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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_max_minutes,
> glob_start,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> glob_html_log,
> days_in_year,
> glob_optimal_expect_sec,
> glob_initial_pass,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> glob_warned2,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug,
> glob_log10relerr,
> glob_log10abserr,
> glob_subiter_method,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_relerr,
> glob_h,
> glob_disp_incr,
> glob_clock_sec,
> glob_warned,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> min_in_hour,
> glob_percent_done,
> glob_normmax,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_last_rel_error,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_y,
> array_x,
> array_pole,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher_work,
> array_poles,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt,
glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass,
glob_clock_start_sec, centuries_in_millinium, glob_display_flag,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2,
glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter,
glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug,
glob_log10relerr, glob_log10abserr, glob_subiter_method,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr,
glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start,
glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour,
glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED,
glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2,
array_const_1, array_const_0D0, array_type_pole, array_last_rel_error,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error,
array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole,
array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial,
array_y_higher, array_complex_pole, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_max_minutes,
> glob_start,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> glob_html_log,
> days_in_year,
> glob_optimal_expect_sec,
> glob_initial_pass,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> glob_warned2,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug,
> glob_log10relerr,
> glob_log10abserr,
> glob_subiter_method,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_relerr,
> glob_h,
> glob_disp_incr,
> glob_clock_sec,
> glob_warned,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> min_in_hour,
> glob_percent_done,
> glob_normmax,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_last_rel_error,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_y,
> array_x,
> array_pole,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher_work,
> array_poles,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt,
glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass,
glob_clock_start_sec, centuries_in_millinium, glob_display_flag,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2,
glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter,
glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug,
glob_log10relerr, glob_log10abserr, glob_subiter_method,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr,
glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start,
glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour,
glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED,
glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2,
array_const_1, array_const_0D0, array_type_pole, array_last_rel_error,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error,
array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole,
array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial,
array_y_higher, array_complex_pole, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_max_minutes,
> glob_start,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> glob_html_log,
> days_in_year,
> glob_optimal_expect_sec,
> glob_initial_pass,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> glob_warned2,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug,
> glob_log10relerr,
> glob_log10abserr,
> glob_subiter_method,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_relerr,
> glob_h,
> glob_disp_incr,
> glob_clock_sec,
> glob_warned,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> min_in_hour,
> glob_percent_done,
> glob_normmax,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_last_rel_error,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_y,
> array_x,
> array_pole,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher_work,
> array_poles,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt,
glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass,
glob_clock_start_sec, centuries_in_millinium, glob_display_flag,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2,
glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter,
glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug,
glob_log10relerr, glob_log10abserr, glob_subiter_method,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr,
glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start,
glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour,
glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED,
glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2,
array_const_1, array_const_0D0, array_type_pole, array_last_rel_error,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error,
array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole,
array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial,
array_y_higher, array_complex_pole, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_max_minutes,
> glob_start,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> glob_html_log,
> days_in_year,
> glob_optimal_expect_sec,
> glob_initial_pass,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> glob_warned2,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug,
> glob_log10relerr,
> glob_log10abserr,
> glob_subiter_method,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_relerr,
> glob_h,
> glob_disp_incr,
> glob_clock_sec,
> glob_warned,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> min_in_hour,
> glob_percent_done,
> glob_normmax,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_last_rel_error,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_y,
> array_x,
> array_pole,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher_work,
> array_poles,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt,
glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass,
glob_clock_start_sec, centuries_in_millinium, glob_display_flag,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2,
glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter,
glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug,
glob_log10relerr, glob_log10abserr, glob_subiter_method,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr,
glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start,
glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour,
glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED,
glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2,
array_const_1, array_const_0D0, array_type_pole, array_last_rel_error,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error,
array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole,
array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial,
array_y_higher, array_complex_pole, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_max_minutes,
> glob_start,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> glob_html_log,
> days_in_year,
> glob_optimal_expect_sec,
> glob_initial_pass,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> glob_warned2,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug,
> glob_log10relerr,
> glob_log10abserr,
> glob_subiter_method,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_relerr,
> glob_h,
> glob_disp_incr,
> glob_clock_sec,
> glob_warned,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> min_in_hour,
> glob_percent_done,
> glob_normmax,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_last_rel_error,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_y,
> array_x,
> array_pole,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher_work,
> array_poles,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt,
glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass,
glob_clock_start_sec, centuries_in_millinium, glob_display_flag,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2,
glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter,
glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug,
glob_log10relerr, glob_log10abserr, glob_subiter_method,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr,
glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start,
glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour,
glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED,
glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2,
array_const_1, array_const_0D0, array_type_pole, array_last_rel_error,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error,
array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole,
array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial,
array_y_higher, array_complex_pole, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_max_minutes,
> glob_start,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> glob_html_log,
> days_in_year,
> glob_optimal_expect_sec,
> glob_initial_pass,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> glob_warned2,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug,
> glob_log10relerr,
> glob_log10abserr,
> glob_subiter_method,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_relerr,
> glob_h,
> glob_disp_incr,
> glob_clock_sec,
> glob_warned,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> min_in_hour,
> glob_percent_done,
> glob_normmax,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_last_rel_error,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_y,
> array_x,
> array_pole,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher_work,
> array_poles,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre exp $eq_no = 1 i = 1
> array_tmp1[1] := exp(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre exp $eq_no = 1 i = 2
> array_tmp1[2] := att(1,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre exp $eq_no = 1 i = 3
> array_tmp1[3] := att(2,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre exp $eq_no = 1 i = 4
> array_tmp1[4] := att(3,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre exp $eq_no = 1 i = 5
> array_tmp1[5] := att(4,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit exp $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt,
glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass,
glob_clock_start_sec, centuries_in_millinium, glob_display_flag,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2,
glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter,
glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug,
glob_log10relerr, glob_log10abserr, glob_subiter_method,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr,
glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start,
glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour,
glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED,
glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2,
array_const_1, array_const_0D0, array_type_pole, array_last_rel_error,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error,
array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole,
array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial,
array_y_higher, array_complex_pole, glob_last;
array_tmp1[1] := exp(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 1.0 + exp(x)
> end;
exact_soln_y := proc(x) 1.0 + exp(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
> DEBUGMASSIVE,
> INFO,
> glob_max_terms,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_curr_iter_when_opt,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_max_minutes,
> glob_start,
> glob_last_good_h,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> glob_html_log,
> days_in_year,
> glob_optimal_expect_sec,
> glob_initial_pass,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_max_sec,
> glob_warned2,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug,
> glob_log10relerr,
> glob_log10abserr,
> glob_subiter_method,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_relerr,
> glob_h,
> glob_disp_incr,
> glob_clock_sec,
> glob_warned,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_look_poles,
> min_in_hour,
> glob_percent_done,
> glob_normmax,
> glob_iter,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_last_rel_error,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_y,
> array_x,
> array_pole,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher_work,
> array_poles,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> INFO := 2;
> glob_max_terms := 30;
> DEBUGL := 3;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_log10_abserr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_dump := false;
> glob_curr_iter_when_opt := 0;
> glob_max_hours := 0.0;
> glob_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_max_minutes := 0.0;
> glob_start := 0;
> glob_last_good_h := 0.1;
> glob_hmax := 1.0;
> glob_reached_optimal_h := false;
> years_in_century := 100.0;
> glob_html_log := true;
> days_in_year := 365.0;
> glob_optimal_expect_sec := 0.1;
> glob_initial_pass := true;
> glob_clock_start_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_display_flag := true;
> glob_max_opt_iter := 10;
> glob_log10normmin := 0.1;
> glob_max_sec := 10000.0;
> glob_warned2 := false;
> glob_smallish_float := 0.1e-100;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_iter := 1000;
> glob_not_yet_start_msg := true;
> glob_not_yet_finished := true;
> hours_in_day := 24.0;
> djd_debug := true;
> glob_log10relerr := 0.0;
> glob_log10abserr := 0.0;
> glob_subiter_method := 3;
> glob_orig_start_sec := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_small_float := 0.1e-50;
> glob_relerr := 0.1e-10;
> glob_h := 0.1;
> glob_disp_incr := 0.1;
> glob_clock_sec := 0.0;
> glob_warned := false;
> glob_optimal_start := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_look_poles := false;
> min_in_hour := 60.0;
> glob_percent_done := 0.0;
> glob_normmax := 0.0;
> glob_iter := 0;
> MAX_UNCHANGED := 10;
> glob_current_iter := 0;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_dump_analytic := false;
> glob_hmin := 0.00000000001;
> glob_optimal_done := false;
> glob_almost_1 := 0.9990;
> sec_in_min := 60.0;
> djd_debug2 := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/exppostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = exp ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 1.0;");
> omniout_str(ALWAYS,"x_end := 10.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"1.0 + exp(x)");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> max_terms := 30;
> Digits := 32;
> #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_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 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_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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 1.0;
> x_end := 10.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = exp ( 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,"2012-06-13T13:42:15-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"exp")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = exp ( 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,"exp diffeq.mxt")
> ;
> logitem_str(html_log_file,"exp 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 DEBUGMASSIVE, INFO, glob_max_terms, DEBUGL, ALWAYS, glob_iolevel,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_curr_iter_when_opt,
glob_max_hours, glob_abserr, glob_large_float, glob_max_minutes, glob_start,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
glob_html_log, days_in_year, glob_optimal_expect_sec, glob_initial_pass,
glob_clock_start_sec, centuries_in_millinium, glob_display_flag,
glob_max_opt_iter, glob_log10normmin, glob_max_sec, glob_warned2,
glob_smallish_float, glob_optimal_clock_start_sec, glob_max_iter,
glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day, djd_debug,
glob_log10relerr, glob_log10abserr, glob_subiter_method,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_small_float, glob_relerr,
glob_h, glob_disp_incr, glob_clock_sec, glob_warned, glob_optimal_start,
glob_max_rel_trunc_err, glob_log10_relerr, glob_look_poles, min_in_hour,
glob_percent_done, glob_normmax, glob_iter, MAX_UNCHANGED,
glob_current_iter, glob_no_eqs, glob_max_trunc_err, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_almost_1, sec_in_min, djd_debug2,
array_const_1, array_const_0D0, array_type_pole, array_last_rel_error,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_1st_rel_error,
array_norms, array_y_init, array_y, array_x, array_pole, array_real_pole,
array_y_higher_work2, array_y_higher_work, array_poles, array_y_set_initial,
array_y_higher, array_complex_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
INFO := 2;
glob_max_terms := 30;
DEBUGL := 3;
ALWAYS := 1;
glob_iolevel := 5;
glob_log10_abserr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_dump := false;
glob_curr_iter_when_opt := 0;
glob_max_hours := 0.;
glob_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_max_minutes := 0.;
glob_start := 0;
glob_last_good_h := 0.1;
glob_hmax := 1.0;
glob_reached_optimal_h := false;
years_in_century := 100.0;
glob_html_log := true;
days_in_year := 365.0;
glob_optimal_expect_sec := 0.1;
glob_initial_pass := true;
glob_clock_start_sec := 0.;
centuries_in_millinium := 10.0;
glob_display_flag := true;
glob_max_opt_iter := 10;
glob_log10normmin := 0.1;
glob_max_sec := 10000.0;
glob_warned2 := false;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_clock_start_sec := 0.;
glob_max_iter := 1000;
glob_not_yet_start_msg := true;
glob_not_yet_finished := true;
hours_in_day := 24.0;
djd_debug := true;
glob_log10relerr := 0.;
glob_log10abserr := 0.;
glob_subiter_method := 3;
glob_orig_start_sec := 0.;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1*10^(-50);
glob_relerr := 0.1*10^(-10);
glob_h := 0.1;
glob_disp_incr := 0.1;
glob_clock_sec := 0.;
glob_warned := false;
glob_optimal_start := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_look_poles := false;
min_in_hour := 60.0;
glob_percent_done := 0.;
glob_normmax := 0.;
glob_iter := 0;
MAX_UNCHANGED := 10;
glob_current_iter := 0;
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_dump_analytic := false;
glob_hmin := 0.1*10^(-10);
glob_optimal_done := false;
glob_almost_1 := 0.9990;
sec_in_min := 60.0;
djd_debug2 := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/exppostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 1.0;");
omniout_str(ALWAYS, "x_end := 10.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "1.0 +\texp(x)");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
max_terms := 30;
Digits := 32;
glob_max_terms := max_terms;
glob_html_log := true;
array_type_pole := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
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_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[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;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 1.0;
x_end := 10.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = exp ( 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, "2012-06-13T13:42:15-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "exp");
logitem_str(html_log_file, "diff ( y , x , 1 ) = exp ( 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,
"exp diffeq.mxt");
logitem_str(html_log_file,
"exp 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/exppostode.ode#################
diff ( y , x , 1 ) = exp ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
max_terms := 30;
Digits := 32;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 1.0;
x_end := 10.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
1.0 + exp(x)
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 1
y[1] (analytic) = 3.7182818284590452353602874713527
y[1] (numeric) = 3.7182818284590452353602874713527
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0001
y[1] (analytic) = 3.718553670233753340476860330281
y[1] (numeric) = 3.7185536702337533404768604624223
absolute error = 1.321413e-25
relative error = 3.5535671048064614376381461241884e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0002
y[1] (analytic) = 3.718825539193998170585580520144
y[1] (numeric) = 3.7188255391939981705855807844399
absolute error = 2.642959e-25
relative error = 7.1069722742971784190449233196766e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0003
y[1] (analytic) = 3.7190974353424984152911619166985
y[1] (numeric) = 3.7190974353424984152911623131621
absolute error = 3.964636e-25
relative error = 1.0660210088405197950413569259573e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0004
y[1] (analytic) = 3.7193693586819730360808727682385
y[1] (numeric) = 3.719369358681973036080873296883
absolute error = 5.286445e-25
relative error = 1.4213283194528840904418162446224e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0005
y[1] (analytic) = 3.7196413092151412663517253104907
y[1] (numeric) = 3.7196413092151412663517259713294
absolute error = 6.608387e-25
relative error = 1.7766194239289151434980099269341e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0006
y[1] (analytic) = 3.7199132869447226114376681006077
y[1] (numeric) = 3.7199132869447226114376688936537
absolute error = 7.930460e-25
relative error = 2.1318937803825870527265940894989e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0007
y[1] (analytic) = 3.7201852918734368486367810705293
y[1] (numeric) = 3.7201852918734368486367819957959
absolute error = 9.252666e-25
relative error = 2.4871519223012889071992866085730e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0008
y[1] (analytic) = 3.7204573240040040272384732999867
y[1] (numeric) = 3.7204573240040040272384743574872
absolute error = 1.0575005e-24
relative error = 2.8423938454477536099861357601398e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0009
y[1] (analytic) = 3.7207293833391444685506835094191
y[1] (numeric) = 3.7207293833391444685506846991666
absolute error = 1.1897475e-24
relative error = 3.1976190080566107112888830564260e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.001
y[1] (analytic) = 3.7210014698815787659270832730755
y[1] (numeric) = 3.7210014698815787659270845950832
absolute error = 1.3220077e-24
relative error = 3.5528276747551863336654151816023e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0011
y[1] (analytic) = 3.7212735836340277847942829525741
y[1] (numeric) = 3.7212735836340277847942844068554
absolute error = 1.4542813e-24
relative error = 3.9080203788183037485333193709641e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0012
y[1] (analytic) = 3.7215457245992126626790403511916
y[1] (numeric) = 3.7215457245992126626790419377596
absolute error = 1.5865680e-24
relative error = 4.2631963098367238514840500710621e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0013
y[1] (analytic) = 3.7218178927798548092354720891528
y[1] (numeric) = 3.7218178927798548092354738080207
absolute error = 1.7188679e-24
relative error = 4.6183557323815329413065357578692e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0014
y[1] (analytic) = 3.7220900881786759062722677001948
y[1] (numeric) = 3.7220900881786759062722695513758
absolute error = 1.8511810e-24
relative error = 4.9734986422798683272350584717538e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0015
y[1] (analytic) = 3.7223623107983979077799064496764
y[1] (numeric) = 3.7223623107983979077799084331839
absolute error = 1.9835075e-24
relative error = 5.3286255726529845751235728651829e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0016
y[1] (analytic) = 3.7226345606417430399578768745059
y[1] (numeric) = 3.722634560641743039957878990353
absolute error = 2.1158471e-24
relative error = 5.6837357133310722191892415838760e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0017
y[1] (analytic) = 3.7229068377114338012418990451582
y[1] (numeric) = 3.7229068377114338012419012933582
absolute error = 2.2482000e-24
relative error = 6.0388295974175548525704732948227e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0018
y[1] (analytic) = 3.723179142010192962331149550055
y[1] (numeric) = 3.7231791420101929623311519306212
absolute error = 2.3805662e-24
relative error = 6.3939072206842598240336565106360e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.18
x[1] = 1.0019
y[1] (analytic) = 3.7234514735407435662154892025794
y[1] (numeric) = 3.7234514735407435662154917155249
absolute error = 2.5129455e-24
relative error = 6.7489680417678801726174852687932e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.002
y[1] (analytic) = 3.7237238323058089282026934709967
y[1] (numeric) = 3.7237238323058089282026961163348
absolute error = 2.6453381e-24
relative error = 7.1040125936566848824237437771029e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0021
y[1] (analytic) = 3.7239962183081126359456856315552
y[1] (numeric) = 3.7239962183081126359456884092991
absolute error = 2.7777439e-24
relative error = 7.4590406035964925187794556157825e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0022
y[1] (analytic) = 3.7242686315503785494697726450381
y[1] (numeric) = 3.7242686315503785494697755552011
absolute error = 2.9101630e-24
relative error = 7.8140523359307894162131731368020e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0023
y[1] (analytic) = 3.7245410720353308011998837570394
y[1] (numeric) = 3.7245410720353308011998867996347
absolute error = 3.0425953e-24
relative error = 8.1690475179464958807013602764940e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0024
y[1] (analytic) = 3.7248135397656937959878118222354
y[1] (numeric) = 3.7248135397656937959878149972763
absolute error = 3.1750409e-24
relative error = 8.5240264139496314953666548237691e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0025
y[1] (analytic) = 3.7250860347441922111394573529259
y[1] (numeric) = 3.7250860347441922111394606604256
absolute error = 3.3074997e-24
relative error = 8.8789887512682145285751910523650e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0026
y[1] (analytic) = 3.7253585569735509964420752921156
y[1] (numeric) = 3.7253585569735509964420787320874
absolute error = 3.4399718e-24
relative error = 9.2339347941708013085154069584456e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0027
y[1] (analytic) = 3.7256311064564953741915245114094
y[1] (numeric) = 3.7256311064564953741915280838665
absolute error = 3.5724571e-24
relative error = 9.5888642700265042872396801894202e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0028
y[1] (analytic) = 3.7259036831957508392195200339938
y[1] (numeric) = 3.7259036831957508392195237389494
absolute error = 3.7049556e-24
relative error = 9.9437771746751557863728680822559e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0029
y[1] (analytic) = 3.7261762871940431589208879829766
y[1] (numeric) = 3.726176287194043158920891820444
absolute error = 3.8374674e-24
relative error = 1.0298673772329122443508685006067e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.003
y[1] (analytic) = 3.726448918454098373280823255358
y[1] (numeric) = 3.7264489184540983732808272253505
absolute error = 3.9699925e-24
relative error = 1.0653554058771144124469845031648e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0031
y[1] (analytic) = 3.7267215769786427949021499219052
y[1] (numeric) = 3.7267215769786427949021540244361
absolute error = 4.1025309e-24
relative error = 1.1008418029784871434109011296561e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0032
y[1] (analytic) = 3.7269942627704030090325843532036
y[1] (numeric) = 3.726994262770403009032588588286
absolute error = 4.2350824e-24
relative error = 1.1363265144529408545738045228672e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0033
y[1] (analytic) = 3.7272669758321058735920010721561
y[1] (numeric) = 3.7272669758321058735920054398034
absolute error = 4.3676473e-24
relative error = 1.1718096203787308077525745412846e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0034
y[1] (analytic) = 3.7275397161664785191997013332053
y[1] (numeric) = 3.7275397161664785191997058334306
absolute error = 4.5002253e-24
relative error = 1.2072910398465656416478209120490e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0035
y[1] (analytic) = 3.7278124837762483492016844285486
y[1] (numeric) = 3.7278124837762483492016890613653
absolute error = 4.6328167e-24
relative error = 1.2427708529231032077593028924174e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0036
y[1] (analytic) = 3.7280852786641430396979217216215
y[1] (numeric) = 3.7280852786641430396979264870427
absolute error = 4.7654212e-24
relative error = 1.2782489787110121566774160994971e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0037
y[1] (analytic) = 3.7283581008328905395696334081194
y[1] (numeric) = 3.7283581008328905395696383061585
absolute error = 4.8980391e-24
relative error = 1.3137254972653540070993380015349e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0038
y[1] (analytic) = 3.7286309502852190705065680048332
y[1] (numeric) = 3.7286309502852190705065730355034
absolute error = 5.0306702e-24
relative error = 1.3492003545202515494210017822221e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0039
y[1] (analytic) = 3.728903827023857127034284566569
y[1] (numeric) = 3.7289038270238571270342897298836
absolute error = 5.1633146e-24
relative error = 1.3846735768782179606949136682991e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.004
y[1] (analytic) = 3.7291767310515334765414376314268
y[1] (numeric) = 3.729176731051533476541442927399
absolute error = 5.2959722e-24
relative error = 1.4201451371028666283640588053859e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0041
y[1] (analytic) = 3.7294496623709771593070648947095
y[1] (numeric) = 3.7294496623709771593070703233526
absolute error = 5.4286431e-24
relative error = 1.4556150615929670267274042623660e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0042
y[1] (analytic) = 3.729722620984917488527877611736
y[1] (numeric) = 3.7297226209849174885278831730634
absolute error = 5.5613274e-24
relative error = 1.4910833767395297362343892506607e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0043
y[1] (analytic) = 3.7299956068960840503455537298316
y[1] (numeric) = 3.7299956068960840503455594238564
absolute error = 5.6940248e-24
relative error = 1.5265500016870751486438168799525e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0044
y[1] (analytic) = 3.7302686201072067038740337497667
y[1] (numeric) = 3.7302686201072067038740395765022
absolute error = 5.8267355e-24
relative error = 1.5620149896423656271592068384080e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0045
y[1] (analytic) = 3.7305416606210155812268193169196
y[1] (numeric) = 3.7305416606210155812268252763791
absolute error = 5.9594595e-24
relative error = 1.5974783401850392578306532708378e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0046
y[1] (analytic) = 3.730814728440241087544274542434
y[1] (numeric) = 3.7308147284402410875442806346308
absolute error = 6.0921968e-24
relative error = 1.6329400528948251474842406005118e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0047
y[1] (analytic) = 3.7310878235676139010209300546455
y[1] (numeric) = 3.7310878235676139010209362795928
absolute error = 6.2249473e-24
relative error = 1.6684001005497084785353946949457e-22 %
h = 0.0001
memory used=7.6MB, alloc=3.9MB, time=0.38
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0048
y[1] (analytic) = 3.7313609460058649729327897810493
y[1] (numeric) = 3.7313609460058649729327961387605
absolute error = 6.3577112e-24
relative error = 1.7038585363352320715968309998599e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0049
y[1] (analytic) = 3.7316340957577255276646404610838
y[1] (numeric) = 3.731634095757725527664646951572
absolute error = 6.4904882e-24
relative error = 1.7393152794317783753975975398153e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.005
y[1] (analytic) = 3.7319072728259270627373638900002
y[1] (numeric) = 3.7319072728259270627373705132788
absolute error = 6.6232786e-24
relative error = 1.7747704098190596972541702690524e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0051
y[1] (analytic) = 3.7321804772132013488352518940949
y[1] (numeric) = 3.7321804772132013488352586501772
absolute error = 6.7560823e-24
relative error = 1.8102239002773867794301338185971e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0052
y[1] (analytic) = 3.7324537089222804298333240375749
y[1] (numeric) = 3.7324537089222804298333309264741
absolute error = 6.8888992e-24
relative error = 1.8456757235950076518162311725540e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0053
y[1] (analytic) = 3.7327269679558966228246480613306
y[1] (numeric) = 3.73272696795589662282465508306
