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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_small_float,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_html_log,
> glob_optimal_clock_start_sec,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> glob_display_flag,
> glob_iter,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_warned2,
> glob_warned,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_dump,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_log10_relerr,
> glob_disp_incr,
> glob_log10normmin,
> glob_start,
> glob_smallish_float,
> glob_relerr,
> glob_abserr,
> centuries_in_millinium,
> glob_subiter_method,
> glob_log10abserr,
> glob_max_hours,
> glob_h,
> glob_clock_sec,
> hours_in_day,
> glob_log10relerr,
> glob_log10_abserr,
> sec_in_min,
> djd_debug,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> years_in_century,
> glob_percent_done,
> glob_normmax,
> glob_current_iter,
> glob_optimal_start,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_initial_pass,
> djd_debug2,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_almost_1,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_norms,
> array_pole,
> array_fact_1,
> array_last_rel_error,
> array_tmp1_g,
> array_type_pole,
> array_1st_rel_error,
> array_m1,
> array_y_init,
> array_y,
> array_x,
> array_poles,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher,
> array_y_higher_work2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax,
glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec,
glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter,
MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned,
glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour,
glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs,
glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start,
glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium,
glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h,
glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr,
sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err,
years_in_century, glob_percent_done, glob_normmax, glob_current_iter,
glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float,
glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes,
glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1,
array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2,
array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g,
array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y,
array_x, array_poles, array_fact_2, array_y_set_initial,
array_y_higher_work, array_y_higher, array_y_higher_work2,
array_complex_pole, array_real_pole, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_small_float,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_html_log,
> glob_optimal_clock_start_sec,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> glob_display_flag,
> glob_iter,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_warned2,
> glob_warned,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_dump,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_log10_relerr,
> glob_disp_incr,
> glob_log10normmin,
> glob_start,
> glob_smallish_float,
> glob_relerr,
> glob_abserr,
> centuries_in_millinium,
> glob_subiter_method,
> glob_log10abserr,
> glob_max_hours,
> glob_h,
> glob_clock_sec,
> hours_in_day,
> glob_log10relerr,
> glob_log10_abserr,
> sec_in_min,
> djd_debug,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> years_in_century,
> glob_percent_done,
> glob_normmax,
> glob_current_iter,
> glob_optimal_start,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_initial_pass,
> djd_debug2,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_almost_1,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_norms,
> array_pole,
> array_fact_1,
> array_last_rel_error,
> array_tmp1_g,
> array_type_pole,
> array_1st_rel_error,
> array_m1,
> array_y_init,
> array_y,
> array_x,
> array_poles,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher,
> array_y_higher_work2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax,
glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec,
glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter,
MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned,
glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour,
glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs,
glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start,
glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium,
glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h,
glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr,
sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err,
years_in_century, glob_percent_done, glob_normmax, glob_current_iter,
glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float,
glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes,
glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1,
array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2,
array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g,
array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y,
array_x, array_poles, array_fact_2, array_y_set_initial,
array_y_higher_work, array_y_higher, array_y_higher_work2,
array_complex_pole, array_real_pole, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_small_float,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_html_log,
> glob_optimal_clock_start_sec,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> glob_display_flag,
> glob_iter,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_warned2,
