152285
absolute error = 4.936637387446124655149896849168
relative error = 11.539732081350732402012010587768 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.289
y[1] (analytic) = 42.782490137856655528068804333626
y[1] (numeric) = 47.73640597107981986870447152285
absolute error = 4.953915833223164340635667189224
relative error = 11.57930690163269859401353454582 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.29
y[1] (analytic) = 42.785500241367407276605463099958
y[1] (numeric) = 47.75669547107981986870447152285
absolute error = 4.971195229712412592099008422892
relative error = 11.618878362221376715435723654742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.291
y[1] (analytic) = 42.788510394163521292507383359791
y[1] (numeric) = 47.77698597107981986870447152285
absolute error = 4.988475576916298576197088163059
relative error = 11.65844646369540670356006716214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.292
y[1] (analytic) = 42.791520596242568648550314568666
y[1] (numeric) = 47.79727747107981986870447152285
absolute error = 5.005756874837251220154156954184
relative error = 11.698011206633297253587885140374 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.293
y[1] (analytic) = 42.794530847602120656907525125559
y[1] (numeric) = 47.81756997107981986870447152285
absolute error = 5.023039123477699211796946397291
relative error = 11.737572591613425855214694547363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.294
y[1] (analytic) = 42.797541148239748869114411225297
y[1] (numeric) = 47.83786347107981986870447152285
absolute error = 5.040322322840070999590060297553
relative error = 11.777130619214038829192523271651 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.295
y[1] (analytic) = 42.80055149815302507603311268665
y[1] (numeric) = 47.85815797107981986870447152285
absolute error = 5.0576064729267947926713588362
relative error = 11.816685290013251363880176738366 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.296
y[1] (analytic) = 42.803561897339521307817135754407
y[1] (numeric) = 47.87845347107981986870447152285
absolute error = 5.074891573740298560887335768443
relative error = 11.856236604589047551781461650617 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.297
y[1] (analytic) = 42.806572345796809833875982873686
y[1] (numeric) = 47.89874997107981986870447152285
absolute error = 5.092177625283010034828488649164
relative error = 11.895784563519280426071371439098 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.298
y[1] (analytic) = 42.809582843522463162839789434799
y[1] (numeric) = 47.91904747107981986870447152285
absolute error = 5.109464627557356705864682088051
relative error = 11.935329167381671997110237990483 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.299
y[1] (analytic) = 42.812593390514054042523967486894
y[1] (numeric) = 47.93934597107981986870447152285
absolute error = 5.126752580565765826180504035956
relative error = 11.97487041675381328894585422351 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.3
y[1] (analytic) = 42.81560398676915545989385641875
y[1] (numeric) = 47.95964547107981986870447152285
absolute error = 5.1440414843106644088106151041
relative error = 12.014408312213164375803572079296 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.301
y[1] (analytic) = 42.818614632285340641029380604902
y[1] (numeric) = 47.97994597107981986870447152285
absolute error = 5.161331338794479227675090917948
relative error = 12.053942854337054418564380490965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.302
y[1] (analytic) = 42.821625327060183051089714015471
y[1] (numeric) = 48.00024747107981986870447152285
absolute error = 5.178622144019636817614757507379
relative error = 12.093474043702681701230967895222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.303
y[1] (analytic) = 42.824636071091256394277951787925
y[1] (numeric) = 48.02054997107981986870447152285
absolute error = 5.195913899988563474426519734925
relative error = 12.133001880887113667381773846913 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.304
y[1] (analytic) = 42.827646864376134613805788759093
y[1] (numeric) = 48.04085347107981986870447152285
absolute error = 5.213206606703685254898682763757
relative error = 12.172526366467286956613034295408 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.305
y[1] (analytic) = 42.83065770691239189185820495569
y[1] (numeric) = 48.06115797107981986870447152285
absolute error = 5.23050026416742797684626656716
relative error = 12.212047501020007440968825079886 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.306
y[1] (analytic) = 42.833668598697602649558158041663
y[1] (numeric) = 48.08146347107981986870447152285
absolute error = 5.247794872382217219146313481187
relative error = 12.251565285121950261359108198456 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.307
y[1] (analytic) = 42.836679539729341546931282720627
y[1] (numeric) = 48.10176997107981986870447152285
absolute error = 5.265090431350478321773188802223
relative error = 12.291079719349659863965785404244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.308
y[1] (analytic) = 42.839690530005183482870597091694
y[1] (numeric) = 48.12207747107981986870447152285
absolute error = 5.282386941074636385833874431156
relative error = 12.330590804279550036636763679533 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.309
y[1] (analytic) = 42.84270156952270359510121595696
y[1] (numeric) = 48.14238597107981986870447152285
absolute error = 5.29968440155711627360325556589
relative error = 12.37009854048790394526803713715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.31
y[1] (analytic) = 42.845712658279477260145071078977
y[1] (numeric) = 48.16269547107981986870447152285
absolute error = 5.316982812800342608559400443873
relative error = 12.409602928550874170173789896238 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.311
y[1] (analytic) = 42.848723796273080093285638386454
y[1] (numeric) = 48.18300597107981986870447152285
absolute error = 5.334282174806739775418833136396
relative error = 12.449103969044482742444524477773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.312
y[1] (analytic) = 42.851734983501087948532672126509
y[1] (numeric) = 48.20331747107981986870447152285
absolute error = 5.351582487578731920171799396341
relative error = 12.488601662544621180293220263047 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.313
y[1] (analytic) = 42.85474621996107691858694596175
y[1] (numeric) = 48.22362997107981986870447152285
absolute error = 5.3688837511187429501175255611
relative error = 12.528096009627050525389526556523 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.314
y[1] (analytic) = 42.857757505650623334805001010472
y[1] (numeric) = 48.24394347107981986870447152285
absolute error = 5.386185965429196533899470512378
relative error = 12.567587010867401379181994792465 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.315
y[1] (analytic) = 42.860768840567303767163900828274
y[1] (numeric) = 48.26425797107981986870447152285
absolute error = 5.403489130512516101540570694576
relative error = 12.607074666841173939208354422771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.316
y[1] (analytic) = 42.863780224708695024225993329374
y[1] (numeric) = 48.28457347107981986870447152285
absolute error = 5.420793246371124844478478193476
relative error = 12.646558978123738035393837021579 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.317
y[1] (analytic) = 42.866791658072374153103679645917
y[1] (numeric) = 48.30488997107981986870447152285
absolute error = 5.438098313007445715600791876933
relative error = 12.686039945290333166337553140182 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.318
y[1] (analytic) = 42.869803140655918439424189923575
y[1] (numeric) = 48.32520747107981986870447152285
absolute error = 5.455404330423901429280281599275
relative error = 12.725517568916068535586926443876 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.319
y[1] (analytic) = 42.872814672456905407294366051736
y[1] (numeric) = 48.34552597107981986870447152285
absolute error = 5.472711298622914461410105471114
relative error = 12.764991849575923087900189660408 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.32
y[1] (analytic) = 42.875826253472912819265451326544
y[1] (numeric) = 48.36584547107981986870447152285
absolute error = 5.490019217606907049439020196306
relative error = 12.804462787844745545496946867843 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.321
y[1] (analytic) = 42.878837883701518676297887045132
y[1] (numeric) = 48.38616597107981986870447152285
absolute error = 5.507328087378301192406584477718
relative error = 12.843930384297254444296806647518 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.322
y[1] (analytic) = 42.881849563140301217726116029312
y[1] (numeric) = 48.40648747107981986870447152285
absolute error = 5.524637907939518650978355493538
relative error = 12.88339463950803817014609062602 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.323
y[1] (analytic) = 42.884861291786838921223393077012
y[1] (numeric) = 48.42680997107981986870447152285
absolute error = 5.541948679292980947481078445838
relative error = 12.922855554051554995032621928112 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.324
y[1] (analytic) = 42.887873069638710502766602339778
y[1] (numeric) = 48.44713347107981986870447152285
absolute error = 5.559260401441109365937869183072
relative error = 12.962313128502133113288598060533 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.325
y[1] (analytic) = 42.890884896693494916601081624626
y[1] (numeric) = 48.46745797107981986870447152285
absolute error = 5.576573074386324952103389898224
relative error = 13.001767363433970677781552744718 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.326
y[1] (analytic) = 42.893896772948771355205453618534
y[1] (numeric) = 48.48778347107981986870447152285
absolute error = 5.593886698131048513499017904316
relative error = 13.041218259421135836093411214573 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=3.6MB, time=1.09
NO POLE
x[1] = 20.327
y[1] (analytic) = 42.896908698402119249256464033889
y[1] (numeric) = 48.50810997107981986870447152285
absolute error = 5.611201272677700619448007488961
relative error = 13.080665817037566766687643493413 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.328
y[1] (analytic) = 42.899920673051118267593826673159
y[1] (numeric) = 48.52843747107981986870447152285
absolute error = 5.628516798028701601110644849691
relative error = 13.120110036857071715064520162351 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.329
y[1] (analytic) = 42.902932696893348317185075411115
y[1] (numeric) = 48.54876597107981986870447152285
absolute error = 5.645833274186471551519396111735
relative error = 13.159550919453329029904475130384 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.33
y[1] (analytic) = 42.905944769926389543090423092897
y[1] (numeric) = 48.56909547107981986870447152285
absolute error = 5.663150701153430325614048429953
relative error = 13.198988465399887199199579914521 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.331
y[1] (analytic) = 42.908956892147822328427627346202
y[1] (numeric) = 48.58942597107981986870447152285
absolute error = 5.680469078931997540276844176648
relative error = 13.238422675270164886373133936444 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.332
y[1] (analytic) = 42.911969063555227294336863305915
y[1] (numeric) = 48.60975747107981986870447152285
absolute error = 5.697788407524592574367608216935
relative error = 13.277853549637450966387375340148 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.333
y[1] (analytic) = 42.914981284146185299945603249489
y[1] (numeric) = 48.63008997107981986870447152285
absolute error = 5.715108686933634568758868273361
relative error = 13.317281089074904561839316833084 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.334
y[1] (analytic) = 42.917993553918277442333503141341
y[1] (numeric) = 48.65042347107981986870447152285
absolute error = 5.732429917161542426370968381509
relative error = 13.356705294155555079044711051552 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.335
y[1] (analytic) = 42.921005872869085056497296084599
y[1] (numeric) = 48.67075797107981986870447152285
absolute error = 5.749752098210734812207175438251
relative error = 13.396126165452302244110149948936 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.336
y[1] (analytic) = 42.924018240996189715315692678493
y[1] (numeric) = 48.69109347107981986870447152285
absolute error = 5.767075230083630153388778844357
relative error = 13.43554370353791613899330270359 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.337
y[1] (analytic) = 42.927030658297173229514288279675
y[1] (numeric) = 48.71142997107981986870447152285
absolute error = 5.784399312782646639190183243175
relative error = 13.474957908985037237551296641265 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.338
y[1] (analytic) = 42.930043124769617647630477165799
y[1] (numeric) = 48.73176747107981986870447152285
absolute error = 5.801724346310202221073994357051
relative error = 13.514368782366176441577245664923 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.339
y[1] (analytic) = 42.933055640411105255978373599639
y[1] (numeric) = 48.75210597107981986870447152285
absolute error = 5.819050330668714612726097923211
relative error = 13.553776324253715116824930682997 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.34
y[1] (analytic) = 42.936068205219218578613739792057
y[1] (numeric) = 48.77244547107981986870447152285
absolute error = 5.836377265860601290090731730793
relative error = 13.59318053521990512902163652515 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.341
y[1] (analytic) = 42.93908081919154037729892076214
y[1] (numeric) = 48.79278597107981986870447152285
absolute error = 5.85370515188827949140555076071
relative error = 13.632581415836868879869149832639 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.342
y[1] (analytic) = 42.942093482325653651467786092775
y[1] (numeric) = 48.81312747107981986870447152285
absolute error = 5.871033988754166217236685430075
relative error = 13.671978966676599343032922408602 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.343
y[1] (analytic) = 42.945106194619141638190678580023
y[1] (numeric) = 48.83346997107981986870447152285
absolute error = 5.888363776460678230513792942827
relative error = 13.711373188310960100119404511426 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.344
y[1] (analytic) = 42.948118956069587812139369774524
y[1] (numeric) = 48.85381347107981986870447152285
absolute error = 5.905694515010232056565101748326
relative error = 13.750764081311685376641552572766 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.345
y[1] (analytic) = 42.95113176667457588555202241331
y[1] (numeric) = 48.87415797107981986870447152285
absolute error = 5.92302620440524398315244910954
relative error = 13.790151646250380077972515819495 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.346
y[1] (analytic) = 42.954144626431689808198159740293
y[1] (numeric) = 48.89450347107981986870447152285
absolute error = 5.940358844648130060506311782557
relative error = 13.829535883698519825287506277238 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.347
y[1] (analytic) = 42.957157535338513767343641713734
y[1] (numeric) = 48.91484997107981986870447152285
absolute error = 5.957692435741306101360829809116
relative error = 13.8689167942274509914938566311 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.348
y[1] (analytic) = 42.960170493392632187715648099024
y[1] (numeric) = 48.93519747107981986870447152285
absolute error = 5.975026977687187680988823423826
relative error = 13.908294378408390737149270417253 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.349
y[1] (analytic) = 42.963183500591629731467668445068
y[1] (numeric) = 48.95554597107981986870447152285
absolute error = 5.992362470488190137236803077782
relative error = 13.947668636812427046368269017206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.35
y[1] (analytic) = 42.966196556933091298144498942579
y[1] (numeric) = 48.97589547107981986870447152285
absolute error = 6.009698914146728570559972580271
relative error = 13.987039570010518762716839924645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.351
y[1] (analytic) = 42.969209662414602024647246162604
y[1] (numeric) = 48.99624597107981986870447152285
absolute error = 6.027036308665217844057225360246
relative error = 14.026407178573495625095290752761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.352
y[1] (analytic) = 42.972222817033747285198337673575
y[1] (numeric) = 49.01659747107981986870447152285
absolute error = 6.044374654046072583506133849275
relative error = 14.065771463072058303609313448175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.353
y[1] (analytic) = 42.975236020788112691306539535217
y[1] (numeric) = 49.03694997107981986870447152285
absolute error = 6.061713950291707177397931987633
relative error = 14.105132424076778435429263175516 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.354
y[1] (analytic) = 42.978249273675284091731980667594
y[1] (numeric) = 49.05730347107981986870447152285
absolute error = 6.079054197404535776972490855256
relative error = 14.144490062158098660637656334969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.355
y[1] (analytic) = 42.981262575692847572451184093637
y[1] (numeric) = 49.07765797107981986870447152285
absolute error = 6.096395395386972296253287429213
relative error = 14.183844377886332658064892173011 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.356
y[1] (analytic) = 42.984275926838389456622105053443
y[1] (numeric) = 49.09801347107981986870447152285
absolute error = 6.113737544241430412082366469407
relative error = 14.223195371831665181113202444805 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.357
y[1] (analytic) = 42.987289327109496304549175988658
y[1] (numeric) = 49.11836997107981986870447152285
absolute error = 6.131080643970323564155295534192
relative error = 14.262543044564152093568833584732 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.358
y[1] (analytic) = 42.99030277650375491364835839527
y[1] (numeric) = 49.13872747107981986870447152285
absolute error = 6.14842469457606495505611312758
relative error = 14.301887396653720405402465839619 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.359
y[1] (analytic) = 42.993316275018752318412201543113
y[1] (numeric) = 49.15908597107981986870447152285
absolute error = 6.165769696061067550292269979737
relative error = 14.341228428670168308557873817377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.36
y[1] (analytic) = 42.996329822652075790374908060407
y[1] (numeric) = 49.17944547107981986870447152285
absolute error = 6.183115648427744078329563462443
relative error = 14.380566141183165212728832901778 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.361
y[1] (analytic) = 42.999343419401312838077406381626
y[1] (numeric) = 49.19980597107981986870447152285
absolute error = 6.200462551678507030627065141224
relative error = 14.419900534762251781124275982309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.362
y[1] (analytic) = 43.002357065264051207032430057037
y[1] (numeric) = 49.22016747107981986870447152285
absolute error = 6.217810405815768661672041465813
relative error = 14.459231609976839966221704945986 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.363
y[1] (analytic) = 43.005370760237878879689603922216
y[1] (numeric) = 49.24052997107981986870447152285
absolute error = 6.235159210841940989014867600634
relative error = 14.498559367396213045508861376203 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.364
y[1] (analytic) = 43.008384504320384075400537125828
y[1] (numeric) = 49.26089347107981986870447152285
absolute error = 6.252508966759435793303934397022
relative error = 14.537883807589525657213660901866 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.365
y[1] (analytic) = 43.011398297509155250383923014035
y[1] (numeric) = 49.28125797107981986870447152285
absolute error = 6.269859673570664618320548508815
relative error = 14.577204931125803836022395637917 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.366
y[1] (analytic) = 43.01441213980178109769064586982
y[1] (numeric) = 49.30162347107981986870447152285
absolute error = 6.28721133127803877101382565303
relative error = 14.616522738573945048786209156697 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.367
y[1] (analytic) = 43.017426031195850547168894505539
y[1] (numeric) = 49.32198997107981986870447152285
absolute error = 6.304563939883969321535577017311
relative error = 14.655837230502718230215848427605 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.368
y[1] (analytic) = 43.020439971688952765429282707035
y[1] (numeric) = 49.34235747107981986870447152285
absolute error = 6.321917499390867103275188815815
relative error = 14.695148407480763818564697160562 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.369
y[1] (analytic) = 43.023453961278677155809976527635
y[1] (numeric) = 49.36272597107981986870447152285
absolute error = 6.339272009801142712894494995215
relative error = 14.734456270076593791300094986937 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.37
y[1] (analytic) = 43.026467999962613358341828430317
y[1] (numeric) = 49.38309547107981986870447152285
absolute error = 6.356627471117206510362643092533
relative error = 14.773760818858591700762946909778 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.371
y[1] (analytic) = 43.029482087738351249713518276411
y[1] (numeric) = 49.40346597107981986870447152285
absolute error = 6.373983883341468618990953246439
relative error = 14.813062054395012709815627453076 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.372
y[1] (analytic) = 43.03249622460348094323670115911
y[1] (numeric) = 49.42383747107981986870447152285
absolute error = 6.39134124647633892546777036374
relative error = 14.852359977253983627478183938174 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.373
y[1] (analytic) = 43.035510410555592788811162080153
y[1] (numeric) = 49.44420997107981986870447152285
absolute error = 6.408699560524227079893309442697
relative error = 14.891654588003502944552843313249 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.374
y[1] (analytic) = 43.038524645592277372889977467963
y[1] (numeric) = 49.46458347107981986870447152285
absolute error = 6.426058825487542495814494054887
relative error = 14.930945887211440869236826960181 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.375
y[1] (analytic) = 43.041538929711125518444683535579
y[1] (numeric) = 49.48495797107981986870447152285
absolute error = 6.443419041368694350259787987271
relative error = 14.970233875445539362723477901015 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.376
y[1] (analytic) = 43.044553262909728284930451476714
y[1] (numeric) = 49.50533347107981986870447152285
absolute error = 6.460780208170091583774020046136
relative error = 15.009518553273412174791704824416 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.377
y[1] (analytic) = 43.047567645185676968251269498233
y[1] (numeric) = 49.52570997107981986870447152285
absolute error = 6.478142325894142900453202024617
relative error = 15.048799921262544879383747350664 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.378