absolute error = 7.0217294e-24
relative error = 1.8811259061482377366726227218959e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0054
y[1] (analytic) = 3.7330002543167825181476630538896
y[1] (numeric) = 3.7330002543167825181476702084624
absolute error = 7.1545728e-24
relative error = 1.9165744207294293767770884093140e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0055
y[1] (analytic) = 3.7332735680076709794135053548233
y[1] (numeric) = 3.7332735680076709794135126422529
absolute error = 7.2874296e-24
relative error = 1.9520213204972998337301976351345e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0056
y[1] (analytic) = 3.7335469090312951435333371908818
y[1] (numeric) = 3.7335469090312951435333446111814
absolute error = 7.4202996e-24
relative error = 1.9874665514582401484979996774692e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0057
y[1] (analytic) = 3.7338202773903884207456780451276
y[1] (numeric) = 3.7338202773903884207456855983106
absolute error = 7.5531830e-24
relative error = 2.0229101667633048998750448393740e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0058
y[1] (analytic) = 3.7340936730876844946437387593441
y[1] (numeric) = 3.7340936730876844946437464454237
absolute error = 7.6860796e-24
relative error = 2.0583521124269113736352093192583e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0059
y[1] (analytic) = 3.73436709612591732220275836999
y[1] (numeric) = 3.7343670961259173222027661889796
absolute error = 7.8189896e-24
relative error = 2.0937924415924521798823987558885e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.006
y[1] (analytic) = 3.7346405465078211338073436779749
y[1] (numeric) = 3.7346405465078211338073516298878
absolute error = 7.9519129e-24
relative error = 2.1292311270587087539533070430260e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0061
y[1] (analytic) = 3.734914024236130433278811552528
y[1] (numeric) = 3.7349140242361304332788196373774
absolute error = 8.0848494e-24
relative error = 2.1646681416323965088979254105180e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0062
y[1] (analytic) = 3.735187529313579997902533969434
y[1] (numeric) = 3.7351875293135799979025421872332
absolute error = 8.2177992e-24
relative error = 2.2001035116729989342990825170014e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0063
y[1] (analytic) = 3.7354610617429048784552857839095
y[1] (numeric) = 3.7354610617429048784552941346719
absolute error = 8.3507624e-24
relative error = 2.2355372635322481978760246453028e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0064
y[1] (analytic) = 3.735734621526840399232595238394
y[1] (numeric) = 3.7357346215268403992326037221328
absolute error = 8.4837388e-24
relative error = 2.2709693432486358630338865470324e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0065
y[1] (analytic) = 3.7360082086681221580760972055273
y[1] (numeric) = 3.7360082086681221580761058222558
absolute error = 8.6167285e-24
relative error = 2.3063997771760364407333541943489e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0066
y[1] (analytic) = 3.7362818231694860264008891665893
y[1] (numeric) = 3.7362818231694860264008979163208
absolute error = 8.7497315e-24
relative error = 2.3418285648959978846926720478127e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0067
y[1] (analytic) = 3.7365554650336681492228899256734
y[1] (numeric) = 3.7365554650336681492228988084212
absolute error = 8.8827478e-24
relative error = 2.3772557059901590943330896824954e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0068
y[1] (analytic) = 3.7368291342634049451862010598685
y[1] (numeric) = 3.7368291342634049451862100756459
absolute error = 9.0157774e-24
relative error = 2.4126812000402499111835548480248e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0069
y[1] (analytic) = 3.7371028308614331065904711057229
y[1] (numeric) = 3.7371028308614331065904802545432
absolute error = 9.1488203e-24
relative error = 2.4481050466280911152833740327938e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.007
y[1] (analytic) = 3.7373765548304895994182624822638
y[1] (numeric) = 3.7373765548304895994182717641402
absolute error = 9.2818764e-24
relative error = 2.4835272185788578356608625385441e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0071
y[1] (analytic) = 3.7376503061733116633624211508451
y[1] (numeric) = 3.7376503061733116633624305657911
absolute error = 9.4149460e-24
relative error = 2.5189477957447624763418332834887e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0072
y[1] (analytic) = 3.7379240848926368118534490120995
y[1] (numeric) = 3.7379240848926368118534585601283
absolute error = 9.5480288e-24
relative error = 2.5543666974376888535263783104991e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0073
y[1] (analytic) = 3.7381978909912028320868790402657
y[1] (numeric) = 3.7381978909912028320868887213907
absolute error = 9.6811250e-24
relative error = 2.5897839767474157949820953349628e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0074
y[1] (analytic) = 3.7384717244717477850506531551669
y[1] (numeric) = 3.7384717244717477850506629694013
absolute error = 9.8142344e-24
relative error = 2.6251995797525437998834606064904e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0075
y[1] (analytic) = 3.7387455853370100055525028321126
y[1] (numeric) = 3.7387455853370100055525127794698
absolute error = 9.9473572e-24
relative error = 2.6606135595351954416358018807899e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0076
memory used=11.4MB, alloc=4.0MB, time=0.59
y[1] (analytic) = 3.7390194735897281022473324499995
y[1] (numeric) = 3.7390194735897281022473425304927
absolute error = 1.00804932e-23
relative error = 2.6960258621819907768866777225286e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0077
y[1] (analytic) = 3.7392933892326409576646053778824
y[1] (numeric) = 3.739293389232640957664615591525
absolute error = 1.02136426e-23
relative error = 2.7314365407673968391453693099351e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0078
y[1] (analytic) = 3.7395673322684877282357328002926
y[1] (numeric) = 3.7395673322684877282357431470979
absolute error = 1.03468053e-23
relative error = 2.7668455681271139949712358045975e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0079
y[1] (analytic) = 3.7398413027000078443214652815741
y[1] (numeric) = 3.7398413027000078443214757615554
absolute error = 1.04799813e-23
relative error = 2.8022529438438724846021208837401e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.008
y[1] (analytic) = 3.7401153005299410102392870695142
y[1] (numeric) = 3.7401153005299410102392976826849
absolute error = 1.06131707e-23
relative error = 2.8376586942376370816325930892346e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0081
y[1] (analytic) = 3.7403893257610272042908131385416
y[1] (numeric) = 3.7403893257610272042908238849149
absolute error = 1.07463733e-23
relative error = 2.8730627654150737572977471052409e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0082
y[1] (analytic) = 3.7406633783960066787891889727645
y[1] (numeric) = 3.7406633783960066787891998523538
absolute error = 1.08795893e-23
relative error = 2.9084652104315140948358054807711e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0083
y[1] (analytic) = 3.7409374584376199600864930891256
y[1] (numeric) = 3.7409374584376199600865041019442
absolute error = 1.10128186e-23
relative error = 2.9438660021329085469160528752466e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0084
y[1] (analytic) = 3.7412115658886078486011423009455
y[1] (numeric) = 3.7412115658886078486011534470067
absolute error = 1.11460612e-23
relative error = 2.9792651401024420850792457490399e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0085
y[1] (analytic) = 3.7414857007517114188452997221297
y[1] (numeric) = 3.7414857007517114188453110014469
absolute error = 1.12793172e-23
relative error = 3.0146626506507411378157610640158e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0086
y[1] (analytic) = 3.7417598630296720194522855123131
y[1] (numeric) = 3.7417598630296720194522969248996
absolute error = 1.14125865e-23
relative error = 3.0500585066299051817748007505478e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0087
y[1] (analytic) = 3.7420340527252312732039903632159
y[1] (numeric) = 3.742034052725231273204001909085
absolute error = 1.15458691e-23
relative error = 3.0854527076233920931833326697822e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0088
y[1] (analytic) = 3.7423082698411310770582917264857
y[1] (numeric) = 3.7423082698411310770583034056507
absolute error = 1.16791650e-23
relative error = 3.1208452532147506180846962296091e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0089
y[1] (analytic) = 3.7425825143801136021764727832987
y[1] (numeric) = 3.7425825143801136021764845957729
absolute error = 1.18124742e-23
relative error = 3.1562361429876203687006802499435e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.009
y[1] (analytic) = 3.7428567863449212939506441559956
y[1] (numeric) = 3.7428567863449212939506561017924
absolute error = 1.19457968e-23
relative error = 3.1916254032432916165837977174239e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0091
y[1] (analytic) = 3.7431310857382968720311683620257
y[1] (numeric) = 3.7431310857382968720311804411584
absolute error = 1.20791327e-23
relative error = 3.2270130068441101338141082459373e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0092
y[1] (analytic) = 3.7434054125629833303540870104731
y[1] (numeric) = 3.7434054125629833303540992229551
absolute error = 1.22124820e-23
relative error = 3.2623989800876325060050663457563e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0093
y[1] (analytic) = 3.7436797668217239371685507414401
y[1] (numeric) = 3.7436797668217239371685630872847
absolute error = 1.23458446e-23
relative error = 3.2977832958403025239454808291233e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0094
y[1] (analytic) = 3.7439541485172622350642519085617
y[1] (numeric) = 3.7439541485172622350642643877822
absolute error = 1.24792205e-23
relative error = 3.3331659536862146232022176627457e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0095
y[1] (analytic) = 3.744228557652342040998860004925
y[1] (numeric) = 3.7442285576523420409988726175348
absolute error = 1.26126098e-23
relative error = 3.3685469799173253802839862473522e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0096
y[1] (analytic) = 3.7445029942297074463254598326694
y[1] (numeric) = 3.7445029942297074463254725786818
absolute error = 1.27460124e-23
relative error = 3.4039263474062247661958648937348e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0097
y[1] (analytic) = 3.7447774582521028168199924165395
y[1] (numeric) = 3.7447774582521028168200052959679
absolute error = 1.28794284e-23
relative error = 3.4393040824411365469494048787607e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0098
y[1] (analytic) = 3.7450519497222727927086986616681
y[1] (numeric) = 3.7450519497222727927087116745258
absolute error = 1.30128577e-23
relative error = 3.4746801578987477640954265495812e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0099
y[1] (analytic) = 3.7453264686429622886955657558611
y[1] (numeric) = 3.7453264686429622886955789021615
absolute error = 1.31463004e-23
relative error = 3.5100546000635497233499756271357e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.01
y[1] (analytic) = 3.7456010150169164939897763166604
y[1] (numeric) = 3.7456010150169164939897895964168
absolute error = 1.32797564e-23
relative error = 3.5454273818163261574736399777247e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0101
y[1] (analytic) = 3.7458755888468808723331602834584
y[1] (numeric) = 3.7458755888468808723331736966841
absolute error = 1.34132257e-23
relative error = 3.5807985027418081564829438412732e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0102
y[1] (analytic) = 3.7461501901356011620276495549394
y[1] (numeric) = 3.7461501901356011620276631016478
absolute error = 1.35467084e-23
relative error = 3.6161679891188888554914798756537e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0103
y[1] (analytic) = 3.7464248188858233759627353721219
y[1] (numeric) = 3.7464248188858233759627490523262
absolute error = 1.36802043e-23
relative error = 3.6515357871423817376561034565408e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0104
y[1] (analytic) = 3.7466994751002938016429284472758
y[1] (numeric) = 3.7466994751002938016429422609895
absolute error = 1.38137137e-23
relative error = 3.6869019764736339266961443482778e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0105
y[1] (analytic) = 3.7469741587817590012152218389912
y[1] (numeric) = 3.7469741587817590012152357862276
absolute error = 1.39472364e-23
relative error = 3.7222665033095978603532745637155e-22 %
h = 0.0001
memory used=15.2MB, alloc=4.1MB, time=0.81
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0106
y[1] (analytic) = 3.7472488699329658114965565736706
y[1] (numeric) = 3.7472488699329658114965706544431
absolute error = 1.40807725e-23
relative error = 3.7576293939217038544648963682021e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0107
y[1] (analytic) = 3.7475236085566613440012900137215
y[1] (numeric) = 3.7475236085566613440013042280435
absolute error = 1.42143220e-23
relative error = 3.7929906478893591344019054331635e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0108
y[1] (analytic) = 3.7477983746555929849686669727228
y[1] (numeric) = 3.7477983746555929849686813206076
absolute error = 1.43478848e-23
relative error = 3.8283502381097304035204042408414e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0109
y[1] (analytic) = 3.7480731682325083953902935778402
y[1] (numeric) = 3.7480731682325083953903080593012
absolute error = 1.44814610e-23
relative error = 3.8637081908486519194572579808177e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.011
y[1] (analytic) = 3.748347989290155511037613879765
y[1] (numeric) = 3.7483479892901555110376284948155
absolute error = 1.46150505e-23
relative error = 3.8990644790073851794460496762524e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0111
y[1] (analytic) = 3.7486228378312825424893892104515
y[1] (numeric) = 3.7486228378312825424894039591049
absolute error = 1.47486534e-23
relative error = 3.9344191288480340822701759647140e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0112
y[1] (analytic) = 3.7488977138586379751591802889277
y[1] (numeric) = 3.7488977138586379751591951711973
absolute error = 1.48822696e-23
relative error = 3.9697721132759545394439398261842e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0113
y[1] (analytic) = 3.7491726173749705693228320754534
y[1] (numeric) = 3.7491726173749705693228470913527
absolute error = 1.50158993e-23
relative error = 4.0051234852220720160397016570884e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0114
y[1] (analytic) = 3.7494475483830293601459613743022
y[1] (numeric) = 3.7494475483830293601459765238444
absolute error = 1.51495422e-23
relative error = 4.0404731642487775239604079529666e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0115
y[1] (analytic) = 3.7497225068855636577114471854399
y[1] (numeric) = 3.7497225068855636577114624686384
absolute error = 1.52831985e-23
relative error = 4.0758212032852227457710616540652e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0116
y[1] (analytic) = 3.7499974928853230470469238053765
y[1] (numeric) = 3.7499974928853230470469392222447
absolute error = 1.54168682e-23
relative error = 4.1111676019116357776366736727850e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0117
y[1] (analytic) = 3.7502725063850573881522766774655
y[1] (numeric) = 3.7502725063850573881522922280168
absolute error = 1.55505513e-23
relative error = 4.1465123597083360269365915145675e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0118
y[1] (analytic) = 3.7505475473875168160271409919258
y[1] (numeric) = 3.7505475473875168160271566761735
absolute error = 1.56842477e-23
relative error = 4.1818554495929606438043612116637e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0119
y[1] (analytic) = 3.7508226158954517406984030358606
y[1] (numeric) = 3.7508226158954517406984188538181
absolute error = 1.58179575e-23
relative error = 4.2171968978126958683130676853867e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.012
y[1] (analytic) = 3.7510977119116128472477042935493
y[1] (numeric) = 3.75109771191161284724772024523
absolute error = 1.59516807e-23
relative error = 4.2525367039481347456929716710585e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0121
y[1] (analytic) = 3.7513728354387510958389482972872
y[1] (numeric) = 3.7513728354387510958389643827044
absolute error = 1.60854172e-23
relative error = 4.2878748409230537637895845278254e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0122
y[1] (analytic) = 3.7516479864796177217458102290468
y[1] (numeric) = 3.7516479864796177217458264482139
absolute error = 1.62191671e-23
relative error = 4.3232113349790465199822419824904e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0123
y[1] (analytic) = 3.7519231650369642353792492732381
y[1] (numeric) = 3.7519231650369642353792656261685
absolute error = 1.63529304e-23
relative error = 4.3585461856969796642625456674563e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0124
y[1] (analytic) = 3.7521983711135424223150237208408
y[1] (numeric) = 3.7521983711135424223150402075479
absolute error = 1.64867071e-23
relative error = 4.3938793926578111321283250116412e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0125
y[1] (analytic) = 3.752473604712104343321208825185
y[1] (numeric) = 3.7524736047121043433212254456821
absolute error = 1.66204971e-23
relative error = 4.4292109287935019569348533297114e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0126
y[1] (analytic) = 3.7527488658354023343857174096545
y[1] (numeric) = 3.7527488658354023343857341639551
absolute error = 1.67543006e-23
relative error = 4.4645408469853236913757810419545e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0127
y[1] (analytic) = 3.7530241544861890067438232275895
y[1] (numeric) = 3.7530241544861890067438401157068
absolute error = 1.68881173e-23
relative error = 4.4998690668731073474193551053749e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0128
y[1] (analytic) = 3.7532994706672172469056870746615
y[1] (numeric) = 3.753299470667217246905704096609
absolute error = 1.70219475e-23
relative error = 4.5351956679795761760070982830601e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0129
y[1] (analytic) = 3.7535748143812402166838856539986
y[1] (numeric) = 3.7535748143812402166839028097897
absolute error = 1.71557911e-23
relative error = 4.5705206232390107163688442868285e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.013
y[1] (analytic) = 3.7538501856310113532209431943337
y[1] (numeric) = 3.7538501856310113532209604839818
absolute error = 1.72896481e-23
relative error = 4.6058439322329162658358027479376e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0131
y[1] (analytic) = 3.7541255844192843690168658214529
y[1] (numeric) = 3.7541255844192843690168832449714
absolute error = 1.74235185e-23
relative error = 4.6411655945428893814515763178610e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0132
y[1] (analytic) = 3.7544010107488132519566786832185
y[1] (numeric) = 3.7544010107488132519566962406207
absolute error = 1.75574022e-23
relative error = 4.6764855831152105999404081700276e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0133
y[1] (analytic) = 3.7546764646223522653379658284421
y[1] (numeric) = 3.7546764646223522653379835197414
absolute error = 1.76912993e-23
relative error = 4.7118039241709743633356839720057e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0134
y[1] (analytic) = 3.7549519460426559478984128398835
y[1] (numeric) = 3.7549519460426559478984306650933
absolute error = 1.78252098e-23
relative error = 4.7471206172920507117140371751295e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=1.03
NO POLE
x[1] = 1.0135
y[1] (analytic) = 3.7552274550124791138433522216505
y[1] (numeric) = 3.7552274550124791138433701807842
absolute error = 1.79591337e-23
relative error = 4.7824356620604009300748576635737e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0136
y[1] (analytic) = 3.7555029915345768528733115412751
y[1] (numeric) = 3.7555029915345768528733296343461
absolute error = 1.80930710e-23
relative error = 4.8177490580580775446411971231058e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0137
y[1] (analytic) = 3.7557785556117045302115643267417
y[1] (numeric) = 3.7557785556117045302115825537635
absolute error = 1.82270218e-23
relative error = 4.8530608314928622579516046431799e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0138
y[1] (analytic) = 3.7560541472466177866316837187432
y[1] (numeric) = 3.756054147246617786631702079729
absolute error = 1.83609858e-23
relative error = 4.8883709020700762511922197451921e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0139
y[1] (analytic) = 3.756329766442072538485098878439
y[1] (numeric) = 3.7563297664420725384851173734023
absolute error = 1.84949633e-23
relative error = 4.9236793492489595684211429054855e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.014
y[1] (analytic) = 3.7566054132008249777286541509929
y[1] (numeric) = 3.7566054132008249777286727799471
absolute error = 1.86289542e-23
relative error = 4.9589861459862917249317178902857e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0141
y[1] (analytic) = 3.7568810875256315719521709851641
y[1] (numeric) = 3.7568810875256315719521897481226
absolute error = 1.87629585e-23
relative error = 4.9942912918645813975080924091009e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0142
y[1] (analytic) = 3.7571567894192490644060126092286
y[1] (numeric) = 3.7571567894192490644060315062048
absolute error = 1.88969762e-23
relative error = 5.0295947864664284819210378417125e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0143
y[1] (analytic) = 3.7574325188844344740286514635058
y[1] (numeric) = 3.757432518884434474028670494513
absolute error = 1.90310072e-23
relative error = 5.0648966027606063415475874375284e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0144
y[1] (analytic) = 3.7577082759239450954742393897659
y[1] (numeric) = 3.7577082759239450954742585548176
absolute error = 1.91650517e-23
relative error = 5.1001967935596858398054027926122e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0145
y[1] (analytic) = 3.757984060540538499140180577795
y[1] (numeric) = 3.7579840605405384991401998769045
absolute error = 1.92991095e-23
relative error = 5.1354953052206578745771960590844e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0146
y[1] (analytic) = 3.7582598727369725311947072693914
y[1] (numeric) = 3.7582598727369725311947267025722
absolute error = 1.94331808e-23
relative error = 5.1707921905484635393115449040615e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0147
y[1] (analytic) = 3.7585357125160053136044582200715
y[1] (numeric) = 3.758535712516005313604477787337
absolute error = 1.95672655e-23
relative error = 5.2060874225141940667805839665994e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0148
y[1] (analytic) = 3.7588115798803952441620599187588
y[1] (numeric) = 3.7588115798803952441620796201224
absolute error = 1.97013636e-23
relative error = 5.2413810007009965886192307481348e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0149
y[1] (analytic) = 3.7590874748329009965137105657334
y[1] (numeric) = 3.7590874748329009965137304012085
absolute error = 1.98354751e-23
relative error = 5.2766729246921094294138861078194e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.015
y[1] (analytic) = 3.7593633973762815201867668091167
y[1] (numeric) = 3.7593633973762815201867867787168
absolute error = 1.99696001e-23
relative error = 5.3119632206711104508180858682251e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0151
y[1] (analytic) = 3.7596393475132960406173332401683
y[1] (numeric) = 3.7596393475132960406173533439067
absolute error = 2.01037384e-23
relative error = 5.3472518350189712505157991237845e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0152
y[1] (analytic) = 3.7599153252467040591778546476696
y[1] (numeric) = 3.7599153252467040591778748855598
absolute error = 2.02378902e-23
relative error = 5.3825388205177481820806402060264e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0153
y[1] (analytic) = 3.7601913305792653532047110316718
y[1] (numeric) = 3.7601913305792653532047314037272
absolute error = 2.03720554e-23
relative error = 5.4178241501507962309093153637151e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0154
y[1] (analytic) = 3.7604673635137399760258153768822
y[1] (numeric) = 3.7604673635137399760258358831162
absolute error = 2.05062340e-23
relative error = 5.4531078235018099045493547898762e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0155
y[1] (analytic) = 3.7607434240528882569882141859666
y[1] (numeric) = 3.7607434240528882569882348263926
absolute error = 2.06404260e-23
relative error = 5.4883898401545748811186117933794e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0156
y[1] (analytic) = 3.7610195121994708014856907730425
y[1] (numeric) = 3.761019512199470801485711547674
absolute error = 2.07746315e-23
relative error = 5.5236702262815032885213549578947e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0157
y[1] (analytic) = 3.7612956279562484909863713176405
y[1] (numeric) = 3.7612956279562484909863922264908
absolute error = 2.09088503e-23
relative error = 5.5589489282875407112621336982590e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0158
y[1] (analytic) = 3.7615717713259824830603336794078
y[1] (numeric) = 3.7615717713259824830603547224904
absolute error = 2.10430826e-23
relative error = 5.5942259989318652078079716623286e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0159
y[1] (analytic) = 3.7618479423114342114072189738327
y[1] (numeric) = 3.761847942311434211407240151161
absolute error = 2.11773283e-23
relative error = 5.6295014112100920923889800929404e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.016
y[1] (analytic) = 3.7621241409153653858838459092636
y[1] (numeric) = 3.762124140915365385883867220851
absolute error = 2.13115874e-23
relative error = 5.6647751647064631140569544372848e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0161
y[1] (analytic) = 3.7624003671405379925318278855001
y[1] (numeric) = 3.7624003671405379925318493313601
absolute error = 2.14458600e-23
relative error = 5.7000472855840880788292559772407e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0162
y[1] (analytic) = 3.7626766209897142936051928542328
y[1] (numeric) = 3.7626766209897142936052144343788
absolute error = 2.15801460e-23
relative error = 5.7353177468447113181839847400411e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0163
y[1] (analytic) = 3.7629529024656568275980059416058
y[1] (numeric) = 3.7629529024656568275980276560512
absolute error = 2.17144454e-23
relative error = 5.7705865480728482885074040873082e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=1.26
NO POLE
x[1] = 1.0164
y[1] (analytic) = 3.7632292115711284092719948331808
y[1] (numeric) = 3.7632292115711284092720166819391
absolute error = 2.18487583e-23
relative error = 5.8058537154260285643395085073017e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0165
y[1] (analytic) = 3.7635055483088921296841779215776
y[1] (numeric) = 3.7635055483088921296841999046621
absolute error = 2.19830845e-23
relative error = 5.8411191953411527831264245673832e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0166
y[1] (analytic) = 3.7637819126817113562144952170666
y[1] (numeric) = 3.7637819126817113562145173344908
absolute error = 2.21174242e-23
relative error = 5.8763830405469048196522897998197e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0167
y[1] (analytic) = 3.7640583046923497325934420213919
y[1] (numeric) = 3.7640583046923497325934642731693
absolute error = 2.22517774e-23
relative error = 5.9116452506223118247278751152012e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0168
y[1] (analytic) = 3.7643347243435711789297053650993
y[1] (numeric) = 3.7643347243435711789297277512432
absolute error = 2.23861439e-23
relative error = 5.9469057720162545707039270666122e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0169
y[1] (analytic) = 3.7646111716381398917378032086454
y[1] (numeric) = 3.7646111716381398917378257291694
absolute error = 2.25205240e-23
relative error = 5.9821646840091529006910789476706e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.017
y[1] (analytic) = 3.7648876465788203439657264075669
y[1] (numeric) = 3.7648876465788203439657490624844
absolute error = 2.26549175e-23
relative error = 6.0174219330520212201105144943047e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0171
y[1] (analytic) = 3.7651641491683772850225834419828
y[1] (numeric) = 3.7651641491683772850226062313072
absolute error = 2.27893244e-23
relative error = 6.0526775187301047979565785498957e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0172
y[1] (analytic) = 3.7654406794095757408062479107087
y[1] (numeric) = 3.7654406794095757408062708344534
absolute error = 2.29237447e-23
relative error = 6.0879314406287400100153949976981e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0173
y[1] (analytic) = 3.7657172373051810137310087902586
y[1] (numeric) = 3.7657172373051810137310318484371
absolute error = 2.30581785e-23
relative error = 6.1231837248887204707497919465270e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0174
y[1] (analytic) = 3.7659938228579586827552234590109
y[1] (numeric) = 3.7659938228579586827552466516367
absolute error = 2.31926258e-23
relative error = 6.1584343710897138479547341369552e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0175
y[1] (analytic) = 3.7662704360706746034089734868152
y[1] (numeric) = 3.7662704360706746034089968139016
absolute error = 2.33270864e-23
relative error = 6.1936833257085482130563542982370e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0176
y[1] (analytic) = 3.7665470769460949078217231903156
y[1] (numeric) = 3.7665470769460949078217466518761
absolute error = 2.34615605e-23
relative error = 6.2289306414358062410588821720491e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0177
y[1] (analytic) = 3.7668237454869860047499809542688
y[1] (numeric) = 3.7668237454869860047500045503169
absolute error = 2.35960481e-23
relative error = 6.2641763178514299723148010790524e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0178
y[1] (analytic) = 3.7671004416961145796049633191324
y[1] (numeric) = 3.7671004416961145796049870496815
absolute error = 2.37305491e-23
relative error = 6.2994203279898375469480597503126e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0179
y[1] (analytic) = 3.7673771655762475944802618351996
y[1] (numeric) = 3.7673771655762475944802857002632
absolute error = 2.38650636e-23
relative error = 6.3346626979806694927622925732693e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.018
y[1] (analytic) = 3.7676539171301522881795126835586
y[1] (numeric) = 3.7676539171301522881795366831502
absolute error = 2.39995916e-23
relative error = 6.3699034274041424631838950561117e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0181
y[1] (analytic) = 3.767930696360596176244069064152
y[1] (numeric) = 3.7679306963605961762440931982849
absolute error = 2.41341329e-23
relative error = 6.4051424627610321948527293884380e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0182
y[1] (analytic) = 3.768207503270347050980676351213
y[1] (numeric) = 3.7682075032703470509807006199008
absolute error = 2.42686878e-23
relative error = 6.4403798832568861034312919060640e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0183
y[1] (analytic) = 3.7684843378621729814891500163565
y[1] (numeric) = 3.7684843378621729814891744196126
absolute error = 2.44032561e-23
relative error = 6.4756156353946122718498300427641e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0184
y[1] (analytic) = 3.7687612001388423136900563195999
y[1] (numeric) = 3.7687612001388423136900808574377
absolute error = 2.45378378e-23
relative error = 6.5108497187606417092595360027921e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0185
y[1] (analytic) = 3.7690380901031236703523957685918
y[1] (numeric) = 3.7690380901031236703524204410248
absolute error = 2.46724330e-23
relative error = 6.5460821594734650137979261881930e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0186
y[1] (analytic) = 3.7693150077577859511212893463255
y[1] (numeric) = 3.7693150077577859511213141533672
absolute error = 2.48070417e-23
relative error = 6.5813129571138476888691138164907e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0187
y[1] (analytic) = 3.7695919531055983325456675076128
y[1] (numeric) = 3.7695919531055983325456924492767
absolute error = 2.49416639e-23
relative error = 6.6165421112626468368929251152959e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0188
y[1] (analytic) = 3.7698689261493302681059619445968
y[1] (numeric) = 3.7698689261493302681059870208963
absolute error = 2.50762995e-23
relative error = 6.6517695949746899669803914165902e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0189
y[1] (analytic) = 3.7701459268917514882418001215789