> glob_warned,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_dump,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_log10_relerr,
> glob_disp_incr,
> glob_log10normmin,
> glob_start,
> glob_smallish_float,
> glob_relerr,
> glob_abserr,
> centuries_in_millinium,
> glob_subiter_method,
> glob_log10abserr,
> glob_max_hours,
> glob_h,
> glob_clock_sec,
> hours_in_day,
> glob_log10relerr,
> glob_log10_abserr,
> sec_in_min,
> djd_debug,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> years_in_century,
> glob_percent_done,
> glob_normmax,
> glob_current_iter,
> glob_optimal_start,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_initial_pass,
> djd_debug2,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_almost_1,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_norms,
> array_pole,
> array_fact_1,
> array_last_rel_error,
> array_tmp1_g,
> array_type_pole,
> array_1st_rel_error,
> array_m1,
> array_y_init,
> array_y,
> array_x,
> array_poles,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher,
> array_y_higher_work2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax,
glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec,
glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter,
MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned,
glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour,
glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs,
glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start,
glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium,
glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h,
glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr,
sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err,
years_in_century, glob_percent_done, glob_normmax, glob_current_iter,
glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float,
glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes,
glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1,
array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2,
array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g,
array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y,
array_x, array_poles, array_fact_2, array_y_set_initial,
array_y_higher_work, array_y_higher, array_y_higher_work2,
array_complex_pole, array_real_pole, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_small_float,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_html_log,
> glob_optimal_clock_start_sec,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> glob_display_flag,
> glob_iter,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_warned2,
> glob_warned,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_dump,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_log10_relerr,
> glob_disp_incr,
> glob_log10normmin,
> glob_start,
> glob_smallish_float,
> glob_relerr,
> glob_abserr,
> centuries_in_millinium,
> glob_subiter_method,
> glob_log10abserr,
> glob_max_hours,
> glob_h,
> glob_clock_sec,
> hours_in_day,
> glob_log10relerr,
> glob_log10_abserr,
> sec_in_min,
> djd_debug,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> years_in_century,
> glob_percent_done,
> glob_normmax,
> glob_current_iter,
> glob_optimal_start,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_initial_pass,
> djd_debug2,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_almost_1,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_norms,
> array_pole,
> array_fact_1,
> array_last_rel_error,
> array_tmp1_g,
> array_type_pole,
> array_1st_rel_error,
> array_m1,
> array_y_init,
> array_y,
> array_x,
> array_poles,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher,
> array_y_higher_work2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax,
glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec,
glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter,
MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned,
glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour,
glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs,
glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start,
glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium,
glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h,
glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr,
sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err,
years_in_century, glob_percent_done, glob_normmax, glob_current_iter,
glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float,
glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes,
glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1,
array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2,
array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g,
array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y,
array_x, array_poles, array_fact_2, array_y_set_initial,
array_y_higher_work, array_y_higher, array_y_higher_work2,
array_complex_pole, array_real_pole, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_small_float,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_html_log,
> glob_optimal_clock_start_sec,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> glob_display_flag,
> glob_iter,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_warned2,
> glob_warned,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_dump,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_log10_relerr,
> glob_disp_incr,
> glob_log10normmin,
> glob_start,
> glob_smallish_float,
> glob_relerr,
> glob_abserr,
> centuries_in_millinium,
> glob_subiter_method,
> glob_log10abserr,
> glob_max_hours,
> glob_h,
> glob_clock_sec,
> hours_in_day,
> glob_log10relerr,
> glob_log10_abserr,
> sec_in_min,