y[1] (analytic) = 43.050582076536563100725131687401
y[1] (numeric) = 49.54608747107981986870447152285
absolute error = 6.495505394543256767979339835449
relative error = 15.088077979980294910171266951762 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.379
y[1] (analytic) = 43.053596556959978451049233712201
y[1] (numeric) = 49.56646597107981986870447152285
absolute error = 6.512869414119841417655237810649
relative error = 15.127352729993891596109767941412 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.38
y[1] (analytic) = 43.056611086453515024265175353076
y[1] (numeric) = 49.58684547107981986870447152285
absolute error = 6.530234384626304844439296169774
relative error = 15.166624171870436196981352947646 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.381
y[1] (analytic) = 43.059625665014765061724169864377
y[1] (numeric) = 49.60722597107981986870447152285
absolute error = 6.547600306065054806980301658473
relative error = 15.205892306176901938925817279148 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.382
y[1] (analytic) = 43.062640292641321041052260163875
y[1] (numeric) = 49.62760747107981986870447152285
absolute error = 6.564967178438498827652211358975
relative error = 15.245157133480134049960086594257 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.383
y[1] (analytic) = 43.065654969330775676115541848658
y[1] (numeric) = 49.64798997107981986870447152285
absolute error = 6.582335001749044192588929674192
relative error = 15.284418654346849795486002279838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.384
y[1] (analytic) = 43.068669695080721916985393035719
y[1] (numeric) = 49.66837347107981986870447152285
absolute error = 6.599703775999097951719078487131
relative error = 15.323676869343638513786458945356 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.385
y[1] (analytic) = 43.071684469888752949903711025581
y[1] (numeric) = 49.68875797107981986870447152285
absolute error = 6.617073501191066918800760497269
relative error = 15.362931779036961651509898435525 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.386
y[1] (analytic) = 43.074699293752462197248155787283
y[1] (numeric) = 49.70914347107981986870447152285
absolute error = 6.634444177327357671456315735567
relative error = 15.402183383993152799143164763055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.387
y[1] (analytic) = 43.077714166669443317497400263027
y[1] (numeric) = 49.72952997107981986870447152285
absolute error = 6.651815804410376551207071259823
relative error = 15.44143168477841772647272436122 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.388
y[1] (analytic) = 43.080729088637290205196387490872
y[1] (numeric) = 49.74991747107981986870447152285
absolute error = 6.669188382442529663508084031978
relative error = 15.480676681958834418034256053847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.389
y[1] (analytic) = 43.08374405965359699092159454373
y[1] (numeric) = 49.77030597107981986870447152285
absolute error = 6.68656191142622287778287697912
relative error = 15.519918376100353108550615138816 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.39
y[1] (analytic) = 43.08675907971595804124630328305
y[1] (numeric) = 49.79069547107981986870447152285
absolute error = 6.7039363913638618274581682398
relative error = 15.559156767768796318358175978919 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.391
y[1] (analytic) = 43.089774148821967958705877925498
y[1] (numeric) = 49.81108597107981986870447152285
absolute error = 6.721311822257851909998593597352
relative error = 15.598391857529858888821557492254 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.392
y[1] (analytic) = 43.092789266969221581763049420947
y[1] (numeric) = 49.83147747107981986870447152285
absolute error = 6.738688204110598286941422101903
relative error = 15.637623645949108017736735932451 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.393
y[1] (analytic) = 43.095804434155313984773206640143
y[1] (numeric) = 49.85186997107981986870447152285
absolute error = 6.756065536924505883931264882707
relative error = 15.676852133591983294722549347006 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.394
y[1] (analytic) = 43.098819650377840477949694370336
y[1] (numeric) = 49.87226347107981986870447152285
absolute error = 6.773443820701979390754777152514
relative error = 15.716077321023796736600598100337 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.395
y[1] (analytic) = 43.101834915634396607329118117246
y[1] (numeric) = 49.89265797107981986870447152285
absolute error = 6.790823055445423261375353405604
relative error = 15.755299208809732822763545846058 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.396
y[1] (analytic) = 43.104850229922578154736655711659
y[1] (numeric) = 49.91305347107981986870447152285
absolute error = 6.808203241157241713967815811191
relative error = 15.794517797514848530531825331349 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=22.8MB, alloc=3.6MB, time=1.31
x[1] = 20.397
y[1] (analytic) = 43.107865593239981137751375719021
y[1] (numeric) = 49.93344997107981986870447152285
absolute error = 6.825584377839838730953095803829
relative error = 15.833733087704073370498753414176 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.398
y[1] (analytic) = 43.110881005584201809671562650331
y[1] (numeric) = 49.95384747107981986870447152285
absolute error = 6.842966465495618059032908872519
relative error = 15.872945079942209421864059672462 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.399
y[1] (analytic) = 43.113896466952836659480048972676
y[1] (numeric) = 49.97424597107981986870447152285
absolute error = 6.860349504126983209224422550174
relative error = 15.912153774793931367755832982308 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.4
y[1] (analytic) = 43.116911977343482411809553917763
y[1] (numeric) = 49.99464547107981986870447152285
absolute error = 6.877733493736337456894917605087
relative error = 15.951359172823786530540890440472 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.401
y[1] (analytic) = 43.119927536753736026908029086744
y[1] (numeric) = 50.01504597107981986870447152285
absolute error = 6.895118434326083841796442436106
relative error = 15.990561274596194907123573004603 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.402
y[1] (analytic) = 43.122943145181194700604010849697
y[1] (numeric) = 50.03544747107981986870447152285
absolute error = 6.912504325898625168100460673153
relative error = 16.029760080675449204232972222671 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.403
y[1] (analytic) = 43.125958802623455864271979538077
y[1] (numeric) = 50.05584997107981986870447152285
absolute error = 6.929891168456364004432491984773
relative error = 16.068955591625714873698592421312 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.404
y[1] (analytic) = 43.12897450907811718479772542851
y[1] (numeric) = 50.07625347107981986870447152285
absolute error = 6.94727896200170268390674609434
relative error = 16.108147808011030147714452720777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.405
y[1] (analytic) = 43.131990264542776564543721516202
y[1] (numeric) = 50.09665797107981986870447152285
absolute error = 6.964667706537043304160750006648
relative error = 16.147336730395306074091633242573 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.406
y[1] (analytic) = 43.13500606901503214131450307637
y[1] (numeric) = 50.11706347107981986870447152285
absolute error = 6.98205740206478772738996844648
relative error = 16.18652235934232655149926987368 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.407
y[1] (analytic) = 43.138021922492482288322054011977
y[1] (numeric) = 50.13746997107981986870447152285
absolute error = 6.999448048587337580382417510873
relative error = 16.225704695415748364694001949678 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.408
y[1] (analytic) = 43.141037824972725614151199986138
y[1] (numeric) = 50.15787747107981986870447152285
absolute error = 7.016839646107094254553271536712
relative error = 16.26488373917910121973787721703 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.409
y[1] (analytic) = 43.144053776453360962725008337529
y[1] (numeric) = 50.17828597107981986870447152285
absolute error = 7.034232194626458905979463185321
relative error = 16.304059491195787779204718433028 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.41
y[1] (analytic) = 43.147069776931987413270194777128
y[1] (numeric) = 50.19869547107981986870447152285
absolute error = 7.051625694147832455434276745722
relative error = 16.34323195202908369737495596001 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.411
y[1] (analytic) = 43.150085826406204280282536864629
y[1] (numeric) = 50.21910597107981986870447152285
absolute error = 7.069020144673615588421934658221
relative error = 16.382401122242137655418930708616 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.412
y[1] (analytic) = 43.153101924873611113492294262895
y[1] (numeric) = 50.23951747107981986870447152285
absolute error = 7.086415546206208755212177259955
relative error = 16.421567002397971396568671782877 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.413
y[1] (analytic) = 43.156118072331807697829635768738
y[1] (numeric) = 50.25992997107981986870447152285
absolute error = 7.103811898748012170874835754112
relative error = 16.46072959305947976127815317832 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.414
y[1] (analytic) = 43.159134268778394053390073118416
y[1] (numeric) = 50.28034347107981986870447152285
absolute error = 7.121209202301425815314398404434
relative error = 16.499888894789430722372033882131 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.415
y[1] (analytic) = 43.162150514210970435399901566158
y[1] (numeric) = 50.30075797107981986870447152285
absolute error = 7.138607456868849433304569956692
relative error = 16.539044908150465420182885722758 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.416
y[1] (analytic) = 43.16516680862713733418164723407
y[1] (numeric) = 50.32117347107981986870447152285
absolute error = 7.15600666245268253452282428878
relative error = 16.578197633705098197676913314387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.417
y[1] (analytic) = 43.16818315202449547511952123176
y[1] (numeric) = 50.34158997107981986870447152285
absolute error = 7.17340681905532439358495029109
relative error = 16.617347072015716635568170439918 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.418
y[1] (analytic) = 43.171199544400645818624880544022
y[1] (numeric) = 50.36200747107981986870447152285
absolute error = 7.190807926679174050079590978828
relative error = 16.656493223644581587421277214172 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.419
y[1] (analytic) = 43.174215985753189560101695684937
y[1] (numeric) = 50.38242597107981986870447152285
absolute error = 7.208209985326630308602775837913
relative error = 16.695636089153827214742642367211 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.42
y[1] (analytic) = 43.1772324760797281299120251167
y[1] (numeric) = 50.40284547107981986870447152285
absolute error = 7.22561299500009173879244640615
relative error = 16.734775669105461022060194985885 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.421
y[1] (analytic) = 43.180249015377863193341496431563
y[1] (numeric) = 50.42326597107981986870447152285
absolute error = 7.243016955701956675362975091287
relative error = 16.773911964061363891991630049692 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.422
y[1] (analytic) = 43.183265603645196650564794295193
y[1] (numeric) = 50.44368747107981986870447152285
absolute error = 7.260421867434623218139677227657
relative error = 16.813044974583290120301172095395 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.423
y[1] (analytic) = 43.186282240879330636611155149819
y[1] (numeric) = 50.46410997107981986870447152285
absolute error = 7.277827730200489232093316373031
relative error = 16.852174701232867450944861342828 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.424
y[1] (analytic) = 43.189298927077867521329868675508
y[1] (numeric) = 50.48453347107981986870447152285
absolute error = 7.295234544001952347374602847342
relative error = 16.89130114457159711110436661254 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.425
y[1] (analytic) = 43.192315662238409909355786007904
y[1] (numeric) = 50.50495797107981986870447152285
absolute error = 7.312642308841409959348685514946
relative error = 16.93042430516085384620932936409 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.426
y[1] (analytic) = 43.195332446358560640074834710785
y[1] (numeric) = 50.52538347107981986870447152285
absolute error = 7.330051024721259228629636812065
relative error = 16.969544183561885954948243181945 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.427
y[1] (analytic) = 43.198349279435922787589540501786
y[1] (numeric) = 50.54580997107981986870447152285
absolute error = 7.347460691643897081114931021064
relative error = 17.008660780335815324267873034047 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.428
y[1] (analytic) = 43.201366161468099660684555729634
y[1] (numeric) = 50.56623747107981986870447152285
absolute error = 7.364871309611720208019915793216
relative error = 17.047774096043637464361218626334 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.429
y[1] (analytic) = 43.204383092452694802792194601234
y[1] (numeric) = 50.58666597107981986870447152285
absolute error = 7.382282878627125065912276921616
relative error = 17.086884131246221543644026174629 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.43
y[1] (analytic) = 43.207400072387311991957975156959
y[1] (numeric) = 50.60709547107981986870447152285
absolute error = 7.399695398692507876746496365891
relative error = 17.125990886504310423719852913469 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.431
y[1] (analytic) = 43.210417101269555240806167992513
y[1] (numeric) = 50.62752597107981986870447152285
absolute error = 7.417108869810264627898303530337
relative error = 17.165094362378520694333688659519 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.432
y[1] (analytic) = 43.213434179097028796505351725667
y[1] (numeric) = 50.64795747107981986870447152285
absolute error = 7.434523291982791072199119797183
relative error = 17.20419455942934270831413874562 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.433
y[1] (analytic) = 43.216451305867337140733975206273
y[1] (numeric) = 50.66838997107981986870447152285
absolute error = 7.451938665212482727970496316577
relative error = 17.243291478217140616504172639329 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.434
y[1] (analytic) = 43.219468481578084989645926467874
y[1] (numeric) = 50.68882347107981986870447152285
absolute error = 7.469354989501734879058545054976
relative error = 17.282385119302152402680442558256 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.435
y[1] (analytic) = 43.222485706226877293836108419247
y[1] (numeric) = 50.70925797107981986870447152285
absolute error = 7.486772264852942574868363103603
relative error = 17.3214754832444899184611763926 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.436
y[1] (analytic) = 43.225502979811319238306021274287
y[1] (numeric) = 50.72969347107981986870447152285
absolute error = 7.504190491268500630398450248563
relative error = 17.36056257060413891820264924324 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.437
y[1] (analytic) = 43.228520302329016242429351718512
y[1] (numeric) = 50.75012997107981986870447152285
absolute error = 7.521609668750803626275119804338
relative error = 17.399646381940959093884237882264 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.438
y[1] (analytic) = 43.231537673777573959917568810587
y[1] (numeric) = 50.77056747107981986870447152285
absolute error = 7.539029797302245908786902712263
relative error = 17.438726917814684109982062440679 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.439
y[1] (analytic) = 43.234555094154598278785526617217
y[1] (numeric) = 50.79100597107981986870447152285
absolute error = 7.556450876925221589918944905633
relative error = 17.477804178784921638331219626282 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.44
y[1] (analytic) = 43.237572563457695321317073579735
y[1] (numeric) = 50.81144547107981986870447152285
absolute error = 7.573872907622124547387397943115
relative error = 17.516878165411153392976611772992 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.441
y[1] (analytic) = 43.240590081684471444030668610769
y[1] (numeric) = 50.83188597107981986870447152285
absolute error = 7.591295889395348424673802912081
relative error = 17.555948878252735165012376020862 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.442
y[1] (analytic) = 43.243607648832533237645003919314
y[1] (numeric) = 50.85232747107981986870447152285
absolute error = 7.608719822247286631059467603536
relative error = 17.595016317868896857409917924382 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.443
y[1] (analytic) = 43.246625264899487527044634562595
y[1] (numeric) = 50.87276997107981986870447152285
absolute error = 7.626144706180332341659836960255
relative error = 17.634080484818742519834553784661 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.444
y[1] (analytic) = 43.249642929882941371245614723041
y[1] (numeric) = 50.89321347107981986870447152285
absolute error = 7.643570541196878497458856799809
relative error = 17.673141379661250383450765999422 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.445
y[1] (analytic) = 43.252660643780502063361140708756
y[1] (numeric) = 50.91365797107981986870447152285
absolute error = 7.660997327299317805343330814094
relative error = 17.712199002955272895716075722755 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.446
y[1] (analytic) = 43.255678406589777130567200675821
y[1] (numeric) = 50.93410347107981986870447152285
absolute error = 7.678425064490042738137270847029
relative error = 17.751253355259536755163537124863 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.447
y[1] (analytic) = 43.258696218308374334068231070788
y[1] (numeric) = 50.95454997107981986870447152285
absolute error = 7.695853752771445534636240452062
relative error = 17.790304437132642946172857540157 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.448
y[1] (analytic) = 43.261714078933901669062779791737
y[1] (numeric) = 50.97499747107981986870447152285
absolute error = 7.713283392145918199641691731113
relative error = 17.829352249133066773730147790175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.449
y[1] (analytic) = 43.264731988463967364709176066235
y[1] (numeric) = 50.99544597107981986870447152285
absolute error = 7.730713982615852503995295456615
relative error = 17.868396791819157898176306966102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.45
y[1] (analytic) = 43.26774994689617988409120704456
y[1] (numeric) = 51.01589547107981986870447152285
absolute error = 7.74814552418363998461326447829
relative error = 17.907438065749140369944045953731 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.451
y[1] (analytic) = 43.270767954228147924183801106557
y[1] (numeric) = 51.03634597107981986870447152285
absolute error = 7.765578016851671944520670416293
relative error = 17.946476071481112664283553981895 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.452
y[1] (analytic) = 43.273786010457480415818717880469
y[1] (numeric) = 51.05679747107981986870447152285
absolute error = 7.783011460622339452885753642381
relative error = 17.985510809573047715976812473659 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.453
y[1] (analytic) = 43.276804115581786523650244972111
y[1] (numeric) = 51.07724997107981986870447152285
absolute error = 7.800445855498033345054226550739
relative error = 18.024542280582792954040560477625 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.454
y[1] (analytic) = 43.279822269598675646120901402762
y[1] (numeric) = 51.09770347107981986870447152285
absolute error = 7.817881201481144222583570120088
relative error = 18.063570485068070336417915954904 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.455
y[1] (analytic) = 43.282840472505757415427147754093
y[1] (numeric) = 51.11815797107981986870447152285
absolute error = 7.835317498574062453277323768757
relative error = 18.102595423586476384658657195626 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.456
y[1] (analytic) = 43.28585872430064169748510301854
y[1] (numeric) = 51.13861347107981986870447152285
absolute error = 7.85275474677917817121936850431
relative error = 18.141617096695482218588168636785 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.457
y[1] (analytic) = 43.288877024980938591896268153447
y[1] (numeric) = 51.15906997107981986870447152285
absolute error = 7.870192946098881276808203369403
relative error = 18.180635504952433590965055351653 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.458
y[1] (analytic) = 43.29189537454425843191325633736
y[1] (numeric) = 51.17952747107981986870447152285
absolute error = 7.88763209653556143679121518549
relative error = 18.21965064891455092212743047898 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.459
y[1] (analytic) = 43.294913772988211784405529926833
y[1] (numeric) = 51.19998597107981986870447152285
absolute error = 7.905072198091608084298941596017
relative error = 18.258662529138929334627879858492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.46
y[1] (analytic) = 43.297932220310409449825144112089
y[1] (numeric) = 51.22044547107981986870447152285
absolute error = 7.922513250769410418879327410761
relative error = 18.297671146182538687857108137377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.461
y[1] (analytic) = 43.300950716508462462172497269925
y[1] (numeric) = 51.24090597107981986870447152285
absolute error = 7.939955254571357406531974252925
relative error = 18.336676500602223612656270610552 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.462
y[1] (analytic) = 43.30396926157998208896208801222
y[1] (numeric) = 51.26136747107981986870447152285
absolute error = 7.95739820949983777974238351063
relative error = 18.375678592954703545917995055736 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.463
y[1] (analytic) = 43.306987855522579831188278928378
y[1] (numeric) = 51.28182997107981986870447152285
absolute error = 7.974842115557240037516192594472
relative error = 18.414677423796572765176097822641 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.464
y[1] (analytic) = 43.310006498333867423291067020115
y[1] (numeric) = 51.30229347107981986870447152285
absolute error = 7.992286972745952445413404502735
relative error = 18.453672993684300423183998433562 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.465
y[1] (analytic) = 43.313025190011456833121860826943
y[1] (numeric) = 51.32275797107981986870447152285
absolute error = 8.009732781068363035582610695907
relative error = 18.492665303174230582481836950969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.466
y[1] (analytic) = 43.316043930552960261909264240677
y[1] (numeric) = 51.34322347107981986870447152285
absolute error = 8.027179540526859606795207282173
relative error = 18.531654352822582249952298365999 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=26.7MB, alloc=3.6MB, time=1.53
x[1] = 20.467
y[1] (analytic) = 43.319062719955990144224867007392