y[1] (numeric) = 3.7701459268917514882418253325274
absolute error = 2.52109485e-23
relative error = 6.6869954078368641620572097769828e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.019
y[1] (analytic) = 3.7704229553356320003797025794385
y[1] (numeric) = 3.7704229553356320003797279250495
absolute error = 2.53456110e-23
relative error = 6.7222195759583709612571823324760e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0191
y[1] (analytic) = 3.7707000114837420889607830099209
y[1] (numeric) = 3.7707000114837420889608084902079
absolute error = 2.54802870e-23
relative error = 6.7574420989204332762913850114541e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0192
y[1] (analytic) = 3.7709770953388523154684511000721
y[1] (numeric) = 3.7709770953388523154684767150485
absolute error = 2.56149764e-23
relative error = 6.7926629497860395864505353884159e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=1.47
NO POLE
x[1] = 1.0193
y[1] (analytic) = 3.7712542069037335184561181470954
y[1] (numeric) = 3.7712542069037335184561438967747
absolute error = 2.57496793e-23
relative error = 6.8278821546588191028898369534761e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0194
y[1] (analytic) = 3.771531346181156813574905443909
y[1] (numeric) = 3.7715313461811568135749313283046
absolute error = 2.58843956e-23
relative error = 6.8630996866058402181784634243280e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0195
y[1] (analytic) = 3.7718085131738935936013554356799
y[1] (numeric) = 3.7718085131738935936013814548054
absolute error = 2.60191255e-23
relative error = 6.8983155982394981966110880353797e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0196
y[1] (analytic) = 3.772085707884715528465145647613
y[1] (numeric) = 3.7720857078847155284651718014818
absolute error = 2.61538688e-23
relative error = 6.9335298361145637900303013984910e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0197
y[1] (analytic) = 3.7723629303163945652768053842703
y[1] (numeric) = 3.772362930316394565276831672896
absolute error = 2.62886257e-23
relative error = 6.9687424528358218600957866197724e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0198
y[1] (analytic) = 3.7726401804717029283554352007001
y[1] (numeric) = 3.772640180471702928355461624096
absolute error = 2.64233959e-23
relative error = 7.0039533684593834459009537475374e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0199
y[1] (analytic) = 3.7729174583534131192564291456501
y[1] (numeric) = 3.7729174583534131192564557038298
absolute error = 2.65581797e-23
relative error = 7.0391626620929557496394979370520e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.02
y[1] (analytic) = 3.7731947639642979167991997771454
y[1] (numeric) = 3.7731947639642979167992264701224
absolute error = 2.66929770e-23
relative error = 7.0743703068100011169439334193009e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0201
y[1] (analytic) = 3.7734720973071303770949059507052
y[1] (numeric) = 3.7734720973071303770949327784929
absolute error = 2.68277877e-23
relative error = 7.1095762756918653206783631273453e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0202
y[1] (analytic) = 3.7737494583846838335741833804776
y[1] (numeric) = 3.7737494583846838335742103430895
absolute error = 2.69626119e-23
relative error = 7.1447805948254655995067136363308e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0203
y[1] (analytic) = 3.774026847199731897014877973569
y[1] (numeric) = 3.7740268471997318970149050710186
absolute error = 2.70974496e-23
relative error = 7.1799832637931227525757780005134e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0204
y[1] (analytic) = 3.774304263755048455569781937846
y[1] (numeric) = 3.7743042637550484555698091701467
absolute error = 2.72323007e-23
relative error = 7.2151842556822998430043828359935e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0205
y[1] (analytic) = 3.7745817080534076747943726634859
y[1] (numeric) = 3.7745817080534076747944000306512
absolute error = 2.73671653e-23
relative error = 7.2503835965743449395054672743627e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0206
y[1] (analytic) = 3.7748591800975839976745543785551
y[1] (numeric) = 3.7748591800975839976745818805985
absolute error = 2.75020434e-23
relative error = 7.2855812860518531588572104198802e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0207
y[1] (analytic) = 3.7751366798903521446544025788909
y[1] (numeric) = 3.775136679890352144654430215826
absolute error = 2.76369351e-23
relative error = 7.3207773501866182858074924899093e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0208
y[1] (analytic) = 3.7754142074344871136639112325658
y[1] (numeric) = 3.775414207434487113663939004406
absolute error = 2.77718402e-23
relative error = 7.3559717355812569978004503515992e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0209
y[1] (analytic) = 3.77569176273276418014674275921
y[1] (numeric) = 3.7756917627327641801467706659688
absolute error = 2.79067588e-23
relative error = 7.3911644683096933981257847348653e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.021
y[1] (analytic) = 3.7759693457879588970879807844716
y[1] (numeric) = 3.7759693457879588970880088261625
absolute error = 2.80416909e-23
relative error = 7.4263555479548886732421972902431e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0211
y[1] (analytic) = 3.7762469566028470950418856698903
y[1] (numeric) = 3.7762469566028470950419138465268
absolute error = 2.81766365e-23
relative error = 7.4615449740998955174899572796427e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0212
y[1] (analytic) = 3.7765245951802048821596528184635
y[1] (numeric) = 3.776524595180204882159681130059
absolute error = 2.83115955e-23
relative error = 7.4967327198484860294249692313198e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0213
y[1] (analytic) = 3.7768022615228086442171737561807
y[1] (numeric) = 3.7768022615228086442172022027489
absolute error = 2.84465682e-23
relative error = 7.5319188642220122072317130960313e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0214
y[1] (analytic) = 3.7770799556334350446427999898065
y[1] (numeric) = 3.7770799556334350446428285713607
absolute error = 2.85815542e-23
relative error = 7.5671033008902062235492002066819e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0215
y[1] (analytic) = 3.7773576775148610245451096411863
y[1] (numeric) = 3.7773576775148610245451383577401
absolute error = 2.87165538e-23
relative error = 7.6022861088687628627504140423687e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0216
y[1] (analytic) = 3.7776354271698638027406768583559
y[1] (numeric) = 3.7776354271698638027407057099228
absolute error = 2.88515669e-23
relative error = 7.6374672612637669356795541208786e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0217
y[1] (analytic) = 3.7779132046012208757818440037302
y[1] (numeric) = 3.7779132046012208757818729903236
absolute error = 2.89865934e-23
relative error = 7.6726467311891807593549304087736e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0218
y[1] (analytic) = 3.7781910098117100179844966196495
y[1] (numeric) = 3.778191009811710017984525741283
absolute error = 2.91216335e-23
relative error = 7.7078245711699224412384168346756e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0219
y[1] (analytic) = 3.7784688428041092814558411715618
y[1] (numeric) = 3.778468842804109281455870428249
absolute error = 2.92566872e-23
relative error = 7.7430007807839377720748744060787e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.022
y[1] (analytic) = 3.7787467035811969961221855691182
y[1] (numeric) = 3.7787467035811969961222149608724
absolute error = 2.93917542e-23
relative error = 7.7781752802178621952013753416413e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0221
y[1] (analytic) = 3.7790245921457517697567224654584
y[1] (numeric) = 3.7790245921457517697567519922932
absolute error = 2.95268348e-23
relative error = 7.8133481484529039232136276517839e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.1MB, time=1.70
x[1] = 1.0222
y[1] (analytic) = 3.7793025085005524880073153349667
y[1] (numeric) = 3.7793025085005524880073449968956
absolute error = 2.96619289e-23
relative error = 7.8485193586073751013623542489293e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0223
y[1] (analytic) = 3.7795804526483783144242873297729
y[1] (numeric) = 3.7795804526483783144243171268095
absolute error = 2.97970366e-23
relative error = 7.8836889367233892804994025951274e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0224
y[1] (analytic) = 3.7798584245920086904882129152796
y[1] (numeric) = 3.7798584245920086904882428474373
absolute error = 2.99321577e-23
relative error = 7.9188568294673165616489270779436e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0225
y[1] (analytic) = 3.7801364243342233356377122849904
y[1] (numeric) = 3.7801364243342233356377423522827
absolute error = 3.00672923e-23
relative error = 7.9540230628833992262771882891599e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0226
y[1] (analytic) = 3.7804144518778022472972485549194
y[1] (numeric) = 3.7804144518778022472972787573598
absolute error = 3.02024404e-23
relative error = 7.9891876365560621275256295551178e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0227
y[1] (analytic) = 3.7806925072255257009049277378592
y[1] (numeric) = 3.7806925072255257009049580754613
absolute error = 3.03376021e-23
relative error = 8.0243505765200022684424743959767e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0228
y[1] (analytic) = 3.7809705903801742499403014977852
y[1] (numeric) = 3.7809705903801742499403319705625
absolute error = 3.04727773e-23
relative error = 8.0595118559057559676220760925586e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0229
y[1] (analytic) = 3.7812487013445287259521726846739
y[1] (numeric) = 3.7812487013445287259522032926399
absolute error = 3.06079660e-23
relative error = 8.0946714742980226811478134789864e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.023
y[1] (analytic) = 3.7815268401213702385864036500145
y[1] (numeric) = 3.7815268401213702385864343931827
absolute error = 3.07431682e-23
relative error = 8.1298294312815933000910782174033e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0231
y[1] (analytic) = 3.7818050067134801756137273432902
y[1] (numeric) = 3.7818050067134801756137582216742
absolute error = 3.08783840e-23
relative error = 8.1649857528837499590397761270636e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0232
y[1] (analytic) = 3.7820832011236402029575611897096
y[1] (numeric) = 3.7820832011236402029575922033228
absolute error = 3.10136132e-23
relative error = 8.2001403858027217890437036322189e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0233
y[1] (analytic) = 3.7823614233546322647218237494628
y[1] (numeric) = 3.7823614233546322647218548983189
absolute error = 3.11488561e-23
relative error = 8.2352934089449386941193821955899e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0234
y[1] (analytic) = 3.782639673409238583218754158785
y[1] (numeric) = 3.7826396734092385832187854428974
absolute error = 3.12841124e-23
relative error = 8.2704447425741930854432571449702e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0235
y[1] (analytic) = 3.7829179512902416589967343531013
y[1] (numeric) = 3.7829179512902416589967657724836
absolute error = 3.14193823e-23
relative error = 8.3055944391508084524741038831706e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0236
y[1] (analytic) = 3.783196257000424270868114072534
y[1] (numeric) = 3.7831962570004242708681456271996
absolute error = 3.15546656e-23
relative error = 8.3407424453889390877460838380686e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0237
y[1] (analytic) = 3.7834745905425694759370386500491
y[1] (numeric) = 3.7834745905425694759370703400116
absolute error = 3.16899625e-23
relative error = 8.3758888137413124256826241257766e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0238
y[1] (analytic) = 3.7837529519194606096272795825212
y[1] (numeric) = 3.7837529519194606096273114077941
absolute error = 3.18252729e-23
relative error = 8.4110335173588308605547137667989e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0239
y[1] (analytic) = 3.7840313411338812857100678849942
y[1] (numeric) = 3.7840313411338812857100998455911
absolute error = 3.19605969e-23
relative error = 8.4461765822539510038993554153077e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.024
y[1] (analytic) = 3.784309758188615396331930228417
y[1] (numeric) = 3.7843097581886153963319623243514
absolute error = 3.20959344e-23
relative error = 8.4813179815816474840183658767412e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0241
y[1] (analytic) = 3.7845882030864471120425278611318
y[1] (numeric) = 3.7845882030864471120425600924172
absolute error = 3.22312854e-23
relative error = 8.5164577149277175468995649665622e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0242
y[1] (analytic) = 3.7848666758301608818224983143939
y[1] (numeric) = 3.7848666758301608818225306810439
absolute error = 3.23666500e-23
relative error = 8.5515958082990597503128356056306e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0243
y[1] (analytic) = 3.7851451764225414331112998922014
y[1] (numeric) = 3.7851451764225414331113323942295
absolute error = 3.25020281e-23
relative error = 8.5867322348567562196300370660140e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0244
y[1] (analytic) = 3.7854237048663737718350589457129
y[1] (numeric) = 3.7854237048663737718350915831327
absolute error = 3.26374198e-23
relative error = 8.6218670206040006741340493423300e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0245
y[1] (analytic) = 3.785702261164443182434419932532
y[1] (numeric) = 3.7857022611644431824344527053571
absolute error = 3.27728251e-23
relative error = 8.6570001651211247599252717358370e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0246
y[1] (analytic) = 3.7859808453195352278923982611372
y[1] (numeric) = 3.785980845319535227892431169381
absolute error = 3.29082438e-23
relative error = 8.6921316151620829828785000187519e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0247
y[1] (analytic) = 3.7862594573344357497622359207346
y[1] (numeric) = 3.7862594573344357497622689644107
absolute error = 3.30436761e-23
relative error = 8.7272614231416343696650658323168e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0248
y[1] (analytic) = 3.7865380972119308681952598968142
y[1] (numeric) = 3.7865380972119308681952930759362
absolute error = 3.31791220e-23
relative error = 8.7623895886403857742605294632752e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0249
y[1] (analytic) = 3.7868167649548069819687433726863
y[1] (numeric) = 3.7868167649548069819687766872676
absolute error = 3.33145813e-23
relative error = 8.7975160584242280605458964875743e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.025
y[1] (analytic) = 3.787095460565850768513769717277
y[1] (numeric) = 3.7870954605658507685138031673312
absolute error = 3.34500542e-23
relative error = 8.8326408848965331777707957988940e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.1MB, time=1.92
x[1] = 1.0251
y[1] (analytic) = 3.7873741840478491839430992594628
y[1] (numeric) = 3.7873741840478491839431328450034
absolute error = 3.35855406e-23
relative error = 8.8677640412346657974756267784534e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0252
y[1] (analytic) = 3.787652935403589463079038849221
y[1] (numeric) = 3.7876529354035894630790725702616
absolute error = 3.37210406e-23
relative error = 8.9028855534270035223378416559783e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0253
y[1] (analytic) = 3.7879317146358591194813142058764
y[1] (numeric) = 3.7879317146358591194813480624305
absolute error = 3.38565541e-23
relative error = 8.9380053946549807734563209836630e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0254
y[1] (analytic) = 3.7882105217474459454749450537212
y[1] (numeric) = 3.7882105217474459454749790458025
absolute error = 3.39920813e-23
relative error = 8.9731236173009602213717427029614e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0255
y[1] (analytic) = 3.7884893567411380121781230452893
y[1] (numeric) = 3.7884893567411380121781571729113
absolute error = 3.41276220e-23
relative error = 9.0082401681488717342340671766688e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0256
y[1] (analytic) = 3.7887682196197236695300924725606
y[1] (numeric) = 3.7887682196197236695301267357368
absolute error = 3.42631762e-23
relative error = 9.0433550467858849049172649619712e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0257
y[1] (analytic) = 3.7890471103859915463190337663771
y[1] (numeric) = 3.789047110385991546319068165121
absolute error = 3.43987439e-23
relative error = 9.0784682527992606565648524311671e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0258
y[1] (analytic) = 3.7893260290427305502099497843478
y[1] (numeric) = 3.7893260290427305502099843186731
absolute error = 3.45343253e-23
relative error = 9.1135798385561855593809578910224e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0259
y[1] (analytic) = 3.7896049755927298677725548875223
y[1] (numeric) = 3.7896049755927298677725895574425
absolute error = 3.46699202e-23
relative error = 9.1486897508564987921155817443517e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.026
y[1] (analytic) = 3.7898839500387789645091668061106
y[1] (numeric) = 3.7898839500387789645092016116393
absolute error = 3.48055287e-23
relative error = 9.1837980156737680114692774196776e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0261
y[1] (analytic) = 3.7901629523836675848826012945301
y[1] (numeric) = 3.7901629523836675848826362356808
absolute error = 3.49411507e-23
relative error = 9.2189046062057030877953580265215e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0262
y[1] (analytic) = 3.7904419826301857523440695760567
y[1] (numeric) = 3.7904419826301857523441046528429
absolute error = 3.50767862e-23
relative error = 9.2540095220400223625303928475481e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0263
y[1] (analytic) = 3.79072104078112376936107857736
y[1] (numeric) = 3.7907210407811237693611137897954
absolute error = 3.52124354e-23
relative error = 9.2891128155249464580798729702292e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0264
y[1] (analytic) = 3.7910001268392722174453339532022
y[1] (numeric) = 3.7910001268392722174453693013003
absolute error = 3.53480981e-23
relative error = 9.3242144334801971136830520560725e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0265
y[1] (analytic) = 3.7912792408074219571806459015777
y[1] (numeric) = 3.7912792408074219571806813853521
absolute error = 3.54837744e-23
relative error = 9.3593144018700885898800339546397e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0266
y[1] (analytic) = 3.7915583826883641282508377695751
y[1] (numeric) = 3.7915583826883641282508733890394
absolute error = 3.56194643e-23
relative error = 9.3944127202768793545054858900370e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0267
y[1] (analytic) = 3.7918375524848901494676574502383
y[1] (numeric) = 3.791837552484890149467693205406
absolute error = 3.57551677e-23
relative error = 9.4295093619104819172107168354011e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0268
y[1] (analytic) = 3.7921167501997917187986915707072
y[1] (numeric) = 3.7921167501997917187987274615919
absolute error = 3.58908847e-23
relative error = 9.4646043527296596099311983473011e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0269
y[1] (analytic) = 3.7923959758358608133952824719172
y[1] (numeric) = 3.7923959758358608133953184985324
absolute error = 3.60266152e-23
relative error = 9.4996976659483916317391173738892e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.027
y[1] (analytic) = 3.7926752293958896896204479801354
y[1] (numeric) = 3.7926752293958896896204841424948
absolute error = 3.61623594e-23
relative error = 9.5347893538883540407917136166769e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0271
y[1] (analytic) = 3.7929545108826708830768039706147
y[1] (numeric) = 3.7929545108826708830768402687318
absolute error = 3.62981171e-23
relative error = 9.5698793633970965107545680029270e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0272
y[1] (analytic) = 3.7932338202989972086344897236425
y[1] (numeric) = 3.7932338202989972086345261575309
absolute error = 3.64338884e-23
relative error = 9.6049677204259824569865965605505e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0273
y[1] (analytic) = 3.7935131576476617604590960732658
y[1] (numeric) = 3.7935131576476617604591326429391
absolute error = 3.65696733e-23
relative error = 9.6400544245579126063037202659930e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0274
y[1] (analytic) = 3.7937925229314579120395963489704
y[1] (numeric) = 3.7937925229314579120396330544421
absolute error = 3.67054717e-23
relative error = 9.6751394490170316198769356625747e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0275
y[1] (analytic) = 3.7940719161531793162162801105936
y[1] (numeric) = 3.7940719161531793162163169518773
absolute error = 3.68412837e-23
relative error = 9.7102228197491538292083088863409e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0276
y[1] (analytic) = 3.7943513373156199052086896767507
y[1] (numeric) = 3.79435133731561990520872665386
absolute error = 3.69771093e-23
relative error = 9.7453045363374551169064181244887e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0277
y[1] (analytic) = 3.7946307864215738906435594470537
y[1] (numeric) = 3.7946307864215738906435965600021
absolute error = 3.71129484e-23
relative error = 9.7803845720121781629340794678679e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0278
y[1] (analytic) = 3.7949102634738357635827580184015
y[1] (numeric) = 3.7949102634738357635827952672027
absolute error = 3.72488012e-23
relative error = 9.8154629790646732360945415523931e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0279
y[1] (analytic) = 3.7951897684752002945512330956226
y[1] (numeric) = 3.7951897684752002945512704802901
absolute error = 3.73846675e-23
relative error = 9.8505397043742821955755031746355e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.028
y[1] (analytic) = 3.795469301428462533564959196747
y[1] (numeric) = 3.7954693014284625335649967172945
absolute error = 3.75205475e-23
relative error = 9.8856148002247757969281055175121e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=2.14
NO POLE
x[1] = 1.0281
y[1] (analytic) = 3.7957488623364178101588881531901
y[1] (numeric) = 3.7957488623364178101589258096311
absolute error = 3.76564410e-23
relative error = 9.9206882135034422084861524002852e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0282
y[1] (analytic) = 3.7960284512018617334149024051249
y[1] (numeric) = 3.796028451201861733414940197473
absolute error = 3.77923481e-23
relative error = 9.9557599701431513414555823769493e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0283
y[1] (analytic) = 3.7963080680275901919897710923242
y[1] (numeric) = 3.7963080680275901919898090205931
absolute error = 3.79282689e-23
relative error = 9.9908300960691030724623137406614e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0284
y[1] (analytic) = 3.7965877128163993541431089407521
y[1] (numeric) = 3.7965877128163993541431470049553
absolute error = 3.80642032e-23
relative error = 1.0025898538180503627127868864453e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0285
y[1] (analytic) = 3.7968673855710856677653379451827
y[1] (numeric) = 3.7968673855710856677653761453338
absolute error = 3.82001511e-23
relative error = 1.0060965322404676743928631210640e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0286
y[1] (analytic) = 3.7971470862944458604056518481281
y[1] (numeric) = 3.7971470862944458604056901842407
absolute error = 3.83361126e-23
relative error = 1.0096030448325715878776752662732e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0287
y[1] (analytic) = 3.7974268149892769392999834153536
y[1] (numeric) = 3.7974268149892769393000218874413
absolute error = 3.84720877e-23
relative error = 1.0131093915527806250826659673118e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0288
y[1] (analytic) = 3.7977065716583761913989745082602
y[1] (numeric) = 3.7977065716583761913990131163366
absolute error = 3.86080764e-23
relative error = 1.0166155723595224838535975997156e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0289
y[1] (analytic) = 3.7979863563045411833959489534145
y[1] (numeric) = 3.7979863563045411833959876974931
absolute error = 3.87440786e-23
relative error = 1.0201215845782598607694382439089e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.029
y[1] (analytic) = 3.7982661689305697617548882095049
y[1] (numeric) = 3.7982661689305697617549270895994
absolute error = 3.88800945e-23
relative error = 1.0236274334335811252561868177300e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0291
y[1] (analytic) = 3.7985460095392600527384098320052
y[1] (numeric) = 3.7985460095392600527384488481292
absolute error = 3.90161240e-23
relative error = 1.0271331162507733473029629237474e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0292
y[1] (analytic) = 3.7988258781334104624357487358239
y[1] (numeric) = 3.798825878133410462435787887991
absolute error = 3.91521671e-23
relative error = 1.0306386329883009245334204948382e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0293
y[1] (analytic) = 3.7991057747158196767907412562196
y[1] (numeric) = 3.7991057747158196767907805444435
absolute error = 3.92882239e-23
relative error = 1.0341439862368357912471376823149e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0294
y[1] (analytic) = 3.7993856992892866616298120082633
y[1] (numeric) = 3.7993856992892866616298514325574
absolute error = 3.94242941e-23
relative error = 1.0376491680582656044338268125472e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0295
y[1] (analytic) = 3.7996656518566106626899635451252
y[1] (numeric) = 3.7996656518566106626900031055032
absolute error = 3.95603780e-23
relative error = 1.0411541863076773705593999692990e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0296
y[1] (analytic) = 3.7999456324205912056467688154686
y[1] (numeric) = 3.7999456324205912056468085119442
absolute error = 3.96964756e-23
relative error = 1.0446590409429904165744628300804e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0297
y[1] (analytic) = 3.800225640984028096142366420229
y[1] (numeric) = 3.8002256409840280961424062528157
absolute error = 3.98325867e-23
relative error = 1.0481637266592879057597151425464e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0298
y[1] (analytic) = 3.8005056775497214198134586690583
y[1] (numeric) = 3.8005056775497214198134986377698
absolute error = 3.99687115e-23
relative error = 1.0516682486781285860881311414840e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0299
y[1] (analytic) = 3.8007857421204715423193124367158
y[1] (numeric) = 3.8007857421204715423193525415656
absolute error = 4.01048498e-23
relative error = 1.0551726016953895764379224691463e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.03
y[1] (analytic) = 3.8010658346990791093697628196836
y[1] (numeric) = 3.8010658346990791093698030606854
absolute error = 4.02410018e-23
relative error = 1.0586767909318723922646239683533e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0301
y[1] (analytic) = 3.8013459552883450467532195932887
y[1] (numeric) = 3.8013459552883450467532599704561
absolute error = 4.03771674e-23
relative error = 1.0621808137148952083760042065812e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0302
y[1] (analytic) = 3.8016261038910705603646764696105
y[1] (numeric) = 3.8016261038910705603647169829571
absolute error = 4.05133466e-23
relative error = 1.0656846700030141717301778630842e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0303
y[1] (analytic) = 3.8019062805100571362337231564535
y[1] (numeric) = 3.801906280510057136233763805993
absolute error = 4.06495395e-23
relative error = 1.0691883623850540697145893646532e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0304
y[1] (analytic) = 3.8021864851481065405525602176674
y[1] (numeric) = 3.8021864851481065405526010034133
absolute error = 4.07857459e-23
relative error = 1.0726918855588766093231410655892e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0305
y[1] (analytic) = 3.8024667178080208197040167350916
y[1] (numeric) = 3.8024667178080208197040576570575
absolute error = 4.09219659e-23
relative error = 1.0761952421135187646419238378171e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0306
y[1] (analytic) = 3.8027469784926023002895707724074
y[1] (numeric) = 3.802746978492602300289611830607
absolute error = 4.10581996e-23
relative error = 1.0796984346372513421214113745087e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0307
y[1] (analytic) = 3.803027267204653589157372641176
y[1] (numeric) = 3.8030272672046535891574138356229
absolute error = 4.11944469e-23
relative error = 1.0832014604586107305805539609019e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0308
y[1] (analytic) = 3.8033075839469775734302709693433
y[1] (numeric) = 3.8033075839469775734303123000512
absolute error = 4.13307079e-23
relative error = 1.0867043221654984873621589537411e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0309
y[1] (analytic) = 3.8035879287223774205338415724918
y[1] (numeric) = 3.8035879287223774205338830394742
absolute error = 4.14669824e-23
relative error = 1.0902070144577604383037421630654e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.1MB, time=2.36
NO POLE
x[1] = 1.031
y[1] (analytic) = 3.8038683015336565782244191281195
y[1] (numeric) = 3.8038683015336565782244607313902
absolute error = 4.16032707e-23
relative error = 1.0937095451813158624250575085238e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0311
y[1] (analytic) = 3.8041487023836187746171316532272
y[1] (numeric) = 3.8041487023836187746171733927996
absolute error = 4.17395724e-23
relative error = 1.0972119037788047313764142034962e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0312
y[1] (analytic) = 3.8044291312750680182139377854922
y[1] (numeric) = 3.8044291312750680182139796613801
absolute error = 4.18758879e-23
relative error = 1.1007141007240985595569727297457e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0313
y[1] (analytic) = 3.8047095882108085979316668683123
y[1] (numeric) = 3.8047095882108085979317088805293
absolute error = 4.20122170e-23
relative error = 1.1042161307180488398605728057070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0314
y[1] (analytic) = 3.8049900731936450831300618399967
y[1] (numeric) = 3.8049900731936450831301039885564
absolute error = 4.21485597e-23
relative error = 1.1077179937193218156975613764853e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0315
y[1] (analytic) = 3.805270586226382323639824927387
y[1] (numeric) = 3.8052705862263823236398672123031
absolute error = 4.22849161e-23
relative error = 1.1112196923145269081212996538658e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0316
y[1] (analytic) = 3.8055511273118254497906661441879
y[1] (numeric) = 3.8055511273118254497907085654739
absolute error = 4.24212860e-23
relative error = 1.1147212212062869373206949229174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0317
y[1] (analytic) = 3.8058316964527798724393545942871
y[1] (numeric) = 3.8058316964527798724393971519568
absolute error = 4.25576697e-23
relative error = 1.1182225882365165207083464030435e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0318
y[1] (analytic) = 3.8061122936520512829977725803471
y[1] (numeric) = 3.806112293652051282997815274414
absolute error = 4.26940669e-23
relative error = 1.1217237854806977358164332066465e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0319
y[1] (analytic) = 3.8063929189124456534609725179466
y[1] (numeric) = 3.8063929189124456534610153484244
absolute error = 4.28304778e-23
relative error = 1.1252248181524421135733079315424e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.032
y[1] (analytic) = 3.8066735722367692364352366555551
y[1] (numeric) = 3.8066735722367692364352796224574
absolute error = 4.29669023e-23
relative error = 1.1287256835829243731522221685157e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0321
y[1] (analytic) = 3.8069542536278285651661396006186
y[1] (numeric) = 3.8069542536278285651661827039592
absolute error = 4.31033406e-23
relative error = 1.1322263869844185206751761309021e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0322
y[1] (analytic) = 3.8072349630884304535666136520393
y[1] (numeric) = 3.8072349630884304535666568918317
absolute error = 4.32397924e-23
relative error = 1.1357269204347678063961244799652e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0323
y[1] (analytic) = 3.8075157006213819962450169393275
y[1] (numeric) = 3.8075157006213819962450603155854
absolute error = 4.33762579e-23
relative error = 1.1392272891460709335731997964326e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0324
y[1] (analytic) = 3.8077964662294905685332043687095
y[1] (numeric) = 3.8077964662294905685332478814464
absolute error = 4.35127369e-23
relative error = 1.1427274878241233230717331008033e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0325