> djd_debug,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> years_in_century,
> glob_percent_done,
> glob_normmax,
> glob_current_iter,
> glob_optimal_start,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_initial_pass,
> djd_debug2,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_almost_1,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_norms,
> array_pole,
> array_fact_1,
> array_last_rel_error,
> array_tmp1_g,
> array_type_pole,
> array_1st_rel_error,
> array_m1,
> array_y_init,
> array_y,
> array_x,
> array_poles,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher,
> array_y_higher_work2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax,
glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec,
glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter,
MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned,
glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour,
glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs,
glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start,
glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium,
glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h,
glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr,
sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err,
years_in_century, glob_percent_done, glob_normmax, glob_current_iter,
glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float,
glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes,
glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1,
array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2,
array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g,
array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y,
array_x, array_poles, array_fact_2, array_y_set_initial,
array_y_higher_work, array_y_higher, array_y_higher_work2,
array_complex_pole, array_real_pole, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_small_float,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_html_log,
> glob_optimal_clock_start_sec,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> glob_display_flag,
> glob_iter,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_warned2,
> glob_warned,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_dump,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_log10_relerr,
> glob_disp_incr,
> glob_log10normmin,
> glob_start,
> glob_smallish_float,
> glob_relerr,
> glob_abserr,
> centuries_in_millinium,
> glob_subiter_method,
> glob_log10abserr,
> glob_max_hours,
> glob_h,
> glob_clock_sec,
> hours_in_day,
> glob_log10relerr,
> glob_log10_abserr,
> sec_in_min,
> djd_debug,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> years_in_century,
> glob_percent_done,
> glob_normmax,
> glob_current_iter,
> glob_optimal_start,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_initial_pass,
> djd_debug2,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_almost_1,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_norms,
> array_pole,
> array_fact_1,
> array_last_rel_error,
> array_tmp1_g,
> array_type_pole,
> array_1st_rel_error,
> array_m1,
> array_y_init,
> array_y,
> array_x,
> array_poles,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher,
> array_y_higher_work2,
> array_complex_pole,
> array_real_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sinh $eq_no = 1
> array_tmp1[1] := sinh(array_x[1]);
> array_tmp1_g[1] := cosh(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 sinh $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := att(1,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sinh $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := att(2,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sinh $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := att(3,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sinh $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := att(4,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sinh $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax,
glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec,
glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter,
MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned,
glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour,
glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs,
glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start,
glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium,
glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h,
glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr,
sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err,
years_in_century, glob_percent_done, glob_normmax, glob_current_iter,
glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float,
glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes,
glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1,
array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2,
array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g,
array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y,
array_x, array_poles, array_fact_2, array_y_set_initial,
array_y_higher_work, array_y_higher, array_y_higher_work2,
array_complex_pole, array_real_pole, glob_last;
array_tmp1[1] := sinh(array_x[1]);
array_tmp1_g[1] := cosh(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 17
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 13
> if array_fact_1[nnn] = 0 then # if number 14
> ret := nnn!;
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> if array_fact_2[mmm,nnn] = 0 then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 1.0 + cosh(x);
> end;