y[1] (numeric) = 51.36368997107981986870447152285
absolute error = 8.044627251123829724479604515458
relative error = 18.570640143185449411365148259638 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.468
y[1] (analytic) = 43.322081558218159147949041915158
y[1] (numeric) = 51.38415747107981986870447152285
absolute error = 8.062075912861660720755429607692
relative error = 18.609622674818801065910483986847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.469
y[1] (analytic) = 43.325100445337080174236748665915
y[1] (numeric) = 51.40462597107981986870447152285
absolute error = 8.079525525742739694467722856935
relative error = 18.64860194827848126072070563199 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.47
y[1] (analytic) = 43.328119381310366357483344429888
y[1] (numeric) = 51.42509547107981986870447152285
absolute error = 8.096976089769453511221127092962
relative error = 18.687577964120209125381210982009 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.471
y[1] (analytic) = 43.331138366135631065290401080882
y[1] (numeric) = 51.44556597107981986870447152285
absolute error = 8.114427604944188803414070441968
relative error = 18.726550722899578906429818762139 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.472
y[1] (analytic) = 43.334157399810487898431529110828
y[1] (numeric) = 51.46603747107981986870447152285
absolute error = 8.131880071269331970272942412022
relative error = 18.765520225172060001844924377088 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.473
y[1] (analytic) = 43.337176482332550690818208221963
y[1] (numeric) = 51.48650997107981986870447152285
absolute error = 8.149333488747269177886263300887
relative error = 18.804486471492996995522392398737 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.474
y[1] (analytic) = 43.340195613699433509465624594997
y[1] (numeric) = 51.50698347107981986870447152285
absolute error = 8.166787857380386359238846927853
relative error = 18.843449462417609691741190039721 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.475
y[1] (analytic) = 43.343214793908750654458514831651
y[1] (numeric) = 51.52745797107981986870447152285
absolute error = 8.184243177171069214245956691199
relative error = 18.882409198500993149617765850355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.476
y[1] (analytic) = 43.34623402295811665891701656993
y[1] (numeric) = 51.54793347107981986870447152285
absolute error = 8.20169944812170320978745495292
relative error = 18.921365680298117717549177874603 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.477
y[1] (analytic) = 43.349253300845146288962525770483
y[1] (numeric) = 51.56840997107981986870447152285
absolute error = 8.219156670234673579741945752367
relative error = 18.960318908363829067644975499055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.478
y[1] (analytic) = 43.352272627567454543683560672464
y[1] (numeric) = 51.58888747107981986870447152285
absolute error = 8.236614843512365325020910850386
relative error = 18.999268883252848230147839226877 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.479
y[1] (analytic) = 43.355292003122656655101632417225
y[1] (numeric) = 51.60936597107981986870447152285
absolute error = 8.254073967957163213602839105625
relative error = 19.038215605519771627842982607131 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.48
y[1] (analytic) = 43.358311427508368088137122338226
y[1] (numeric) = 51.62984547107981986870447152285
absolute error = 8.271534043571451780567349184624
relative error = 19.07715907571907111045632054793 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.481
y[1] (analytic) = 43.361330900722204540575165915554
y[1] (numeric) = 51.65032597107981986870447152285
absolute error = 8.288995070357615328129305607296
relative error = 19.116099294405093989041408240057 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.482
y[1] (analytic) = 43.364350422761781943031543393386
y[1] (numeric) = 51.67080747107981986870447152285
absolute error = 8.306457048318037925672928129464
relative error = 19.155036262132063070355154916056 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.483
y[1] (analytic) = 43.367369993624716458918577058799
y[1] (numeric) = 51.69128997107981986870447152285
absolute error = 8.323919977455103409785894464051
relative error = 19.193969979454076691222316667786 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.484
y[1] (analytic) = 43.370389613308624484411035180303
y[1] (numeric) = 51.71177347107981986870447152285
absolute error = 8.341383857771195384293436342547
relative error = 19.232900446925108752888772543761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.485
y[1] (analytic) = 43.373409281811122648412042604432
y[1] (numeric) = 51.73225797107981986870447152285
absolute error = 8.358848689268697220292428918418
relative error = 19.27182766509900875536358814585 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.486
y[1] (analytic) = 43.376428999129827812518998008841
y[1] (numeric) = 51.75274347107981986870447152285
absolute error = 8.376314471949992056185473514009
relative error = 19.310751634529501831749870942876 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.487
y[1] (analytic) = 43.379448765262357070989497810185
y[1] (numeric) = 51.77322997107981986870447152285
absolute error = 8.393781205817462797714973712665
relative error = 19.349672355770188782564421517271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.488
y[1] (analytic) = 43.382468580206327750707266725264
y[1] (numeric) = 51.79371747107981986870447152285
absolute error = 8.411248890873492117997204797586
relative error = 19.388589829374546110046184958623 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.489
y[1] (analytic) = 43.385488443959357411148094983714
y[1] (numeric) = 51.81420597107981986870447152285
absolute error = 8.428717527120462457556376539136
relative error = 19.427504055895926052453506616701 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.49
y[1] (analytic) = 43.388508356519063844345782190696
y[1] (numeric) = 51.83469547107981986870447152285
absolute error = 8.446187114560756024358689332154
relative error = 19.466415035887556618350196424282 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.491
y[1] (analytic) = 43.391528317883065074858087837903
y[1] (numeric) = 51.85518597107981986870447152285
absolute error = 8.463657653196754793846383684947
relative error = 19.505322769902541620880405998681 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.492
y[1] (analytic) = 43.394548328048979359732688461308
y[1] (numeric) = 51.87567747107981986870447152285
absolute error = 8.481129143030840508971783061542
relative error = 19.544227258493860712032322728814 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.493
y[1] (analytic) = 43.397568387014425188473141443998
y[1] (numeric) = 51.89616997107981986870447152285
absolute error = 8.498601584065394680231330078852
relative error = 19.583128502214369416890685053039 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.494
y[1] (analytic) = 43.400588494777021283004855462492
y[1] (numeric) = 51.91666347107981986870447152285
absolute error = 8.516074976302798585699616060358
relative error = 19.622026501616799167878123131109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.495
y[1] (analytic) = 43.403608651334386597641067574909
y[1] (numeric) = 51.93715797107981986870447152285
absolute error = 8.533549319745433271063403947941
relative error = 19.66092125725375733898532911185 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.496
y[1] (analytic) = 43.406628856684140319048826949381
y[1] (numeric) = 51.95765347107981986870447152285
absolute error = 8.551024614395679549655644573469
relative error = 19.699812769677727279990061196321 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.497
y[1] (analytic) = 43.409649110823901866214985231084
y[1] (numeric) = 51.97814997107981986870447152285
absolute error = 8.568500860255918002489486291766
relative error = 19.738701039441068350664985694495 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.498
y[1] (analytic) = 43.412669413751290890412193546247
y[1] (numeric) = 51.99864747107981986870447152285
absolute error = 8.585978057328528978292277976603
relative error = 19.777586067096015954974361271739 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.499
y[1] (analytic) = 43.415689765463927275164906141571
y[1] (numeric) = 52.01914597107981986870447152285
absolute error = 8.603456205615892593539565381279
relative error = 19.816467853194681575259569579407 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.5
y[1] (analytic) = 43.418710165959431136215390657374
y[1] (numeric) = 52.03964547107981986870447152285
absolute error = 8.620935305120388732489080865476
relative error = 19.855346398289052806413496462374 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.501
y[1] (analytic) = 43.421730615235422821489745032906
y[1] (numeric) = 52.06014597107981986870447152285
absolute error = 8.638415355844397047214726489944
relative error = 19.894221702930993390043767934228 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.502
y[1] (analytic) = 43.424751113289522911063921042174
y[1] (numeric) = 52.08064747107981986870447152285
absolute error = 8.655896357790296957640550480676
relative error = 19.933093767672243248624845109333 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.503
y[1] (analytic) = 43.427771660119352217129754458668
y[1] (numeric) = 52.10114997107981986870447152285
absolute error = 8.673378310960467651574717064182
relative error = 19.971962593064418519638982279048 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.504
y[1] (analytic) = 43.4307922557225317839610018474
y[1] (numeric) = 52.12165347107981986870447152285
absolute error = 8.69086121535728808474346967545
relative error = 20.010828179659011589706052317567 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.505
y[1] (analytic) = 43.433812900096682887879383982589
y[1] (numeric) = 52.14215797107981986870447152285
absolute error = 8.708345070983136980825087540261
relative error = 20.049690528007391128702243601281 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.506
y[1] (analytic) = 43.436833593239427037220635889439
y[1] (numeric) = 52.16266347107981986870447152285
absolute error = 8.725829877840392831483835633411
relative error = 20.088549638660802123867632623446 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.507
y[1] (analytic) = 43.439854335148385972300563508322
y[1] (numeric) = 52.18316997107981986870447152285
absolute error = 8.743315635931433896403908014528
relative error = 20.127405512170365913902636484587 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.508
y[1] (analytic) = 43.442875125821181665381106979825
y[1] (numeric) = 52.20367747107981986870447152285
absolute error = 8.760802345258638203323364543025
relative error = 20.166258149087080223053349436834 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.509
y[1] (analytic) = 43.445895965255436320636410548987
y[1] (numeric) = 52.22418597107981986870447152285
absolute error = 8.778290005824383548068060973863
relative error = 20.205107549961819195185767659018 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.51
y[1] (analytic) = 43.44891685344877237411889908715
y[1] (numeric) = 52.24469547107981986870447152285
absolute error = 8.7957786176310474945855724357
relative error = 20.243953715345333427848906437288 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.511
y[1] (analytic) = 43.451937790398812493725361229805
y[1] (numeric) = 52.26520597107981986870447152285
absolute error = 8.813268180681007374979110293045
relative error = 20.282796645788250006326813924367 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.512
y[1] (analytic) = 43.454958776103179579163039128783
y[1] (numeric) = 52.28571747107981986870447152285
absolute error = 8.830758694976640289541432394067
relative error = 20.321636341841072537679485648875 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.513
y[1] (analytic) = 43.457979810559496761915724817246
y[1] (numeric) = 52.30622997107981986870447152285
absolute error = 8.848250160520323106788746705604
relative error = 20.360472804054181184772683944083 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.514
y[1] (analytic) = 43.46100089376538740520986318581
y[1] (numeric) = 52.32674347107981986870447152285
absolute error = 8.86574257731443246349460833704
relative error = 20.399306032977832700296666464041 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.515
y[1] (analytic) = 43.464022025718475103980661568202
y[1] (numeric) = 52.34725797107981986870447152285
absolute error = 8.883235945361344764723809954648
relative error = 20.438136029162160460773827953042 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.516
y[1] (analytic) = 43.467043206416383684838205934857
y[1] (numeric) = 52.36777347107981986870447152285
absolute error = 8.900730264663436183866265587993
relative error = 20.47696279315717450055525943263 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.517
y[1] (analytic) = 43.470064435856737206033583692834
y[1] (numeric) = 52.38828997107981986870447152285
absolute error = 8.918225535223082662670887830016
relative error = 20.515786325512761545806228968644 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.518
y[1] (analytic) = 43.47308571403715995742501309043
y[1] (numeric) = 52.40880747107981986870447152285
absolute error = 8.93572175704265991127945843242
relative error = 20.554606626778685048480588179029 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.519
y[1] (analytic) = 43.476107040955276460443979224907
y[1] (numeric) = 52.42932597107981986870447152285
absolute error = 8.953218930124543408260492297943
relative error = 20.593423697504585220284108641294 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.52
y[1] (analytic) = 43.479128416608711468061376651688
y[1] (numeric) = 52.44984547107981986870447152285
absolute error = 8.970717054471108400643094871162
relative error = 20.632237538239979066626752356869 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.521
y[1] (analytic) = 43.482149840995089964753658593454
y[1] (numeric) = 52.47036597107981986870447152285
absolute error = 8.988216130084729903950812929396
relative error = 20.67104814953426042056388042766 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.522
y[1] (analytic) = 43.485171314112037166468992747518
y[1] (numeric) = 52.49088747107981986870447152285
absolute error = 9.005716156967782702235478775332
relative error = 20.709855531936699976726404098485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.523
y[1] (analytic) = 43.488192835957178520593423689828
y[1] (numeric) = 52.51140997107981986870447152285
absolute error = 9.023217135122641348111047833022
relative error = 20.748659685996445325239882317374 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.524
y[1] (analytic) = 43.491214406528139705917041874082
y[1] (numeric) = 52.53193347107981986870447152285
absolute error = 9.040719064551680162787429648768
relative error = 20.787460612262520985632569963598 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.525
y[1] (analytic) = 43.494236025822546632600159224247
y[1] (numeric) = 52.55245797107981986870447152285
absolute error = 9.058221945257273236104312298603
relative error = 20.826258311283828440732420892045 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.526
y[1] (analytic) = 43.497257693838025442139491318952
y[1] (numeric) = 52.57298347107981986870447152285
absolute error = 9.075725777241794426564980203898
relative error = 20.865052783609146170553049940343 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.527
y[1] (analytic) = 43.500279410572202507334346166111
y[1] (numeric) = 52.59350997107981986870447152285
absolute error = 9.093230560507617361370125356739
relative error = 20.903844029787129686168658043633 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.528
y[1] (analytic) = 43.50330117602270443225281956618
y[1] (numeric) = 52.61403747107981986870447152285
absolute error = 9.11073629505711543645165195667
relative error = 20.942632050366311563577924600059 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.529
y[1] (analytic) = 43.50632299018715805219799706245
y[1] (numeric) = 52.63456597107981986870447152285
absolute error = 9.1282429808926618165064744604
relative error = 20.981416845895101477556871228239 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.53
y[1] (analytic) = 43.509344853063190433674162476754
y[1] (numeric) = 52.65509547107981986870447152285
absolute error = 9.145750618016629435030309046096
relative error = 21.020198416921786235500701056342 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.531
y[1] (analytic) = 43.512366764648428874353013029015
y[1] (numeric) = 52.67562597107981986870447152285
absolute error = 9.163259206431390994351458493835
relative error = 21.058976763994529811254617680452 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.532
y[1] (analytic) = 43.515388724940500903039881038981
y[1] (numeric) = 52.69615747107981986870447152285
absolute error = 9.180768746139318965664590483869
relative error = 21.09775188766137337893362792841 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.533
y[1] (analytic) = 43.518410733937034279639962208614
y[1] (numeric) = 52.71668997107981986870447152285
absolute error = 9.198279237142785589064509314236
relative error = 21.136523788470235346731332563215 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.534
y[1] (analytic) = 43.521432791635656995124550483457
y[1] (numeric) = 52.73722347107981986870447152285
absolute error = 9.215790679444162873579921039393
relative error = 21.17529246696891139071770905871 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.535
y[1] (analytic) = 43.524454898033997271497279491435
y[1] (numeric) = 52.75775797107981986870447152285
absolute error = 9.233303073045822597207192031415
relative error = 21.214057923705074488625890578166 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.536
y[1] (analytic) = 43.527477053129683561760370557456
y[1] (numeric) = 52.77829347107981986870447152285
absolute error = 9.250816417950136306944100965394
relative error = 21.252820159226274953627945284869 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.537
y[1] (analytic) = 43.530499256920344549880887292222
y[1] (numeric) = 52.79882997107981986870447152285
absolute error = 9.268330714159475318823584230628
relative error = 21.291579174079940468099660111947 %
h = 0.001
memory used=30.5MB, alloc=3.6MB, time=1.77
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.538
y[1] (analytic) = 43.53352150940360915075699675364
y[1] (numeric) = 52.81936747107981986870447152285
absolute error = 9.28584596167621071794747476921
relative error = 21.330334968813376117374333116971 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.539
y[1] (analytic) = 43.536543810577106510184237179258
y[1] (numeric) = 52.83990597107981986870447152285
absolute error = 9.303362160502713358520234343592
relative error = 21.369087543973764423485578545027 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.54
y[1] (analytic) = 43.539566160438466004821792288098
y[1] (numeric) = 52.86044547107981986870447152285
absolute error = 9.320879310641353863882679234752
relative error = 21.407836900108165378899148722349 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.541
y[1] (analytic) = 43.542588558985317242158772150287
y[1] (numeric) = 52.88098597107981986870447152285
absolute error = 9.338397412094502626545699372563
relative error = 21.446583037763516480233776900769 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.542
y[1] (analytic) = 43.545611006215290060480500622926
y[1] (numeric) = 52.90152747107981986870447152285
absolute error = 9.355916464864529808223970899924
relative error = 21.485325957486632761971045171411 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.543
y[1] (analytic) = 43.548633502126014528834809350542
y[1] (numeric) = 52.92206997107981986870447152285
absolute error = 9.373436468953805339869662172308
relative error = 21.524065659824206830154281564525 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.544
y[1] (analytic) = 43.551656046715120946998338328577
y[1] (numeric) = 52.94261347107981986870447152285
absolute error = 9.390957424364698921706133194273
relative error = 21.562802145322808896076490450362 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.545
y[1] (analytic) = 43.554678639980239845442843028269
y[1] (numeric) = 52.96315797107981986870447152285
absolute error = 9.408479331099580023261628494581
relative error = 21.601535414528886809957320354487 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.546
y[1] (analytic) = 43.557701281919001985301508081389
y[1] (numeric) = 52.98370347107981986870447152285
absolute error = 9.426002189160817883402963441461
relative error = 21.640265467988766094609073298894 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.547
y[1] (analytic) = 43.560723972529038358335267523157
y[1] (numeric) = 53.00424997107981986870447152285
absolute error = 9.443525998550781510369203999693
relative error = 21.678992306248649979091759778927 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.548
y[1] (analytic) = 43.563746711807980186899131591822
y[1] (numeric) = 53.02479747107981986870447152285
absolute error = 9.461050759271839681805339931028
relative error = 21.717715929854619432357203483836 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.549
y[1] (analytic) = 43.566769499753458923908520083262
y[1] (numeric) = 53.04534597107981986870447152285
absolute error = 9.478576471326360944795951439588
relative error = 21.756436339352633196882199867388 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.55
y[1] (analytic) = 43.569792336363106252805602259014
y[1] (numeric) = 53.06589547107981986870447152285
absolute error = 9.496103134716713615898869263836
relative error = 21.795153535288527822290732673091 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.551
y[1] (analytic) = 43.572815221634554087525643306156
y[1] (numeric) = 53.08644597107981986870447152285
absolute error = 9.513630749445265781178828216694
relative error = 21.833867518208017698965252516795 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.552
y[1] (analytic) = 43.575838155565434572463357347433
y[1] (numeric) = 53.10699747107981986870447152285
absolute error = 9.531159315514385296241114175417
relative error = 21.872578288656695091647021627788 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.553
y[1] (analytic) = 43.578861138153380082439267000042
y[1] (numeric) = 53.12754997107981986870447152285
absolute error = 9.548688832926439786265204522808
relative error = 21.9112858471800301730255288477 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.554
y[1] (analytic) = 43.581884169396023222666069481473
y[1] (numeric) = 53.14810347107981986870447152285
absolute error = 9.566219301683796646038402041377
relative error = 21.949990194323371057316978984847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.555
y[1] (analytic) = 43.584907249290996828715009260828
y[1] (numeric) = 53.16865797107981986870447152285
absolute error = 9.583750721788823039989462262022
relative error = 21.988691330631943833831860619826 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.556
y[1] (analytic) = 43.587930377835933966482257254006
y[1] (numeric) = 53.18921347107981986870447152285
absolute error = 9.601283093243885902222214268844