y[1] (analytic) = 3.8080772599155638265146013764686
y[1] (numeric) = 3.8080772599155638265146450256983
absolute error = 4.36492297e-23
relative error = 1.1462275243062644863712830016760e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0326
y[1] (analytic) = 3.8083580816824097070522804898037
y[1] (numeric) = 3.8083580816824097070523242755398
absolute error = 4.37857361e-23
relative error = 1.1497273932985018764440042841902e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0327
y[1] (analytic) = 3.8086389315328364278170406954826
y[1] (numeric) = 3.8086389315328364278170846177388
absolute error = 4.39222562e-23
relative error = 1.1532270973852308692287111086543e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0328
y[1] (analytic) = 3.8089198094696524873154896165741
y[1] (numeric) = 3.808919809469652487315533675364
absolute error = 4.40587899e-23
relative error = 1.1567266338992490086433174244463e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0329
y[1] (analytic) = 3.8092007154956666649181284975368
y[1] (numeric) = 3.8092007154956666649181726928741
absolute error = 4.41953373e-23
relative error = 1.1602260054245827908125640959622e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.033
y[1] (analytic) = 3.8094816496136880208874399979479
y[1] (numeric) = 3.8094816496136880208874843298463
absolute error = 4.43318984e-23
relative error = 1.1637252119194644210347598344126e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0331
y[1] (analytic) = 3.8097626118265258964059787951517
y[1] (numeric) = 3.8097626118265258964060232636248
absolute error = 4.44684731e-23
relative error = 1.1672242507172998579960831048197e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0332
y[1] (analytic) = 3.8100436021369899136044649961078
y[1] (numeric) = 3.8100436021369899136045096011693
absolute error = 4.46050615e-23
relative error = 1.1707231244015623578508014792790e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0333
y[1] (analytic) = 3.8103246205478899755898803587226
y[1] (numeric) = 3.8103246205478899755899251003861
absolute error = 4.47416635e-23
relative error = 1.1742218303060634319541273807368e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0334
y[1] (analytic) = 3.8106056670620362664735673229417
y[1] (numeric) = 3.8106056670620362664736122012209
absolute error = 4.48782792e-23
relative error = 1.1777203710139075445909771326096e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0335
y[1] (analytic) = 3.8108867416822392513993308518873
y[1] (numeric) = 3.8108867416822392513993758667959
absolute error = 4.50149086e-23
relative error = 1.1812187464833729118323140667642e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0336
y[1] (analytic) = 3.8111678444113096765715430833196
y[1] (numeric) = 3.8111678444113096765715882348712
absolute error = 4.51515516e-23
relative error = 1.1847169540488793158492370454774e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0337
y[1] (analytic) = 3.8114489752520585692832507917036
y[1] (numeric) = 3.811448975252058569283296079912
absolute error = 4.52882084e-23
relative error = 1.1882149989166522234164683396130e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0338
y[1] (analytic) = 3.8117301342072972379442856611636
y[1] (numeric) = 3.8117301342072972379443310860423
absolute error = 4.54248787e-23
relative error = 1.1917128731739751261646861796636e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.1MB, time=2.57
NO POLE
x[1] = 1.0339
y[1] (analytic) = 3.8120113212798372721093773696043
y[1] (numeric) = 3.812011321279837272109422931167
absolute error = 4.55615627e-23
relative error = 1.1952105820268983223015280109344e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.034
y[1] (analytic) = 3.8122925364724905425062694842819
y[1] (numeric) = 3.8122925364724905425063151825423
absolute error = 4.56982604e-23
relative error = 1.1987081254337460286408451025987e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0341
y[1] (analytic) = 3.8125737797880692010638381691049
y[1] (numeric) = 3.8125737797880692010638840040766
absolute error = 4.58349717e-23
relative error = 1.2022055007299516108656517933845e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0342
y[1] (analytic) = 3.8128550512293856809402137039462
y[1] (numeric) = 3.8128550512293856809402596756429
absolute error = 4.59716967e-23
relative error = 1.2057027104971447451809127541035e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0343
y[1] (analytic) = 3.813136350799252696550904816248
y[1] (numeric) = 3.8131363507992526965509509246834
absolute error = 4.61084354e-23
relative error = 1.2091997546936772495408893090025e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0344
y[1] (analytic) = 3.8134176785004832435969258252002
y[1] (numeric) = 3.813417678500483243596972070388
absolute error = 4.62451878e-23
relative error = 1.2126966332779101506745571521921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0345
y[1] (analytic) = 3.8136990343358905990929265987741
y[1] (numeric) = 3.8136990343358905990929729807279
absolute error = 4.63819538e-23
relative error = 1.2161933435860875248107057475668e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0346
y[1] (analytic) = 3.8139804183082883213953253238921
y[1] (numeric) = 3.8139804183082883213953718426257
absolute error = 4.65187336e-23
relative error = 1.2196898908210345853264775821065e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0347
y[1] (analytic) = 3.8142618304204902502304440900158
y[1] (numeric) = 3.8142618304204902502304907455428
absolute error = 4.66555270e-23
relative error = 1.2231862696970810992743596989658e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0348
y[1] (analytic) = 3.8145432706753105067226472864321
y[1] (numeric) = 3.8145432706753105067226940787661
absolute error = 4.67923340e-23
relative error = 1.2266824801732052269330894350943e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0349
y[1] (analytic) = 3.8148247390755634934224828135206
y[1] (numeric) = 3.8148247390755634934225297426754
absolute error = 4.69291548e-23
relative error = 1.2301785274510990878138135301700e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.035
y[1] (analytic) = 3.8151062356240638943348261082825
y[1] (numeric) = 3.8151062356240638943348731742718
absolute error = 4.70659893e-23
relative error = 1.2336744088674396622826863622939e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0351
y[1] (analytic) = 3.8153877603236266749470269844131
y[1] (numeric) = 3.8153877603236266749470741872504
absolute error = 4.72028373e-23
relative error = 1.2371701191387212365537699409265e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0352
y[1] (analytic) = 3.8156693131770670822570592871979
y[1] (numeric) = 3.8156693131770670822571066268971
absolute error = 4.73396992e-23
relative error = 1.2406656687076275862759590874710e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0353
y[1] (analytic) = 3.8159508941872006448016733635169
y[1] (numeric) = 3.8159508941872006448017208400916
absolute error = 4.74765747e-23
relative error = 1.2441610496697057992237109520963e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0354
y[1] (analytic) = 3.8162325033568431726845513472347
y[1] (numeric) = 3.8162325033568431726845989606986
absolute error = 4.76134639e-23
relative error = 1.2476562646043744940345472718312e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0355
y[1] (analytic) = 3.8165141406888107576044652602612
y[1] (numeric) = 3.816514140688810757604513010628
absolute error = 4.77503668e-23
relative error = 1.2511513134700959121537124538372e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0356
y[1] (analytic) = 3.8167958061859197728834379295628
y[1] (numeric) = 3.8167958061859197728834858168462
absolute error = 4.78872834e-23
relative error = 1.2546461962253414989601136681725e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0357
y[1] (analytic) = 3.8170774998509868734949067204059
y[1] (numeric) = 3.8170774998509868734949547446195
absolute error = 4.80242136e-23
relative error = 1.2581409102087865678949864438638e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0358
y[1] (analytic) = 3.8173592216868289960918900861148
y[1] (numeric) = 3.8173592216868289960919382472724
absolute error = 4.81611576e-23
relative error = 1.2616354606187249840560162963188e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0359
y[1] (analytic) = 3.8176409716962633590351569346256
y[1] (numeric) = 3.8176409716962633590352052327408
absolute error = 4.82981152e-23
relative error = 1.2651298421742384549843900925882e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.036
y[1] (analytic) = 3.8179227498821074624213988121168
y[1] (numeric) = 3.8179227498821074624214472472034
absolute error = 4.84350866e-23
relative error = 1.2686240600728658822851399892412e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0361
y[1] (analytic) = 3.8182045562471790881114049040005
y[1] (numeric) = 3.8182045562471790881114534760722
absolute error = 4.85720717e-23
relative error = 1.2721181116535127315979983223563e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0362
y[1] (analytic) = 3.8184863907942962997582398535532
y[1] (numeric) = 3.8184863907942962997582885626235
absolute error = 4.87090703e-23
relative error = 1.2756119916370282296895838028820e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0363
y[1] (analytic) = 3.8187682535262774428354243984698
y[1] (numeric) = 3.8187682535262774428354732445525
absolute error = 4.88460827e-23
relative error = 1.2791057078390442770244409260863e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0364
y[1] (analytic) = 3.8190501444459411446651188256228
y[1] (numeric) = 3.8190501444459411446651678087317
absolute error = 4.89831089e-23
relative error = 1.2825992602175260199338094483319e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0365
y[1] (analytic) = 3.8193320635561063144463092443073
y[1] (numeric) = 3.819332063556106314446358364456
absolute error = 4.91201487e-23
relative error = 1.2860926434939301479610780279559e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0366
y[1] (analytic) = 3.8196140108595921432829966782539
y[1] (numeric) = 3.8196140108595921432830459354561
absolute error = 4.92572022e-23
relative error = 1.2895858602454655166698776653928e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0367
y[1] (analytic) = 3.8198959863592181042123889766926
y[1] (numeric) = 3.8198959863592181042124383709621
absolute error = 4.93942695e-23
relative error = 1.2930789130485770887316703945359e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=49.5MB, alloc=4.1MB, time=2.80
x[1] = 1.0368
y[1] (analytic) = 3.8201779900578039522330955447485
y[1] (numeric) = 3.8201779900578039522331450760989
absolute error = 4.95313504e-23
relative error = 1.2965717966259087906532483574329e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0369
y[1] (analytic) = 3.8204600219581697243333248934508
y[1] (numeric) = 3.8204600219581697243333745618959
absolute error = 4.96684451e-23
relative error = 1.3000645161716030795560359233222e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.037
y[1] (analytic) = 3.820742082063135739519085009639
y[1] (numeric) = 3.8207420820631357395191348151925
absolute error = 4.98055535e-23
relative error = 1.3035570690263878849390724345269e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0371
y[1] (analytic) = 3.8210241703755225988423865460463
y[1] (numeric) = 3.8210241703755225988424364887219
absolute error = 4.99426756e-23
relative error = 1.3070494551488726625319854977416e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0372
y[1] (analytic) = 3.821306286898151185429448831843
y[1] (numeric) = 3.8213062868981511854294989116544
absolute error = 5.00798114e-23
relative error = 1.3105416744976760655021771711571e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0373
y[1] (analytic) = 3.8215884316338426645089087039224
y[1] (numeric) = 3.8215884316338426645089589208833
absolute error = 5.02169609e-23
relative error = 1.3140337270314259440471466528188e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0374
y[1] (analytic) = 3.8218706045854184834400321592107
y[1] (numeric) = 3.8218706045854184834400825133348
absolute error = 5.03541241e-23
relative error = 1.3175256127087593449866150788370e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0375
y[1] (analytic) = 3.822152805755700371740928828283
y[1] (numeric) = 3.822152805755700371740979319584
absolute error = 5.04913010e-23
relative error = 1.3210173314883225113544524739221e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0376
y[1] (analytic) = 3.822435035147510341116769270568
y[1] (numeric) = 3.8224350351475103411168198990597
absolute error = 5.06284917e-23
relative error = 1.3245088859449042912045397585990e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0377
y[1] (analytic) = 3.8227172927636706854880050914234
y[1] (numeric) = 3.8227172927636706854880558571195
absolute error = 5.07656961e-23
relative error = 1.3280002734206495751683732805176e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0378
y[1] (analytic) = 3.8229995786070039810185918813637
y[1] (numeric) = 3.8229995786070039810186427842779
absolute error = 5.09029142e-23
relative error = 1.3314914938742322201025231180887e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0379
y[1] (analytic) = 3.8232818926803330861442149777232
y[1] (numeric) = 3.8232818926803330861442660178693
absolute error = 5.10401461e-23
relative error = 1.3349825498798892127024835039007e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.038
y[1] (analytic) = 3.8235642349864811416005180490368
y[1] (numeric) = 3.8235642349864811416005692264285
absolute error = 5.11773917e-23
relative error = 1.3384734387803725841918122060238e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0381
y[1] (analytic) = 3.8238466055282715704513345024195
y[1] (numeric) = 3.8238466055282715704513858170705
absolute error = 5.13146510e-23
relative error = 1.3419641605343838015764479923480e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0382
y[1] (analytic) = 3.8241290043085280781169217142285
y[1] (numeric) = 3.8241290043085280781169731661525
absolute error = 5.14519240e-23
relative error = 1.3454547151006335252168838941648e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0383
y[1] (analytic) = 3.8244114313300746524021980842892
y[1] (numeric) = 3.8244114313300746524022496735
absolute error = 5.15892108e-23
relative error = 1.3489451050526230406877237657473e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0384
y[1] (analytic) = 3.8246938865957355635249829139682
y[1] (numeric) = 3.8246938865957355635250346404794
absolute error = 5.17265112e-23
relative error = 1.3524353251193254265732222803270e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0385
y[1] (analytic) = 3.8249763701083353641442391083744
y[1] (numeric) = 3.8249763701083353641442909721999
absolute error = 5.18638255e-23
relative error = 1.3559253831032439371302817094813e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0386
y[1] (analytic) = 3.825258881870698889388318702973
y[1] (numeric) = 3.8252588818706988893883707041264
absolute error = 5.20011534e-23
relative error = 1.3594152711193610410230564942275e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0387
y[1] (analytic) = 3.8255414218856512568832112148919
y[1] (numeric) = 3.8255414218856512568832633533869
absolute error = 5.21384950e-23
relative error = 1.3629049917410217164270410121865e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0388
y[1] (analytic) = 3.8258239901560178667807948192054
y[1] (numeric) = 3.8258239901560178667808470950558
absolute error = 5.22758504e-23
relative error = 1.3663945475408078136683370614980e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0389
y[1] (analytic) = 3.8261065866846244017870903504765
y[1] (numeric) = 3.826106586684624401787142763696
absolute error = 5.24132195e-23
relative error = 1.3698839358632922386370364189442e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.039
y[1] (analytic) = 3.8263892114742968271905181298406
y[1] (numeric) = 3.826389211474296827190570680443
absolute error = 5.25506024e-23
relative error = 1.3733731592806891457661887730820e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0391
y[1] (analytic) = 3.8266718645278613908901576179135
y[1] (numeric) = 3.8266718645278613908902103059125
absolute error = 5.26879990e-23
relative error = 1.3768622151379759892715913733475e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0392
y[1] (analytic) = 3.8269545458481446234240098938054
y[1] (numeric) = 3.8269545458481446234240627192147
absolute error = 5.28254093e-23
relative error = 1.3803511033939554234290015932637e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0393
y[1] (analytic) = 3.8272372554379733379972629605245
y[1] (numeric) = 3.8272372554379733379973159233579
absolute error = 5.29628334e-23
relative error = 1.3838398266202901110403091291430e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0394
y[1] (analytic) = 3.8275199933001746305105598770528
y[1] (numeric) = 3.8275199933001746305106129773241
absolute error = 5.31002713e-23
relative error = 1.3873283847752220519108561787301e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0395
y[1] (analytic) = 3.8278027594375758795882697173758
y[1] (numeric) = 3.8278027594375758795883229550986
absolute error = 5.32377228e-23
relative error = 1.3908167725920728736762230893556e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0396
y[1] (analytic) = 3.8280855538530047466067613567495
y[1] (numeric) = 3.8280855538530047466068147319377
absolute error = 5.33751882e-23
relative error = 1.3943049978670764620191479582965e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0397
y[1] (analytic) = 3.8283683765492891757226800854884
y[1] (numeric) = 3.8283683765492891757227335981557
absolute error = 5.35126673e-23
relative error = 1.3977930553337658760361751529590e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.1MB, time=3.03
NO POLE
x[1] = 1.0398
y[1] (analytic) = 3.8286512275292573939012270505547
y[1] (numeric) = 3.8286512275292573939012807007149
absolute error = 5.36501602e-23
relative error = 1.4012809475628848387577157524433e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0399
y[1] (analytic) = 3.8289341067957379109444415252345
y[1] (numeric) = 3.8289341067957379109444953129013
absolute error = 5.37876668e-23
relative error = 1.4047686719010286127032340989013e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.04
y[1] (analytic) = 3.8292170143515595195194860071813
y[1] (numeric) = 3.8292170143515595195195399323685
absolute error = 5.39251872e-23
relative error = 1.4082562309185734010994718724644e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0401
y[1] (analytic) = 3.8294999501995512951869341451116
y[1] (numeric) = 3.8294999501995512951869882078329
absolute error = 5.40627213e-23
relative error = 1.4117436219625188222722096759566e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0402
y[1] (analytic) = 3.8297829143425425964290614944339
y[1] (numeric) = 3.829782914342542596429115694703
absolute error = 5.42002691e-23
relative error = 1.4152308449917595386217308785329e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0403
y[1] (analytic) = 3.8300659067833630646781391020952
y[1] (numeric) = 3.8300659067833630646781934399258
absolute error = 5.43378306e-23
relative error = 1.4187178999651993972684207445009e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0404
y[1] (analytic) = 3.8303489275248426243447299209271
y[1] (numeric) = 3.8303489275248426243447843963331
absolute error = 5.44754060e-23
relative error = 1.4222047920632078500397922292518e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0405
y[1] (analytic) = 3.8306319765698114828459880537755
y[1] (numeric) = 3.8306319765698114828460426667706
absolute error = 5.46129951e-23
relative error = 1.4256915160224790550785833239198e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0406
y[1] (analytic) = 3.830915053921100130633960827695
y[1] (numeric) = 3.830915053921100130634015578293
absolute error = 5.47505980e-23
relative error = 1.4291780744122868675260208067439e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0407
y[1] (analytic) = 3.8311981595815393412238936984937
y[1] (numeric) = 3.8311981595815393412239485867083
absolute error = 5.48882146e-23
relative error = 1.4326644645808437420145392545772e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0408
y[1] (analytic) = 3.8314812935539601712225379859085
y[1] (numeric) = 3.8314812935539601712225930117535
absolute error = 5.50258450e-23
relative error = 1.4361506890970561547686065800387e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0409
y[1] (analytic) = 3.831764455841193960356461439697
y[1] (numeric) = 3.8317644558411939603565166031861
absolute error = 5.51634891e-23
relative error = 1.4396367453095407621391438043498e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.041
y[1] (analytic) = 3.832047646446072331500361636926
y[1] (numeric) = 3.832047646446072331500416938073
absolute error = 5.53011470e-23
relative error = 1.4431226357868366966577164868785e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0411
y[1] (analytic) = 3.8323308653714271907053822107427
y[1] (numeric) = 3.8323308653714271907054376495614
absolute error = 5.54388187e-23
relative error = 1.4466083604873428173100256111108e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0412
y[1] (analytic) = 3.8326141126200907272274319109094
y[1] (numeric) = 3.8326141126200907272274874874135
absolute error = 5.55765041e-23
relative error = 1.4500939167602820246068231364248e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0413
y[1] (analytic) = 3.8328973881948954135555064963862
y[1] (numeric) = 3.8328973881948954135555622105895
absolute error = 5.57142033e-23
relative error = 1.4535793071736425154183298817536e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0414
y[1] (analytic) = 3.8331806920986740054400134602447
y[1] (numeric) = 3.833180692098674005440069312161
absolute error = 5.58519163e-23
relative error = 1.4570645316858508287805963128087e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0415
y[1] (analytic) = 3.8334640243342595419210995871955
y[1] (numeric) = 3.8334640243342595419211555768386
absolute error = 5.59896431e-23
relative error = 1.4605495902553427388075050939009e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0416
y[1] (analytic) = 3.8337473849044853453569813440136
y[1] (numeric) = 3.8337473849044853453570374713972
absolute error = 5.61273836e-23
relative error = 1.4640344802321493458977201410589e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0417
y[1] (analytic) = 3.8340307738121850214522781031437
y[1] (numeric) = 3.8340307738121850214523343682816
absolute error = 5.62651379e-23
relative error = 1.4675192041835243985582309113375e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0418
y[1] (analytic) = 3.8343141910601924592863481997704
y[1] (numeric) = 3.8343141910601924592864046026764
absolute error = 5.64029060e-23
relative error = 1.4710037620679313459896017707742e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0419
y[1] (analytic) = 3.8345976366513418313416278226354
y[1] (numeric) = 3.8345976366513418313416843633232
absolute error = 5.65406878e-23
relative error = 1.4744881512360073304135338740063e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.042
y[1] (analytic) = 3.834881110588467593531972738885
y[1] (numeric) = 3.8348811105884675935320294173684
absolute error = 5.66784834e-23
relative error = 1.4779723742544553496251007580654e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0421
y[1] (analytic) = 3.8351646128744044852310028532329
y[1] (numeric) = 3.8351646128744044852310596695257
absolute error = 5.68162928e-23
relative error = 1.4814564310817665241816716280789e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0422
y[1] (analytic) = 3.8354481435119875293004496017196
y[1] (numeric) = 3.8354481435119875293005065558357
absolute error = 5.69541161e-23
relative error = 1.4849403242836984622506942340174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0423
y[1] (analytic) = 3.8357317025040520321185061803537
y[1] (numeric) = 3.8357317025040520321185632723067
absolute error = 5.70919530e-23
relative error = 1.4884240459969889820414683397172e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0424
y[1] (analytic) = 3.8360152898534335836081806089169
y[1] (numeric) = 3.8360152898534335836082378387207
absolute error = 5.72298038e-23
relative error = 1.4919076040019286656978544709010e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0425
y[1] (analytic) = 3.8362989055629680572656516302184
y[1] (numeric) = 3.8362989055629680572657089978867
absolute error = 5.73676683e-23
relative error = 1.4953909930431092511009559127544e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0426
y[1] (analytic) = 3.8365825496354916101886274450798
y[1] (numeric) = 3.8365825496354916101886849506264
absolute error = 5.75055466e-23
relative error = 1.4988742156861325001046924141223e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.1MB, time=3.25
NO POLE
x[1] = 1.0427
y[1] (analytic) = 3.8368662220738406831047072833359
y[1] (numeric) = 3.8368662220738406831047649267746
absolute error = 5.76434387e-23
relative error = 1.5023572718895448924453930455653e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0428
y[1] (analytic) = 3.8371499228808520003997458111346
y[1] (numeric) = 3.8371499228808520003998035924792
absolute error = 5.77813446e-23
relative error = 1.5058401616119021375474626246554e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0429
y[1] (analytic) = 3.8374336520593625701462203748188
y[1] (numeric) = 3.8374336520593625701462782940832
absolute error = 5.79192644e-23
relative error = 1.5093228874176774207905894099222e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.043
y[1] (analytic) = 3.8377174096122096841316010816751
y[1] (numeric) = 3.8377174096122096841316591388729
absolute error = 5.80571978e-23
relative error = 1.5128054414477201696793105122404e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0431
y[1] (analytic) = 3.8380011955422309178867237178316
y[1] (numeric) = 3.8380011955422309178867819129767
absolute error = 5.81951451e-23
relative error = 1.5162878314783385202559924307928e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0432
y[1] (analytic) = 3.8382850098522641307141655035906
y[1] (numeric) = 3.8382850098522641307142238366968
absolute error = 5.83331062e-23
relative error = 1.5197700548622168498554644825267e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0433
y[1] (analytic) = 3.8385688525451474657166236864776
y[1] (numeric) = 3.8385688525451474657166821575587
absolute error = 5.84710811e-23
relative error = 1.5232521115579570101030674417987e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0434
y[1] (analytic) = 3.838852723623719349825296972292
y[1] (numeric) = 3.8388527236237193498253555813618
absolute error = 5.86090698e-23
relative error = 1.5267340015241700798150600686900e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0435
y[1] (analytic) = 3.8391366230908184938282697944428
y[1] (numeric) = 3.839136623090818493828328541515
absolute error = 5.87470722e-23
relative error = 1.5302157221147240513001150693722e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0436
y[1] (analytic) = 3.8394205509492838923988994218528
y[1] (numeric) = 3.8394205509492838923989583069414
absolute error = 5.88850886e-23
relative error = 1.5336972811025053963503437172759e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0437
y[1] (analytic) = 3.8397045072019548241242059057165
y[1] (numeric) = 3.8397045072019548241242649288352
absolute error = 5.90231187e-23
relative error = 1.5371786706318959330078091394727e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0438
y[1] (analytic) = 3.8399884918516708515332648653933
y[1] (numeric) = 3.8399884918516708515333240265559
absolute error = 5.91611626e-23
relative error = 1.5406598932662959579632617084487e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0439
y[1] (analytic) = 3.8402725049012718211256031137222
y[1] (numeric) = 3.8402725049012718211256624129425
absolute error = 5.92992203e-23
relative error = 1.5441409489643626797303631847473e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.044
y[1] (analytic) = 3.8405565463535978633995971220407
y[1] (numeric) = 3.8405565463535978633996565593325
absolute error = 5.94372918e-23
relative error = 1.5476218376847625315094396917258e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0441
y[1] (analytic) = 3.8408406162114893928808743251923
y[1] (numeric) = 3.8408406162114893928809339005694
absolute error = 5.95753771e-23
relative error = 1.5511025593861711707694168857911e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0442
y[1] (analytic) = 3.8411247144777871081507172668062
y[1] (numeric) = 3.8411247144777871081507769802825
absolute error = 5.97134763e-23
relative error = 1.5545831166306776230138044187592e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0443
y[1] (analytic) = 3.8414088411553319918744705851342
y[1] (numeric) = 3.8414088411553319918745304367234
absolute error = 5.98515892e-23
relative error = 1.5580635041699751459572277935490e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0444
y[1] (analytic) = 3.8416929962469653108299508397275
y[1] (numeric) = 3.8416929962469653108300108294434
absolute error = 5.99897159e-23
relative error = 1.5615437245663637794465523262654e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0445
y[1] (analytic) = 3.8419771797555286159358591792386
y[1] (numeric) = 3.8419771797555286159359193070951
absolute error = 6.01278565e-23
relative error = 1.5650237803813825697119654819073e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0446
y[1] (analytic) = 3.842261391683863742280196850632
y[1] (numeric) = 3.8422613916838637422802571166429
absolute error = 6.02660109e-23
relative error = 1.5685036689705417314637837599175e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0447
y[1] (analytic) = 3.8425456320348128091486835500882
y[1] (numeric) = 3.8425456320348128091487439542672
absolute error = 6.04041790e-23
relative error = 1.5719833876901308435364450742839e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0448
y[1] (analytic) = 3.8428299008112182200531786158839
y[1] (numeric) = 3.8428299008112182200532391582449
absolute error = 6.05423610e-23
relative error = 1.5754629417039655480642441036856e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0449
y[1] (analytic) = 3.843114198015922662760105063535
y[1] (numeric) = 3.8431141980159226627601657440918
absolute error = 6.06805568e-23
relative error = 1.5789423283681613443920197285091e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.045
y[1] (analytic) = 3.843398523651769109318876463484
y[1] (numeric) = 3.8433985236517691093189372822505
absolute error = 6.08187665e-23
relative error = 1.5824215502433408505607894809935e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0451
y[1] (analytic) = 3.8436828777216008160903266616181
y[1] (numeric) = 3.8436828777216008160903876186082
absolute error = 6.09569901e-23
relative error = 1.5859006072876945169332331945937e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0452
y[1] (analytic) = 3.8439672602282613237751423429014
y[1] (numeric) = 3.8439672602282613237752034381287
absolute error = 6.10952273e-23
relative error = 1.5893794916549851502256994475919e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0453
y[1] (analytic) = 3.8442516711745944574422984384048
y[1] (numeric) = 3.8442516711745944574423596718832
absolute error = 6.12334784e-23
relative error = 1.5928582111090134673050420393500e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0454
y[1] (analytic) = 3.8445361105634443265574963760202
y[1] (numeric) = 3.8445361105634443265575577477635
absolute error = 6.13717433e-23
relative error = 1.5963367630069036099152679052038e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0455
y[1] (analytic) = 3.8448205783976553250116051751407
y[1] (numeric) = 3.8448205783976553250116666851628
absolute error = 6.15100221e-23
relative error = 1.5998151499083619882260993398030e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=61.0MB, alloc=4.2MB, time=3.47
x[1] = 1.0456
y[1] (analytic) = 3.8451050746800721311491053855934
y[1] (numeric) = 3.8451050746800721311491670339081
absolute error = 6.16483147e-23
relative error = 1.6032933691709161499940601297133e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0457
y[1] (analytic) = 3.8453895994135397077965358711075
y[1] (numeric) = 3.8453895994135397077965976577286
absolute error = 6.17866211e-23
relative error = 1.6067714207533893670797902859206e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0458
y[1] (analytic) = 3.8456741526009033022909434376036
y[1] (numeric) = 3.845674152600903302291005362545
absolute error = 6.19249414e-23
relative error = 1.6102493072149384417691661978787e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0459
y[1] (analytic) = 3.845958734245008446508335306588
y[1] (numeric) = 3.8459587342450084465083973698635
absolute error = 6.20632755e-23
relative error = 1.6137270259136959445837801347647e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.046
y[1] (analytic) = 3.8462433443487009568921344339362
y[1] (numeric) = 3.8462433443487009568921966355597
absolute error = 6.22016235e-23