exact_soln_y := proc(x) 1.0 + cosh(x) end proc
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_small_float,
> glob_hmax,
> glob_not_yet_start_msg,
> glob_html_log,
> glob_optimal_clock_start_sec,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> glob_display_flag,
> glob_iter,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_warned2,
> glob_warned,
> glob_optimal_done,
> glob_reached_optimal_h,
> days_in_year,
> min_in_hour,
> glob_dump,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_log10_relerr,
> glob_disp_incr,
> glob_log10normmin,
> glob_start,
> glob_smallish_float,
> glob_relerr,
> glob_abserr,
> centuries_in_millinium,
> glob_subiter_method,
> glob_log10abserr,
> glob_max_hours,
> glob_h,
> glob_clock_sec,
> hours_in_day,
> glob_log10relerr,
> glob_log10_abserr,
> sec_in_min,
> djd_debug,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> years_in_century,
> glob_percent_done,
> glob_normmax,
> glob_current_iter,
> glob_optimal_start,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_initial_pass,
> djd_debug2,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_almost_1,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_norms,
> array_pole,
> array_fact_1,
> array_last_rel_error,
> array_tmp1_g,
> array_type_pole,
> array_1st_rel_error,
> array_m1,
> array_y_init,
> array_y,
> array_x,
> array_poles,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher,
> array_y_higher_work2,
> array_complex_pole,
> array_real_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGL := 3;
> INFO := 2;
> glob_curr_iter_when_opt := 0;
> glob_max_sec := 10000.0;
> glob_small_float := 0.1e-50;
> glob_hmax := 1.0;
> glob_not_yet_start_msg := true;
> glob_html_log := true;
> glob_optimal_clock_start_sec := 0.0;
> glob_look_poles := false;
> glob_last_good_h := 0.1;
> glob_hmin := 0.00000000001;
> glob_display_flag := true;
> glob_iter := 0;
> MAX_UNCHANGED := 10;
> glob_orig_start_sec := 0.0;
> glob_warned2 := false;
> glob_warned := false;
> glob_optimal_done := false;
> glob_reached_optimal_h := false;
> days_in_year := 365.0;
> min_in_hour := 60.0;
> glob_dump := false;
> glob_optimal_expect_sec := 0.1;
> glob_unchanged_h_cnt := 0;
> glob_no_eqs := 0;
> glob_log10_relerr := 0.1e-10;
> glob_disp_incr := 0.1;
> glob_log10normmin := 0.1;
> glob_start := 0;
> glob_smallish_float := 0.1e-100;
> glob_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> centuries_in_millinium := 10.0;
> glob_subiter_method := 3;
> glob_log10abserr := 0.0;
> glob_max_hours := 0.0;
> glob_h := 0.1;
> glob_clock_sec := 0.0;
> hours_in_day := 24.0;
> glob_log10relerr := 0.0;
> glob_log10_abserr := 0.1e-10;
> sec_in_min := 60.0;
> djd_debug := true;
> glob_max_trunc_err := 0.1e-10;
> glob_max_rel_trunc_err := 0.1e-10;
> years_in_century := 100.0;
> glob_percent_done := 0.0;
> glob_normmax := 0.0;
> glob_current_iter := 0;
> glob_optimal_start := 0.0;
> glob_max_iter := 1000;
> glob_dump_analytic := false;
> glob_large_float := 9.0e100;
> glob_initial_pass := true;
> djd_debug2 := true;
> glob_max_opt_iter := 10;
> glob_max_minutes := 0.0;
> glob_hmin_init := 0.001;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> glob_almost_1 := 0.9990;
> #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/sinhpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 10.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"1.0 + cosh(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_fact_1[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_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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
> ;
> 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 <=max_terms do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while iiif <= glob_max_terms do # do number 2
> jjjf := 0;
> while jjjf <= glob_max_terms do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 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 := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sinh ( x ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-18T01:21:32-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sinh")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh ( x ) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 092 | ")
> ;
> logitem_str(html_log_file,"sinh diffeq.mxt")
> ;
> logitem_str(html_log_file,"sinh maple results")
> ;
> logitem_str(html_log_file,"Mostly affecting speed of factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_curr_iter_when_opt, glob_max_sec, glob_small_float, glob_hmax,
glob_not_yet_start_msg, glob_html_log, glob_optimal_clock_start_sec,
glob_look_poles, glob_last_good_h, glob_hmin, glob_display_flag, glob_iter,
MAX_UNCHANGED, glob_orig_start_sec, glob_warned2, glob_warned,
glob_optimal_done, glob_reached_optimal_h, days_in_year, min_in_hour,
glob_dump, glob_optimal_expect_sec, glob_unchanged_h_cnt, glob_no_eqs,
glob_log10_relerr, glob_disp_incr, glob_log10normmin, glob_start,
glob_smallish_float, glob_relerr, glob_abserr, centuries_in_millinium,
glob_subiter_method, glob_log10abserr, glob_max_hours, glob_h,
glob_clock_sec, hours_in_day, glob_log10relerr, glob_log10_abserr,
sec_in_min, djd_debug, glob_max_trunc_err, glob_max_rel_trunc_err,
years_in_century, glob_percent_done, glob_normmax, glob_current_iter,
glob_optimal_start, glob_max_iter, glob_dump_analytic, glob_large_float,
glob_initial_pass, djd_debug2, glob_max_opt_iter, glob_max_minutes,
glob_hmin_init, glob_not_yet_finished, glob_clock_start_sec, glob_almost_1,
array_const_0D0, array_const_1, array_tmp0, array_tmp1, array_tmp2,
array_norms, array_pole, array_fact_1, array_last_rel_error, array_tmp1_g,