relative error = 22.027389256650852600531596456554 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.557
y[1] (analytic) = 43.59095355502846793215529656119
y[1] (numeric) = 53.20976997107981986870447152285
absolute error = 9.61881641605135193654917496166
relative error = 22.066083972925079497574280311057 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.558
y[1] (analytic) = 43.593976780866232252179314745
y[1] (numeric) = 53.23032747107981986870447152285
absolute error = 9.63635069021358761652515677785
relative error = 22.104775479999484740849504828786 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.559
y[1] (analytic) = 43.597000055346860683223602647788
y[1] (numeric) = 53.25088597107981986870447152285
absolute error = 9.653885915732959185480868875062
relative error = 22.143463778418806655502284019197 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.56
y[1] (analytic) = 43.600023378467987212147959746412
y[1] (numeric) = 53.27144547107981986870447152285
absolute error = 9.671422092611832656556511776438
relative error = 22.182148868727661709446074694984 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.561
y[1] (analytic) = 43.603046750227246055969106042946
y[1] (numeric) = 53.29200597107981986870447152285
absolute error = 9.688959220852573812735365479904
relative error = 22.220830751470544546864900901286 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.562
y[1] (analytic) = 43.606070170622271661827100489736
y[1] (numeric) = 53.31256747107981986870447152285
absolute error = 9.706497300457548206877371033114
relative error = 22.259509427191828021704585418599 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.563
y[1] (analytic) = 43.609093639650698706951765947176
y[1] (numeric) = 53.33312997107981986870447152285
absolute error = 9.724036331429121161752705575674
relative error = 22.298184896435763231153092421475 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.564
y[1] (analytic) = 43.612117157310162098629120672658
y[1] (numeric) = 53.35369347107981986870447152285
absolute error = 9.741576313769657770075350850192
relative error = 22.336857159746479549109985373158 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.565
y[1] (analytic) = 43.615140723598296974167816339089
y[1] (numeric) = 53.37425797107981986870447152285
absolute error = 9.759117247481522894536655183761
relative error = 22.375526217667984659645004234749 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.566
y[1] (analytic) = 43.618164338512738700865582581385
y[1] (numeric) = 53.39482347107981986870447152285
absolute error = 9.776659132567081167838888941465
relative error = 22.41419207074416459044576606569 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.567
y[1] (analytic) = 43.621188002051122875975678069354
y[1] (numeric) = 53.41538997107981986870447152285
absolute error = 9.794201969028696992728793453496
relative error = 22.452854719518783746254593090662 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.568
y[1] (analytic) = 43.624211714211085326673348105399
y[1] (numeric) = 53.43595747107981986870447152285
absolute error = 9.811745756868734542031123417451
relative error = 22.491514164535484942294472306192 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.569
y[1] (analytic) = 43.62723547499026211002228874543
y[1] (numeric) = 53.45652597107981986870447152285
absolute error = 9.82929049608955775868218277742
relative error = 22.530170406337789437684150698657 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.57
y[1] (analytic) = 43.630259284386289512941117441422
y[1] (numeric) = 53.47709547107981986870447152285
absolute error = 9.846836186693530355763354081428
relative error = 22.568823445469096968842370143516 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.571
y[1] (analytic) = 43.633283142396804052169850204002
y[1] (numeric) = 53.49766597107981986870447152285
absolute error = 9.864382828683015816534621318848
relative error = 22.607473282472685782881246054043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.572
y[1] (analytic) = 43.636307049019442474236385283543
y[1] (numeric) = 53.51823747107981986870447152285
absolute error = 9.881930422060377394468086239307
relative error = 22.646119917891712670988793845819 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.573
y[1] (analytic) = 43.639331004251841755422993368079
y[1] (numeric) = 53.53880997107981986870447152285
absolute error = 9.899478966827978113281478154771
relative error = 22.684763352269213001800607282009 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.574
y[1] (analytic) = 43.642355008091639101732814296584
y[1] (numeric) = 53.55938347107981986870447152285
absolute error = 9.917028462988180766971657226266
relative error = 22.723403586148100754760692762055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.575
y[1] (analytic) = 43.645379060536471948856360285905
y[1] (numeric) = 53.57995797107981986870447152285
absolute error = 9.934578910543347919848111236945
relative error = 22.762040620071168553471463615438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.576
y[1] (analytic) = 43.648403161583977962138025669865
y[1] (numeric) = 53.60053347107981986870447152285
absolute error = 9.952130309495841906566445852985
relative error = 22.80067445458108769903289845979 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.577
y[1] (analytic) = 43.651427311231795036542603148904
y[1] (numeric) = 53.62110997107981986870447152285
absolute error = 9.969682659848024832161868373946
relative error = 22.839305090220408203370867681327 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.578
y[1] (analytic) = 43.654451509477561296621806548673
y[1] (numeric) = 53.64168747107981986870447152285
absolute error = 9.987235961602258572082664974177
relative error = 22.877932527531558822554632093746 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.579
y[1] (analytic) = 43.657475756318915096480800086034
y[1] (numeric) = 53.66226597107981986870447152285
absolute error = 10.004790214760904772223671436816
relative error = 22.916556767056847090103517829901 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.58
y[1] (analytic) = 43.660500051753495019744734140848
y[1] (numeric) = 53.68284547107981986870447152285
absolute error = 10.022345419326324848959737382002
relative error = 22.955177809338459350282771519024 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.581
y[1] (analytic) = 43.663524395778939879525287531996
y[1] (numeric) = 53.70342597107981986870447152285
absolute error = 10.039901575300879989179183990854
relative error = 22.993795654918460791388599800428 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.582
y[1] (analytic) = 43.666548788392888718387216296034
y[1] (numeric) = 53.72400747107981986870447152285
absolute error = 10.057458682686931150317255226816
relative error = 23.032410304338795479022397222967 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.583
y[1] (analytic) = 43.669573229592980808314908966922
y[1] (numeric) = 53.74458997107981986870447152285
absolute error = 10.075016741486839060389562555928
relative error = 23.071021758141286389354166577761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.584
y[1] (analytic) = 43.672597719376855650678948355227
y[1] (numeric) = 53.76517347107981986870447152285
absolute error = 10.092575751702964218025523167623
relative error = 23.109630016867635442375135710068 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.585
y[1] (analytic) = 43.675622257742152976202679825232
y[1] (numeric) = 53.78575797107981986870447152285
absolute error = 10.110135713337666892501791697618
relative error = 23.148235081059423535139574854385 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.586
y[1] (analytic) = 43.678646844686512744928786068387
y[1] (numeric) = 53.80634347107981986870447152285
absolute error = 10.127696626393307123775685454463
relative error = 23.186836951258110574995818535136 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.587
y[1] (analytic) = 43.681671480207575146185868371492
y[1] (numeric) = 53.82692997107981986870447152285
absolute error = 10.145258490872244722518603151358
relative error = 23.225435628005035512806496073742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.588
y[1] (analytic) = 43.684696164302980598555034378052
y[1] (numeric) = 53.84751747107981986870447152285
absolute error = 10.162821306776839270149437144798
relative error = 23.264031111841416376157974740992 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.589
y[1] (analytic) = 43.687720896970369749836492341242
y[1] (numeric) = 53.86810597107981986870447152285
absolute error = 10.180385074109450118867979181608
relative error = 23.302623403308350302559019591947 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.59
y[1] (analytic) = 43.690745678207383477016151866873
y[1] (numeric) = 53.88869547107981986870447152285
absolute error = 10.197949792872436391688319655977
relative error = 23.341212502946813572628674019033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.591
y[1] (analytic) = 43.693770508011662886232231144814
y[1] (numeric) = 53.90928597107981986870447152285
absolute error = 10.215515463068156982472240378036
relative error = 23.379798411297661643273365057086 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.592
y[1] (analytic) = 43.696795386380849312741870667274
y[1] (numeric) = 53.92987747107981986870447152285
absolute error = 10.233082084698970555962600855576
relative error = 23.418381128901629180853237472553 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.593
y[1] (analytic) = 43.699820313312584320887753432373
y[1] (numeric) = 53.95046997107981986870447152285
absolute error = 10.250649657767235547816718090477
relative error = 23.456960656299330094337720667278 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.594
y[1] (analytic) = 43.702845288804509704064731631438
y[1] (numeric) = 53.97106347107981986870447152285
absolute error = 10.268218182275310164639739891412
relative error = 23.495536994031257568450332425572 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.595
y[1] (analytic) = 43.705870312854267484686459818435
y[1] (numeric) = 53.99165797107981986870447152285
absolute error = 10.285787658225552384018011704415
relative error = 23.53411014263778409680272353164 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.596
y[1] (analytic) = 43.708895385459499914152034559978
y[1] (numeric) = 54.01225347107981986870447152285
absolute error = 10.303358085620319954552436962872
relative error = 23.572680102659161515017967282653 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.597
y[1] (analytic) = 43.711920506617849472812640564321
y[1] (numeric) = 54.03284997107981986870447152285
absolute error = 10.320929464461970395891830958529
relative error = 23.611246874635521033843097921129 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.598
y[1] (analytic) = 43.714945676326958869938203287786
y[1] (numeric) = 54.05344747107981986870447152285
absolute error = 10.338501794752860998766268235064
relative error = 23.649810459106873272250902008485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.599
y[1] (analytic) = 43.717970894584471043684048017041
y[1] (numeric) = 54.07404597107981986870447152285
absolute error = 10.356075076495348825020423505809
relative error = 23.688370856613108290530966760002 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.6
y[1] (analytic) = 43.720996161388029161057565425642
y[1] (numeric) = 54.09464547107981986870447152285
absolute error = 10.373649309691790707646906097208
relative error = 23.726928067693995623369989359766 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.601
y[1] (analytic) = 43.724021476735276617884883603301
y[1] (numeric) = 54.11524597107981986870447152285
absolute error = 10.391224494344543250819587919549
relative error = 23.765482092889184312921351272297 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.602
y[1] (analytic) = 43.727046840623857038777546556279
y[1] (numeric) = 54.13584747107981986870447152285
absolute error = 10.408800630455962829926924966571
relative error = 23.80403293273820294186396156608 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.603
y[1] (analytic) = 43.730072253051414277099199177358
y[1] (numeric) = 54.15644997107981986870447152285
absolute error = 10.426377718028405591605272345492
relative error = 23.842580587780459666450373262326 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.604
y[1] (analytic) = 43.733097714015592414932278683783
y[1] (numeric) = 54.17705347107981986870447152285
absolute error = 10.443955757064227453772192839067
relative error = 23.881125058555242249544176720809 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.605
y[1] (analytic) = 43.736123223514035763044712521662
y[1] (numeric) = 54.19765797107981986870447152285
absolute error = 10.461534747565784105659759001188
relative error = 23.919666345601718093646674072633 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.606
y[1] (analytic) = 43.739148781544388860856622735203
y[1] (numeric) = 54.21826347107981986870447152285
absolute error = 10.479114689535431007847848787647
relative error = 23.958204449458934273912838708393 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.607
y[1] (analytic) = 43.742174388104296476407036799237
y[1] (numeric) = 54.23886997107981986870447152285
absolute error = 10.496695582975523392297434723613
relative error = 23.996739370665817571156563828324 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=3.6MB, time=2.00
x[1] = 20.608
y[1] (analytic) = 43.745200043191403606320604913486
y[1] (numeric) = 54.25947747107981986870447152285
absolute error = 10.514277427888416262383866609364
relative error = 24.035271109761174504845204059286 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.609
y[1] (analytic) = 43.74822574680335547577432375695
y[1] (numeric) = 54.28008597107981986870447152285
absolute error = 10.5318602242764643929301477659
relative error = 24.073799667283691366083414141995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.61
y[1] (analytic) = 43.751251498937797538464266700907
y[1] (numeric) = 54.30069547107981986870447152285
absolute error = 10.549443972142022330240204821943
relative error = 24.112325043771934250586288689879 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.611
y[1] (analytic) = 43.754277299592375476572320478913
y[1] (numeric) = 54.32130597107981986870447152285
absolute error = 10.567028671487444392132151043937
relative error = 24.150847239764349091641807019538 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.612
y[1] (analytic) = 43.757303148764735200732928312267
y[1] (numeric) = 54.34191747107981986870447152285
absolute error = 10.584614322315084667971543210583
relative error = 24.18936625579926169306258705089 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.613
y[1] (analytic) = 43.760329046452522849999839489346
y[1] (numeric) = 54.36252997107981986870447152285
absolute error = 10.602200924627297018704632033504
relative error = 24.227882092414877762126952273564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.614
y[1] (analytic) = 43.763354992653384791812865397287
y[1] (numeric) = 54.38314347107981986870447152285
absolute error = 10.619788478426435076891606125563
relative error = 24.266394750149282942509315774188 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.615
y[1] (analytic) = 43.766380987364967621964642004394
y[1] (numeric) = 54.40375797107981986870447152285
absolute error = 10.637376983714852246739829518456
relative error = 24.304904229540442847199885317851 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.616
y[1] (analytic) = 43.769407030584918164567398791752
y[1] (numeric) = 54.42437347107981986870447152285
absolute error = 10.654966440494901704137072731098
relative error = 24.343410531126203091413693474997 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.617
y[1] (analytic) = 43.772433122310883472019734132473
y[1] (numeric) = 54.44498997107981986870447152285
absolute error = 10.672556848768936396684737390377
relative error = 24.381913655444289325488956783507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.618
y[1] (analytic) = 43.775459262540510824973397116994
y[1] (numeric) = 54.46560747107981986870447152285
absolute error = 10.690148208539309043731074405856
relative error = 24.420413603032307267774767934054 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.619
y[1] (analytic) = 43.778485451271447732300075822876
y[1] (numeric) = 54.48622597107981986870447152285
absolute error = 10.707740519808372136404395699974
relative error = 24.458910374427742737508124965037 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.62
y[1] (analytic) = 43.781511688501341931058192027545
y[1] (numeric) = 54.50684547107981986870447152285
absolute error = 10.725333782578477937646279495305
relative error = 24.497403970167961687680301451748 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.621
y[1] (analytic) = 43.784537974227841386459702362404
y[1] (numeric) = 54.52746597107981986870447152285
absolute error = 10.742927996851978482244769160446
relative error = 24.535894390790210237892561672772 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.622
y[1] (analytic) = 43.787564308448594291836905906771
y[1] (numeric) = 54.54808747107981986870447152285
absolute error = 10.760523162631225576867565616079
relative error = 24.574381636831614707201224734878 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.623
y[1] (analytic) = 43.790590691161249068609258220036
y[1] (numeric) = 54.56870997107981986870447152285
absolute error = 10.778119279918570800095213302814
relative error = 24.612865708829181646952081636123 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.624
y[1] (analytic) = 43.793617122363454366250191810553
y[1] (numeric) = 54.58933347107981986870447152285
absolute error = 10.795716348716365502454279712297
relative error = 24.6513466073197978736041692449 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.625
y[1] (analytic) = 43.796643602052859062253943039623
y[1] (numeric) = 54.60995797107981986870447152285
absolute error = 10.813314369026960806450528483227
relative error = 24.689824332840230501542905171404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.626
y[1] (analytic) = 43.799670130227112262102385459071
y[1] (numeric) = 54.63058347107981986870447152285
absolute error = 10.830913340852707606602086063779
relative error = 24.728298885927126975882587505911 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.627
y[1] (analytic) = 43.802696706883863299231869580821
y[1] (numeric) = 54.65120997107981986870447152285
absolute error = 10.848513264195956569472601942029
relative error = 24.766770267117015105258263396857 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.628
y[1] (analytic) = 43.805723332020761735000069076935
y[1] (numeric) = 54.67183747107981986870447152285
absolute error = 10.866114139059058133704402445915
relative error = 24.805238476946303094606970439868 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.629
y[1] (analytic) = 43.808750005635457358652833408532
y[1] (numeric) = 54.69246597107981986870447152285
absolute error = 10.883715965444362510051638114318
relative error = 24.843703515951279577938354847329 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.63
y[1] (analytic) = 43.811776727725600187291046882042
y[1] (numeric) = 54.71309547107981986870447152285
absolute error = 10.901318743354219681413424640808
relative error = 24.882165384668113651094670366322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.631
y[1] (analytic) = 43.814803498288840465837494131255
y[1] (numeric) = 54.73372597107981986870447152285
absolute error = 10.918922472790979402866977391595
relative error = 24.920624083632854904500161911062 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.632
y[1] (analytic) = 43.817830317322828667003732023563
y[1] (numeric) = 54.75435747107981986870447152285
absolute error = 10.936527153756991201700739499287
relative error = 24.959079613381433455899837874448 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.633
y[1] (analytic) = 43.820857184825215491256967988883
y[1] (numeric) = 54.77498997107981986870447152285
absolute error = 10.954132786254604377447503533967
relative error = 24.997531974449659983087635081448 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.634
y[1] (analytic) = 43.823884100793651866786944769684
y[1] (numeric) = 54.79562347107981986870447152285
absolute error = 10.971739370286168001917526753166
relative error = 25.035981167373225756623980345522 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.635
y[1] (analytic) = 43.82691106522578894947283159055
y[1] (numeric) = 54.81625797107981986870447152285
absolute error = 10.9893469058540309192316399323
relative error = 25.074427192687702672542752587592 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.636
y[1] (analytic) = 43.829938078119278122850121745766
y[1] (numeric) = 54.83689347107981986870447152285
absolute error = 11.006955392960541745854349777084
relative error = 25.112870050928543285047649475264 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.637
y[1] (analytic) = 43.832965139471770998077536603309
y[1] (numeric) = 54.85752997107981986870447152285
absolute error = 11.024564831608048870626934919541
relative error = 25.151309742631080839197962538606 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.638
y[1] (analytic) = 43.835992249280919413903936023758
y[1] (numeric) = 54.87816747107981986870447152285
absolute error = 11.042175221798900454800535499092
relative error = 25.189746268330529303583764716757 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.639
y[1] (analytic) = 43.839019407544375436635235192502
y[1] (numeric) = 54.89880597107981986870447152285
absolute error = 11.059786563535444432069236330348
relative error = 25.228179628561983402990514288351 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.64
y[1] (analytic) = 43.842046614259791360101327863757
y[1] (numeric) = 54.91944547107981986870447152285
absolute error = 11.077398856820028508603143659093
relative error = 25.266609823860418651053079136712 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.641
y[1] (analytic) = 43.84507386942481970562301601478
y[1] (numeric) = 54.94008597107981986870447152285
absolute error = 11.09501210165500016308145550807
relative error = 25.30503685476069138289918529942 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.642
y[1] (analytic) = 43.848101173037113221978945908779
y[1] (numeric) = 54.96072747107981986870447152285
absolute error = 11.112626298042706646725525614071
relative error = 25.343460721797538787782293749929 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.643
y[1] (analytic) = 43.851128525094324885372550564915
y[1] (numeric) = 54.98136997107981986870447152285
absolute error = 11.130241445985494983331920957935
relative error = 25.381881425505578941703909357468 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.644
y[1] (analytic) = 43.854155925594107899398998633898
y[1] (numeric) = 55.00201347107981986870447152285
absolute error = 11.147857545485711969305472888952
relative error = 25.420298966419310840025325969562 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.645
y[1] (analytic) = 43.857183374534115695012149677578
y[1] (numeric) = 55.02265797107981986870447152285
absolute error = 11.165474596545704173692321845272