relative error = 1.6172045794084523258572926288263e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0461
y[1] (analytic) = 3.8465279829148269344816376743512
y[1] (numeric) = 3.8465279829148269344817000143365
absolute error = 6.23399853e-23
relative error = 1.6206819650577434655814101185213e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0462
y[1] (analytic) = 3.8468126499462327649404767917798
y[1] (numeric) = 3.8468126499462327649405392701407
absolute error = 6.24783609e-23
relative error = 1.6241591828204387724878646376254e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0463
y[1] (analytic) = 3.847097345445765118585082316073
y[1] (numeric) = 3.8470973454457651185851449328233
absolute error = 6.26167503e-23
relative error = 1.6276362326554168703357781732267e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0464
y[1] (analytic) = 3.8473820694162709504131502461736
y[1] (numeric) = 3.8473820694162709504132130013272
absolute error = 6.27551536e-23
relative error = 1.6311131171207355836186893005018e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0465
y[1] (analytic) = 3.8476668218605975001321116001174
y[1] (numeric) = 3.8476668218605975001321744936881
absolute error = 6.28935707e-23
relative error = 1.6345898335757372676846325536679e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0466
y[1] (analytic) = 3.8479516027815922921876048121308
y[1] (numeric) = 3.8479516027815922921876678441324
absolute error = 6.30320016e-23
relative error = 1.6380663819793282165489461441408e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0467
y[1] (analytic) = 3.8482364121821031357919509771111
y[1] (numeric) = 3.8482364121821031357920141475576
absolute error = 6.31704465e-23
relative error = 1.6415427674876098320395781279893e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0468
y[1] (analytic) = 3.8485212500649781249526319427736
y[1] (numeric) = 3.8485212500649781249526952516787
absolute error = 6.33089051e-23
relative error = 1.6450189822631510092405111558415e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0469
y[1] (analytic) = 3.8488061164330656385007712497498
y[1] (numeric) = 3.8488061164330656385008346971274
absolute error = 6.34473776e-23
relative error = 1.6484950314618792937489221797584e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.047
y[1] (analytic) = 3.8490910112892143401196179199226
y[1] (numeric) = 3.8490910112892143401196815057865
absolute error = 6.35858639e-23
relative error = 1.6519709124441449385777237238742e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0471
y[1] (analytic) = 3.8493759346362731783730330932825
y[1] (numeric) = 3.8493759346362731783730968176466
absolute error = 6.37243641e-23
relative error = 1.6554466277667240469955998513418e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0472
y[1] (analytic) = 3.8496608864770913867339795135899
y[1] (numeric) = 3.8496608864770913867340433764681
absolute error = 6.38628782e-23
relative error = 1.6589221773880013695071752546074e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0473
y[1] (analytic) = 3.8499458668145184836130138631286
y[1] (numeric) = 3.8499458668145184836130778645347
absolute error = 6.40014061e-23
relative error = 1.6623975586689318039753978759712e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0474
y[1] (analytic) = 3.850230875651404272386781946835
y[1] (numeric) = 3.8502308756514042723868460867828
absolute error = 6.41399478e-23
relative error = 1.6658727715684954501195911815062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0475
y[1] (analytic) = 3.8505159129905988414265167260882
y[1] (numeric) = 3.8505159129905988414265810045916
absolute error = 6.42785034e-23
relative error = 1.6693478186427362009339548886861e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0476
y[1] (analytic) = 3.8508009788349525641265392024463
y[1] (numeric) = 3.8508009788349525641266036195192
absolute error = 6.44170729e-23
relative error = 1.6728226998500758138716508691352e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0477
y[1] (analytic) = 3.8510860731873160989327621516133
y[1] (numeric) = 3.8510860731873160989328267072695
absolute error = 6.45556562e-23
relative error = 1.6762974125522752261864661788183e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0478
y[1] (analytic) = 3.8513711960505403893711967079219
y[1] (numeric) = 3.8513711960505403893712614021753
absolute error = 6.46942534e-23
relative error = 1.6797719593048292795930013330445e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0479
y[1] (analytic) = 3.8516563474274766640764617996174
y[1] (numeric) = 3.8516563474274766640765266324819
absolute error = 6.48328645e-23
relative error = 1.6832463400661874961737318735867e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.048
y[1] (analytic) = 3.8519415273209764368202964352279
y[1] (numeric) = 3.8519415273209764368203614067172
absolute error = 6.49714893e-23
relative error = 1.6867205496026218489575162153289e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0481
y[1] (analytic) = 3.8522267357338915065400748413048
y[1] (numeric) = 3.8522267357338915065401399514329
absolute error = 6.51101281e-23
relative error = 1.6901945956614572277620934248921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0482
y[1] (analytic) = 3.852511972669073957367324451821
y[1] (numeric) = 3.8525119726690739573673897006018
absolute error = 6.52487808e-23
relative error = 1.6936684756048852923743115585396e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0483
y[1] (analytic) = 3.8527972381293761586562467495098
y[1] (numeric) = 3.8527972381293761586563121369571
absolute error = 6.53874473e-23
relative error = 1.6971421867958757769382742736989e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0484
y[1] (analytic) = 3.8530825321176507650122409594303
y[1] (numeric) = 3.8530825321176507650123064855579
absolute error = 6.55261276e-23
relative error = 1.7006157291935010278852066392471e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=64.8MB, alloc=4.2MB, time=3.70
x[1] = 1.0485
y[1] (analytic) = 3.8533678546367507163204305950455
y[1] (numeric) = 3.8533678546367507163204962598673
absolute error = 6.56648218e-23
relative error = 1.7040891053519750573736135611009e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0486
y[1] (analytic) = 3.8536532056895292377741928570973
y[1] (numeric) = 3.8536532056895292377742586606272
absolute error = 6.58035299e-23
relative error = 1.7075623152298121383051777771793e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0487
y[1] (analytic) = 3.8539385852788398399036908855639
y[1] (numeric) = 3.8539385852788398399037568278158
absolute error = 6.59422519e-23
relative error = 1.7110353587855358038837785222009e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0488
y[1] (analytic) = 3.8542239934075363186044088649854
y[1] (numeric) = 3.8542239934075363186044749459731
absolute error = 6.60809877e-23
relative error = 1.7145082333831228439322554592107e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0489
y[1] (analytic) = 3.8545094300784727551656899834421
y[1] (numeric) = 3.8545094300784727551657562031796
absolute error = 6.62197375e-23
relative error = 1.7179809441704194512734124409600e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.049
y[1] (analytic) = 3.8547948952945035162992772454722
y[1] (numeric) = 3.8547948952945035162993436039733
absolute error = 6.63585011e-23
relative error = 1.7214534859170570462353427906668e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0491
y[1] (analytic) = 3.8550803890584832541678571392126
y[1] (numeric) = 3.8550803890584832541679236364912
absolute error = 6.64972786e-23
relative error = 1.7249258611761521745117946574744e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0492
y[1] (analytic) = 3.8553659113732669064136061580498
y[1] (numeric) = 3.8553659113732669064136727941197
absolute error = 6.66360699e-23
relative error = 1.7283980673124871130715903961670e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0493
y[1] (analytic) = 3.8556514622417096961867401770651
y[1] (numeric) = 3.8556514622417096961868069519402
absolute error = 6.67748751e-23
relative error = 1.7318701068788126375079037053621e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0494
y[1] (analytic) = 3.8559370416666671321740666845611
y[1] (numeric) = 3.8559370416666671321741335982553
absolute error = 6.69136942e-23
relative error = 1.7353419798337170357764118902921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0495
y[1] (analytic) = 3.8562226496509950086275398689531
y[1] (numeric) = 3.8562226496509950086276069214803
absolute error = 6.70525272e-23
relative error = 1.7388136861357978527324244951922e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0496
y[1] (analytic) = 3.8565082861975494053928185613128
y[1] (numeric) = 3.8565082861975494053928857526869
absolute error = 6.71913741e-23
relative error = 1.7422852257436618897049731207020e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0497
y[1] (analytic) = 3.8567939513091866879378270338483
y[1] (numeric) = 3.8567939513091866879378943640832
absolute error = 6.73302349e-23
relative error = 1.7457565986159252040707049864413e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0498
y[1] (analytic) = 3.8570796449887635073813186546075
y[1] (numeric) = 3.8570796449887635073813861237171
absolute error = 6.74691096e-23
relative error = 1.7492278047112131088275802819271e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0499
y[1] (analytic) = 3.8573653672391368005214423986893
y[1] (numeric) = 3.8573653672391368005215100066874
absolute error = 6.76079981e-23
relative error = 1.7526988413957171319184992266071e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.05
y[1] (analytic) = 3.8576511180631637898643122162488
y[1] (numeric) = 3.8576511180631637898643799631493
absolute error = 6.77469005e-23
relative error = 1.7561697112209082006970576147390e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0501
y[1] (analytic) = 3.8579368974637019836525792575823
y[1] (numeric) = 3.8579368974637019836526471433992
absolute error = 6.78858169e-23
relative error = 1.7596404167374983500782674382461e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0502
y[1] (analytic) = 3.8582227054436091758940069555778
y[1] (numeric) = 3.858222705443609175894074980325
absolute error = 6.80247472e-23
relative error = 1.7631109553117068710279331554546e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0503
y[1] (analytic) = 3.8585085420057434463900489658164
y[1] (numeric) = 3.8585085420057434463901171295076
absolute error = 6.81636912e-23
relative error = 1.7665813217188554133528845532836e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0504
y[1] (analytic) = 3.8587944071529631607644299646103
y[1] (numeric) = 3.8587944071529631607644982672595
absolute error = 6.83026492e-23
relative error = 1.7700515236932257024026491241755e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0505
y[1] (analytic) = 3.8590803008881269704917293052642
y[1] (numeric) = 3.8590803008881269704917977468853
absolute error = 6.84416211e-23
relative error = 1.7735215586016408290486608349628e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0506
y[1] (analytic) = 3.8593662232140938129259675328451
y[1] (numeric) = 3.859366223214093812926036113452
absolute error = 6.85806069e-23
relative error = 1.7769914264028001081421784289634e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0507
y[1] (analytic) = 3.8596521741337229113291957577457
y[1] (numeric) = 3.8596521741337229113292644773524
absolute error = 6.87196067e-23
relative error = 1.7804611296463191489221550647067e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0508
y[1] (analytic) = 3.8599381536498737749000878883295
y[1] (numeric) = 3.8599381536498737749001567469498
absolute error = 6.88586203e-23
relative error = 1.7839306631089097260479851734619e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0509
y[1] (analytic) = 3.8602241617654061988025357229408
y[1] (numeric) = 3.8602241617654061988026047205885
absolute error = 6.89976477e-23
relative error = 1.7874000267498747826696035419609e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.051
y[1] (analytic) = 3.8605101984831802641942469015675
y[1] (numeric) = 3.8605101984831802641943160382566
absolute error = 6.91366891e-23
relative error = 1.7908692257091888491326523226668e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0511
y[1] (analytic) = 3.8607962638060563382553457174423
y[1] (numeric) = 3.8607962638060563382554149931868
absolute error = 6.92757445e-23
relative error = 1.7943382599450216761146008071809e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0512
y[1] (analytic) = 3.8610823577368950742169767888678
y[1] (numeric) = 3.8610823577368950742170462036815
absolute error = 6.94148137e-23
relative error = 1.7978071242356576300707370434445e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0513
y[1] (analytic) = 3.8613684802785574113899115915512
y[1] (numeric) = 3.8613684802785574113899811454481
absolute error = 6.95538969e-23
relative error = 1.8012758237199474082166177359125e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0514
y[1] (analytic) = 3.8616546314339045751931578517367
y[1] (numeric) = 3.8616546314339045751932275447306
absolute error = 6.96929939e-23
relative error = 1.8047443531769615593317671946446e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.2MB, time=3.92
NO POLE
x[1] = 1.0515
y[1] (analytic) = 3.8619408112057980771825718004187
y[1] (numeric) = 3.8619408112057980771826416325235
absolute error = 6.98321048e-23
relative error = 1.8082127151554299934826046976118e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0516
y[1] (analytic) = 3.8622270195970997150794732889245
y[1] (numeric) = 3.8622270195970997150795432601542
absolute error = 6.99712297e-23
relative error = 1.8116809122033242768085132107276e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0517
y[1] (analytic) = 3.8625132566106715727992637661515
y[1] (numeric) = 3.86251325661067157279933387652
absolute error = 7.01103685e-23
relative error = 1.8151489416898819675955878876323e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0518
y[1] (analytic) = 3.8627995222493760204800471177449
y[1] (numeric) = 3.862799522249376020480117367266
absolute error = 7.02495211e-23
relative error = 1.8186168009851173890127082791691e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0519
y[1] (analytic) = 3.8630858165160757145112533675024
y[1] (numeric) = 3.8630858165160757145113237561901
absolute error = 7.03886877e-23
relative error = 1.8220844952256340044573719886499e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.052
y[1] (analytic) = 3.8633721394136335975622652412928
y[1] (numeric) = 3.863372139413633597562335769161
absolute error = 7.05278682e-23
relative error = 1.8255520217812727643355677653062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0521
y[1] (analytic) = 3.8636584909449128986110475937732
y[1] (numeric) = 3.8636584909449128986111182608359
absolute error = 7.06670627e-23
relative error = 1.8290193831990922140236973615153e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0522
y[1] (analytic) = 3.863944871112777132972779698193
y[1] (numeric) = 3.863944871112777132972850504464
absolute error = 7.08062710e-23
relative error = 1.8324865742613069020527697514249e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0523
y[1] (analytic) = 3.8642312799200901023284903995691
y[1] (numeric) = 3.8642312799200901023285613450624
absolute error = 7.09454933e-23
relative error = 1.8359536001030225251719074609297e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0524
y[1] (analytic) = 3.8645177173697158947536961315204
y[1] (numeric) = 3.8645177173697158947537672162499
absolute error = 7.10847295e-23
relative error = 1.8394204580948844488134083448102e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0525
y[1] (analytic) = 3.8648041834645188847470417970467
y[1] (numeric) = 3.8648041834645188847471130210263
absolute error = 7.12239796e-23
relative error = 1.8428871481957677536506241207948e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0526
y[1] (analytic) = 3.8650906782073637332589445135388
y[1] (numeric) = 3.8650906782073637332590158767824
absolute error = 7.13632436e-23
relative error = 1.8463536703645567639634173895935e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0527
y[1] (analytic) = 3.865377201601115387720240222307
y[1] (numeric) = 3.8653772016011153877203117248285
absolute error = 7.15025215e-23
relative error = 1.8498200245601450472061870371278e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0528
y[1] (analytic) = 3.8656637536486390820708331629129
y[1] (numeric) = 3.8656637536486390820709048047263
absolute error = 7.16418134e-23
relative error = 1.8532862133283132791327887088844e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0529
y[1] (analytic) = 3.8659503343528003367883482125926
y[1] (numeric) = 3.8659503343528003367884199937119
absolute error = 7.17811193e-23
relative error = 1.8567522366273982208860252507044e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.053
y[1] (analytic) = 3.8662369437164649589167860910568
y[1] (numeric) = 3.8662369437164649589168580114959
absolute error = 7.19204391e-23
relative error = 1.8602180918292515837825341083687e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0531
y[1] (analytic) = 3.8665235817424990420951814309545
y[1] (numeric) = 3.8665235817424990420952534907273
absolute error = 7.20597728e-23
relative error = 1.8636837788928039591862417121228e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0532
y[1] (analytic) = 3.8668102484337689665862637142874
y[1] (numeric) = 3.8668102484337689665863359134078
absolute error = 7.21991204e-23
relative error = 1.8671492977769951794751229851319e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0533
y[1] (analytic) = 3.8670969437931413993051210750611
y[1] (numeric) = 3.867096943793141399305193413543
absolute error = 7.23384819e-23
relative error = 1.8706146484407743176080566999460e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0534
y[1] (analytic) = 3.8673836678234832938478669684596
y[1] (numeric) = 3.867383667823483293847939446317
absolute error = 7.24778574e-23
relative error = 1.8740798334288271083589306539470e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0535
y[1] (analytic) = 3.8676704205276618905203097068308
y[1] (numeric) = 3.8676704205276618905203823240776
absolute error = 7.26172468e-23
relative error = 1.8775448501140102663794630714264e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0536
y[1] (analytic) = 3.8679572019085447163666248627681
y[1] (numeric) = 3.8679572019085447163666976194182
absolute error = 7.27566501e-23
relative error = 1.8810096984553006115421229927487e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0537
y[1] (analytic) = 3.8682440119689995851980305395759
y[1] (numeric) = 3.8682440119689995851981034356434
absolute error = 7.28960675e-23
relative error = 1.8844743835819888519418271284428e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0538
y[1] (analytic) = 3.8685308507118945976214655094065
y[1] (numeric) = 3.8685308507118945976215385449052
absolute error = 7.30354987e-23
relative error = 1.8879388976970382692153156293061e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0539
y[1] (analytic) = 3.8688177181400981410682702193523
y[1] (numeric) = 3.8688177181400981410683433942962
absolute error = 7.31749439e-23
relative error = 1.8914032459295664136623909594147e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.054
y[1] (analytic) = 3.8691046142564788898228706657838
y[1] (numeric) = 3.8691046142564788898229439801869
absolute error = 7.33144031e-23
relative error = 1.8948674282380120998310118597430e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0541
y[1] (analytic) = 3.8693915390639058050514651372178
y[1] (numeric) = 3.869391539063905805051538591094
absolute error = 7.34538762e-23
relative error = 1.8983314419964377766074163498103e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0542
y[1] (analytic) = 3.8696784925652481348307138260029
y[1] (numeric) = 3.8696784925652481348307874193661
absolute error = 7.35933632e-23
relative error = 1.9017952871638757737656458068861e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0543
y[1] (analytic) = 3.8699654747633754141764313091102
y[1] (numeric) = 3.8699654747633754141765050419744
absolute error = 7.37328642e-23
relative error = 1.9052589662833700380191229122828e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.2MB, time=4.14
NO POLE
x[1] = 1.0544
y[1] (analytic) = 3.8702524856611574650722818983154
y[1] (numeric) = 3.8702524856611574650723557706945
absolute error = 7.38723791e-23
relative error = 1.9087224767295857406468352199090e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0545
y[1] (analytic) = 3.8705395252614643964984778600593
y[1] (numeric) = 3.8705395252614643964985518719673
absolute error = 7.40119080e-23
relative error = 1.9121858210452020867316862890282e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0546
y[1] (analytic) = 3.8708265935671666044604805052739
y[1] (numeric) = 3.8708265935671666044605546567248
absolute error = 7.41514509e-23
relative error = 1.9156489991887135569733385774765e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0547
y[1] (analytic) = 3.8711136905811347720177041494609
y[1] (numeric) = 3.8711136905811347720177784404686
absolute error = 7.42910077e-23
relative error = 1.9191120085353879855807978099544e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0548
y[1] (analytic) = 3.8714008163062398693122229433097
y[1] (numeric) = 3.8714008163062398693122973738882
absolute error = 7.44305785e-23
relative error = 1.9225748516273575452732641077201e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0549
y[1] (analytic) = 3.8716879707453531535974805741421
y[1] (numeric) = 3.8716879707453531535975551443054
absolute error = 7.45701633e-23
relative error = 1.9260375284231445578613382104038e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.055
y[1] (analytic) = 3.8719751539013461692670028384709
y[1] (numeric) = 3.8719751539013461692670775482329
absolute error = 7.47097620e-23
relative error = 1.9295000362986194332331492746397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0551
y[1] (analytic) = 3.8722623657770907478831130859587
y[1] (numeric) = 3.8722623657770907478831879353333
absolute error = 7.48493746e-23
relative error = 1.9329623752128977505933771186345e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0552
y[1] (analytic) = 3.8725496063754590082056505350652
y[1] (numeric) = 3.8725496063754590082057255240664
absolute error = 7.49890012e-23
relative error = 1.9364245477073824112177714428632e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0553
y[1] (analytic) = 3.8728368756993233562206914606696
y[1] (numeric) = 3.8728368756993233562207665893114
absolute error = 7.51286418e-23
relative error = 1.9398865537406328337933701109034e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0554
y[1] (analytic) = 3.8731241737515564851692732539554
y[1] (numeric) = 3.8731241737515564851693485222518
absolute error = 7.52682964e-23
relative error = 1.9433483932712177240318313568200e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0555
y[1] (analytic) = 3.8734115005350313755761213548445
y[1] (numeric) = 3.8734115005350313755761967628094
absolute error = 7.54079649e-23
relative error = 1.9468100636760115814304746907375e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0556
y[1] (analytic) = 3.8736988560526212952783790572685
y[1] (numeric) = 3.8736988560526212952784546049158
absolute error = 7.55476473e-23
relative error = 1.9502715649141762258118148158601e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0557
y[1] (analytic) = 3.8739862403071997994543401875639
y[1] (numeric) = 3.8739862403071997994544158749076
absolute error = 7.56873437e-23
relative error = 1.9537328995262031816298355812822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0558
y[1] (analytic) = 3.8742736533016407306521846562793
y[1] (numeric) = 3.8742736533016407306522604833334
absolute error = 7.58270541e-23
relative error = 1.9571940674706982427655626906944e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0559
y[1] (analytic) = 3.874561095038818218818716883681
y[1] (numeric) = 3.8745610950388182188187928504595
absolute error = 7.59667785e-23
relative error = 1.9606550687062764879475809049020e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.056
y[1] (analytic) = 3.8748485655216066813281070992449
y[1] (numeric) = 3.8748485655216066813281832057618
absolute error = 7.61065169e-23
relative error = 1.9641159031915622803164932253765e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0561
y[1] (analytic) = 3.8751360647528808230106355154223
y[1] (numeric) = 3.8751360647528808230107117616915
absolute error = 7.62462692e-23
relative error = 1.9675765683046347179613161340314e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0562
y[1] (analytic) = 3.8754235927355156361814393759666
y[1] (numeric) = 3.8754235927355156361815157620021
absolute error = 7.63860355e-23
relative error = 1.9710370665850741969765768687449e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0563
y[1] (analytic) = 3.8757111494723864006692628791085
y[1] (numeric) = 3.8757111494723864006693394049243
absolute error = 7.65258158e-23
relative error = 1.9744973979915329033288478248106e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0564
y[1] (analytic) = 3.8759987349663686838452099758676
y[1] (numeric) = 3.8759987349663686838452866414777
absolute error = 7.66656101e-23
relative error = 1.9779575624826723056514652334285e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0565
y[1] (analytic) = 3.8762863492203383406515000437875
y[1] (numeric) = 3.8762863492203383406515768492058
absolute error = 7.68054183e-23
relative error = 1.9814175574373743830080755081641e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0566
y[1] (analytic) = 3.8765739922371715136302264363816
y[1] (numeric) = 3.8765739922371715136303033816221
absolute error = 7.69452405e-23
relative error = 1.9848773853944907821420430966156e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0567
y[1] (analytic) = 3.8768616640197446329521179085782
y[1] (numeric) = 3.8768616640197446329521949936549
absolute error = 7.70850767e-23
relative error = 1.9883370463127107892688164945727e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0568
y[1] (analytic) = 3.8771493645709344164453029184518
y[1] (numeric) = 3.8771493645709344164453801433787
absolute error = 7.72249269e-23
relative error = 1.9917965401507329715222361257065e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0569
y[1] (analytic) = 3.8774370938936178696240768055282
y[1] (numeric) = 3.8774370938936178696241541703193
absolute error = 7.73647911e-23
relative error = 1.9952558668672651765172386974678e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.057
y[1] (analytic) = 3.8777248519906722857176718459518
y[1] (numeric) = 3.8777248519906722857177493506211
absolute error = 7.75046693e-23
relative error = 1.9987150264210245319123666601754e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0571
y[1] (analytic) = 3.8780126388649752456990301848014
y[1] (numeric) = 3.8780126388649752456991078293628
absolute error = 7.76445614e-23
relative error = 2.0021740161920970610338755695992e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0572
y[1] (analytic) = 3.8783004545194046183135796458439
y[1] (numeric) = 3.8783004545194046183136574303114
absolute error = 7.77844675e-23
relative error = 2.0056328387182415653370548518277e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=76.2MB, alloc=4.2MB, time=4.35
x[1] = 1.0573
y[1] (analytic) = 3.8785882989568385601080124190126
y[1] (numeric) = 3.8785882989568385601080903434002
absolute error = 7.79243876e-23
relative error = 2.0090914939582029821809609157085e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0574
y[1] (analytic) = 3.8788761721801555154590666258977
y[1] (numeric) = 3.8788761721801555154591446902195
absolute error = 7.80643218e-23
relative error = 2.0125499844488018423302453343052e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0575
y[1] (analytic) = 3.8791640741922342166023107635384
y[1] (numeric) = 3.8791640741922342166023889678083
absolute error = 7.82042699e-23
relative error = 2.0160083049924776713185291959571e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0576
y[1] (analytic) = 3.8794520049959536836609310268018
y[1] (numeric) = 3.8794520049959536836610093710338
absolute error = 7.83442320e-23
relative error = 2.0194664581262609021826828961823e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0577
y[1] (analytic) = 3.8797399645941932246745215096392
y[1] (numeric) = 3.8797399645941932246745999938474
absolute error = 7.84842082e-23
relative error = 2.0229244463864259125199269117151e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0578
y[1] (analytic) = 3.8800279529898324356278772855061
y[1] (numeric) = 3.8800279529898324356279559097044
absolute error = 7.86241983e-23
relative error = 2.0263822645765880574102168745051e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0579
y[1] (analytic) = 3.8803159701857512004797903672338
y[1] (numeric) = 3.8803159701857512004798691314362
absolute error = 7.87642024e-23
relative error = 2.0298399152332315862833281885069e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.058
y[1] (analytic) = 3.8806040161848296911918485466416
y[1] (numeric) = 3.880604016184829691191927450862
absolute error = 7.89042204e-23
relative error = 2.0332973957382479475959264596870e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0581
y[1] (analytic) = 3.8808920909899483677572371141764
y[1] (numeric) = 3.8808920909899483677573161584289
absolute error = 7.90442525e-23
relative error = 2.0367547112044844303107788228503e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0582
y[1] (analytic) = 3.8811801946039879782295434588689
y[1] (numeric) = 3.8811801946039879782296226431676
absolute error = 7.91842987e-23
relative error = 2.0402118615901956142359425321746e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0583
y[1] (analytic) = 3.8814683270298295587515645488934
y[1] (numeric) = 3.8814683270298295587516438732522
absolute error = 7.93243588e-23
relative error = 2.0436688417009561908033416905299e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0584
y[1] (analytic) = 3.8817564882703544335841172930196
y[1] (numeric) = 3.8817564882703544335841967574525
absolute error = 7.94644329e-23
relative error = 2.0471256540723402800216448835324e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0585
y[1] (analytic) = 3.8820446783284442151348517832447
y[1] (numeric) = 3.8820446783284442151349313877658
absolute error = 7.96045211e-23
relative error = 2.0505823012391662395751757077475e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0586
y[1] (analytic) = 3.8823328972069808039870674188944
y[1] (numeric) = 3.8823328972069808039871471635177
absolute error = 7.97446233e-23
relative error = 2.0540387805839550089911100752943e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0587
y[1] (analytic) = 3.8826211449088463889285319124795
y[1] (numeric) = 3.8826211449088463889286117972189
absolute error = 7.98847394e-23
relative error = 2.0574950894900017619846417047548e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0588
y[1] (analytic) = 3.8829094214369234469803031775975
y[1] (numeric) = 3.8829094214369234469803832024671
absolute error = 8.00248696e-23
relative error = 2.0609512330675411042996420562944e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0589
y[1] (analytic) = 3.8831977267940947434255540991677
y[1] (numeric) = 3.8831977267940947434256342641814
absolute error = 8.01650137e-23
relative error = 2.0644072061244983046033802564821e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.059
y[1] (analytic) = 3.8834860609832433318384001862864
y[1] (numeric) = 3.8834860609832433318384804914583
absolute error = 8.03051719e-23
relative error = 2.0678630137703616426925024196957e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0591
y[1] (analytic) = 3.8837744240072525541127301079925
y[1] (numeric) = 3.8837744240072525541128105533366
absolute error = 8.04453441e-23
relative error = 2.0713186533886545953992284501630e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0592
y[1] (analytic) = 3.8840628158690060404910391122302
y[1] (numeric) = 3.8840628158690060404911196977605
absolute error = 8.05855303e-23
relative error = 2.0747741249382983402584617753165e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0593
y[1] (analytic) = 3.8843512365713877095932653282979
y[1] (numeric) = 3.8843512365713877095933460540285
absolute error = 8.07257306e-23
relative error = 2.0782294309526558080389429656476e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0594
y[1] (analytic) = 3.8846396861172817684456289530719
y[1] (numeric) = 3.8846396861172817684457098190168
absolute error = 8.08659449e-23
relative error = 2.0816845688158519092118702889229e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0595
y[1] (analytic) = 3.8849281645095727125094743212924
y[1] (numeric) = 3.8849281645095727125095553274656
absolute error = 8.10061732e-23
relative error = 2.0851395384868356575904268706300e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0596
y[1] (analytic) = 3.8852166717511453257101148602012
y[1] (numeric) = 3.8852166717511453257101960066167