array_type_pole, array_1st_rel_error, array_m1, array_y_init, array_y,
array_x, array_poles, array_fact_2, array_y_set_initial,
array_y_higher_work, array_y_higher, array_y_higher_work2,
array_complex_pole, array_real_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGL := 3;
INFO := 2;
glob_curr_iter_when_opt := 0;
glob_max_sec := 10000.0;
glob_small_float := 0.1*10^(-50);
glob_hmax := 1.0;
glob_not_yet_start_msg := true;
glob_html_log := true;
glob_optimal_clock_start_sec := 0.;
glob_look_poles := false;
glob_last_good_h := 0.1;
glob_hmin := 0.1*10^(-10);
glob_display_flag := true;
glob_iter := 0;
MAX_UNCHANGED := 10;
glob_orig_start_sec := 0.;
glob_warned2 := false;
glob_warned := false;
glob_optimal_done := false;
glob_reached_optimal_h := false;
days_in_year := 365.0;
min_in_hour := 60.0;
glob_dump := false;
glob_optimal_expect_sec := 0.1;
glob_unchanged_h_cnt := 0;
glob_no_eqs := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_log10normmin := 0.1;
glob_start := 0;
glob_smallish_float := 0.1*10^(-100);
glob_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
centuries_in_millinium := 10.0;
glob_subiter_method := 3;
glob_log10abserr := 0.;
glob_max_hours := 0.;
glob_h := 0.1;
glob_clock_sec := 0.;
hours_in_day := 24.0;
glob_log10relerr := 0.;
glob_log10_abserr := 0.1*10^(-10);
sec_in_min := 60.0;
djd_debug := true;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_rel_trunc_err := 0.1*10^(-10);
years_in_century := 100.0;
glob_percent_done := 0.;
glob_normmax := 0.;
glob_current_iter := 0;
glob_optimal_start := 0.;
glob_max_iter := 1000;
glob_dump_analytic := false;
glob_large_float := 0.90*10^101;
glob_initial_pass := true;
djd_debug2 := true;
glob_max_opt_iter := 10;
glob_max_minutes := 0.;
glob_hmin_init := 0.001;
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
glob_almost_1 := 0.9990;
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/sinhpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 10.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "1.0 + \t cosh(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
term := 1;
while term <= max_terms do array_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_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[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_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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
;
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 <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
x_end := 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 := 0.001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sinh ( x ) ;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-18T01:21:32-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sinh");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh ( x ) ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 092 | ");
logitem_str(html_log_file,
"sinh diffeq.mxt");
logitem_str(html_log_file,
"sinh maple results");
logitem_str(html_log_file, "Mostly affecting speed of factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/sinhpostode.ode#################
diff ( y , x , 1 ) = sinh ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 10.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
1.0 + cosh(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 2
y[1] (numeric) = 2
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 2.0000005000000416666680555555804
y[1] (numeric) = 2.000000500000041666716666668254
absolute error = 4.86111126736e-20
relative error = 2.4305550260411928531370563054199e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 2.0000020000006666667555555619048
y[1] (numeric) = 2.0000020000006666668527778210814
absolute error = 9.72222591766e-20
relative error = 4.8611080977202819101361338390097e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 2.0000045000033750010125001627232
y[1] (numeric) = 2.0000045000033750011583336508434
absolute error = 1.458334881202e-19
relative error = 7.2916579997671958472433341038629e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 2.0000080000106666723555571809527
y[1] (numeric) = 2.0000080000106666725500020290681
absolute error = 1.944448481154e-19
relative error = 9.7222035169040806039331534881948e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 2.0000125000260416883680652436783
y[1] (numeric) = 2.0000125000260416886111216314521
absolute error = 2.430563877738e-19
relative error = 1.2152743433885299238218615101705e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 2.0000180000540000648000416571595
y[1] (numeric) = 2.0000180000540000650917098128664
absolute error = 2.916681557069e-19
relative error = 1.4583276535462431899156958428176e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 2.0000245001000418300681985318487
y[1] (numeric) = 2.000024500100041830408478732375
absolute error = 3.402802005263e-19
relative error = 1.7013801606394275745561647200906e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 2.0000320001706670307559716574388
y[1] (numeric) = 2.000032000170667031144864228283
absolute error = 3.888925708442e-19
relative error = 1.9444317431471844489935220484395e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 2.0000405002733757381135676279698
y[1] (numeric) = 2.0000405002733757385510729432428
absolute error = 4.375053152730e-19
relative error = 2.1874822795498368244131625717739e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 2.0000500004166680555580357170414
y[1] (numeric) = 2.0000500004166680560441541994669
absolute error = 4.861184824255e-19