relative error = 25.458713345073114430068811560084 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.646
y[1] (analytic) = 43.860210871912001930491515851006
y[1] (numeric) = 55.04330347107981986870447152285
absolute error = 11.183092599167817938212955671844
relative error = 25.497124562001250643708237383901 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.647
y[1] (analytic) = 43.863238417725420491409229985426
y[1] (numeric) = 55.06394997107981986870447152285
absolute error = 11.200711553354399377295241537424
relative error = 25.535532617737861429949155077534 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.648
y[1] (analytic) = 43.866266011972025490597020070597
y[1] (numeric) = 55.08459747107981986870447152285
absolute error = 11.218331459107794378107451452253
relative error = 25.573937512816969787498325643798 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.649
y[1] (analytic) = 43.869293654649471268113190134962
y[1] (numeric) = 55.10524597107981986870447152285
absolute error = 11.235952316430348600591281387888
relative error = 25.612339247772479797322704256349 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.65
y[1] (analytic) = 43.872321345755412391209607522069
y[1] (numeric) = 55.12589547107981986870447152285
absolute error = 11.253574125324407477494864000781
relative error = 25.650737823138176655197884818768 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.651
y[1] (analytic) = 43.8753490852875036542986965617
y[1] (numeric) = 55.14654597107981986870447152285
absolute error = 11.27119688579231621440577496115
relative error = 25.689133239447726704246008210965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.652
y[1] (analytic) = 43.878376873243400078920438634183
y[1] (numeric) = 55.16719747107981986870447152285
absolute error = 11.288820597836419789784032888667
relative error = 25.727525497234677467463138154017 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.653
y[1] (analytic) = 43.881404709620756913709378626319
y[1] (numeric) = 55.18784997107981986870447152285
absolute error = 11.306445261459062954995092896531
relative error = 25.765914597032457680236108622974 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.654
y[1] (analytic) = 43.884432594417229634361637777375
y[1] (numeric) = 55.20850347107981986870447152285
absolute error = 11.324070876662590234342833745475
relative error = 25.804300539374377322848846735492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.655
y[1] (analytic) = 43.887460527630473943601932913613
y[1] (numeric) = 55.22915797107981986870447152285
absolute error = 11.341697443449345925102538609237
relative error = 25.842683324793627652978175042422 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.656
y[1] (analytic) = 43.890488509258145771150602069797
y[1] (numeric) = 55.24981347107981986870447152285
absolute error = 11.359324961821674097553869453053
relative error = 25.881062953823281238179097144916 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.657
y[1] (analytic) = 43.893516539297901273690636496125
y[1] (numeric) = 55.27046997107981986870447152285
absolute error = 11.376953431781918595013835026725
relative error = 25.919439426996291988359570560939 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.658
y[1] (analytic) = 43.896544617747396834834719049058
y[1] (numeric) = 55.29112747107981986870447152285
absolute error = 11.394582853332423033869752473792
relative error = 25.957812744845495188244770762348 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.659
y[1] (analytic) = 43.899572744604289065092268964491
y[1] (numeric) = 55.31178597107981986870447152285
absolute error = 11.412213226475530803612202558359
relative error = 25.996182907903607529830850302135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.66
y[1] (analytic) = 43.902600919866234801836493011713
y[1] (numeric) = 55.33244547107981986870447152285
absolute error = 11.429844551213585066867978511137
relative error = 26.034549916703227144828196949755 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.661
y[1] (analytic) = 43.905629143530891109271443026632
y[1] (numeric) = 55.35310597107981986870447152285
absolute error = 11.447476827548928759433028496218
relative error = 26.072913771776833637094194750744 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.662
y[1] (analytic) = 43.908657415595915278399079822711
y[1] (numeric) = 55.37376747107981986870447152285
absolute error = 11.465110055483904590305391700139
relative error = 26.111274473656788115055491925248 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.663
y[1] (analytic) = 43.911685736058964826986343478053
y[1] (numeric) = 55.39442997107981986870447152285
absolute error = 11.482744235020855041718128044797
relative error = 26.149632022875333224119779518482 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.664
y[1] (analytic) = 43.914714104917697499532229997132
y[1] (numeric) = 55.41509347107981986870447152285
absolute error = 11.500379366162122369172241525718
relative error = 26.187986419964593179077084714285 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.665
y[1] (analytic) = 43.917742522169771267234874345589
y[1] (numeric) = 55.43575797107981986870447152285
absolute error = 11.518015448910048601469597177261
relative error = 26.226337665456573796490582721551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.666
y[1] (analytic) = 43.920770987812844327958639856582
y[1] (numeric) = 55.45642347107981986870447152285
absolute error = 11.535652483266975540745831666268
relative error = 26.264685759883162527076931141437 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.667
y[1] (analytic) = 43.923799501844575106201214007119
y[1] (numeric) = 55.47708997107981986870447152285
absolute error = 11.553290469235244762503257515731
relative error = 26.303030703776128488076130721789 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.668
y[1] (analytic) = 43.926828064262622253060710562851
y[1] (numeric) = 55.49775747107981986870447152285
absolute error = 11.570929406817197615643760959999
relative error = 26.341372497667122495610916403442 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.669
y[1] (analytic) = 43.929856675064644646202778089798
y[1] (numeric) = 55.51842597107981986870447152285
absolute error = 11.588569296015175222501693433052
relative error = 26.379711142087677097035682561409 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.67
y[1] (analytic) = 43.932885334248301389827714831423
y[1] (numeric) = 55.53909547107981986870447152285
absolute error = 11.606210136831518478876756691427
relative error = 26.418046637569206603274946342506 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.671
y[1] (analytic) = 43.935914041811251814637589949564
y[1] (numeric) = 55.55976597107981986870447152285
absolute error = 11.623851929268568054066881573286
relative error = 26.45637898464300712115135299904 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.672
y[1] (analytic) = 43.938942797751155477803371127653
y[1] (numeric) = 55.58043747107981986870447152285
absolute error = 11.641494673328664390901100395197
relative error = 26.494708183840256585703227116764 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.673
y[1] (analytic) = 43.941971602065672162932058534699
y[1] (numeric) = 55.60110997107981986870447152285
absolute error = 11.659138369014147705772412988151
relative error = 26.533034235692014792491673633545 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.674
y[1] (analytic) = 43.945000454752461880033825148476
y[1] (numeric) = 55.62178347107981986870447152285
absolute error = 11.676783016327357988670646374374
relative error = 26.571357140729223429897232543647 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.675
y[1] (analytic) = 43.948029355809184865489163436418
y[1] (numeric) = 55.64245797107981986870447152285
absolute error = 11.694428615270635003215308086432
relative error = 26.609676899482706111406091180683 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.676
y[1] (analytic) = 43.95105830523350158201603839263
y[1] (numeric) = 55.66313347107981986870447152285
absolute error = 11.71207516584631828668843313022
relative error = 26.647993512483168407885857970983 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.677
y[1] (analytic) = 43.954087303023072718637046929524
y[1] (numeric) = 55.68380997107981986870447152285
absolute error = 11.729722668056747150067424593326
relative error = 26.686306980261197879850901547122 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=38.1MB, alloc=3.7MB, time=2.23
x[1] = 20.678
y[1] (analytic) = 43.957116349175559190646583622522
y[1] (numeric) = 55.70448747107981986870447152285
absolute error = 11.747371121904260678057887900328
relative error = 26.724617303347264109717259109973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.679
y[1] (analytic) = 43.960145443688622139578012806292
y[1] (numeric) = 55.72516597107981986870447152285
absolute error = 11.765020527391197729126458716558
relative error = 26.762924482271718734047117925896 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.68
y[1] (analytic) = 43.963174586559922933170847020972
y[1] (numeric) = 55.74584547107981986870447152285
absolute error = 11.782670884519896935533624501878
relative error = 26.801228517564795475782873844097 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.681
y[1] (analytic) = 43.966203777787123165337931806881
y[1] (numeric) = 55.76652597107981986870447152285
absolute error = 11.800322193292696703366539715969
relative error = 26.839529409756610176470770717409 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.682
y[1] (analytic) = 43.969233017367884656132636846134
y[1] (numeric) = 55.78720747107981986870447152285
absolute error = 11.817974453711935212571834676716
relative error = 26.877827159377160828474124608372 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.683
y[1] (analytic) = 43.972262305299869451716053449661
y[1] (numeric) = 55.80788997107981986870447152285
absolute error = 11.835627665779950416988418073189
relative error = 26.916121766956327607176136660582 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.684
y[1] (analytic) = 43.975291641580739824324198388089
y[1] (numeric) = 55.82857347107981986870447152285
absolute error = 11.853281829499080044380273134761
relative error = 26.954413233023872903172298513796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.685
y[1] (analytic) = 43.978321026208158272235224064943
y[1] (numeric) = 55.84925797107981986870447152285
absolute error = 11.870936944871661596469247457907
relative error = 26.992701558109441354452394139636 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.686
y[1] (analytic) = 43.98135045917978751973663503065
y[1] (numeric) = 55.86994347107981986870447152285
absolute error = 11.8885930119000323489678364922
relative error = 27.030986742742559878572101973027 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.687
y[1] (analytic) = 43.984379940493290517092510835787
y[1] (numeric) = 55.89062997107981986870447152285
absolute error = 11.906250030586529351611960687063
relative error = 27.069268787452637704814201213 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.688
y[1] (analytic) = 43.987409470146330440510735222083
y[1] (numeric) = 55.91131747107981986870447152285
absolute error = 11.923908000933489428193736300767
relative error = 27.107547692768966406339386164655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.689
y[1] (analytic) = 43.990439048136570692110231649581
y[1] (numeric) = 55.93200597107981986870447152285
absolute error = 11.941566922943249176594239873269
relative error = 27.145823459220719932326692492752 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.69
y[1] (analytic) = 43.99346867446167489988820515851
y[1] (numeric) = 55.95269547107981986870447152285
absolute error = 11.95922679661814496881626636434
relative error = 27.184096087336954640103539255363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.691
y[1] (analytic) = 43.996498349119306917687390564251
y[1] (numeric) = 55.97338597107981986870447152285
absolute error = 11.976887621960512951017080958599
relative error = 27.222365577646609327265390584843 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.692
y[1] (analytic) = 43.999528072107130825163306983932
y[1] (numeric) = 55.99407747107981986870447152285
absolute error = 11.994549398972689043541164538918
relative error = 27.260631930678505263785040881346 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.693
y[1] (analytic) = 44.00255784342281092775151869309
y[1] (numeric) = 56.01476997107981986870447152285
absolute error = 12.01221212765700894095295282976
relative error = 27.298895146961346224111527382742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.694
y[1] (analytic) = 44.005587663064011756634902310873
y[1] (numeric) = 56.03546347107981986870447152285
absolute error = 12.029875808015808112069569211977
relative error = 27.337155227023718519258673973075 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.695
y[1] (analytic) = 44.008617531028398068710920312267
y[1] (numeric) = 56.05615797107981986870447152285
absolute error = 12.047540440051421799993551210583
relative error = 27.37541217139409102888327009004 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.696
y[1] (analytic) = 44.0116474473136348465589008658
y[1] (numeric) = 56.07685347107981986870447152285
absolute error = 12.06520602376618502214557065705
relative error = 27.413665980600815233352888590417 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.697
y[1] (analytic) = 44.014677411917387298407323995208
y[1] (numeric) = 56.09754997107981986870447152285
absolute error = 12.082872559162432570297147527642
relative error = 27.451916655172125245803346430709 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.698
y[1] (analytic) = 44.017707424837320858101114063539
y[1] (numeric) = 56.11824747107981986870447152285
absolute error = 12.100540046242499010603357459311
relative error = 27.490164195636137844185812018596 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.699
y[1] (analytic) = 44.020737486071101185068938578154
y[1] (numeric) = 56.13894597107981986870447152285
absolute error = 12.118208485008718683635532944696
relative error = 27.528408602520852503303563089277 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.7
y[1] (analytic) = 44.023767595616394164290513315098
y[1] (numeric) = 56.15964547107981986870447152285
absolute error = 12.135877875463425704413958207752
relative error = 27.566649876354151426838398959088 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.701
y[1] (analytic) = 44.026797753470865906263913761337
y[1] (numeric) = 56.18034597107981986870447152285
absolute error = 12.153548217608953962440557761513
relative error = 27.604888017663799579366711007112 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.702
y[1] (analytic) = 44.029827959632182746972892873312
y[1] (numeric) = 56.20104747107981986870447152285
absolute error = 12.171219511447637121731578649538
relative error = 27.643123026977444718365215233991 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.703
y[1] (analytic) = 44.032858214098011247854205150285
y[1] (numeric) = 56.22174997107981986870447152285
absolute error = 12.188891756981808620850266372565
relative error = 27.681354904822617426206350745483 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.704
y[1] (analytic) = 44.035888516866018195764937020968
y[1] (numeric) = 56.24245347107981986870447152285
absolute error = 12.206564954213801672939534501882
relative error = 27.719583651726731142143348006613 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.705
y[1] (analytic) = 44.038918867933870602949843541902
y[1] (numeric) = 56.26315797107981986870447152285
absolute error = 12.224239103145949265754627980948
relative error = 27.757809268217082194284970710759 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.706
y[1] (analytic) = 44.041949267299235707008691406048
y[1] (numeric) = 56.28386347107981986870447152285
absolute error = 12.241914203780584161695780116802
relative error = 27.796031754820849831559935106357 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.707
y[1] (analytic) = 44.044979714959780970863608260101
y[1] (numeric) = 56.30456997107981986870447152285
absolute error = 12.259590256120038897840863262749
relative error = 27.834251112065096255671010622216 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.708
y[1] (analytic) = 44.048010210913174082726438328954
y[1] (numeric) = 56.32527747107981986870447152285
absolute error = 12.277267260166645785978033193896
relative error = 27.872467340476766653038805630994 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.709
y[1] (analytic) = 44.051040755157082956066104345848
y[1] (numeric) = 56.34598597107981986870447152285
absolute error = 12.294945215922736912638367177002
relative error = 27.910680440582689226735242188521 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.71
y[1] (analytic) = 44.054071347689175729575975786623
y[1] (numeric) = 56.36669547107981986870447152285
absolute error = 12.312624123390644139128495736227
relative error = 27.948890412909575228406723585333 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.711
y[1] (analytic) = 44.05710198850712076714124340661
y[1] (numeric) = 56.38740597107981986870447152285
absolute error = 12.33030398257269910156322811624
relative error = 27.987097257984018990186998544851 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.712
y[1] (analytic) = 44.06013267760858665780630007858
y[1] (numeric) = 56.40811747107981986870447152285
absolute error = 12.34798479347123321089817144427
relative error = 28.025300976332497956599725901358 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.713
y[1] (analytic) = 44.063163414991242215742127930297
y[1] (numeric) = 56.42882997107981986870447152285
absolute error = 12.365666556088577652962343592553
relative error = 28.06350156848137271645074358895 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.714
y[1] (analytic) = 44.066194200652756480213691780081
y[1] (numeric) = 56.44954347107981986870447152285
absolute error = 12.383349270427063388490779742769
relative error = 28.10169903495688703471004577142 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.715
y[1] (analytic) = 44.069225034590798715547338868925
y[1] (numeric) = 56.47025797107981986870447152285
absolute error = 12.401032936489021153157132653925
relative error = 28.139893376285167884383471941056 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.716
y[1] (analytic) = 44.072255916803038411098204887612
y[1] (numeric) = 56.49097347107981986870447152285
absolute error = 12.418717554276781457606266635238
relative error = 28.178084592992225478374111812954 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.717
y[1] (analytic) = 44.075286847287145281217626297312
y[1] (numeric) = 56.51168997107981986870447152285
absolute error = 12.436403123792674587486845225538
relative error = 28.216272685603953301333429839807 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.718
y[1] (analytic) = 44.07831782604078926522055894215
y[1] (numeric) = 56.53240747107981986870447152285
absolute error = 12.4540896450390306034839125807
relative error = 28.254457654646128141502113170427 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.719
y[1] (analytic) = 44.081348853061640527353002952243
y[1] (numeric) = 56.55312597107981986870447152285
absolute error = 12.471777118018179341351468570607
relative error = 28.292639500644410122540646873673 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.72
y[1] (analytic) = 44.084379928347369456759433935634
y[1] (numeric) = 56.57384547107981986870447152285
absolute error = 12.489465542732450411945037587216
relative error = 28.330818224124342735349620248051 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.721
y[1] (analytic) = 44.087411051895646667450240457676
y[1] (numeric) = 56.59456597107981986870447152285
absolute error = 12.507154919184173201254231065174
relative error = 28.368993825611352869879768035243 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.722
y[1] (analytic) = 44.090442223704142998269167806288
y[1] (numeric) = 56.61528747107981986870447152285
absolute error = 12.524845247375676870435303716562
relative error = 28.407166305630750846931750354662 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.723
y[1] (analytic) = 44.093473443770529512860768041615
y[1] (numeric) = 56.63600997107981986870447152285
absolute error = 12.542536527309290355843703481235
relative error = 28.44533566470773044994567517415 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.724
y[1] (analytic) = 44.09650471209247749963785632852
y[1] (numeric) = 56.65673347107981986870447152285
absolute error = 12.56022875898734236906661519433
relative error = 28.483501903367368956780367130659 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.725
y[1] (analytic) = 44.099536028667658471748973550463
y[1] (numeric) = 56.67745797107981986870447152285
absolute error = 12.577921942412161396955497972387
relative error = 28.521665022134627171482386512796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.726
y[1] (analytic) = 44.102567393493744167045855203183
y[1] (numeric) = 56.69818347107981986870447152285
absolute error = 12.595616077586075701658616319667
relative error = 28.559825021534349456044802215885 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.727
y[1] (analytic) = 44.10559880656840654805090656672
y[1] (numeric) = 56.71890997107981986870447152285
absolute error = 12.61331116451141332065356495613
relative error = 28.597981902091263762155722478261 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.728
y[1] (analytic) = 44.108630267889317801924684154213
y[1] (numeric) = 56.73963747107981986870447152285
absolute error = 12.631007203190502066779787368637
relative error = 28.636135664329981662936587206224 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.729
y[1] (analytic) = 44.111661777454150340433383436027
y[1] (numeric) = 56.76036597107981986870447152285
absolute error = 12.648704193625669528271088086823
relative error = 28.6742863087749983846702256931 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.73
y[1] (analytic) = 44.114693335260576799916332837621
y[1] (numeric) = 56.78109547107981986870447152285
absolute error = 12.666402135819243068788138685229
relative error = 28.712433835950692838518683536697 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.731
y[1] (analytic) = 44.11772494130627004125349400969
y[1] (numeric) = 56.80182597107981986870447152285
absolute error = 12.68410102977354982745097751316
relative error = 28.750578246381327652230822557495 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.732
y[1] (analytic) = 44.120756595588903149832968369068
y[1] (numeric) = 56.82255747107981986870447152285
absolute error = 12.701800875490916718871503153782
relative error = 28.788719540591049201839697518422 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.733
y[1] (analytic) = 44.123788298106149435518509908863
y[1] (numeric) = 56.84328997107981986870447152285
absolute error = 12.719501672973670433185961613987
relative error = 28.826857719103887643349713445548 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.734
y[1] (analytic) = 44.126820048855682432617044276294
y[1] (numeric) = 56.86402347107981986870447152285
absolute error = 12.737203422224137436087427246556
relative error = 28.864992782443756944413567347401 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.735