absolute error = 8.11464155e-23
relative error = 2.0885943399245653355895064359983e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0597
y[1] (analytic) = 3.8855052078448846804656809288185
y[1] (numeric) = 3.8855052078448846804657622154903
absolute error = 8.12866718e-23
relative error = 2.0920489730880084937829764238871e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0598
y[1] (analytic) = 3.8857937727936761377159705421485
y[1] (numeric) = 3.8857937727936761377160519690907
absolute error = 8.14269422e-23
relative error = 2.0955034405096187185833488874397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0599
y[1] (analytic) = 3.8860823666004053469513029806017
y[1] (numeric) = 3.8860823666004053469513845478283
absolute error = 8.15672266e-23
relative error = 2.0989577395745230970059773080329e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.06
y[1] (analytic) = 3.8863709892679582462413752849215
y[1] (numeric) = 3.8863709892679582462414569924465
absolute error = 8.17075250e-23
relative error = 2.1024118702417170092695387938853e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0601
y[1] (analytic) = 3.8866596407992210622641216369058
y[1] (numeric) = 3.8866596407992210622642034847432
absolute error = 8.18478374e-23
relative error = 2.1058658324702051019799212117945e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0602
memory used=80.1MB, alloc=4.2MB, time=4.58
y[1] (analytic) = 3.8869483211970803103345756262099
y[1] (numeric) = 3.8869483211970803103346576143738
absolute error = 8.19881639e-23
relative error = 2.1093196287917136506129835968627e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0603
y[1] (analytic) = 3.8872370304644227944337354035214
y[1] (numeric) = 3.8872370304644227944338175320258
absolute error = 8.21285044e-23
relative error = 2.1127732565921713140730706403037e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0604
y[1] (analytic) = 3.8875257686041356072374317203939
y[1] (numeric) = 3.8875257686041356072375139892529
absolute error = 8.22688590e-23
relative error = 2.1162267184029407792791154950439e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0605
y[1] (analytic) = 3.8878145356191061301451988560295
y[1] (numeric) = 3.887814535619106130145281265257
absolute error = 8.24092275e-23
relative error = 2.1196800090382122902522180766533e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0606
y[1] (analytic) = 3.8881033315122220333091484312979
y[1] (numeric) = 3.8881033315122220333092309809081
absolute error = 8.25496102e-23
relative error = 2.1231331361734543438252063514637e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0607
y[1] (analytic) = 3.8883921562863712756628461102822
y[1] (numeric) = 3.888392156286371275662928800289
absolute error = 8.26900068e-23
relative error = 2.1265860920513097619808077142786e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0608
y[1] (analytic) = 3.888681009944442104950191189638
y[1] (numeric) = 3.8886810099444421049502740200555
absolute error = 8.28304175e-23
relative error = 2.1300388817745532891229982240264e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0609
y[1] (analytic) = 3.8889698924893230577542990760569
y[1] (numeric) = 3.8889698924893230577543820468991
absolute error = 8.29708422e-23
relative error = 2.1334915027303156643186445690477e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.061
y[1] (analytic) = 3.8892588039239029595263866521213
y[1] (numeric) = 3.8892588039239029595264697634024
absolute error = 8.31112811e-23
relative error = 2.1369439600200529908000150550992e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0611
y[1] (analytic) = 3.8895477442510709246146605308412
y[1] (numeric) = 3.8895477442510709246147437825751
absolute error = 8.32517339e-23
relative error = 2.1403962458887376330154044635830e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0612
y[1] (analytic) = 3.8898367134737163562932081991599
y[1] (numeric) = 3.8898367134737163562932915913606
absolute error = 8.33922007e-23
relative error = 2.1438483628668512608327463204176e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0613
y[1] (analytic) = 3.8901257115947289467908920507189
y[1] (numeric) = 3.8901257115947289467909755834005
absolute error = 8.35326816e-23
relative error = 2.1473003134841208081765860690911e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0614
y[1] (analytic) = 3.890414738616998677320246308171
y[1] (numeric) = 3.8904147386169986773203299813476
absolute error = 8.36731766e-23
relative error = 2.1507520976990985274423744601279e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0615
y[1] (analytic) = 3.8907037945434158181063768353295
y[1] (numeric) = 3.8907037945434158181064606490151
absolute error = 8.38136856e-23
relative error = 2.1542037129001169157074588753239e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0616
y[1] (analytic) = 3.8909928793768709284158638394433
y[1] (numeric) = 3.890992879376870928415947793652
absolute error = 8.39542087e-23
relative error = 2.1576551616163578427459677908395e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0617
y[1] (analytic) = 3.8912819931202548565856674638869
y[1] (numeric) = 3.8912819931202548565857515586327
absolute error = 8.40947458e-23
relative error = 2.1611064412365543138478825660434e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0618
y[1] (analytic) = 3.8915711357764587400520362715539
y[1] (numeric) = 3.8915711357764587400521205068509
absolute error = 8.42352970e-23
relative error = 2.1645575542895248575807514897695e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0619
y[1] (analytic) = 3.8918603073483740053794186192439
y[1] (numeric) = 3.8918603073483740053795029951062
absolute error = 8.43758623e-23
relative error = 2.1680085007338682454161153653002e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.062
y[1] (analytic) = 3.8921495078388923682893769233309
y[1] (numeric) = 3.8921495078388923682894614397724
absolute error = 8.45164415e-23
relative error = 2.1714592753896438094417854996777e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0621
y[1] (analytic) = 3.8924387372509058336895048170028
y[1] (numeric) = 3.8924387372509058336895894740377
absolute error = 8.46570349e-23
relative error = 2.1749098859238648106878931418371e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0622
y[1] (analytic) = 3.8927279955873066957023471993618
y[1] (numeric) = 3.8927279955873066957024319970042
absolute error = 8.47976424e-23
relative error = 2.1783603297256926354289822207104e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0623
y[1] (analytic) = 3.8930172828509875376943231766739
y[1] (numeric) = 3.8930172828509875376944081149378
absolute error = 8.49382639e-23
relative error = 2.1818106041850616080129671667882e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0624
y[1] (analytic) = 3.893306599044841232304651896057
y[1] (numeric) = 3.8933065990448412323047369749564
absolute error = 8.50788994e-23
relative error = 2.1852607092611896854337082806933e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0625
y[1] (analytic) = 3.8935959441717609414742812718972
y[1] (numeric) = 3.8935959441717609414743664914462
absolute error = 8.52195490e-23
relative error = 2.1887106474816239942574206957402e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0626
y[1] (analytic) = 3.8938853182346401164748196052827
y[1] (numeric) = 3.8938853182346401164749049654953
absolute error = 8.53602126e-23
relative error = 2.1921604162368993591923461232570e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0627
y[1] (analytic) = 3.8941747212363724979374700967436
y[1] (numeric) = 3.8941747212363724979375555976339
absolute error = 8.55008903e-23
relative error = 2.1956100180541997246291494771675e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0628
y[1] (analytic) = 3.8944641531798521158819682525883
y[1] (numeric) = 3.8944641531798521158820538941705
absolute error = 8.56415822e-23
relative error = 2.1990594554599549048629484681987e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0629
y[1] (analytic) = 3.894753614067973289745522185125
y[1] (numeric) = 3.8947536140679732897456079674131
absolute error = 8.57822881e-23
relative error = 2.2025087232771711438960463861063e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.063
y[1] (analytic) = 3.8950431039036306284117558070577
y[1] (numeric) = 3.8950431039036306284118417300657
absolute error = 8.59230080e-23
relative error = 2.2059578214651220375826593131208e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0631
y[1] (analytic) = 3.8953326226897190302396549203467
y[1] (numeric) = 3.8953326226897190302397409840887
absolute error = 8.60637420e-23
relative error = 2.2094067525502652998412123255786e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.2MB, time=4.82
NO POLE
x[1] = 1.0632
y[1] (analytic) = 3.8956221704291336830925161998224
y[1] (numeric) = 3.8956221704291336830926024043125
absolute error = 8.62044901e-23
relative error = 2.2128555164913206051644601273101e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0633
y[1] (analytic) = 3.8959117471247700643668990718429
y[1] (numeric) = 3.8959117471247700643669854170951
absolute error = 8.63452522e-23
relative error = 2.2163041106802236794748948112780e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0634
y[1] (analytic) = 3.8962013527795239410215804882829
y[1] (numeric) = 3.8962013527795239410216669743114
absolute error = 8.64860285e-23
relative error = 2.2197525402094901156338477539175e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0635
y[1] (analytic) = 3.8964909873962913696065125961464
y[1] (numeric) = 3.8964909873962913696065992229653
absolute error = 8.66268189e-23
relative error = 2.2232008024708834541642725793500e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0636
y[1] (analytic) = 3.89678065097796869629178330309
y[1] (numeric) = 3.8967806509779686962918700707133
absolute error = 8.67676233e-23
relative error = 2.2266488948569396851211572866511e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0637
y[1] (analytic) = 3.8970703435274525568965797391478
y[1] (numeric) = 3.8970703435274525568966666475895
absolute error = 8.69084417e-23
relative error = 2.2300968173269973052610999690086e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0638
y[1] (analytic) = 3.8973600650476398769181546149475
y[1] (numeric) = 3.8973600650476398769182416642218
absolute error = 8.70492743e-23
relative error = 2.2335445749720828556180933747252e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0639
y[1] (analytic) = 3.8976498155414278715607954767074
y[1] (numeric) = 3.8976498155414278715608826668283
absolute error = 8.71901209e-23
relative error = 2.2369921626191115618977056708476e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.064
y[1] (analytic) = 3.8979395950117140457647968583027
y[1] (numeric) = 3.8979395950117140457648841892844
absolute error = 8.73309817e-23
relative error = 2.2404395853583655618870229333512e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0641
y[1] (analytic) = 3.8982294034613961942354353306936
y[1] (numeric) = 3.89822940346139619423552280255
absolute error = 8.74718564e-23
relative error = 2.2438868354522744729877884127119e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0642
y[1] (analytic) = 3.898519240893372401471947449001
y[1] (numeric) = 3.8985192408933724014720350617463
absolute error = 8.76127453e-23
relative error = 2.2473339205560247276049091457669e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0643
y[1] (analytic) = 3.8988091073105410417965105975241
y[1] (numeric) = 3.8988091073105410417965983511724
absolute error = 8.77536483e-23
relative error = 2.2507808380629803873319768709399e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0644
y[1] (analytic) = 3.8990990027158007793832267329858
y[1] (numeric) = 3.8990990027158007793833146275511
absolute error = 8.78945653e-23
relative error = 2.2542275853672776625452131505262e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0645
y[1] (analytic) = 3.8993889271120505682871090262977
y[1] (numeric) = 3.8993889271120505682871970617943
absolute error = 8.80354966e-23
relative error = 2.2576741701218423566166936243273e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0646
y[1] (analytic) = 3.8996788805021896524730714031351
y[1] (numeric) = 3.8996788805021896524731595795769
absolute error = 8.81764418e-23
relative error = 2.2611205820271254336490621344489e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0647
y[1] (analytic) = 3.8999688628891175658449209836094
y[1] (numeric) = 3.8999688628891175658450093010106
absolute error = 8.83174012e-23
relative error = 2.2645668287354992357735241984722e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0648
y[1] (analytic) = 3.900258874275734132274353421331
y[1] (numeric) = 3.9002588742757341322744418797057
absolute error = 8.84583747e-23
relative error = 2.2680129076413278686702079642446e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0649
y[1] (analytic) = 3.9005489146649394656299511421502
y[1] (numeric) = 3.9005489146649394656300397415125
absolute error = 8.85993623e-23
relative error = 2.2714588187034891230416350245267e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.065
y[1] (analytic) = 3.9008389840596339698061844828672
y[1] (numeric) = 3.9008389840596339698062732232311
absolute error = 8.87403639e-23
relative error = 2.2749045593173190073404269437612e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0651
y[1] (analytic) = 3.9011290824627183387524157302009
y[1] (numeric) = 3.9011290824627183387525046115805
absolute error = 8.88813796e-23
relative error = 2.2783501320056462596748292570036e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0652
y[1] (analytic) = 3.9014192098770935565019060603067
y[1] (numeric) = 3.9014192098770935565019950827162
absolute error = 8.90224095e-23
relative error = 2.2817955392905463687723053804957e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0653
y[1] (analytic) = 3.9017093663056608972008253791335
y[1] (numeric) = 3.901709366305660897200914542587
absolute error = 8.91634535e-23
relative error = 2.2852407785673832409441387690134e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0654
y[1] (analytic) = 3.9019995517513219251372650639094
y[1] (numeric) = 3.901999551751321925137354368421
absolute error = 8.93045116e-23
relative error = 2.2886858497950811633236761885521e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0655
y[1] (analytic) = 3.9022897662169784947702536060468
y[1] (numeric) = 3.9022897662169784947703430516305
absolute error = 8.94455837e-23
relative error = 2.2921307503699757082488555392440e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0656
y[1] (analytic) = 3.9025800097055327507587751557567
y[1] (numeric) = 3.9025800097055327507588647424267
absolute error = 8.95866700e-23
relative error = 2.2955754853763963697964970121026e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0657
y[1] (analytic) = 3.9028702822198871279907909686632
y[1] (numeric) = 3.9028702822198871279908806964336
absolute error = 8.97277704e-23
relative error = 2.2990200522105067194560153136391e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0658
y[1] (analytic) = 3.9031605837629443516122637547069
y[1] (numeric) = 3.9031605837629443516123536235918
absolute error = 8.98688849e-23
relative error = 2.3024644508312682333854802400344e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0659
y[1] (analytic) = 3.9034509143376074370561849296288
y[1] (numeric) = 3.9034509143376074370562749396423
absolute error = 9.00100135e-23
relative error = 2.3059086811976516838698111543888e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.066
y[1] (analytic) = 3.9037412739467796900716047693244
y[1] (numeric) = 3.9037412739467796900716949204806
absolute error = 9.01511562e-23
relative error = 2.3093527432686371388686315412146e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=87.7MB, alloc=4.2MB, time=5.04
x[1] = 1.0661
y[1] (analytic) = 3.9040316625933647067526654673584
y[1] (numeric) = 3.9040316625933647067527557596715
absolute error = 9.02923131e-23
relative error = 2.3127966395646685972461665671257e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0662
y[1] (analytic) = 3.9043220802802663735676370959306
y[1] (numeric) = 3.9043220802802663735677275294147
absolute error = 9.04334841e-23
relative error = 2.3162403674829090206345358663706e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0663
y[1] (analytic) = 3.9046125270103888673879564705823
y[1] (numeric) = 3.9046125270103888673880470452515
absolute error = 9.05746692e-23
relative error = 2.3196839269823663891811834304088e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0664
y[1] (analytic) = 3.9049030027866366555172689189352
y[1] (numeric) = 3.9049030027866366555173596348036
absolute error = 9.07158684e-23
relative error = 2.3231273180220579768988396348633e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0665
y[1] (analytic) = 3.9051935076119144957204729537519
y[1] (numeric) = 3.9051935076119144957205638108336
absolute error = 9.08570817e-23
relative error = 2.3265705405610103512124120677480e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0666
y[1] (analytic) = 3.9054840414891274362527678506092
y[1] (numeric) = 3.9054840414891274362528588489184
absolute error = 9.09983092e-23
relative error = 2.3300135971187614495253318834043e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0667
y[1] (analytic) = 3.9057746044211808158887041304744
y[1] (numeric) = 3.9057746044211808158887952700252
absolute error = 9.11395508e-23
relative error = 2.3334564850934733800034568287762e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0668
y[1] (analytic) = 3.9060651964109802639512369474748
y[1] (numeric) = 3.9060651964109802639513282282813
absolute error = 9.12808065e-23
relative error = 2.3368992044442006154702408086579e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0669
y[1] (analytic) = 3.9063558174614317003407823821514
y[1] (numeric) = 3.9063558174614317003408738042278
absolute error = 9.14220764e-23
relative error = 2.3403417576899375736950684421593e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.067
y[1] (analytic) = 3.9066464675754413355642766404877
y[1] (numeric) = 3.906646467575441335564368203848
absolute error = 9.15633603e-23
relative error = 2.3437841396697055475826590940615e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0671
y[1] (analytic) = 3.9069371467559156707642381590028
y[1] (numeric) = 3.9069371467559156707643298636611
absolute error = 9.17046583e-23
relative error = 2.3472263529027080020012313474642e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0672
y[1] (analytic) = 3.907227855005761497747832616201
y[1] (numeric) = 3.9072278550057614977479244621715
absolute error = 9.18459705e-23
relative error = 2.3506683999073958867720122350010e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0673
y[1] (analytic) = 3.9075185923278858990159408506679
y[1] (numeric) = 3.9075185923278858990160328379647
absolute error = 9.19872968e-23
relative error = 2.3541102780831299586784017063395e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0674
y[1] (analytic) = 3.907809358725196247792229686103
y[1] (numeric) = 3.9078093587251962477923218147403
absolute error = 9.21286373e-23
relative error = 2.3575519899479989276679056408379e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0675
y[1] (analytic) = 3.9081001542006002080522256635809
y[1] (numeric) = 3.9081001542006002080523179335729
absolute error = 9.22699920e-23
relative error = 2.3609935354605510976310188031893e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0676
y[1] (analytic) = 3.9083909787570057345523916813308
y[1] (numeric) = 3.9083909787570057345524840926916
absolute error = 9.24113608e-23
relative error = 2.3644349120207464598810194128080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0677
y[1] (analytic) = 3.9086818323973210728592065423253
y[1] (numeric) = 3.9086818323973210728592990950689
absolute error = 9.25527436e-23
relative error = 2.3678761170293159130646323977457e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0678
y[1] (analytic) = 3.9089727151244547593782474099691
y[1] (numeric) = 3.9089727151244547593783401041098
absolute error = 9.26941407e-23
relative error = 2.3713171581206287068382844130667e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0679
y[1] (analytic) = 3.9092636269413156213832751721797
y[1] (numeric) = 3.9092636269413156213833680077315
absolute error = 9.28355518e-23
relative error = 2.3747580275786197826595260171020e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.068
y[1] (analytic) = 3.9095545678508127770453227141486
y[1] (numeric) = 3.9095545678508127770454156911257
absolute error = 9.29769771e-23
relative error = 2.3781987304786985810488004629152e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0681
y[1] (analytic) = 3.9098455378558556354617861000763
y[1] (numeric) = 3.9098455378558556354618792184928
absolute error = 9.31184165e-23
relative error = 2.3816392642218235574452286887801e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0682
y[1] (analytic) = 3.9101365369593538966855186641702
y[1] (numeric) = 3.9101365369593538966856119240403
absolute error = 9.32598701e-23
relative error = 2.3850796313246347880941238243399e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0683
y[1] (analytic) = 3.9104275651642175517539280111976
y[1] (numeric) = 3.9104275651642175517540214125355
absolute error = 9.34013379e-23
relative error = 2.3885198317457551782870086288178e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0684
y[1] (analytic) = 3.910718622473356882718075926884
y[1] (numeric) = 3.9107186224733568827181694697038
absolute error = 9.35428198e-23
relative error = 2.3919598628867421839579169306577e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0685
y[1] (analytic) = 3.9110097088896824626717811984478
y[1] (numeric) = 3.9110097088896824626718748827636
absolute error = 9.36843158e-23
relative error = 2.3953997247068083406147198521694e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0686
y[1] (analytic) = 3.9113008244161051557807253455628
y[1] (numeric) = 3.9113008244161051557808191713889
absolute error = 9.38258261e-23
relative error = 2.3988394222785638000059473359273e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0687
y[1] (analytic) = 3.9115919690555361173115612620397
y[1] (numeric) = 3.9115919690555361173116552293901
absolute error = 9.39673504e-23
relative error = 2.4022789478905862725823728259094e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0688
y[1] (analytic) = 3.911883142810886793661024768516
y[1] (numeric) = 3.9118831428108867936611188774049
absolute error = 9.41088889e-23
relative error = 2.4057183066153142250221844118265e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0689
y[1] (analytic) = 3.9121743456850689223850490764485
y[1] (numeric) = 3.9121743456850689223851433268901
absolute error = 9.42504416e-23
relative error = 2.4091574984114265154784208510975e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=91.5MB, alloc=4.2MB, time=5.25
x[1] = 1.069
y[1] (analytic) = 3.9124655776809945322278821636965
y[1] (numeric) = 3.9124655776809945322279765557049
absolute error = 9.43920084e-23
relative error = 2.4125965206816783096118124500273e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0691
y[1] (analytic) = 3.9127568388015759431512070619884
y[1] (numeric) = 3.9127568388015759431513015955778
absolute error = 9.45335894e-23
relative error = 2.4160353759410806925394087371045e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0692
y[1] (analytic) = 3.9130481290497257663632650565632
y[1] (numeric) = 3.9130481290497257663633597317477
absolute error = 9.46751845e-23
relative error = 2.4194740615927879884482905769445e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0693
y[1] (analytic) = 3.9133394484283569043479817982768
y[1] (numeric) = 3.9133394484283569043480766150706
absolute error = 9.48167938e-23
relative error = 2.4229125801514493786025749883685e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0694
y[1] (analytic) = 3.9136307969403825508940963284658
y[1] (numeric) = 3.9136307969403825508941912868831
absolute error = 9.49584173e-23
relative error = 2.4263509315757903499491195471873e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0695
y[1] (analytic) = 3.913922174588716191124293016859
y[1] (numeric) = 3.913922174588716191124388116914
absolute error = 9.51000550e-23
relative error = 2.4297891158245457249852075870491e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0696
y[1] (analytic) = 3.9142135813762716015243364128288
y[1] (numeric) = 3.9142135813762716015244316545355
absolute error = 9.52417067e-23
relative error = 2.4332271277468764502174521711586e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0697
y[1] (analytic) = 3.9145050173059628499722090102725
y[1] (numeric) = 3.9145050173059628499723043936451
absolute error = 9.53833726e-23
relative error = 2.4366649724118800485914429312615e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0698
y[1] (analytic) = 3.9147964823807042957672519264171
y[1] (numeric) = 3.9147964823807042957673474514699
absolute error = 9.55250528e-23
relative error = 2.4401026523327304957315184055435e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0699
y[1] (analytic) = 3.9150879766034105896593084948368
y[1] (numeric) = 3.9150879766034105896594041615839
absolute error = 9.56667471e-23
relative error = 2.4435401623591872995945775843970e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.07
y[1] (analytic) = 3.9153794999769966738778707729755
y[1] (numeric) = 3.915379499976996673877966581431
absolute error = 9.58084555e-23
relative error = 2.4469775024506024566717950273091e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0701
y[1] (analytic) = 3.9156710525043777821612289644662
y[1] (numeric) = 3.9156710525043777821613249146443
absolute error = 9.59501781e-23
relative error = 2.4504146751201779144719524972679e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0702
y[1] (analytic) = 3.915962634188469439785623756538
y[1] (numeric) = 3.9159626341884694397857198484529
absolute error = 9.60919149e-23
relative error = 2.4538516803267137478237267440047e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0703
y[1] (analytic) = 3.9162542450321874635944015728032
y[1] (numeric) = 3.9162542450321874635944978064691
absolute error = 9.62336659e-23
relative error = 2.4572885180290193634466140097003e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0704
y[1] (analytic) = 3.9165458850384479620271727417147
y[1] (numeric) = 3.9165458850384479620272691171457
absolute error = 9.63754310e-23
relative error = 2.4607251856326432727350744508360e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0705
y[1] (analytic) = 3.9168375542101673351489725809865
y[1] (numeric) = 3.9168375542101673351490690981968
absolute error = 9.65172103e-23
relative error = 2.4641616856500640325383087800691e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0706
y[1] (analytic) = 3.9171292525502622746794253982685
y[1] (numeric) = 3.9171292525502622746795220572722
absolute error = 9.66590037e-23
relative error = 2.4675980154872290394883199954040e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0707
y[1] (analytic) = 3.9174209800616497640219114083666
y[1] (numeric) = 3.917420980061649764022008209178
absolute error = 9.68008114e-23
relative error = 2.4710341802089550574419092969201e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0708
y[1] (analytic) = 3.9177127367472470782927365673016
y[1] (numeric) = 3.9177127367472470782928335099348
absolute error = 9.69426332e-23
relative error = 2.4744701746685082608508128449563e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0709
y[1] (analytic) = 3.9180045226099717843503053234958
y[1] (numeric) = 3.918004522609971784350402407965
absolute error = 9.70844692e-23
relative error = 2.4779060013776439574225045762133e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.071
y[1] (analytic) = 3.9182963376527417408242962863816
y[1] (numeric) = 3.9182963376527417408243935127011
absolute error = 9.72263195e-23
relative error = 2.4813416628473663918832783241365e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0711
y[1] (analytic) = 3.918588181878475098144840812723
y[1] (numeric) = 3.9185881818784750981449381809069
absolute error = 9.73681839e-23
relative error = 2.4847771539321103122143651373708e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0712
y[1] (analytic) = 3.9188800552900902985717045109407
y[1] (numeric) = 3.9188800552900902985718020210031
absolute error = 9.75100624e-23
relative error = 2.4882124745913392596385445305622e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0713
y[1] (analytic) = 3.9191719578905060762234716637341
y[1] (numeric) = 3.9191719578905060762235693156893
absolute error = 9.76519552e-23
relative error = 2.4916476298876448216475234510112e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0714
y[1] (analytic) = 3.9194638896826414571067325692919
y[1] (numeric) = 3.9194638896826414571068303631541
absolute error = 9.77938622e-23
relative error = 2.4950826172279994608655006716678e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0715
y[1] (analytic) = 3.919755850669415759145273801382
y[1] (numeric) = 3.9197558506694157591453717371654
absolute error = 9.79357834e-23
relative error = 2.4985174365713244750843099942172e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0716
y[1] (analytic) = 3.9200478408537485922092713886138
y[1] (numeric) = 3.9200478408537485922093694663325
absolute error = 9.80777187e-23
relative error = 2.5019520853255612128902618866365e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0717
y[1] (analytic) = 3.9203398602385598581444869131641
y[1] (numeric) = 3.9203398602385598581445851328323
absolute error = 9.82196682e-23
relative error = 2.5053865660010189362046008234397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0718
y[1] (analytic) = 3.9206319088267697508014665292593
y[1] (numeric) = 3.9206319088267697508015648908913
absolute error = 9.83616320e-23
relative error = 2.5088208811072561380892169577812e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0719
y[1] (analytic) = 3.9209239866212987560647429017051
y[1] (numeric) = 3.9209239866212987560648414053151
absolute error = 9.85036100e-23
relative error = 2.5122550280522421421290328921325e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.2MB, time=5.48
NO POLE
x[1] = 1.072
y[1] (analytic) = 3.9212160936250676518820400647562
y[1] (numeric) = 3.9212160936250676518821387103583
absolute error = 9.86456021e-23
relative error = 2.5156890042447156153837829536110e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0721
y[1] (analytic) = 3.9215082298409975082934812016178
y[1] (numeric) = 3.9215082298409975082935799892262
absolute error = 9.87876084e-23
relative error = 2.5191228121942630231464847949173e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0722
y[1] (analytic) = 3.9218003952720096874607993448711
y[1] (numeric) = 3.9218003952720096874608982745
absolute error = 9.89296289e-23
relative error = 2.5225564518598709070524670560891e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0723
y[1] (analytic) = 3.9220925899210258436965509981152
y[1] (numeric) = 3.9220925899210258436966500697789
absolute error = 9.90716637e-23
relative error = 2.5259899257501944703495980947435e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0724
y[1] (analytic) = 3.922384813790967923493332679117
y[1] (numeric) = 3.9223848137909679234934318928297
absolute error = 9.92137127e-23
relative error = 2.5294232312741996533737982626077e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0725
y[1] (analytic) = 3.9226770668847581655530003847613
y[1] (numeric) = 3.9226770668847581655530997405371
absolute error = 9.93557758e-23
relative error = 2.5328563658416215514562390159939e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0726
y[1] (analytic) = 3.9229693492053191008158919780937
y[1] (numeric) = 3.9229693492053191008159914759469
absolute error = 9.94978532e-23
relative error = 2.5362893345102328390456720671526e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0727
y[1] (analytic) = 3.9232616607555735524900524977488
y[1] (numeric) = 3.9232616607555735524901521376935
absolute error = 9.96399447e-23
relative error = 2.5397221321406977291136993596832e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0728
y[1] (analytic) = 3.9235540015384446360804623900544
y[1] (numeric) = 3.9235540015384446360805621721048
absolute error = 9.97820504e-23
relative error = 2.5431547612413381334488513059246e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0729
y[1] (analytic) = 3.9238463715568557594182686641059
y[1] (numeric) = 3.9238463715568557594183685882763
absolute error = 9.99241704e-23
relative error = 2.5465872243197255994904950131338e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.073
y[1] (analytic) = 3.9241387708137306226900189701024
y[1] (numeric) = 3.924138770813730622690119036407
absolute error = 1.000663046e-22
relative error = 2.5500195187860216852388602065343e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0731
y[1] (analytic) = 3.9244311993119932184668986012361
y[1] (numeric) = 3.9244311993119932184669988096891
absolute error = 1.002084530e-22
relative error = 2.5534516445992968478594214882837e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0732
y[1] (analytic) = 3.9247236570545678317339704194288
y[1] (numeric) = 3.9247236570545678317340707700444
absolute error = 1.003506156e-22
relative error = 2.5568836017186308630488298126641e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0733
y[1] (analytic) = 3.9250161440443790399194177052068
y[1] (numeric) = 3.9250161440443790399195181979993
absolute error = 1.004927925e-22
relative error = 2.5603153926508730459334506341826e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0734
y[1] (analytic) = 3.9253086602843517129237899320072
y[1] (numeric) = 3.9253086602843517129238905669908
absolute error = 1.006349836e-22
relative error = 2.5637470148069818654302669988046e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0735
y[1] (analytic) = 3.9256012057774110131492514652077
y[1] (numeric) = 3.9256012057774110131493522423965
absolute error = 1.007771888e-22
relative error = 2.5671784655986845683995009449190e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0736
y[1] (analytic) = 3.9258937805264823955288331861724
y[1] (numeric) = 3.9258937805264823955289341055807
absolute error = 1.009194083e-22
relative error = 2.5706097500800490890530615857205e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0737
y[1] (analytic) = 3.926186384534491607555687041607
y[1] (numeric) = 3.926186384534491607555788103249
absolute error = 1.010616420e-22
relative error = 2.5740408656626314559084742217544e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0738
y[1] (analytic) = 3.9264790178043646893123435185141
y[1] (numeric) = 3.9264790178043646893124447224041
absolute error = 1.012038900e-22
relative error = 2.5774718148523783858119480339666e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0739
y[1] (analytic) = 3.9267716803390279734999720450435
y[1] (numeric) = 3.9267716803390279735000733911957
absolute error = 1.013461522e-22
relative error = 2.5809025950612442594053666495234e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.074
y[1] (analytic) = 3.9270643721414080854676443175278
y[1] (numeric) = 3.9270643721414080854677458059564
absolute error = 1.014884286e-22
relative error = 2.5843332062483834398154238671923e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0741
y[1] (analytic) = 3.9273570932144319432416005539977
y[1] (numeric) = 3.9273570932144319432417021847169
absolute error = 1.016307192e-22
relative error = 2.5877636483729596045238996942617e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0742
y[1] (analytic) = 3.9276498435610267575545186744687
y[1] (numeric) = 3.9276498435610267575546204474928
absolute error = 1.017730241e-22
relative error = 2.5911939239401975566223765540685e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0743
y[1] (analytic) = 3.9279426231841200318747864082925
y[1] (numeric) = 3.9279426231841200318748883236357
absolute error = 1.019153432e-22
relative error = 2.5946240303628482357356739844612e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0744
y[1] (analytic) = 3.9282354320866395624357763288649
y[1] (numeric) = 3.9282354320866395624358783865415
absolute error = 1.020576766e-22
relative error = 2.5980539701457755551455039440337e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0745
y[1] (analytic) = 3.9285282702715134382651238159845
y[1] (numeric) = 3.9285282702715134382652260160086
absolute error = 1.022000241e-22
relative error = 2.6014837381566461797823035437380e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0746
y[1] (analytic) = 3.9288211377416700412140079461527
y[1] (numeric) = 3.9288211377416700412141102885386
absolute error = 1.023423859e-22
relative error = 2.6049133394458251755669822367579e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0747
y[1] (analytic) = 3.9291140345000380459864353111105
y[1] (numeric) = 3.9291140345000380459865377958725
absolute error = 1.024847620e-22
relative error = 2.6083427739719629058850118800097e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0748
y[1] (analytic) = 3.9294069605495464201685267649028
y[1] (numeric) = 3.929406960549546420168629392055
absolute error = 1.026271522e-22
relative error = 2.6117720366038925189332052326194e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.2MB, time=5.71
NO POLE
x[1] = 1.0749
y[1] (analytic) = 3.9296999158931244242578070997638
y[1] (numeric) = 3.9296999158931244242579098693205
absolute error = 1.027695567e-22
relative error = 2.6152011323908685771277373325725e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.075
y[1] (analytic) = 3.9299929005337016116924976511169
y[1] (numeric) = 3.9299929005337016116926005630924
absolute error = 1.029119755e-22
relative error = 2.6186300612915694875332384079362e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0751
y[1] (analytic) = 3.9302859144742078288808118319814
y[1] (numeric) = 3.9302859144742078288809148863899
absolute error = 1.030544085e-22
relative error = 2.6220588207203388662752707505335e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0752
y[1] (analytic) = 3.9305789577175732152302535970788
y[1] (numeric) = 3.9305789577175732152303567939345
absolute error = 1.031968557e-22
relative error = 2.6254874106364429297999354577818e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0753
y[1] (analytic) = 3.9308720302667282031769188369323
y[1] (numeric) = 3.9308720302667282031770221762495
absolute error = 1.033393172e-22
relative error = 2.6289158335431219833975849930417e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0754
y[1] (analytic) = 3.9311651321246035182147997022524
y[1] (numeric) = 3.9311651321246035182149031840453
absolute error = 1.034817929e-22
relative error = 2.6323440868553167319927030865075e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0755
y[1] (analytic) = 3.931458263294130178925091858901
y[1] (numeric) = 3.9314582632941301789251954831839
absolute error = 1.036242829e-22
relative error = 2.6357721730759067857685165893265e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0756
y[1] (analytic) = 3.9317514237782394970055046737278
y[1] (numeric) = 3.931751423778239497005608440515
absolute error = 1.037667872e-22
relative error = 2.6392000921636266545271108852792e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0757
y[1] (analytic) = 3.9320446135798630772995743315722
y[1] (numeric) = 3.9320446135798630772996782408778
absolute error = 1.039093056e-22
relative error = 2.6426278389908079329122469620478e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0758
y[1] (analytic) = 3.9323378327019328178259798837223
y[1] (numeric) = 3.9323378327019328178260839355607
absolute error = 1.040518384e-22
relative error = 2.6460554211463911837448160832202e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0759
y[1] (analytic) = 3.9326310811473809098078622281271
y[1] (numeric) = 3.9326310811473809098079664225125
absolute error = 1.041943854e-22
relative error = 2.6494828335029163162630325134991e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.076
y[1] (analytic) = 3.9329243589191398377021460216515
y[1] (numeric) = 3.9329243589191398377022503585982
absolute error = 1.043369467e-22
relative error = 2.6529100785623613717494751057130e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0761
y[1] (analytic) = 3.9332176660201423792288645246706
y[1] (numeric) = 3.9332176660201423792289690041928
absolute error = 1.044795222e-22
relative error = 2.6563371537410599664711322290287e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0762
y[1] (analytic) = 3.933511002453321605400487378294
y[1] (numeric) = 3.933511002453321605400592000406
absolute error = 1.046221120e-22
relative error = 2.6597640615406295705171847627886e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0763
y[1] (analytic) = 3.9338043682216108805512513145152
y[1] (numeric) = 3.9338043682216108805513560792313
absolute error = 1.047647161e-22
relative error = 2.6631908019198701396404937995903e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0764
y[1] (analytic) = 3.9340977633279438623664937995785
y[1] (numeric) = 3.9340977633279438623665987069129
absolute error = 1.049073344e-22
relative error = 2.6666173722957121133127655909565e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0765
y[1] (analytic) = 3.9343911877752545019119896108566
y[1] (numeric) = 3.9343911877752545019120946608235
absolute error = 1.050499669e-22
relative error = 2.6700437726275428811264324854913e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0766
y[1] (analytic) = 3.9346846415664770436632903475328
y[1] (numeric) = 3.9346846415664770436633955401465
absolute error = 1.051926137e-22
relative error = 2.6734700054162588769993668313973e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0767
y[1] (analytic) = 3.934978124704546025535066875381
y[1] (numeric) = 3.9349781247045460255351722106559
absolute error = 1.053352749e-22
relative error = 2.6768960731620076246409343264377e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0768
y[1] (analytic) = 3.9352716371923962789104547059373
y[1] (numeric) = 3.9352716371923962789105601838875
absolute error = 1.054779502e-22
relative error = 2.6803219681997052512582197129754e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0769
y[1] (analytic) = 3.9355651790329629286704023103549
y[1] (numeric) = 3.9355651790329629286705079309947
absolute error = 1.056206398e-22
relative error = 2.6837476955712072622089661294420e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.077
y[1] (analytic) = 3.9358587502291813932230223682388
y[1] (numeric) = 3.9358587502291813932231281315826
absolute error = 1.057633438e-22
relative error = 2.6871732577761206214402945354746e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0771
y[1] (analytic) = 3.9361523507839873845329459517514
y[1] (numeric) = 3.9361523507839873845330518578133
absolute error = 1.059060619e-22
relative error = 2.6905986471510953085421427042920e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0772
y[1] (analytic) = 3.9364459807003169081506796452826
y[1] (numeric) = 3.9364459807003169081507856940769
absolute error = 1.060487943e-22
relative error = 2.6940238687368776069834590865588e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0773
y[1] (analytic) = 3.9367396399811062632419656009801
y[1] (numeric) = 3.9367396399811062632420717925211
absolute error = 1.061915410e-22
relative error = 2.6974489224923609349638916436877e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0774
y[1] (analytic) = 3.9370333286292920426171445304307
y[1] (numeric) = 3.9370333286292920426172508647327
absolute error = 1.063343020e-22
relative error = 2.7008738083764480655358167681503e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0775
y[1] (analytic) = 3.9373270466478111327605216327886
y[1] (numeric) = 3.9373270466478111327606281098659
absolute error = 1.064770773e-22
relative error = 2.7042985263480511261354487043996e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0776
y[1] (analytic) = 3.9376207940396007138597354596427
y[1] (numeric) = 3.9376207940396007138598420795096
absolute error = 1.066198669e-22
relative error = 2.7077230763660915981137577718833e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0777
y[1] (analytic) = 3.9379145708075982598351297169176
y[1] (numeric) = 3.9379145708075982598352364795883
absolute error = 1.067626707e-22
relative error = 2.7111474558500851460825449201393e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=103.0MB, alloc=4.2MB, time=5.92
x[1] = 1.0778
y[1] (analytic) = 3.9382083769547415383691280041013
y[1] (numeric) = 3.9382083769547415383692349095901
absolute error = 1.069054888e-22
relative error = 2.7145716672987660291213415961499e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0779
y[1] (analytic) = 3.9385022124839686109356114910941
y[1] (numeric) = 3.9385022124839686109357185394153
absolute error = 1.070483212e-22
relative error = 2.7179957106710837595379685941521e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.078
y[1] (analytic) = 3.938796077398217832829299532972
y[1] (numeric) = 3.9387960773982178328294067241398
absolute error = 1.071911678e-22
relative error = 2.7214195833871503552034115066397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0781
y[1] (analytic) = 3.939089971700427853195133222958
y[1] (numeric) = 3.9390899717004278531952405569868
absolute error = 1.073340288e-22
relative error = 2.7248432904838171475604656024654e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0782
y[1] (analytic) = 3.9393838953935376150576618838964
y[1] (numeric) = 3.9393838953935376150577693608004
absolute error = 1.074769040e-22
relative error = 2.7282668268425574146089778258451e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0783
y[1] (analytic) = 3.9396778484804863553504324985225
y[1] (numeric) = 3.939677848480486355350540118316
absolute error = 1.076197935e-22
relative error = 2.7316901949612048924759134962135e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0784
y[1] (analytic) = 3.9399718309642136049453820788228
y[1] (numeric) = 3.9399718309642136049454898415201
absolute error = 1.077626973e-22
relative error = 2.7351133947987558209690777429128e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0785
y[1] (analytic) = 3.9402658428476591886822329747785
y[1] (numeric) = 3.940265842847659188682340880394
absolute error = 1.079056155e-22
relative error = 2.7385364288521156163509629638250e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0786
y[1] (analytic) = 3.9405598841337632253978911227879
y[1] (numeric) = 3.9405598841337632253979991713357
absolute error = 1.080485478e-22
relative error = 2.7419592894665997370061126646412e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0787
y[1] (analytic) = 3.940853954825466127955847234059
y[1] (numeric) = 3.9408539548254661279559554255535
absolute error = 1.081914945e-22
relative error = 2.7453819842149319506932327213680e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0788
y[1] (analytic) = 3.9411480549257086032755809232699
y[1] (numeric) = 3.9411480549257086032756892577254
absolute error = 1.083344555e-22
relative error = 2.7488045105182460663505278056249e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0789
y[1] (analytic) = 3.9414421844374316523619677777874
y[1] (numeric) = 3.9414421844374316523620762552181
absolute error = 1.084774307e-22
relative error = 2.7522268657984426886163319840064e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.079
y[1] (analytic) = 3.9417363433635765703346893677405
y[1] (numeric) = 3.9417363433635765703347979881607
absolute error = 1.086204202e-22
relative error = 2.7556490525520952045135488251798e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0791
y[1] (analytic) = 3.9420305317070849464576461972417
y[1] (numeric) = 3.9420305317070849464577549606658
absolute error = 1.087634241e-22
relative error = 2.7590710732750289746247745917636e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0792
y[1] (analytic) = 3.9423247494708986641683735970508
y[1] (numeric) = 3.942324749470898664168482503493
absolute error = 1.089064422e-22
relative error = 2.7624929228525982532785316066701e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0793
y[1] (analytic) = 3.9426189966579599011074605589742
y[1] (numeric) = 3.9426189966579599011075696084489
absolute error = 1.090494747e-22
relative error = 2.7659146063172215028702307393100e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0794
y[1] (analytic) = 3.9429132732712111291479715122958
y[1] (numeric) = 3.9429132732712111291480807048173
absolute error = 1.091925215e-22
relative error = 2.7693361210912247279369934484608e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0795
y[1] (analytic) = 3.943207579313595114424871042532
y[1] (numeric) = 3.9432075793135951144249803781146
absolute error = 1.093355826e-22
relative error = 2.7727574671337069888558838022658e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0796
y[1] (analytic) = 3.9435019147880549173644515528058
y[1] (numeric) = 3.9435019147880549173645610314638
absolute error = 1.094786580e-22
relative error = 2.7761786444037766904949514442828e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0797
y[1] (analytic) = 3.9437962796975338927137638681343
y[1] (numeric) = 3.943796279697533892713873489882
absolute error = 1.096217477e-22
relative error = 2.7795996528605515817401461476027e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0798
y[1] (analytic) = 3.9440906740449756895700507829238
y[1] (numeric) = 3.9440906740449756895701605477755
absolute error = 1.097648517e-22
relative error = 2.7830204924631587550220421522832e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0799
y[1] (analytic) = 3.9443850978333242514101835519665
y[1] (numeric) = 3.9443850978333242514102934599366
absolute error = 1.099079701e-22
relative error = 2.7864411657059840578465560544841e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.08
y[1] (analytic) = 3.9446795510655238161201013252344
y[1] (numeric) = 3.9446795510655238161202113763371
absolute error = 1.100511027e-22
relative error = 2.7898616674774851989237505473099e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0801
y[1] (analytic) = 3.9449740337445189160242535267623
y[1] (numeric) = 3.9449740337445189160243637210119
absolute error = 1.101942496e-22
relative error = 2.7932820002722559651908465031393e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0802
y[1] (analytic) = 3.9452685458732543779150451779175
y[1] (numeric) = 3.9452685458732543779151555153284
absolute error = 1.103374109e-22
relative error = 2.7967021665841425223706553977921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0803
y[1] (analytic) = 3.9455630874546753230822851653482
y[1] (numeric) = 3.9455630874546753230823956459347
absolute error = 1.104805865e-22
relative error = 2.8001221638372585348772620045991e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0804
y[1] (analytic) = 3.9458576584917271673426374539063
y[1] (numeric) = 3.9458576584917271673427480776826
absolute error = 1.106237763e-22
relative error = 2.8035419894564838960540174697872e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0805
y[1] (analytic) = 3.946152258987355621069075244838
y[1] (numeric) = 3.9461522589873556210691860118186
absolute error = 1.107669806e-22
relative error = 2.8069616510039209530561268045898e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0806
y[1] (analytic) = 3.9464468889445066892203380795389
y[1] (numeric) = 3.946446888944506689220448989738
absolute error = 1.109101991e-22
relative error = 2.8103811408358617224147078319317e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0807
y[1] (analytic) = 3.9467415483661266713703918891653
y[1] (numeric) = 3.9467415483661266713705029425972
absolute error = 1.110534319e-22
relative error = 2.8138004614458206735229496616866e-21 %
memory used=106.8MB, alloc=4.2MB, time=6.15
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0808
y[1] (analytic) = 3.9470362372551621617378919903987
y[1] (numeric) = 3.9470362372551621617380031870778
absolute error = 1.111966791e-22
relative error = 2.8172196153265648756350349150044e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0809
y[1] (analytic) = 3.9473309556145600492156490276569
y[1] (numeric) = 3.9473309556145600492157603675975
absolute error = 1.113399406e-22
relative error = 2.8206385999033993346078090729071e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.081
y[1] (analytic) = 3.9476257034472675174000978620467
y[1] (numeric) = 3.9476257034472675174002093452631
absolute error = 1.114832164e-22
relative error = 2.8240574151355632844142972329033e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0811
y[1] (analytic) = 3.9479204807562320446207694073525
y[1] (numeric) = 3.9479204807562320446208810338591
absolute error = 1.116265066e-22
relative error = 2.8274760635152843796315654331767e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0812
y[1] (analytic) = 3.9482152875444014039697654133566
y[1] (numeric) = 3.9482152875444014039698771831677
absolute error = 1.117698111e-22
relative error = 2.8308945424684631784593518155453e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0813
y[1] (analytic) = 3.9485101238147236633312361967845
y[1] (numeric) = 3.9485101238147236633313481099145
absolute error = 1.119131300e-22
relative error = 2.8343128544869677793062516645504e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0814
y[1] (analytic) = 3.9488049895701471854108613201711
y[1] (numeric) = 3.9488049895701471854109733766343
absolute error = 1.120564632e-22
relative error = 2.8377309969970957355648105187996e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0815
y[1] (analytic) = 3.9490998848136206277653332189421
y[1] (numeric) = 3.9490998848136206277654454187527
absolute error = 1.121998106e-22
relative error = 2.8411489674259104137534401518779e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0816
y[1] (analytic) = 3.9493948095480929428318437770051
y[1] (numeric) = 3.9493948095480929428319561201776
absolute error = 1.123431725e-22
relative error = 2.8445667733293749376891482582367e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0817
y[1] (analytic) = 3.9496897637765133779575738511468
y[1] (numeric) = 3.9496897637765133779576863376954
absolute error = 1.124865486e-22
relative error = 2.8479844070701261322573092140201e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0818
y[1] (analytic) = 3.9499847475018314754291857445287
y[1] (numeric) = 3.9499847475018314754292983744679
absolute error = 1.126299392e-22
relative error = 2.8514018762030112693555407337042e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0819
y[1] (analytic) = 3.9502797607269970725023186295789
y[1] (numeric) = 3.9502797607269970725024314029229
absolute error = 1.127733440e-22
relative error = 2.8548191730918204179642093283710e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.082
y[1] (analytic) = 3.9505748034549603014310869205724
y[1] (numeric) = 3.9505748034549603014311998373356
absolute error = 1.129167632e-22
relative error = 2.8582363027590078896515167071596e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0821
y[1] (analytic) = 3.9508698756886715894975815961975
y[1] (numeric) = 3.9508698756886715894976946563942
absolute error = 1.130601967e-22
relative error = 2.8616532626322603700108196881930e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0822
y[1] (analytic) = 3.9511649774310816590413744724009
y[1] (numeric) = 3.9511649774310816590414876760454
absolute error = 1.132036445e-22
relative error = 2.8650700526709292221044248459491e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0823
y[1] (analytic) = 3.951460108685141527489025425808
y[1] (numeric) = 3.9514601086851415274891387729148
absolute error = 1.133471068e-22
relative error = 2.8684866778957953372117289047172e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0824
y[1] (analytic) = 3.9517552694538025073835925680134
y[1] (numeric) = 3.9517552694538025073837060585968
absolute error = 1.134905834e-22
relative error = 2.8719031332040524590464474316043e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0825
y[1] (analytic) = 3.9520504597400162064141453710358
y[1] (numeric) = 3.9520504597400162064142590051101
absolute error = 1.136340743e-22
relative error = 2.8753194185550800002201954346977e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0826
y[1] (analytic) = 3.9523456795467345274452807442332
y[1] (numeric) = 3.9523456795467345274453945218128
absolute error = 1.137775796e-22
relative error = 2.8787355364384097656366482184001e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0827
y[1] (analytic) = 3.9526409288769096685466420629738
y[1] (numeric) = 3.952640928876909668546755984073
absolute error = 1.139210992e-22
relative error = 2.8821514842829187790103895929339e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0828
y[1] (analytic) = 3.9529362077334941230224411493569
y[1] (numeric) = 3.95293620773349412302255521399
absolute error = 1.140646331e-22
relative error = 2.8855672620480144701970458579638e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0829
y[1] (analytic) = 3.9532315161194406794409832052794
y[1] (numeric) = 3.9532315161194406794410974134609
absolute error = 1.142081815e-22
relative error = 2.8889828747522658176001004252471e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.083
y[1] (analytic) = 3.9535268540377024216641946981439
y[1] (numeric) = 3.953526854037702421664309049888
absolute error = 1.143517441e-22
relative error = 2.8923983147658036823634266700687e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0831
y[1] (analytic) = 3.9538222214912327288771541995021
y[1] (numeric) = 3.9538222214912327288772686948232
absolute error = 1.144953211e-22
relative error = 2.8958135871070267803236858174930e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0832
y[1] (analytic) = 3.9541176184829852756176261769304
y[1] (numeric) = 3.954117618482985275617740815843
absolute error = 1.146389126e-22
relative error = 2.8992286942638222832000890008711e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0833
y[1] (analytic) = 3.9544130450159140318055977394325
y[1] (numeric) = 3.9544130450159140318057125219508
absolute error = 1.147825183e-22
relative error = 2.9026436286080497787185546428894e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0834
y[1] (analytic) = 3.9547085010929732627728183366632
y[1] (numeric) = 3.9547085010929732627729332628016
absolute error = 1.149261384e-22
relative error = 2.9060583951570023110519804346532e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0835
y[1] (analytic) = 3.9550039867171175292923424122711
y[1] (numeric) = 3.9550039867171175292924574820439
absolute error = 1.150697728e-22
relative error = 2.9094729913411434718353374738461e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0836
y[1] (analytic) = 3.9552995018913016876080750116533
y[1] (numeric) = 3.955299501891301687608190225075
absolute error = 1.152134217e-22
relative error = 2.9128874221764625163341792898313e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.2MB, time=6.38
NO POLE
x[1] = 1.0837
y[1] (analytic) = 3.9555950466184808894643203444197
y[1] (numeric) = 3.9555950466184808894644357015046
absolute error = 1.153570849e-22
relative error = 2.9163016825651882317128345347608e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0838
y[1] (analytic) = 3.9558906209016105821353333018599
y[1] (numeric) = 3.9558906209016105821354488026224
absolute error = 1.155007625e-22
relative error = 2.9197157749946972397425172484773e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0839
y[1] (analytic) = 3.956186224743646508454873929711
y[1] (numeric) = 3.9561862247436465084549895741655
absolute error = 1.156444545e-22
relative error = 2.9231296994239330846177697666859e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.084
y[1] (analytic) = 3.9564818581475447068457648565196
y[1] (numeric) = 3.9564818581475447068458806446804
absolute error = 1.157881608e-22
relative error = 2.9265434532843506859102519710786e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0841
y[1] (analytic) = 3.9567775211162615113494516778944
y[1] (numeric) = 3.9567775211162615113495676097759
absolute error = 1.159318815e-22
relative error = 2.9299570390627880759357952870254e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0842
y[1] (analytic) = 3.9570732136527535516555662969459
y[1] (numeric) = 3.9570732136527535516556823725624
absolute error = 1.160756165e-22
relative error = 2.9333704541910966199010430193299e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0843
y[1] (analytic) = 3.9573689357599777531314932212068
y[1] (numeric) = 3.9573689357599777531316094405727
absolute error = 1.162193659e-22
relative error = 2.9367837011557553254413613109086e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0844
y[1] (analytic) = 3.9576646874408913368519388163306
y[1] (numeric) = 3.9576646874408913368520551794604
absolute error = 1.163631298e-22
relative error = 2.9401967824424971831832094539234e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0845
y[1] (analytic) = 3.9579604686984518196285035168637
y[1] (numeric) = 3.9579604686984518196286200237716
absolute error = 1.165069079e-22
relative error = 2.9436096904300941227700520895907e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0846
y[1] (analytic) = 3.9582562795356170140392569943854
y[1] (numeric) = 3.9582562795356170140393736450859
absolute error = 1.166507005e-22
relative error = 2.9470224326577831077099722286315e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0847
y[1] (analytic) = 3.9585521199553450284583162833139
y[1] (numeric) = 3.9585521199553450284584330778214
absolute error = 1.167945075e-22
relative error = 2.9504350065578400395681610368648e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0848
y[1] (analytic) = 3.9588479899605942670854268646717
y[1] (numeric) = 3.9588479899605942670855438030005
absolute error = 1.169383288e-22
relative error = 2.9538474095633054408061915349976e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0849
y[1] (analytic) = 3.9591438895543234299755467081077
y[1] (numeric) = 3.9591438895543234299756637902722
absolute error = 1.170821645e-22
relative error = 2.9572596441595815136895106772531e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.085
y[1] (analytic) = 3.9594398187394915130684332724717
y[1] (numeric) = 3.9594398187394915130685504984863
absolute error = 1.172260146e-22
relative error = 2.9606717103057148669729119662616e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0851
y[1] (analytic) = 3.9597357775190578082182334652364
y[1] (numeric) = 3.9597357775190578082183508351155
absolute error = 1.173698791e-22
relative error = 2.9640836079607614836762108426045e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0852
y[1] (analytic) = 3.9600317658959819032230765610638
y[1] (numeric) = 3.9600317658959819032231940748218
absolute error = 1.175137580e-22
relative error = 2.9674953370837867206032534561900e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0853
y[1] (analytic) = 3.9603277838732236818546700798108
y[1] (numeric) = 3.960327783873223681854787737462
absolute error = 1.176576512e-22
relative error = 2.9709068951088217898163932124126e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0854
y[1] (analytic) = 3.9606238314537433238878986242712
y[1] (numeric) = 3.96062383145374332388801642583
absolute error = 1.178015588e-22
relative error = 2.9743182845203717947535558136884e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0855
y[1] (analytic) = 3.960919908640501305130425677949
y[1] (numeric) = 3.9609199086405013051305436234299
absolute error = 1.179454809e-22
relative error = 2.9777295078021962275757566882283e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0856
y[1] (analytic) = 3.96121601543645839745229836316
y[1] (numeric) = 3.9612160154364583974524164525774
absolute error = 1.180894174e-22
relative error = 2.9811405623883544173644201887362e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0857
y[1] (analytic) = 3.9615121518445756688155551597568
y[1] (numeric) = 3.961512151844575668815673393125
absolute error = 1.182333682e-22
relative error = 2.9845514457136699734489707777073e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0858
y[1] (analytic) = 3.9618083178678144833038365847737
y[1] (numeric) = 3.9618083178678144833039549621071
absolute error = 1.183773334e-22
relative error = 2.9879621602619305021164347811926e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0859
y[1] (analytic) = 3.962104513509136501151998833288
y[1] (numeric) = 3.962104513509136501152117354601
absolute error = 1.185213130e-22
relative error = 2.9913727059922669351426849447025e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.086
y[1] (analytic) = 3.9624007387715036787757303807931
y[1] (numeric) = 3.9624007387715036787758490461001
absolute error = 1.186653070e-22
relative error = 2.9947830828638195742318782608931e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0861
y[1] (analytic) = 3.9626969936578782688011715473803
y[1] (numeric) = 3.9626969936578782688012903566957
absolute error = 1.188093154e-22
relative error = 2.9981932908357380905337611803452e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0862
y[1] (analytic) = 3.9629932781712228200945370240246
y[1] (numeric) = 3.9629932781712228200946559773628
absolute error = 1.189533382e-22
relative error = 3.0016033298671815241607856968647e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0863
y[1] (analytic) = 3.9632895923145001777917413612716
y[1] (numeric) = 3.9632895923145001777918604586471
absolute error = 1.190973755e-22
relative error = 3.0050132024404748098876597551408e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0864
y[1] (analytic) = 3.9635859360906734833280274206216
y[1] (numeric) = 3.9635859360906734833281466620487
absolute error = 1.192414271e-22
relative error = 3.0084229034682940241461972418299e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0865
y[1] (analytic) = 3.9638823095027061744675977889063
y[1] (numeric) = 3.9638823095027061744677171743994
absolute error = 1.193854931e-22
relative error = 3.0118324354331714943572917613637e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=114.4MB, alloc=4.2MB, time=6.60
x[1] = 1.0866
y[1] (analytic) = 3.9641787125535619853332491559559
y[1] (numeric) = 3.9641787125535619853333686855294
absolute error = 1.195295735e-22
relative error = 3.0152417982943037316518460805027e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0867