y[1] (analytic) = 44.129851847835175899846194116793
y[1] (numeric) = 56.88475797107981986870447152285
absolute error = 12.754906123244643968858277406057
relative error = 28.903124731134454915998978128791 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.736
y[1] (analytic) = 44.132883695042303820301810682751
y[1] (numeric) = 56.90549347107981986870447152285
absolute error = 12.772609776037516048402660840099
relative error = 28.941253565699663244045208493907 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.737
y[1] (analytic) = 44.135915590474740401425511705509
y[1] (numeric) = 56.92622997107981986870447152285
absolute error = 12.790314380605079467278959817341
relative error = 28.979379286662947521109382631281 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.738
y[1] (analytic) = 44.138947534130160074972225529002
y[1] (numeric) = 56.94696747107981986870447152285
absolute error = 12.808019936949659793732245993848
relative error = 29.017501894547757278002603472118 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.739
y[1] (analytic) = 44.141979526006237496977741503571
y[1] (numeric) = 56.96770597107981986870447152285
absolute error = 12.825726445073582371726730019279
relative error = 29.055621389877426015415873311637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.74
y[1] (analytic) = 44.145011566100647547726266638471
y[1] (numeric) = 56.98844547107981986870447152285
absolute error = 12.843433904979172320978204884379
relative error = 29.09373777317517123553582158141 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.741
y[1] (analytic) = 44.148043654411065331717988511498
y[1] (numeric) = 57.00918597107981986870447152285
absolute error = 12.861142316668754536986483011352
relative error = 29.131851044964094473650243559404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.742
y[1] (analytic) = 44.151075790935166177636644434281
y[1] (numeric) = 57.02992747107981986870447152285
absolute error = 12.878851680144653691067827088569
relative error = 29.169961205767181329743453802507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.743
y[1] (analytic) = 44.154107975670625638317096871716
y[1] (numeric) = 57.05066997107981986870447152285
absolute error = 12.896561995409194230387374651134
relative error = 29.208068256107301500081458084888 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.744
y[1] (analytic) = 44.157140208615119490712915114016
y[1] (numeric) = 57.07141347107981986870447152285
absolute error = 12.914273262464700377991556408834
relative error = 29.246172196507208808786947624007 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.745
y[1] (analytic) = 44.160172489766323735863963199892
y[1] (numeric) = 57.09215797107981986870447152285
absolute error = 12.931985481313496132840508322958
relative error = 29.28427302748954123940411937435 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.746
y[1] (analytic) = 44.163204819121914598863994089358
y[1] (numeric) = 57.11290347107981986870447152285
absolute error = 12.949698651957905269840477433492
relative error = 29.32237074957682096645332616746 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.747
y[1] (analytic) = 44.166237196679568528828250084642
y[1] (numeric) = 57.13364997107981986870447152285
absolute error = 12.967412774400251339876221438208
relative error = 29.360465363291454386975560475269 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.748
y[1] (analytic) = 44.169269622436962198861069497688
y[1] (numeric) = 57.15439747107981986870447152285
absolute error = 12.985127848642857669843402025162
relative error = 29.398556869155732152066775572155 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=3.7MB, time=2.46
NO POLE
x[1] = 20.749
y[1] (analytic) = 44.172302096391772506023499562791
y[1] (numeric) = 57.17514597107981986870447152285
absolute error = 13.002843874688047362680971960059
relative error = 29.43664526769182919840204786938 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.75
y[1] (analytic) = 44.175334618541676571300915592781
y[1] (numeric) = 57.19589547107981986870447152285
absolute error = 13.020560852538143297403555930069
relative error = 29.474730559421804779749584194374 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.751
y[1] (analytic) = 44.178367188884351739570646377352
y[1] (numeric) = 57.21664597107981986870447152285
absolute error = 13.038278782195468129133825145498
relative error = 29.512812744867602498474577785185 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.752
y[1] (analytic) = 44.181399807417475579569605821924
y[1] (numeric) = 57.23739747107981986870447152285
absolute error = 13.055997663662344289134865700926
relative error = 29.550891824551050337032916769481 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.753
y[1] (analytic) = 44.184432474138725883861930825624
y[1] (numeric) = 57.25814997107981986870447152285
absolute error = 13.073717496941093984842540697226
relative error = 29.588967798993860689454748895289 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.754
y[1] (analytic) = 44.187465189045780668806625396833
y[1] (numeric) = 57.27890347107981986870447152285
absolute error = 13.091438282034039199897846126017
relative error = 29.627040668717630392817906279529 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.755
y[1] (analytic) = 44.190497952136318174525211004809
y[1] (numeric) = 57.29965797107981986870447152285
absolute error = 13.109160018943501694179260518041
relative error = 29.665110434243840758711193938578 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.756
y[1] (analytic) = 44.193530763408016864869383165891
y[1] (numeric) = 57.32041347107981986870447152285
absolute error = 13.126882707671803003835088356959
relative error = 29.70317709609385760468754586359 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.757
y[1] (analytic) = 44.196563622858555427388674262764
y[1] (numeric) = 57.34116997107981986870447152285
absolute error = 13.144606348221264441315797260086
relative error = 29.741240654788931285707052401761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.758
y[1] (analytic) = 44.199596530485612773298122595314
y[1] (numeric) = 57.36192747107981986870447152285
absolute error = 13.162330940594207095406348927536
relative error = 29.779301110850196725569862703005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.759
y[1] (analytic) = 44.20262948628686803744594766153
y[1] (numeric) = 57.38268597107981986870447152285
absolute error = 13.18005648479295183125852386132
relative error = 29.817358464798673448338965990158 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.76
y[1] (analytic) = 44.205662490260000578281231666994
y[1] (numeric) = 57.40344547107981986870447152285
absolute error = 13.197782980819819290423239855856
relative error = 29.855412717155265609752855409001 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.761
y[1] (analytic) = 44.208695542402689977821607261436
y[1] (numeric) = 57.42420597107981986870447152285
absolute error = 13.215510428677129890882864261414
relative error = 29.893463868440762028628078212986 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.762
y[1] (analytic) = 44.21172864271261604162095150085
y[1] (numeric) = 57.44496747107981986870447152285
absolute error = 13.233238828367203827083520022
relative error = 29.931511919175836218251676035933 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.763
y[1] (analytic) = 44.214761791187458798737086033693
y[1] (numeric) = 57.46572997107981986870447152285
absolute error = 13.250968179892361069967385489157
relative error = 29.969556869881046417763519004333 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.764
y[1] (analytic) = 44.217794987824898501699483509644
y[1] (numeric) = 57.48649347107981986870447152285
absolute error = 13.268698483254921367004988013206
relative error = 30.007598721076835623528537439404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.765
y[1] (analytic) = 44.220828232622615626476980209451
y[1] (numeric) = 57.50725797107981986870447152285
absolute error = 13.286429738457204242227491313399
relative error = 30.045637473283531620498854897373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.766
y[1] (analytic) = 44.223861525578290872445494894338
y[1] (numeric) = 57.52802347107981986870447152285
absolute error = 13.304161945501528996258976628512
relative error = 30.083673127021347013565826295018 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.767
y[1] (analytic) = 44.226894866689605162355753873493
y[1] (numeric) = 57.54878997107981986870447152285
absolute error = 13.321895104390214706348717649357
relative error = 30.121705682810379258901984865806 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.768
y[1] (analytic) = 44.229928255954239642301022288153
y[1] (numeric) = 57.56955747107981986870447152285
absolute error = 13.339629215125580226403449234697
relative error = 30.159735141170610695292901690388 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.769
y[1] (analytic) = 44.232961693369875681684841610743
y[1] (numeric) = 57.59032597107981986870447152285
absolute error = 13.357364277709944187019629912107
relative error = 30.197761502621908575458961543847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.77
y[1] (analytic) = 44.235995178934194873188773357632
y[1] (numeric) = 57.61109547107981986870447152285
absolute error = 13.375100292145624995515698165218
relative error = 30.235784767684025097367058800175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.771
y[1] (analytic) = 44.239028712644879032740149013962
y[1] (numeric) = 57.63186597107981986870447152285
absolute error = 13.392837258434940835964322508888
relative error = 30.273804936876597435532217133235 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.772
y[1] (analytic) = 44.242062294499610199479826169084
y[1] (numeric) = 57.65263747107981986870447152285
absolute error = 13.410575176580209669224645353766
relative error = 30.311822010719147772309136751644 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.773
y[1] (analytic) = 44.245095924496070635729950861091
y[1] (numeric) = 57.67340997107981986870447152285
absolute error = 13.428314046583749232974520661759
relative error = 30.349835989731083329173672903593 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.774
y[1] (analytic) = 44.248129602631942826961726128955
y[1] (numeric) = 57.69418347107981986870447152285
absolute error = 13.446053868447877041742745393895
relative error = 30.387846874431696397994249385989 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.775
y[1] (analytic) = 44.251163328904909481763186770784
y[1] (numeric) = 57.71495797107981986870447152285
absolute error = 13.463794642174910386941284752066
relative error = 30.425854665340164372293210790719 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.776
y[1] (analytic) = 44.254197103312653531806980306698
y[1] (numeric) = 57.73573347107981986870447152285
absolute error = 13.481536367767166336897491216152
relative error = 30.463859362975549778498117219324 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.777
y[1] (analytic) = 44.257230925852858131818154144817
y[1] (numeric) = 57.75650997107981986870447152285
absolute error = 13.499279045226961736886317378033
relative error = 30.501860967856800307182985195818 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.778
y[1] (analytic) = 44.26026479652320665954194894891
y[1] (numeric) = 57.77728747107981986870447152285
absolute error = 13.51702267455661320916252257394
relative error = 30.539859480502748844299478505667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.779
y[1] (analytic) = 44.263298715321382715711598206155
y[1] (numeric) = 57.79806597107981986870447152285
absolute error = 13.534767255758437152992873316695
relative error = 30.577854901432113502398052687655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.78
y[1] (analytic) = 44.266332682245070124016133993565
y[1] (numeric) = 57.81884547107981986870447152285
absolute error = 13.552512788834749744688337529285
relative error = 30.615847231163497651839056903523 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.781
y[1] (analytic) = 44.269366697291952931068198941576
y[1] (numeric) = 57.83962597107981986870447152285
absolute error = 13.570259273787866937636272581274
relative error = 30.653836470215389951993796908847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.782
y[1] (analytic) = 44.272400760459715406371864393284
y[1] (numeric) = 57.86040747107981986870447152285
absolute error = 13.588006710620104462332607129566
relative error = 30.691822619106164382435562847109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.783
y[1] (analytic) = 44.275434871746042042290454757869
y[1] (numeric) = 57.88118997107981986870447152285
absolute error = 13.605755099333777826414016764981
relative error = 30.729805678354080274120625587197 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.784
y[1] (analytic) = 44.278469031148617554014378056711
y[1] (numeric) = 57.90197347107981986870447152285
absolute error = 13.623504439931202314690093466139
relative error = 30.767785648477282340559205323102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.785
y[1] (analytic) = 44.281503238665126879528962660683
y[1] (numeric) = 57.92275797107981986870447152285
absolute error = 13.641254732414692989175508862167
relative error = 30.80576252999380070897641615311 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.786
y[1] (analytic) = 44.284537494293255179582300217172
y[1] (numeric) = 57.94354347107981986870447152285
absolute error = 13.659005976786564689122171305678
relative error = 30.843736323421550951463190353977 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.787
y[1] (analytic) = 44.287571798030687837653094765303
y[1] (numeric) = 57.96432997107981986870447152285
absolute error = 13.676758173049132031051376757547
relative error = 30.881707029278334116117186064319 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.788
y[1] (analytic) = 44.290606149875110459918518037892
y[1] (numeric) = 57.98511747107981986870447152285
absolute error = 13.694511321204709408785953484958
relative error = 30.919674648081836758173682089672 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.789
y[1] (analytic) = 44.293640549824208875222070948659
y[1] (numeric) = 58.00590597107981986870447152285
absolute error = 13.712265421255610993482400574191
relative error = 30.957639180349630971126463540144 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.79
y[1] (analytic) = 44.296674997875669135041451263162
y[1] (numeric) = 58.02669547107981986870447152285
absolute error = 13.730020473204150733663020259688
relative error = 30.995600626599174417838702010246 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.791
y[1] (analytic) = 44.299709494027177513456427452027
y[1] (numeric) = 58.04748597107981986870447152285
absolute error = 13.747776477052642355248044070823
relative error = 31.033558987347810361643834008542 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.792
y[1] (analytic) = 44.302744038276420507116718724946
y[1] (numeric) = 58.06827747107981986870447152285
absolute error = 13.765533432803399361587752797904
relative error = 31.071514263112767697436441343583 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.793
y[1] (analytic) = 44.305778630621084835209881243964
y[1] (numeric) = 58.08906997107981986870447152285
absolute error = 13.783291340458735033494590278886
relative error = 31.109466454411160982753137170833 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.794
y[1] (analytic) = 44.308813271058857439429200514579
y[1] (numeric) = 58.10986347107981986870447152285
absolute error = 13.801050200020962429275271008271
relative error = 31.147415561759990468843461403761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.795
y[1] (analytic) = 44.311847959587425483941589953166
y[1] (numeric) = 58.13065797107981986870447152285
absolute error = 13.818810011492394384762881569684
relative error = 31.185361585676142131730789190763 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.796
y[1] (analytic) = 44.314882696204476355355495629227
y[1] (numeric) = 58.15145347107981986870447152285
absolute error = 13.836570774875343513348975893623
relative error = 31.223304526676387703263256158048 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.797
y[1] (analytic) = 44.317917480907697662688807181006
y[1] (numeric) = 58.17224997107981986870447152285
absolute error = 13.854332490172122206015664341844
relative error = 31.261244385277384702154704116955 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.798
y[1] (analytic) = 44.320952313694777237336774902968
y[1] (numeric) = 58.19304747107981986870447152285
absolute error = 13.872095157385042631367696619882
relative error = 31.29918116199567646501565093275 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.799
y[1] (analytic) = 44.323987194563403133039933003652
y[1] (numeric) = 58.21384597107981986870447152285
absolute error = 13.889858776516416735664538519198
relative error = 31.33711485734769217737428825038 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.8
y[1] (analytic) = 44.327022123511263625852029032445
y[1] (numeric) = 58.23464547107981986870447152285
absolute error = 13.907623347568556242852442490405
relative error = 31.375045471849746904687510770965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.801
y[1] (analytic) = 44.330057100536047214107959473746
y[1] (numeric) = 58.25544597107981986870447152285
absolute error = 13.925388870543772654596512049104
relative error = 31.412973006018041623341980771551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.802
y[1] (analytic) = 44.333092125635442618391711507101
y[1] (numeric) = 58.27624747107981986870447152285
absolute error = 13.943155345444377250312760015749
relative error = 31.45089746036866325164523155871 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.803
y[1] (analytic) = 44.33612719880713878150431093176
y[1] (numeric) = 58.29704997107981986870447152285
absolute error = 13.96092277227268108720016059109
relative error = 31.488818835417584680806813545466 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.804
y[1] (analytic) = 44.339162320048824868431776254221
y[1] (numeric) = 58.31785347107981986870447152285
absolute error = 13.978691151030995000272695268629
relative error = 31.526737131680664805909486639103 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.805
y[1] (analytic) = 44.342197489358190266313078937255
y[1] (numeric) = 58.33865797107981986870447152285
absolute error = 13.996460481721629602391392585595
relative error = 31.564652349673648556870462626099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.806
y[1] (analytic) = 44.345232706732924584408109808963
y[1] (numeric) = 58.35946347107981986870447152285
absolute error = 14.014230764346895284296361713887
relative error = 31.602564489912166929392701238714 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.807
y[1] (analytic) = 44.348267972170717654065651630335
y[1] (numeric) = 58.38026997107981986870447152285
absolute error = 14.032001998909102214638819892515
relative error = 31.640473552911737015906263586464 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.808
y[1] (analytic) = 44.351303285669259528691357819863
y[1] (numeric) = 58.40107747107981986870447152285
absolute error = 14.049774185410560340013113702987
relative error = 31.678379539187762036499726633902 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.809
y[1] (analytic) = 44.354338647226240483715737333758
y[1] (numeric) = 58.42188597107981986870447152285
absolute error = 14.067547323853579384988734189092
relative error = 31.716282449255531369841662404637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.81
y[1] (analytic) = 44.357374056839351016562145700198
y[1] (numeric) = 58.44269547107981986870447152285
absolute error = 14.085321414240468852142325822652
relative error = 31.754182283630220584092185590302 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.811
y[1] (analytic) = 44.360409514506281846614782206249
y[1] (numeric) = 58.46350597107981986870447152285
absolute error = 14.103096456573538022089689316601
relative error = 31.792079042826891467804573241031 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.812
y[1] (analytic) = 44.363445020224723915186693235877
y[1] (numeric) = 58.48431747107981986870447152285
absolute error = 14.120872450855095953517778286973
relative error = 31.82997272736049206081696021313 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.813
y[1] (analytic) = 44.366480573992368385487781757636
y[1] (numeric) = 58.50512997107981986870447152285
absolute error = 14.138649397087451483216689765214
relative error = 31.867863337745856685134114047576 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.814
y[1] (analytic) = 44.369516175806906642592822960541
y[1] (numeric) = 58.52594347107981986870447152285
absolute error = 14.156427295272913226111648562309
relative error = 31.90575087449770597579929295169 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.815
y[1] (analytic) = 44.372551825666030293409486036613
y[1] (numeric) = 58.54675797107981986870447152285
absolute error = 14.174206145413789575294985486237
relative error = 31.943635338130646911756190554839 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.816
y[1] (analytic) = 44.375587523567431166646362108691
y[1] (numeric) = 58.56757347107981986870447152285
absolute error = 14.191985947512388702058109414159
relative error = 31.981516729159172846700971107179 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.817
y[1] (analytic) = 44.378623269508801312780998301957
y[1] (numeric) = 58.58838997107981986870447152285
absolute error = 14.209766701571018555923473220893
relative error = 32.019395048097663539924398789348 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.818
y[1] (analytic) = 44.38165906348783300402793795776
y[1] (numeric) = 58.60920747107981986870447152285
absolute error = 14.22754840759198686467653356509
relative error = 32.05727029546038518714406479908 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=3.7MB, time=2.68
x[1] = 20.819
y[1] (analytic) = 44.384694905502218734306766988224
y[1] (numeric) = 58.63002597107981986870447152285
absolute error = 14.245331065577601134397704534626
relative error = 32.095142471761490451326715879461 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.82
y[1] (analytic) = 44.387730795549651219210166370182
y[1] (numeric) = 58.65084547107981986870447152285
absolute error = 14.263114675530168649494305152668
relative error = 32.133011577515018493500687951867 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.821
y[1] (analytic) = 44.390766733627823395971970776974
y[1] (numeric) = 58.67166597107981986870447152285
absolute error = 14.280899237451996472732500745876
relative error = 32.17087761323489500355844851508 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.822
y[1] (analytic) = 44.39380271973442842343523334659
y[1] (numeric) = 58.69248747107981986870447152285
absolute error = 14.29868475134539144526923817626
relative error = 32.208740579434932231049251470739 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.823
y[1] (analytic) = 44.396838753867159682020296584748
y[1] (numeric) = 58.71330997107981986870447152285
absolute error = 14.316471217212660186684174938102
relative error = 32.246600476628829015961908033405 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.824