y[1] (analytic) = 3.9644751452462049464360096558515
y[1] (numeric) = 3.9644751452462049464361293295198
absolute error = 1.196736683e-22
relative error = 3.0186509920108966137062135087868e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0868
y[1] (analytic) = 3.9647716075835993847047791720602
y[1] (numeric) = 3.9647716075835993847048989898378
absolute error = 1.198177776e-22
relative error = 3.0220600190643787649413307903274e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0869
y[1] (analytic) = 3.9650680995687099235159726067489
y[1] (numeric) = 3.9650680995687099235160925686501
absolute error = 1.199619012e-22
relative error = 3.0254688743693594322445067952874e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.087
y[1] (analytic) = 3.9653646212045014827231661145728
y[1] (numeric) = 3.9653646212045014827232862206121
absolute error = 1.201060393e-22
relative error = 3.0288775629293107690219708720693e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0871
y[1] (analytic) = 3.9656611724939392786867463012363
y[1] (numeric) = 3.9656611724939392786868665514281
absolute error = 1.202501918e-22
relative error = 3.0322860821812627616476375947822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0872
y[1] (analytic) = 3.9659577534399888243035623871215
y[1] (numeric) = 3.9659577534399888243036827814801
absolute error = 1.203943586e-22
relative error = 3.0356944295630091087840436056998e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0873
y[1] (analytic) = 3.9662543640456159290365813362809
y[1] (numeric) = 3.9662543640456159290367018748209
absolute error = 1.205385400e-22
relative error = 3.0391026125981890028092086507076e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0874
y[1] (analytic) = 3.9665510043137866989445459510925
y[1] (numeric) = 3.9665510043137866989446666338283
absolute error = 1.206827358e-22
relative error = 3.0425106262027787186623875048275e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0875
y[1] (analytic) = 3.9668476742474675367116359328716
y[1] (numeric) = 3.9668476742474675367117567598175
absolute error = 1.208269459e-22
relative error = 3.0459184678151657354880576142114e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0876
y[1] (analytic) = 3.9671443738496251416771319087371
y[1] (numeric) = 3.9671443738496251416772528799077
absolute error = 1.209711706e-22
relative error = 3.0493261449573203727896832471515e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0877
y[1] (analytic) = 3.9674411031232265098650824250296
y[1] (numeric) = 3.9674411031232265098652035404392
absolute error = 1.211154096e-22
relative error = 3.0527336500258620945077250779908e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0878
y[1] (analytic) = 3.9677378620712389340139739075761
y[1] (numeric) = 3.9677378620712389340140951672391
absolute error = 1.212596630e-22
relative error = 3.0561409855009932039700090339630e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0879
y[1] (analytic) = 3.9680346506966300036064035890996
y[1] (numeric) = 3.9680346506966300036065249930305
absolute error = 1.214039309e-22
relative error = 3.0595481538621712788070109667346e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.088
y[1] (analytic) = 3.9683314690023676048987554040703
y[1] (numeric) = 3.9683314690023676048988769522835
absolute error = 1.215482132e-22
relative error = 3.0629551525482076941834615573775e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0881
y[1] (analytic) = 3.9686283169914199209508788512937
y[1] (numeric) = 3.9686283169914199209510005438036
absolute error = 1.216925099e-22
relative error = 3.0663619815184394926532113371717e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0882
y[1] (analytic) = 3.9689251946667554316557708245339
y[1] (numeric) = 3.9689251946667554316558926613549
absolute error = 1.218368210e-22
relative error = 3.0697686407322130760384506259961e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0883
y[1] (analytic) = 3.9692221020313429137692604114684
y[1] (numeric) = 3.969222102031342913769382392615
absolute error = 1.219811466e-22
relative error = 3.0731751326682695512257688729671e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0884
y[1] (analytic) = 3.9695190390881514409396966612712
y[1] (numeric) = 3.9695190390881514409398187867578
absolute error = 1.221254866e-22
relative error = 3.0765814547662117691618937334012e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0885
y[1] (analytic) = 3.9698160058401503837376393211209
y[1] (numeric) = 3.969816005840150383737761590962
absolute error = 1.222698411e-22
relative error = 3.0799876095044226685684101083352e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0886
y[1] (analytic) = 3.9701130022903094096855525419311
y[1] (numeric) = 3.9701130022903094096856749561411
absolute error = 1.224142100e-22
relative error = 3.0833935943229007932918037881008e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0887
y[1] (analytic) = 3.9704100284415984832875015535997
y[1] (numeric) = 3.970410028441598483287624112193
absolute error = 1.225585933e-22
relative error = 3.0867994091810393902956606946924e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0888
y[1] (analytic) = 3.9707070842969878660588523100744
y[1] (numeric) = 3.9707070842969878660589750130655
absolute error = 1.227029911e-22
relative error = 3.0902050565566841985085987636320e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0889
y[1] (analytic) = 3.9710041698594481165559741045312
y[1] (numeric) = 3.9710041698594481165560969519345
absolute error = 1.228474033e-22
relative error = 3.0936105338904272133213544442209e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.089
y[1] (analytic) = 3.9713012851319500904059451549626
y[1] (numeric) = 3.9713012851319500904060681467925
absolute error = 1.229918299e-22
relative error = 3.0970158411416897773276624504644e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0891
y[1] (analytic) = 3.9715984301174649403362611604733
y[1] (numeric) = 3.9715984301174649403363842967443
absolute error = 1.231362710e-22
relative error = 3.1004209807877805094394880835850e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0892
y[1] (analytic) = 3.97189560481896411620454682858
y[1] (numeric) = 3.9718956048189641162046701093065
absolute error = 1.232807265e-22
relative error = 3.1038259502698847680449977166429e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0893
y[1] (analytic) = 3.972192809239419365028270373812
y[1] (numeric) = 3.9721928092394193650283937990085
absolute error = 1.234251965e-22
relative error = 3.1072307520649531457183336097763e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0894
y[1] (analytic) = 3.9724900433818027310144609879114
y[1] (numeric) = 3.9724900433818027310145845575923
absolute error = 1.235696809e-22
relative error = 3.1106353836145665363334789822071e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=118.2MB, alloc=4.2MB, time=6.82
x[1] = 1.0895
y[1] (analytic) = 3.9727873072490865555894292819273
y[1] (numeric) = 3.9727873072490865555895529961071
absolute error = 1.237141798e-22
relative error = 3.1140398473953175415851851842650e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0896
y[1] (analytic) = 3.9730846008442434774284907005043
y[1] (numeric) = 3.9730846008442434774286145591974
absolute error = 1.238586931e-22
relative error = 3.1174441408491825514715726331230e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0897
y[1] (analytic) = 3.9733819241702464324856919086601
y[1] (numeric) = 3.973381924170246432485815911881
absolute error = 1.240032209e-22
relative error = 3.1208482664523962122668889193445e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0898
y[1] (analytic) = 3.973679277230068654023540151351
y[1] (numeric) = 3.9736792772300686540236642991141
absolute error = 1.241477631e-22
relative error = 3.1242522216473303707282422603924e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0899
y[1] (analytic) = 3.9739766600266836726427355861214
y[1] (numeric) = 3.9739766600266836726428598784412
absolute error = 1.242923198e-22
relative error = 3.1276560089098617531687174914964e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.09
y[1] (analytic) = 3.9742740725630653163119065891359
y[1] (numeric) = 3.9742740725630653163120310260268
absolute error = 1.244368909e-22
relative error = 3.1310596256827576237357940911056e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0901
y[1] (analytic) = 3.9745715148421877103973480348902
y[1] (numeric) = 3.9745715148421877103974726163667
absolute error = 1.245814765e-22
relative error = 3.1344630744415368242411878338759e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0902
y[1] (analytic) = 3.9748689868670252776927625498989
y[1] (numeric) = 3.9748689868670252776928872759755
absolute error = 1.247260766e-22
relative error = 3.1378663551451681864483681074214e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0903
y[1] (analytic) = 3.9751664886405527384490047406574
y[1] (numeric) = 3.9751664886405527384491296113484
absolute error = 1.248706910e-22
relative error = 3.1412694627213941343348276827268e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0904
y[1] (analytic) = 3.9754640201657451104038283961748
y[1] (numeric) = 3.9754640201657451104039534114948
absolute error = 1.250153200e-22
relative error = 3.1446724046766208501876973217032e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0905
y[1] (analytic) = 3.9757615814455777088116366653769
y[1] (numeric) = 3.9757615814455777088117618253403
absolute error = 1.251599634e-22
relative error = 3.1480751759387977938052318265022e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0906
y[1] (analytic) = 3.9760591724830261464732352096745
y[1] (numeric) = 3.9760591724830261464733605142958
absolute error = 1.253046213e-22
relative error = 3.1514777789825492649187438148594e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0907
y[1] (analytic) = 3.9763567932810663337655883309965
y[1] (numeric) = 3.9763567932810663337657137802902
absolute error = 1.254492937e-22
relative error = 3.1548802137668910599811319133828e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0908
y[1] (analytic) = 3.9766544438426744786715780755843
y[1] (numeric) = 3.9766544438426744786717036695648
absolute error = 1.255939805e-22
relative error = 3.1582824777361717470144517615600e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0909
y[1] (analytic) = 3.9769521241708270868097663138453
y[1] (numeric) = 3.9769521241708270868098920525271
absolute error = 1.257386818e-22
relative error = 3.1616845733644790125013753300771e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.091
y[1] (analytic) = 3.9772498342685009614641597965635
y[1] (numeric) = 3.9772498342685009614642856799611
absolute error = 1.258833976e-22
relative error = 3.1650865006108568314465990238555e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0911
y[1] (analytic) = 3.9775475741386732036139781877642
y[1] (numeric) = 3.9775475741386732036141042158921
absolute error = 1.260281279e-22
relative error = 3.1684882594343585800819286059832e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0912
y[1] (analytic) = 3.9778453437843212119634250745314
y[1] (numeric) = 3.977845343784321211963551247404
absolute error = 1.261728726e-22
relative error = 3.1718898472801232561058798456711e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0913
y[1] (analytic) = 3.9781431432084226829714619540739
y[1] (numeric) = 3.9781431432084226829715882717057
absolute error = 1.263176318e-22
relative error = 3.1752912666215231951483577870129e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0914
y[1] (analytic) = 3.9784409724139556108815851983405
y[1] (numeric) = 3.978440972413955610881711660746
absolute error = 1.264624055e-22
relative error = 3.1786925174176399461099399108834e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0915
y[1] (analytic) = 3.9787388314038982877516059964794
y[1] (numeric) = 3.978738831403898287751732603673
absolute error = 1.266071936e-22
relative error = 3.1820935971142052185280074091700e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0916
y[1] (analytic) = 3.979036720181229303483433275441
y[1] (numeric) = 3.9790367201812293034835600274373
absolute error = 1.267519963e-22
relative error = 3.1854945106972259980993695486995e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0917
y[1] (analytic) = 3.9793346387489275458528595990224
y[1] (numeric) = 3.9793346387489275458529864958358
absolute error = 1.268968134e-22
relative error = 3.1888952530992816955733797705274e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0918
y[1] (analytic) = 3.9796325871099722005393500456494
y[1] (numeric) = 3.9796325871099722005394770872944
absolute error = 1.270416450e-22
relative error = 3.1922958267928506645216608706607e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0919
y[1] (analytic) = 3.9799305652673427511558340651964
y[1] (numeric) = 3.9799305652673427511559612516875
absolute error = 1.271864911e-22
relative error = 3.1956962317370614171880865859147e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.092
y[1] (analytic) = 3.9802285732240189792785003151405
y[1] (numeric) = 3.9802285732240189792786276464922
absolute error = 1.273313517e-22
relative error = 3.1990964678910518626261796106216e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0921
y[1] (analytic) = 3.9805266109829809644765944763481
y[1] (numeric) = 3.9805266109829809644767219525749
absolute error = 1.274762268e-22
relative error = 3.2024965352139693062075573829441e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0922
y[1] (analytic) = 3.9808246785472090843422200487925
y[1] (numeric) = 3.9808246785472090843423476699088
absolute error = 1.276211163e-22
relative error = 3.2058964311529281444564073045222e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0923
y[1] (analytic) = 3.9811227759196840145201421274992
y[1] (numeric) = 3.9811227759196840145202698935196
absolute error = 1.277660204e-22
relative error = 3.2092961606913671792378430943149e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0924
y[1] (analytic) = 3.981420903103386728737594159019
y[1] (numeric) = 3.9814209031033867287377220699579
absolute error = 1.279109389e-22
relative error = 3.2126957187645653698442085532004e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.2MB, time=7.04
NO POLE
x[1] = 1.0925
y[1] (analytic) = 3.9817190601012984988340876787246
y[1] (numeric) = 3.9817190601012984988342157345965
absolute error = 1.280558719e-22
relative error = 3.2160951078437498785933367221423e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0926
y[1] (analytic) = 3.9820172469164008947912250292311
y[1] (numeric) = 3.9820172469164008947913532300506
absolute error = 1.282008195e-22
relative error = 3.2194943303994049338797638763026e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0927
y[1] (analytic) = 3.9823154635516757847625150602366
y[1] (numeric) = 3.9823154635516757847626434060181
absolute error = 1.283457815e-22
relative error = 3.2228933813679661682362082450681e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0928
y[1] (analytic) = 3.9826137100101053351031918100821
y[1] (numeric) = 3.9826137100101053351033203008401
absolute error = 1.284907580e-22
relative error = 3.2262922632201246641968009302692e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0929
y[1] (analytic) = 3.9829119862946720104000361693288
y[1] (numeric) = 3.9829119862946720104001648050778
absolute error = 1.286357490e-22
relative error = 3.2296909759151028518751310029979e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.093
y[1] (analytic) = 3.9832102924083585735012005266506
y[1] (numeric) = 3.9832102924083585735013293074051
absolute error = 1.287807545e-22
relative error = 3.2330895194121325532694670949153e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0931
y[1] (analytic) = 3.9835086283541480855460363973408
y[1] (numeric) = 3.9835086283541480855461653231153
absolute error = 1.289257745e-22
relative error = 3.2364878936704549817693239241632e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0932
y[1] (analytic) = 3.9838069941350239059949250347301
y[1] (numeric) = 3.9838069941350239059950541055391
absolute error = 1.290708090e-22
relative error = 3.2398860986493207416618410853272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0933
y[1] (analytic) = 3.9841053897539696926591110248156
y[1] (numeric) = 3.9841053897539696926592402406736
absolute error = 1.292158580e-22
relative error = 3.2432841343079898276379741487267e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0934
y[1] (analytic) = 3.9844038152139694017305388643977
y[1] (numeric) = 3.9844038152139694017306682253193
absolute error = 1.293609216e-22
relative error = 3.2466820031155173949616513017967e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0935
y[1] (analytic) = 3.984702270518007287811692523025
y[1] (numeric) = 3.9847022705180072878118220290246
absolute error = 1.295059996e-22
relative error = 3.2500797000114226926734086133425e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0936
y[1] (analytic) = 3.9850007556690679039454379890435
y[1] (numeric) = 3.9850007556690679039455676401356
absolute error = 1.296510921e-22
relative error = 3.2534772274649676473865057330126e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0937
y[1] (analytic) = 3.9852992706701361016448688000502
y[1] (numeric) = 3.9852992706701361016449985962494
absolute error = 1.297961992e-22
relative error = 3.2568745879446716582688454721145e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0938
y[1] (analytic) = 3.9855978155241970309231545580492
y[1] (numeric) = 3.98559781552419703092328449937
absolute error = 1.299413208e-22
relative error = 3.2602717789002439056932142374704e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0939
y[1] (analytic) = 3.9858963902342361403233924296082
y[1] (numeric) = 3.985896390234236140323522516065
absolute error = 1.300864568e-22
relative error = 3.2636687977821547984376035718230e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.094
y[1] (analytic) = 3.9861949948032391769484616313138
y[1] (numeric) = 3.9861949948032391769485918629212
absolute error = 1.302316074e-22
relative error = 3.2670656495676099071948013806214e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0941
y[1] (analytic) = 3.986493629234192186490880900826
y[1] (numeric) = 3.9864936292341921864910112775985
absolute error = 1.303767725e-22
relative error = 3.2704623317069104679363063471490e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0942
y[1] (analytic) = 3.9867922935300815132626689538278
y[1] (numeric) = 3.9867922935300815132627994757799
absolute error = 1.305219521e-22
relative error = 3.2738588441594009948287046189271e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0943
y[1] (analytic) = 3.9870909876938938002252079271702
y[1] (numeric) = 3.9870909876938938002253385943165
absolute error = 1.306671463e-22
relative error = 3.2772551893925296423953000866932e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0944
y[1] (analytic) = 3.9873897117286159890191098085113
y[1] (numeric) = 3.9873897117286159890192406208663
absolute error = 1.308123550e-22
relative error = 3.2806513648571896415689191976683e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0945
y[1] (analytic) = 3.987688465637235319994085852747
y[1] (numeric) = 3.9876884656372353199942168103251
absolute error = 1.309575781e-22
relative error = 3.2840473680050352239774517985466e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0946
y[1] (analytic) = 3.9879872494227393322388189855329
y[1] (numeric) = 3.9879872494227393322389500883487
absolute error = 1.311028158e-22
relative error = 3.2874432038110732824080459278972e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0947
y[1] (analytic) = 3.9882860630881158636108391941965
y[1] (numeric) = 3.9882860630881158636109704422645
absolute error = 1.312480680e-22
relative error = 3.2908388697267889259201079669794e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0948
y[1] (analytic) = 3.9885849066363530507664019063369
y[1] (numeric) = 3.9885849066363530507665332996717
absolute error = 1.313933348e-22
relative error = 3.2942343682187378537516020976216e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0949
y[1] (analytic) = 3.9888837800704393291903693564126
y[1] (numeric) = 3.9888837800704393291905008950286
absolute error = 1.315386160e-22
relative error = 3.2976296942318327400403896673002e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.095
y[1] (analytic) = 3.9891826833933634332260949406148
y[1] (numeric) = 3.9891826833933634332262266245266
absolute error = 1.316839118e-22
relative error = 3.3010248527396150663480859556200e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0951
y[1] (analytic) = 3.9894816166081143961053105603258
y[1] (numeric) = 3.989481616608114396105442389548
absolute error = 1.318292222e-22
relative error = 3.3044198437009503247374763396715e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0952
y[1] (analytic) = 3.9897805797176815499780169544617
y[1] (numeric) = 3.9897805797176815499781489290088
absolute error = 1.319745471e-22
relative error = 3.3078146645683099467742937942959e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0953
y[1] (analytic) = 3.9900795727250545259423770209968
y[1] (numeric) = 3.9900795727250545259425091408832
absolute error = 1.321198864e-22
relative error = 3.3112093127949260610423462738683e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.3MB, time=7.26
NO POLE
x[1] = 1.0954
y[1] (analytic) = 3.9903785956332232540746121279702
y[1] (numeric) = 3.9903785956332232540747443932105
absolute error = 1.322652403e-22
relative error = 3.3146037933528750296449099865605e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0955
y[1] (analytic) = 3.9906776484451779634589014142731
y[1] (numeric) = 3.9906776484451779634590338248819
absolute error = 1.324106088e-22
relative error = 3.3179981062010600061177681005581e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0956
y[1] (analytic) = 3.9909767311639091822172840805157
y[1] (numeric) = 3.9909767311639091822174166365075
absolute error = 1.325559918e-22
relative error = 3.3213922487927412856363144823163e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0957
y[1] (analytic) = 3.991275843792407737539564670272
y[1] (numeric) = 3.9912758437924077375396973716613
absolute error = 1.327013893e-22
relative error = 3.3247862210874042244805607032982e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0958
y[1] (analytic) = 3.991574986333664755713221342003
y[1] (numeric) = 3.9915749863336647557133541888045
absolute error = 1.328468015e-22
relative error = 3.3281800280550970523516989214565e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0959
y[1] (analytic) = 3.9918741587906716621533171319568
y[1] (numeric) = 3.9918741587906716621534501241849
absolute error = 1.329922281e-22
relative error = 3.3315736621389303612837982999261e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.096
y[1] (analytic) = 3.9921733611664201814324142083434
y[1] (numeric) = 3.9921733611664201814325473460127
absolute error = 1.331376693e-22
relative error = 3.3349671283087834234550704593362e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0961
y[1] (analytic) = 3.9924725934639023373104911170859
y[1] (numeric) = 3.9924725934639023373106244002109
absolute error = 1.332831250e-22
relative error = 3.3383604240189024126665530202927e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0962
y[1] (analytic) = 3.9927718556861104527648630194449
y[1] (numeric) = 3.9927718556861104527649964480402
absolute error = 1.334285953e-22
relative error = 3.3417535517333453948601942586677e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0963
y[1] (analytic) = 3.9930711478360371500201049218168
y[1] (numeric) = 3.9930711478360371500202384958969
absolute error = 1.335740801e-22
relative error = 3.3451465089067528318432676395495e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0964
y[1] (analytic) = 3.9933704699166753505779778980041
y[1] (numeric) = 3.9933704699166753505781116175836
absolute error = 1.337195795e-22
relative error = 3.3485392980028261347567758925822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0965
y[1] (analytic) = 3.9936698219310182752473583042583
y[1] (numeric) = 3.9936698219310182752474921693518
absolute error = 1.338650935e-22
relative error = 3.3519319189805626462789520153132e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0966
y[1] (analytic) = 3.9939692038820594441741699873938
y[1] (numeric) = 3.9939692038820594441743039980157
absolute error = 1.340106219e-22
relative error = 3.3553243667914192612275663207723e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0967
y[1] (analytic) = 3.9942686157727926768713194862713
y[1] (numeric) = 3.9942686157727926768714536424363
absolute error = 1.341561650e-22
relative error = 3.3587166489063000511395082138623e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0968
y[1] (analytic) = 3.9945680576062120922486342269527
y[1] (numeric) = 3.9945680576062120922487685286753
absolute error = 1.343017226e-22
relative error = 3.3621087602768684068674256139534e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0969
y[1] (analytic) = 3.9948675293853121086428037118238
y[1] (numeric) = 3.9948675293853121086429381591185
absolute error = 1.344472947e-22
relative error = 3.3655007008627223564468164089550e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.097
y[1] (analytic) = 3.9951670311130874438473237029863
y[1] (numeric) = 3.9951670311130874438474582958677
absolute error = 1.345928814e-22
relative error = 3.3688924731264935595173708226634e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0971
y[1] (analytic) = 3.9954665627925331151424434002177
y[1] (numeric) = 3.9954665627925331151425781387003
absolute error = 1.347384826e-22
relative error = 3.3722840745243992351729575357086e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0972
y[1] (analytic) = 3.9957661244266444393251156137987
y[1] (numeric) = 3.9957661244266444393252504978971
absolute error = 1.348840984e-22
relative error = 3.3756755075187145301878416302062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0973
y[1] (analytic) = 3.9960657160184170327389499325077
y[1] (numeric) = 3.9960657160184170327390849622366
absolute error = 1.350297289e-22
relative error = 3.3790667745709734510746540562328e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0974
y[1] (analytic) = 3.9963653375708468113041688870822
y[1] (numeric) = 3.996365337570846811304304062456
absolute error = 1.351753738e-22
relative error = 3.3824578681328740369878880986722e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0975
y[1] (analytic) = 3.9966649890869299905475671094453
y[1] (numeric) = 3.9966649890869299905477024304786
absolute error = 1.353210333e-22
relative error = 3.3858487931688057220885931536787e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0976
y[1] (analytic) = 3.9969646705696630856324734879992
y[1] (numeric) = 3.9969646705696630856326089547066
absolute error = 1.354667074e-22
relative error = 3.3892395496378694135932095985730e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0977
y[1] (analytic) = 3.9972643820220429113887163192833
y[1] (numeric) = 3.9972643820220429113888519316793
absolute error = 1.356123960e-22
relative error = 3.3926301349974645121083117303218e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0978
y[1] (analytic) = 3.9975641234470665823425914562973
y[1] (numeric) = 3.9975641234470665823427272143965
absolute error = 1.357580992e-22
relative error = 3.3960205517087968668419896910765e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0979
y[1] (analytic) = 3.9978638948477315127468334537894
y[1] (numeric) = 3.9978638948477315127469693576063
absolute error = 1.359038169e-22
relative error = 3.3994107972296598505503252475416e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.098
y[1] (analytic) = 3.9981636962270354166105897108083
y[1] (numeric) = 3.9981636962270354166107257603575
absolute error = 1.360495492e-22
relative error = 3.4028008740209029415197274870083e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0981
y[1] (analytic) = 3.9984635275879763077293976108199
y[1] (numeric) = 3.9984635275879763077295338061161
absolute error = 1.361952962e-22
relative error = 3.4061907845426347736903394546016e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0982
y[1] (analytic) = 3.9987633889335524997151646596877
y[1] (numeric) = 3.9987633889335524997153010007454
absolute error = 1.363410577e-22
relative error = 3.4095805237519038671040442650743e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.3MB, time=7.47
x[1] = 1.0983
y[1] (analytic) = 3.9990632802667626060261516218167
y[1] (numeric) = 3.9990632802667626060262881086504
absolute error = 1.364868337e-22
relative error = 3.4129700916084396654191526572072e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0984
y[1] (analytic) = 3.9993632015906055399969586547609
y[1] (numeric) = 3.9993632015906055399970952873853
absolute error = 1.366326244e-22
relative error = 3.4163594930727771020389544632983e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0985
y[1] (analytic) = 3.9996631529080805148685144425947
y[1] (numeric) = 3.9996631529080805148686512210243
absolute error = 1.367784296e-22
relative error = 3.4197487231031181644877617499248e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0986
y[1] (analytic) = 3.9999631342221870438180683283467
y[1] (numeric) = 3.9999631342221870438182052525961
absolute error = 1.369242494e-22
relative error = 3.4231377841592434874565333540440e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0987
y[1] (analytic) = 4.0002631455359249399891854457975
y[1] (numeric) = 4.0002631455359249399893225158813
absolute error = 1.370700838e-22
relative error = 3.4265266762003575384003844868861e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0988
y[1] (analytic) = 4.0005631868522943165217448509402
y[1] (numeric) = 4.000563186852294316521882066873
absolute error = 1.372159328e-22
relative error = 3.4299153991856742040028456504961e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0989
y[1] (analytic) = 4.0008632581742955865819406534044
y[1] (numeric) = 4.0008632581742955865820780152008
absolute error = 1.373617964e-22
relative error = 3.4333039530744167896739446320381e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.099
y[1] (analytic) = 4.0011633595049294633922861481429
y[1] (numeric) = 4.0011633595049294633924236558174
absolute error = 1.375076745e-22
relative error = 3.4366923353265449073305844375845e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0991
y[1] (analytic) = 4.0014634908471969602616209476819
y[1] (numeric) = 4.0014634908471969602617586012491
absolute error = 1.376535672e-22
relative error = 3.4400805484009487279714218368070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0992
y[1] (analytic) = 4.0017636522040993906151211152345
y[1] (numeric) = 4.001763652204099390615258914709
absolute error = 1.377994745e-22
relative error = 3.4434685922568797820441750247667e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0993
y[1] (analytic) = 4.0020638435786383680243122989773
y[1] (numeric) = 4.0020638435786383680244502443738
absolute error = 1.379453965e-22
relative error = 3.4468564693523097796718322984148e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0994
y[1] (analytic) = 4.002364064973815806237085867791
y[1] (numeric) = 4.002364064973815806237223959124
absolute error = 1.380913330e-22
relative error = 3.4502441746489001274796256068692e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0995
y[1] (analytic) = 4.0026643163926339192077180487639
y[1] (numeric) = 4.002664316392633919207856286048
absolute error = 1.382372841e-22
relative error = 3.4536317106048288077238727317805e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0996
y[1] (analytic) = 4.00296459783809522112689206676
y[1] (numeric) = 4.0029645978380952211270304500098
absolute error = 1.383832498e-22
relative error = 3.4570190771793850146987595163910e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0997
y[1] (analytic) = 4.0032649093132025264517232863507
y[1] (numeric) = 4.0032649093132025264518618155808
absolute error = 1.385292301e-22
relative error = 3.4604062743318673574019690454152e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0998
y[1] (analytic) = 4.0035652508209589499357873564111
y[1] (numeric) = 4.0035652508209589499359260316361
absolute error = 1.386752250e-22
relative error = 3.4637933020215838590310840974857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.0999
y[1] (analytic) = 4.0038656223643679066591513576805
y[1] (numeric) = 4.0038656223643679066592901789151
absolute error = 1.388212346e-22
relative error = 3.4671801627054382750972564106999e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.1
y[1] (analytic) = 4.0041660239464331120584079535887
y[1] (numeric) = 4.0041660239464331120585469208473
absolute error = 1.389672586e-22
relative error = 3.4705668488499984998339699440511e-21 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = exp ( x ) ;
Iterations = 1000
Total Elapsed Time = 7 Seconds
Elapsed Time(since restart) = 7 Seconds
Expected Time Remaining = 11 Minutes 12 Seconds
Optimized Time Remaining = 11 Minutes 11 Seconds
Time to Timeout = 14 Minutes 52 Seconds
Percent Done = 1.112 %
> quit
memory used=132.0MB, alloc=4.3MB, time=7.60