y[1] (analytic) = 44.39987483602371077369286940138
y[1] (numeric) = 58.73413347107981986870447152285
absolute error = 14.33425863505610909501160212147
relative error = 32.284457305330170819497677382363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.825
y[1] (analytic) = 44.402910966201775521932110279082
y[1] (numeric) = 58.75495797107981986870447152285
absolute error = 14.352047004878044346772361243768
relative error = 32.322311066052429754833280710485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.826
y[1] (analytic) = 44.405947144399047971698716572045
y[1] (numeric) = 58.77578347107981986870447152285
absolute error = 14.369836326680771897005754950805
relative error = 32.360161759308964617874042324072 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.827
y[1] (analytic) = 44.408983370613222389403019934001
y[1] (numeric) = 58.79660997107981986870447152285
absolute error = 14.387626600466597479301451588849
relative error = 32.398009385613020917997161446024 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.828
y[1] (analytic) = 44.412019644841993262873087873703
y[1] (numeric) = 58.81743747107981986870447152285
absolute error = 14.405417826237826605831383649147
relative error = 32.435853945477730908785118373201 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.829
y[1] (analytic) = 44.415055967083055301322831436483
y[1] (numeric) = 58.83826597107981986870447152285
absolute error = 14.423210003996764567381640086367
relative error = 32.473695439416113618749218637211 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.83
y[1] (analytic) = 44.41809233733410343532011901041
y[1] (numeric) = 58.85909547107981986870447152285
absolute error = 14.44100313374571643338435251244
relative error = 32.511533867941074882043278816456 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.831
y[1] (analytic) = 44.421128755592832816754896255562
y[1] (numeric) = 58.87992597107981986870447152285
absolute error = 14.458797215486987051949575267288
relative error = 32.549369231565407369167457645711 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.832
y[1] (analytic) = 44.424165221856938818807312154975
y[1] (numeric) = 58.90075747107981986870447152285
absolute error = 14.476592249222881049897159367875
relative error = 32.587201530801790617662236067859 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.833
y[1] (analytic) = 44.427201736124117035915851185769
y[1] (numeric) = 58.92158997107981986870447152285
absolute error = 14.494388234955702832788620337081
relative error = 32.625030766162791062792549871098 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.834
y[1] (analytic) = 44.430238298392063283745471609012
y[1] (numeric) = 58.94242347107981986870447152285
absolute error = 14.512185172687756584958999913838
relative error = 32.662856938160862068222078553179 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.835
y[1] (analytic) = 44.433274908658473599155749876809
y[1] (numeric) = 58.96325797107981986870447152285
absolute error = 14.529983062421346269548721646041
relative error = 32.700680047308343956677694052973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.836
y[1] (analytic) = 44.436311566921044240169031155202
y[1] (numeric) = 58.98409347107981986870447152285
absolute error = 14.547781904158775628535440367648
relative error = 32.738500094117464040604072987841 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.837
y[1] (analytic) = 44.439348273177471685938585961377
y[1] (numeric) = 59.00492997107981986870447152285
absolute error = 14.565581697902348182765885561473
relative error = 32.776317079100336652808476034002 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.838
y[1] (analytic) = 44.442385027425452636716772913717
y[1] (numeric) = 59.02576747107981986870447152285
absolute error = 14.583382443654367231987698609133
relative error = 32.81413100276896317709569808549 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.839
y[1] (analytic) = 44.445421829662684013823207593241
y[1] (numeric) = 59.04660597107981986870447152285
absolute error = 14.601184141417135854881263929609
relative error = 32.851941865635232078893192825729 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.84
y[1] (analytic) = 44.448458679886862959612937514965
y[1] (numeric) = 59.06744547107981986870447152285
absolute error = 14.618986791192956909091534007885
relative error = 32.889749668210918935866375344274 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.841
y[1] (analytic) = 44.451495578095686837444623207701
y[1] (numeric) = 59.08828597107981986870447152285
absolute error = 14.636790392984133031259848315149
relative error = 32.927554411007686468524106429787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.842
y[1] (analytic) = 44.454532524286853231648725400861
y[1] (numeric) = 59.10912747107981986870447152285
absolute error = 14.654594946792966637055746121989
relative error = 32.965356094537084570814362168671 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.843
y[1] (analytic) = 44.457569518458059947495698316757
y[1] (numeric) = 59.12996997107981986870447152285
absolute error = 14.672400452621759921208773206093
relative error = 33.003154719310550340710092477477 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.844
y[1] (analytic) = 44.460606560607005011164189066982
y[1] (numeric) = 59.15081347107981986870447152285
absolute error = 14.690206910472814857540282455868
relative error = 33.04095028583940811078527219541 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.845
y[1] (analytic) = 44.463643650731386669709243151357
y[1] (numeric) = 59.17165797107981986870447152285
absolute error = 14.708014320348433198995228371493
relative error = 33.078742794634869478781148362036 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.846
y[1] (analytic) = 44.466680788828903391030516058027
y[1] (numeric) = 59.19250347107981986870447152285
absolute error = 14.725822682250916477673955464823
relative error = 33.116532246208033338162687303504 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.847
y[1] (analytic) = 44.469717974897253863840490963209
y[1] (numeric) = 59.21334997107981986870447152285
absolute error = 14.743631996182566004863980559641
relative error = 33.154318641069885908665225149296 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.848
y[1] (analytic) = 44.472755208934136997632702529148
y[1] (numeric) = 59.23419747107981986870447152285
absolute error = 14.761442262145682871071768993702
relative error = 33.192101979731300766831325399871 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.849
y[1] (analytic) = 44.475792490937251922649966798802
y[1] (numeric) = 59.25504597107981986870447152285
absolute error = 14.779253480142567946054504724048
relative error = 33.229882262703038876537847164141 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.85
y[1] (analytic) = 44.478829820904297989852617185817
y[1] (numeric) = 59.27589547107981986870447152285
absolute error = 14.797065650175521878851854337033
relative error = 33.267659490495748619513227684103 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.851
y[1] (analytic) = 44.481867198832974770886746558306
y[1] (numeric) = 59.29674597107981986870447152285
absolute error = 14.814878772246845097817724964544
relative error = 33.305433663619965825844982762567 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.852
y[1] (analytic) = 44.484904624720982058052455414985
y[1] (numeric) = 59.31759747107981986870447152285
absolute error = 14.832692846358837810652016107865
relative error = 33.343204782586113804477428708305 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.853
y[1] (analytic) = 44.487942098566019864272106152204
y[1] (numeric) = 59.33844997107981986870447152285
absolute error = 14.850507872513800004432365370646
relative error = 33.380972847904503373699629411471 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.854
y[1] (analytic) = 44.490979620365788423058583420407
y[1] (numeric) = 59.35930347107981986870447152285
absolute error = 14.868323850714031445645888102443
relative error = 33.418737860085332891623572160646 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.855
y[1] (analytic) = 44.494017190117988188483560568569
y[1] (numeric) = 59.38015797107981986870447152285
absolute error = 14.886140780961831680220910954281
relative error = 33.456499819638688286652575811336 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.856
y[1] (analytic) = 44.497054807820319835145772175137
y[1] (numeric) = 59.40101347107981986870447152285
absolute error = 14.903958663259500033558699347713
relative error = 33.494258727074543087939934914251 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.857
y[1] (analytic) = 44.500092473470484258139292664036
y[1] (numeric) = 59.42186997107981986870447152285
absolute error = 14.921777497609335610565178858814
relative error = 33.532014582902758455837803410162 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.858
y[1] (analytic) = 44.503130187066182573021821004261
y[1] (numeric) = 59.44272747107981986870447152285
absolute error = 14.939597284013637295682650518589
relative error = 33.569767387633083212336321496665 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.859
y[1] (analytic) = 44.506167948605116115782971491607
y[1] (numeric) = 59.46358597107981986870447152285
absolute error = 14.957418022474703752921500031243
relative error = 33.607517141775153871492989270655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.86
y[1] (analytic) = 44.509205758084986442812570611082
y[1] (numeric) = 59.48444547107981986870447152285
absolute error = 14.975239712994833425891900911768
relative error = 33.645263845838494669852290748777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.861
y[1] (analytic) = 44.512243615503495330868959978534
y[1] (numeric) = 59.50530597107981986870447152285
absolute error = 14.993062355576324537835511544316
relative error = 33.683007500332517596855571866684 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.862
y[1] (analytic) = 44.51528152085834477704730536005
y[1] (numeric) = 59.52616747107981986870447152285
absolute error = 15.0108859502214750916571661628
relative error = 33.720748105766522425241176056355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.863
y[1] (analytic) = 44.518319474147236998747911767654
y[1] (numeric) = 59.54702997107981986870447152285
absolute error = 15.028710496932582869956559755196
relative error = 33.758485662649696741434840999284 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.864
y[1] (analytic) = 44.521357475367874433644544629864
y[1] (numeric) = 59.56789347107981986870447152285
absolute error = 15.046535995711945435059926892986
relative error = 33.796220171491115975930360151786 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.865
y[1] (analytic) = 44.524395524517959739652757035636
y[1] (numeric) = 59.58875797107981986870447152285
absolute error = 15.064362446561860129051714487214
relative error = 33.833951632799743433660512637251 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.866
y[1] (analytic) = 44.527433621595195794898223050259
y[1] (numeric) = 59.60962347107981986870447152285
absolute error = 15.082189849484624073806248472591
relative error = 33.871680047084430324358265098538 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.867
y[1] (analytic) = 44.530471766597285697685077101718
y[1] (numeric) = 59.63048997107981986870447152285
absolute error = 15.100018204482534171019394421132
relative error = 33.909405414853915792908249102403 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.868
y[1] (analytic) = 44.533509959521932766464259436108
y[1] (numeric) = 59.65135747107981986870447152285
absolute error = 15.117847511557887102240212086742
relative error = 33.947127736616826949688517686096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.869
y[1] (analytic) = 44.536548200366840539801867640605
y[1] (numeric) = 59.67222597107981986870447152285
absolute error = 15.135677770712979328902603882245
relative error = 33.984847012881678900902584635033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.87
y[1] (analytic) = 44.539586489129712776347514232573
y[1] (numeric) = 59.69309547107981986870447152285
absolute error = 15.153508981950107092356957290277
relative error = 34.022563244156874778901750078722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.871
y[1] (analytic) = 44.542624825808253454802690313331
y[1] (numeric) = 59.71396597107981986870447152285
absolute error = 15.171341145271566413901781209519
relative error = 34.060276430950705772497715990787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.872
y[1] (analytic) = 44.545663210400166773889135285146
y[1] (numeric) = 59.73483747107981986870447152285
absolute error = 15.189174260679653094815336237704
relative error = 34.09798657377135115726549517732 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.873
y[1] (analytic) = 44.548701642903157152317212629976
y[1] (numeric) = 59.75570997107981986870447152285
absolute error = 15.207008328176662716387258892874
relative error = 34.135693673126878325836617336402 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.874
y[1] (analytic) = 44.551740123314929228754291748537
y[1] (numeric) = 59.77658347107981986870447152285
absolute error = 15.224843347764890639950179774313
relative error = 34.173397729525242818182635770022 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.875
y[1] (analytic) = 44.554778651633187861793135858228
y[1] (numeric) = 59.79745797107981986870447152285
absolute error = 15.242679319446632006911335664622
relative error = 34.211098743474288351888938328222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.876
y[1] (analytic) = 44.557817227855638129920295948459
y[1] (numeric) = 59.81833347107981986870447152285
absolute error = 15.260516243224181738784175574391
relative error = 34.248796715481746852418866163769 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.877
y[1] (analytic) = 44.560855851979985331484510791933
y[1] (numeric) = 59.83920997107981986870447152285
absolute error = 15.278354119099834537219960730917
relative error = 34.286491646055238483368143874169 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.878
y[1] (analytic) = 44.563894524003934984665113010462
y[1] (numeric) = 59.86008747107981986870447152285
absolute error = 15.296192947075884884039358512388
relative error = 34.324183535702271676709624606235 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.879
y[1] (analytic) = 44.566933243925192827440441193801
y[1] (numeric) = 59.88096597107981986870447152285
absolute error = 15.314032727154627041264030329049
relative error = 34.36187238493024316302835369723 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.88
y[1] (analytic) = 44.569972011741464817556258070123
y[1] (numeric) = 59.90184547107981986870447152285
absolute error = 15.331873459338355051148213452727
relative error = 34.399558194246438001746954424683 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.881
y[1] (analytic) = 44.573010827450457132494174726635
y[1] (numeric) = 59.92272597107981986870447152285
absolute error = 15.349715143629362736210296796215
relative error = 34.437240964158029611341339435887 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.882
y[1] (analytic) = 44.576049691049876169440080878917
y[1] (numeric) = 59.94360747107981986870447152285
absolute error = 15.367557780029943699264390643933
relative error = 34.474920695172079799546751426314 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.883
y[1] (analytic) = 44.5790886025374285452525811875
y[1] (numeric) = 59.96448997107981986870447152285
absolute error = 15.38540136854239132345189033535
relative error = 34.512597387795538793554136634921 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.884
y[1] (analytic) = 44.582127561910821096431437620296
y[1] (numeric) = 59.98537347107981986870447152285
absolute error = 15.403245909168998772273033902554
relative error = 34.550271042535245270196854722525 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.885
y[1] (analytic) = 44.585166569167760879086017859348
y[1] (numeric) = 60.00625797107981986870447152285
absolute error = 15.421091401912058989618453663502
relative error = 34.587941659897926386127728598383 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.886
y[1] (analytic) = 44.588205624305955168903749750546
y[1] (numeric) = 60.02714347107981986870447152285
absolute error = 15.438937846773864699800721772304
relative error = 34.62560924039019780798643775809 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.887
y[1] (analytic) = 44.591244727323111461118581794775
y[1] (numeric) = 60.04802997107981986870447152285
absolute error = 15.456785243756708407585889728075
relative error = 34.663273784518563742557258694952 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.888
y[1] (analytic) = 44.594283878216937470479449679119
y[1] (numeric) = 60.06891747107981986870447152285
absolute error = 15.474633592862882398225021843731
relative error = 34.700935292789416966917155945057 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.889
y[1] (analytic) = 44.597323076985141131218748846633
y[1] (numeric) = 60.08980597107981986870447152285
absolute error = 15.492482894094678737485722676217
relative error = 34.738593765709038858574227325082 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=3.7MB, time=2.92
NO POLE
x[1] = 20.89
y[1] (analytic) = 44.600362323625430597020813103247
y[1] (numeric) = 60.11069547107981986870447152285
absolute error = 15.510333147454389271683658419603
relative error = 34.776249203783599425596506920277 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.891
y[1] (analytic) = 44.603401618135514240990399260374
y[1] (numeric) = 60.13158597107981986870447152285
absolute error = 15.528184352944305627714072262476
relative error = 34.81390160751915733673112937852 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.892
y[1] (analytic) = 44.606440960513100655621177811747
y[1] (numeric) = 60.15247747107981986870447152285
absolute error = 15.546036510566719213083293711103
relative error = 34.851550977421659951513859065026 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.893
y[1] (analytic) = 44.609480350755898652764229643074
y[1] (numeric) = 60.17336997107981986870447152285
absolute error = 15.563889620323921215940241879776
relative error = 34.889197313996943350368987630597 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.894
y[1] (analytic) = 44.612519788861617263596548773035
y[1] (numeric) = 60.19426347107981986870447152285
absolute error = 15.581743682218202605107922749815
relative error = 34.926840617750732364699603545036 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.895
y[1] (analytic) = 44.615559274827965738589551124206
y[1] (numeric) = 60.21515797107981986870447152285
absolute error = 15.599598696251854130114920398644
relative error = 34.964480889188640606968237145661 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.896
y[1] (analytic) = 44.618598808652653547477589322455
y[1] (numeric) = 60.23605347107981986870447152285
absolute error = 15.617454662427166321226882200395
relative error = 35.002118128816170500767884749519 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.897
y[1] (analytic) = 44.621638390333390379226473523353
y[1] (numeric) = 60.25694997107981986870447152285
absolute error = 15.635311580746429489477997999497
relative error = 35.039752337138713310883415376407 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.898
y[1] (analytic) = 44.624678019867886142001998264189
y[1] (numeric) = 60.27784747107981986870447152285
absolute error = 15.653169451211933726702473258661
relative error = 35.077383514661549173343363628203 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.899
y[1] (analytic) = 44.627717697253850963138475340116
y[1] (numeric) = 60.29874597107981986870447152285
absolute error = 15.671028273825968905565996182734
relative error = 35.115011661889847125462112268717 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.9
y[1] (analytic) = 44.630757422488995189107272703024
y[1] (numeric) = 60.31964547107981986870447152285
absolute error = 15.688888048590824679597198819826
relative error = 35.152636779328665135872468046586 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.901
y[1] (analytic) = 44.63379719557102938548535938164
y[1] (numeric) = 60.34054597107981986870447152285
absolute error = 15.70674877550879048321911214121
relative error = 35.190258867482950134548634302545 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.902
y[1] (analytic) = 44.636837016497664336923856421486
y[1] (numeric) = 60.36144747107981986870447152285
absolute error = 15.724610454582155531780615101364
relative error = 35.227877926857538042819583900547 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.903
y[1] (analytic) = 44.639876885266611047116593843203
y[1] (numeric) = 60.38234997107981986870447152285
absolute error = 15.742473085813208821587877679647
relative error = 35.265493957957153803372836021096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.904
y[1] (analytic) = 44.642916801875580738768673617816
y[1] (numeric) = 60.40325347107981986870447152285
absolute error = 15.760336669204239129935797905034
relative error = 35.303106961286411410248640353471 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.905
y[1] (analytic) = 44.64595676632228485356503865752
y[1] (numeric) = 60.42415797107981986870447152285
absolute error = 15.77820120475753501513943286533
relative error = 35.34071693734981393882457222205 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.906
y[1] (analytic) = 44.648996778604435052139047820502
y[1] (numeric) = 60.44506347107981986870447152285
absolute error = 15.796066692475384816565423702348
relative error = 35.378323886651753575790542180654 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.907
y[1] (analytic) = 44.652036838719743214041056928425
y[1] (numeric) = 60.46596997107981986870447152285
absolute error = 15.813933132360076654663414594425
relative error = 35.415927809696511649114223607019 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.908
y[1] (analytic) = 44.655076946665921437707005795078
y[1] (numeric) = 60.48687747107981986870447152285
absolute error = 15.831800524413898430997465727772
relative error = 35.453528706988258657996901828421 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.909
y[1] (analytic) = 44.658117102440682040427011264774
y[1] (numeric) = 60.50778597107981986870447152285
absolute error = 15.849668868639137828277460258076
relative error = 35.491126579031054302819748307742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.91
y[1] (analytic) = 44.661157306041737558313966259089
y[1] (numeric) = 60.52869547107981986870447152285
absolute error = 15.867538165038082310390505263761
relative error = 35.528721426328847515080523417805 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.911
y[1] (analytic) = 44.664197557466800746272144830446
y[1] (numeric) = 60.54960597107981986870447152285
absolute error = 15.885408413613019122432326692404
relative error = 35.566313249385476487320711330556 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.912
y[1] (analytic) = 44.667237856713584577965813221166
y[1] (numeric) = 60.57051747107981986870447152285
absolute error = 15.903279614366235290738658301684
relative error = 35.603902048704668703043090545882 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.913
y[1] (analytic) = 44.670278203779802245787846926509
y[1] (numeric) = 60.59142997107981986870447152285
absolute error = 15.921151767300017622916624596341
relative error = 35.641487824790040966619743583685 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.914
y[1] (analytic) = 44.673318598663167160828353760295
y[1] (numeric) = 60.61234347107981986870447152285
absolute error = 15.939024872416652707876117762555
relative error = 35.67907057814509943319050936112 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.915
y[1] (analytic) = 44.67635904136139295284330292165
y[1] (numeric) = 60.63325797107981986870447152285
absolute error = 15.9568989297184269158611686012
relative error = 35.716650309273239638551881775649 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.916
y[1] (analytic) = 44.679399531872193470223160061468
y[1] (numeric) = 60.65417347107981986870447152285
absolute error = 15.974773939207626398481311461382
relative error = 35.754227018677746529036358012867 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.917
y[1] (analytic) = 44.682440070193282779961528347114
y[1] (numeric) = 60.67508997107981986870447152285
absolute error = 15.992649900886537088742943175736
relative error = 35.791800706861794491382240096886 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.918
y[1] (analytic) = 44.685480656322375167623795523989
y[1] (numeric) = 60.69600747107981986870447152285
absolute error = 16.010526814757444701080675998861
relative error = 35.829371374328447382593893199224 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.919
y[1] (analytic) = 44.688521290257185137315786972473
y[1] (numeric) = 60.71692597107981986870447152285
absolute error = 16.028404680822634731388684550377
relative error = 35.86693902158065855979246422105 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.92
y[1] (analytic) = 44.691561971995427411652424758838
y[1] (numeric) = 60.73784547107981986870447152285
absolute error = 16.046283499084392457052046764012
relative error = 35.904503649121270910057064161941 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.921
y[1] (analytic) = 44.694602701534816931726392678703
y[1] (numeric) = 60.75876597107981986870447152285
absolute error = 16.064163269545002936978078844147
relative error = 35.94206525745301688025641778687 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.922
y[1] (analytic) = 44.697643478873068857076807291575
y[1] (numeric) = 60.77968747107981986870447152285
absolute error = 16.082043992206751011627664231275
relative error = 35.979623847078518506870984101814 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.923
y[1] (analytic) = 44.700684304007898565657894945077
y[1] (numeric) = 60.80060997107981986870447152285
absolute error = 16.099925667071921303046576577773
relative error = 36.017179418500287445805551146693 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.924
y[1] (analytic) = 44.703725176937021653807674787399
y[1] (numeric) = 60.82153347107981986870447152285
absolute error = 16.117808294142798214896796735451
relative error = 36.054731972220725002192308613129 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.925
y[1] (analytic) = 44.706766097658153936216647766565
y[1] (numeric) = 60.84245797107981986870447152285
absolute error = 16.135691873421665932487823756285
relative error = 36.092281508742122160184401792847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.926
y[1] (analytic) = 44.709807066169011445896491615074
y[1] (numeric) = 60.86338347107981986870447152285
absolute error = 16.153576404910808422807979907776
relative error = 36.129828028566659612739970361203 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.927
y[1] (analytic) = 44.712848082467310434148761818479
y[1] (numeric) = 60.88430997107981986870447152285
absolute error = 16.171461888612509434555709704371
relative error = 36.167371532196407791396675498854 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.928
y[1] (analytic) = 44.715889146550767370533598566506
y[1] (numeric) = 60.90523747107981986870447152285
absolute error = 16.189348324529052498170872956344
relative error = 36.204912020133326896036718852995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.929
y[1] (analytic) = 44.718930258417098942838439685229
y[1] (numeric) = 60.92616597107981986870447152285
absolute error = 16.207235712662720925866031837621
relative error = 36.242449492879266924642356838404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.93
y[1] (analytic) = 44.721971418064022057046739548928
y[1] (numeric) = 60.94709547107981986870447152285
absolute error = 16.225124053015797811657731973922
relative error = 36.279983950935967703041913776744 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.931
y[1] (analytic) = 44.725012625489253837306693970167
y[1] (numeric) = 60.96802597107981986870447152285
absolute error = 16.243013345590566031397777552683
relative error = 36.317515394805058914646297371375 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.932
y[1] (analytic) = 44.728053880690511625899971066675
y[1] (numeric) = 60.98895747107981986870447152285
absolute error = 16.260903590389308242804500456175
relative error = 36.355043824988060130176020013353 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.933
y[1] (analytic) = 44.731095183665512983210448103601
y[1] (numeric) = 61.00988997107981986870447152285
absolute error = 16.278794787414306885494023419249
relative error = 36.392569241986380837378729412861 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.934
y[1] (analytic) = 44.734136534411975687692954309712
y[1] (numeric) = 61.03082347107981986870447152285
absolute error = 16.296686936667844181011517213138
relative error = 36.430091646301320470737252048875 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.935
y[1] (analytic) = 44.737177932927617735842019666126
y[1] (numeric) = 61.05175797107981986870447152285
absolute error = 16.314580038152202132862451856724
relative error = 36.467611038434068441168152928345 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.936
y[1] (analytic) = 44.740219379210157342160629666116
y[1] (numeric) = 61.07269347107981986870447152285
absolute error = 16.332474091869662526543841856734
relative error = 36.505127418885704165710815144891 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.937
y[1] (analytic) = 44.743260873257312939128986044604
y[1] (numeric) = 61.09362997107981986870447152285
absolute error = 16.350369097822506929575485478246
relative error = 36.542640788157197097207042725298 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.938
y[1] (analytic) = 44.746302415066803177173273475877
y[1] (numeric) = 61.11456747107981986870447152285
absolute error = 16.368265056013016691531198046973
relative error = 36.580151146749406753971190250938 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.939
y[1] (analytic) = 44.749344004636346924634432238137
y[1] (numeric) = 61.13550597107981986870447152285
absolute error = 16.386161966443472944070039284713
relative error = 36.617658495163082749450822739504 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.94
y[1] (analytic) = 44.752385641963663267736936843432
y[1] (numeric) = 61.15644547107981986870447152285
absolute error = 16.404059829116156600967534679418
relative error = 36.655162833898864821877909271247 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.941
y[1] (analytic) = 44.755427327046471510557580631557
y[1] (numeric) = 61.17738597107981986870447152285
absolute error = 16.421958644033348358146890891293
relative error = 36.692664163457282863910553842277 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.942
y[1] (analytic) = 44.758469059882491174994266326502
y[1] (numeric) = 61.19832747107981986870447152285
absolute error = 16.439858411197328693710205196348
relative error = 36.730162484338756952265266926121 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.943
y[1] (analytic) = 44.761510840469442000734802554014
y[1] (numeric) = 61.21926997107981986870447152285
absolute error = 16.457759130610377867969668968836
relative error = 36.767657797043597377339781223283 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.944
y[1] (analytic) = 44.764552668805043945225706318862
y[1] (numeric) = 61.24021347107981986870447152285
absolute error = 16.475660802274775923478765203988
relative error = 36.80515010207200467282641507705 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.945
y[1] (analytic) = 44.767594544887017183641011440374
y[1] (numeric) = 61.26115797107981986870447152285
absolute error = 16.493563426192802685063460082476
relative error = 36.842639399924069645315987032408 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.946
y[1] (analytic) = 44.770636468713082108851082944824
y[1] (numeric) = 61.28210347107981986870447152285
absolute error = 16.511467002366737759853388578026
relative error = 36.880125691099773403892285013445 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.947
y[1] (analytic) = 44.77367844028095933139143741324
y[1] (numeric) = 61.30304997107981986870447152285
absolute error = 16.52937153079886053731303410961
relative error = 36.917608976098987389717093593206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.948
y[1] (analytic) = 44.776720459588369679431569283249
y[1] (numeric) = 61.32399747107981986870447152285
absolute error = 16.547277011491450189272902239601
relative error = 36.955089255421473405605782828383 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.949
y[1] (analytic) = 44.779762526633034198743783103478
y[1] (numeric) = 61.34494597107981986870447152285
absolute error = 16.565183444446785669960688419372
relative error = 36.99256652956688364559346213006 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.95
y[1] (analytic) = 44.782804641412674152672031739126
y[1] (numeric) = 61.36589547107981986870447152285
absolute error = 16.583090829667145716032439783724
relative error = 37.030040799034760724491702640027 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.951
y[1] (analytic) = 44.785846803925011022100760527303
y[1] (numeric) = 61.38684597107981986870447152285
absolute error = 16.600999167154808846603710995547
relative error = 37.067512064324537707435831580761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.952
y[1] (analytic) = 44.788889014167766505423757380679
y[1] (numeric) = 61.40779747107981986870447152285
absolute error = 16.618908456912053363280714142171
relative error = 37.104980325935538139422802045909 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.953
y[1] (analytic) = 44.79193127213866251851300883803
y[1] (numeric) = 61.42874997107981986870447152285
absolute error = 16.63681869894115735019146268482
relative error = 37.142445584366976074839641696541 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.954
y[1] (analytic) = 44.794973577835421194687562060297
y[1] (numeric) = 61.44970347107981986870447152285
absolute error = 16.654729893244398674016909462553
relative error = 37.17990784011795610698248382689 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.955
y[1] (analytic) = 44.798015931255764884682392770687
y[1] (numeric) = 61.47065797107981986870447152285
absolute error = 16.672642039824054984022078752163
relative error = 37.21736709368747339756618426213 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.956
y[1] (analytic) = 44.801058332397416156617279137455
y[1] (numeric) = 61.49161347107981986870447152285
absolute error = 16.690555138682403712087192385395
relative error = 37.254823345574413706224527548994 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.957
y[1] (analytic) = 44.804100781258097795965681597874
y[1] (numeric) = 61.51256997107981986870447152285
absolute error = 16.708469189821722072738789924976
relative error = 37.292276596277553420001025898952 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.958
y[1] (analytic) = 44.807143277835532805523628622077
y[1] (numeric) = 61.53352747107981986870447152285
absolute error = 16.726384193244287063180842900773
relative error = 37.329726846295559582830314341733 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.959
y[1] (analytic) = 44.810185822127444405378608415242
y[1] (numeric) = 61.55448597107981986870447152285
absolute error = 16.744300148952375463325863107608
relative error = 37.367174096126989925010145546161 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=3.7MB, time=3.15
x[1] = 20.96
y[1] (analytic) = 44.813228414131556032878466556798
y[1] (numeric) = 61.57544547107981986870447152285
absolute error = 16.762217056948263835826004966052
relative error = 37.404618346270292892663987763231 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.961
y[1] (analytic) = 44.816271053845591342600309575175
y[1] (numeric) = 61.59640597107981986870447152285
absolute error = 16.780134917234228526104161947675
relative error = 37.442059597223807677194229345356 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.962
y[1] (analytic) = 44.819313741267274206319414456706
y[1] (numeric) = 61.61736747107981986870447152285
absolute error = 16.798053729812545662385057066144
relative error = 37.479497849485764244725993294061 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.963
y[1] (analytic) = 44.822356476394328712978144087278
y[1] (numeric) = 61.63832997107981986870447152285
absolute error = 16.815973494685491155726327435572
relative error = 37.516933103554283365541565286969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.964
y[1] (analytic) = 44.825399259224479168654868625279
y[1] (numeric) = 61.65929347107981986870447152285
absolute error = 16.833894211855340700049602897571
relative error = 37.55436535992737664350543863365 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.965
y[1] (analytic) = 44.828442089755450096532892804459
y[1] (numeric) = 61.68025797107981986870447152285
absolute error = 16.851815881324369772171578718391
relative error = 37.59179461910294654547997960827 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.966
y[1] (analytic) = 44.831484967984966236869389165294
y[1] (numeric) = 61.70122347107981986870447152285
absolute error = 16.869738503094853631835082357556
relative error = 37.629220881578786430731716605611 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.967
y[1] (analytic) = 44.834527893910752546964337213396
y[1] (numeric) = 61.72218997107981986870447152285
absolute error = 16.887662077169067321740134309454
relative error = 37.666644147852580580328256565761 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.968
y[1] (analytic) = 44.837570867530534201129468503616
y[1] (numeric) = 61.74315747107981986870447152285
absolute error = 16.905586603549285667575003019234
relative error = 37.704064418421904226525832111002 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.969
y[1] (analytic) = 44.840613888842036590657217648384
y[1] (numeric) = 61.76412597107981986870447152285
absolute error = 16.923512082237783278047253874466
relative error = 37.741481693784223582147482837342 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.97
y[1] (analytic) = 44.843656957842985323789679248875
y[1] (numeric) = 61.78509547107981986870447152285
absolute error = 16.941438513236834544914792273975
relative error = 37.778895974436895869951874201539 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.971
y[1] (analytic) = 44.846700074531106225687570747618
y[1] (numeric) = 61.80606597107981986870447152285
absolute error = 16.959365896548713643016900775232
relative error = 37.816307260877169351992757442956 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.972
y[1] (analytic) = 44.849743238904125338399201201113
y[1] (numeric) = 61.82703747107981986870447152285
absolute error = 16.977294232175694530305270321737
relative error = 37.853715553602183358969073978339 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.973
y[1] (analytic) = 44.852786450959768920829445971037
y[1] (numeric) = 61.84800997107981986870447152285
absolute error = 16.995223520120050947875025551813
relative error = 37.891120853108968319565707706109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.974
y[1] (analytic) = 44.855829710695763448708727332654
y[1] (numeric) = 61.86898347107981986870447152285
absolute error = 17.013153760384056419995744190196
relative error = 37.928523159894445789784888655228 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.975
y[1] (analytic) = 44.858873018109835614562000999007
y[1] (numeric) = 61.88995797107981986870447152285
absolute error = 17.031084952969984254142470523843
relative error = 37.965922474455428482268251412416 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.976
y[1] (analytic) = 44.861916373199712327677748559467
y[1] (numeric) = 61.91093347107981986870447152285
absolute error = 17.049017097880107541026722963383
relative error = 38.003318797288620295609551760033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.977
y[1] (analytic) = 44.864959775963120714076975831246
y[1] (numeric) = 61.93190997107981986870447152285
absolute error = 17.066950195116699154627495691604
relative error = 38.04071212889061634365804495547 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.978
y[1] (analytic) = 44.868003226397788116482217122471
y[1] (numeric) = 61.95288747107981986870447152285
absolute error = 17.084884244682031752222254400379
relative error = 38.078102469757902984812529081442 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.979
y[1] (analytic) = 44.871046724501442094286545405383
y[1] (numeric) = 61.97386597107981986870447152285
absolute error = 17.102819246578377774417926117467
relative error = 38.115489820386857851306056895311 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.98
y[1] (analytic) = 44.874090270271810423522588398286
y[1] (numeric) = 61.99484547107981986870447152285
absolute error = 17.120755200808009445181883124564
relative error = 38.152874181273749878481319603913 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.981
y[1] (analytic) = 44.877133863706621096831550554802
y[1] (numeric) = 62.01582597107981986870447152285
absolute error = 17.138692107373198771872920968048
relative error = 38.190255552914739334056705989173 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.982
y[1] (analytic) = 44.880177504803602323432240959057
y[1] (numeric) = 62.03680747107981986870447152285
absolute error = 17.156629966276217545272230563793
relative error = 38.227633935805877847383040308155 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.983
y[1] (analytic) = 44.883221193560482529090107125378
y[1] (numeric) = 62.05778997107981986870447152285
absolute error = 17.174568777519337339614364397472
relative error = 38.265009330443108438691002389917 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.984
y[1] (analytic) = 44.886264929974990356086274701077
y[1] (numeric) = 62.07877347107981986870447152285
absolute error = 17.192508541104829512618196821773
relative error = 38.302381737322265548329233350114 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.985
y[1] (analytic) = 44.889308714044854663186593070952
y[1] (numeric) = 62.09975797107981986870447152285
absolute error = 17.210449257034965205517878451898
relative error = 38.339751156939075065993130342735 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.986
y[1] (analytic) = 44.892352545767804525610686862054
y[1] (numeric) = 62.12074347107981986870447152285
absolute error = 17.228390925312015343093784660796
relative error = 38.377117589789154359944333767161 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.987
y[1] (analytic) = 44.89539642514156923500101334736
y[1] (numeric) = 62.14172997107981986870447152285
absolute error = 17.24633354593825063370345817549
relative error = 38.414481036368012306220910347054 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.988
y[1] (analytic) = 44.898440352163878299391925746916
y[1] (numeric) = 62.16271747107981986870447152285
absolute error = 17.264277118915941569312545775934
relative error = 38.451841497171049317838235496401 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.989
y[1] (analytic) = 44.901484326832461443178742425048
y[1] (numeric) = 62.18370597107981986870447152285
absolute error = 17.282221644247358425525729097802
relative error = 38.489198972693557373980578386488 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.99
y[1] (analytic) = 44.90452834914504860708682198225
y[1] (numeric) = 62.20469547107981986870447152285
absolute error = 17.3001671219347712616176495406
relative error = 38.526553463430720049183393126188 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.991
y[1] (analytic) = 44.907572419099369948140644240336
y[1] (numeric) = 62.22568597107981986870447152285
absolute error = 17.318113551980449920563827282514
relative error = 38.563904969877612542506319466518 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.992
y[1] (analytic) = 44.910616536693155839632897119449
y[1] (numeric) = 62.24667747107981986870447152285
absolute error = 17.336060934386664029071574403401
relative error = 38.601253492529201706696896439074 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.993
y[1] (analytic) = 44.913660701924136871093569405533
y[1] (numeric) = 62.26766997107981986870447152285
absolute error = 17.354009269155682997610902117317
relative error = 38.638599031880346077344992336418 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.994
y[1] (analytic) = 44.916704914790043848259049406854
y[1] (numeric) = 62.28866347107981986870447152285
absolute error = 17.371958556289776020445422115996
relative error = 38.675941588425795902027954441206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.995
y[1] (analytic) = 44.919749175288607793041229498185
y[1] (numeric) = 62.30965797107981986870447152285
absolute error = 17.389908795791212075663242024665
relative error = 38.71328116266019316944648190929 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.996
y[1] (analytic) = 44.922793483417559943496616551223
y[1] (numeric) = 62.33065347107981986870447152285
absolute error = 17.407859987662259925207854971627
relative error = 38.750617755078071638551225210802 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.997
y[1] (analytic) = 44.925837839174631753795448249871
y[1] (numeric) = 62.35164997107981986870447152285
absolute error = 17.425812131905188114909023272979
relative error = 38.787951366173856867660115531586 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.998
y[1] (analytic) = 44.92888224255755489419081528896
y[1] (numeric) = 62.37264747107981986870447152285
absolute error = 17.44376522852226497451365623389
relative error = 38.825281996441866243566427536128 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 20.999
y[1] (analytic) = 44.931926693564061250987789455017
y[1] (numeric) = 62.39364597107981986870447152285
absolute error = 17.461719277515758617716682067833
relative error = 38.862609646376309010637578891619 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 21
y[1] (analytic) = 44.93497119219188292651255758768
y[1] (numeric) = 62.41464547107981986870447152285
absolute error = 17.47967427888793694219191393517
relative error = 38.899934316471286299904669951404 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = log ( x ) ;
Iterations = 1000
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Expected Time Remaining = 29 Seconds
Optimized Time Remaining = 29 Seconds
Time to Timeout = 14 Minutes 56 Seconds
Percent Done = 10.01 %
> quit
memory used=55.6MB, alloc=3.7MB, time=3.29