relative error = 2.4305316483299293038264547823902e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 2.0000605006100441271733720032042
y[1] (numeric) = 2.0000605006100441277081041241188
absolute error = 5.347321209146e-19
relative error = 2.6735797279707280796864274025255e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 2.0000720008640041472106642456342
y[1] (numeric) = 2.0000720008640041477940105249884
absolute error = 5.833462793542e-19
relative error = 2.9166263969607207626334652778816e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 2.0000845011900483705882870102372
y[1] (numeric) = 2.0000845011900483712202480165955
absolute error = 6.319610063583e-19
relative error = 3.1596715337891164296408818473526e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=3.8MB, alloc=3.0MB, time=0.18
x[1] = 0.014
y[1] (analytic) = 2.0000980016006771243921575463776
y[1] (numeric) = 2.0000980016006771250727338969194
absolute error = 6.805763505418e-19
relative error = 3.4027150169498454133461009507791e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 2.00011250210939082037606391449
y[1] (numeric) = 2.00011250210939082110525627501
absolute error = 7.291923605200e-19
relative error = 3.6457567249390592934593657715165e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 2.0001280027306899684620778649013
y[1] (numeric) = 2.0001280027306899692398869498101
absolute error = 7.778090849088e-19
relative error = 3.8887965362561307621588761563099e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 2.0001445034800751912410659682783
y[1] (numeric) = 2.0001445034800751920674925406034
absolute error = 8.264265723251e-19
relative error = 4.1318343294056533695026630777249e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 2.0001620043740472394733134982132
y[1] (numeric) = 2.0001620043740472403483583695994
absolute error = 8.750448713862e-19
relative error = 4.3748699828944415643662391501815e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 2.000180505430107008589276566571
y[1] (numeric) = 2.0001805054301070095129405972816
absolute error = 9.236640307106e-19
relative error = 4.6179033752355302519674955747643e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 2.0002000066667555561904790123542
y[1] (numeric) = 2.0002000066667555571627631112715
absolute error = 9.722840989173e-19
relative error = 4.8609343849446748729590741212497e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 2.0002205081034941205505715449809
y[1] (numeric) = 2.0002205081034941215714766696073
absolute error = 1.0209051246264e-18
relative error = 5.1039628905433509580437032678271e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 2.0002420097608241401165716430391
y[1] (numeric) = 2.000242009760824141186098799498
absolute error = 1.0695271564589e-18
relative error = 5.3469887705577539774725490446703e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 2.0002645116602472740103037097573
y[1] (numeric) = 2.0002645116602472751284539527943
absolute error = 1.1181502430370e-18
relative error = 5.5900119035202989106152140197659e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 2.000288013824265423530059986634
y[1] (numeric) = 2.0002880138242654246968344196177
absolute error = 1.1667744329837e-18
relative error = 5.8330321679676202057037000940392e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 2.0003125162763807546525037268886
y[1] (numeric) = 2.0003125162763807558679035018117
absolute error = 1.2153997749231e-18
relative error = 6.0760494424420713217153793086748e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 2.0003380190410957215348371306378
y[1] (numeric) = 2.0003380190410957227988634481186
absolute error = 1.2640263174808e-18
relative error = 6.3190636054937240692957633583413e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 2.0003645221439130910172575439702
y[1] (numeric) = 2.0003645221439130923299116532532
absolute error = 1.3126541092830e-18
relative error = 6.5620745356758689654891063066106e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 2.0003920256113359681257264243733
y[1] (numeric) = 2.000392025611335969487009623331
absolute error = 1.3612831989577e-18
relative error = 6.8050821115510138764724870911207e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 2.0004205294708678225750765752876
y[1] (numeric) = 2.0004205294708678239849902104216
absolute error = 1.4099136351340e-18
relative error = 7.0480862116873841541051997459931e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 2.0004500337510125162724841528952
y[1] (numeric) = 2.0004500337510125177310296193375
absolute error = 1.4585454664423e-18
relative error = 7.2910867146599220356844435516512e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 2.0004805384812743318213329486178
y[1] (numeric) = 2.0004805384812743333285116901322
absolute error = 1.5071787415144e-18
relative error = 7.5340834990507860657368728601849e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 2.0005120436921580020254994511908
y[1] (numeric) = 2.0005120436921580035813129601745
absolute error = 1.5558135089837e-18
relative error = 7.7770764434503503297839573907328e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 2.0005445494151687403940881926011
y[1] (numeric) = 2.000544549415168741998538010086
absolute error = 1.6044498174849e-18
relative error = 8.0200654264557042558616921406166e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 2.000578055682812272646647882626
y[1] (numeric) = 2.0005780556828122742997355982802
absolute error = 1.6530877156542e-18
relative error = 8.2630503266716518228786145627560e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 2.0006125625285948692188998371924
y[1] (numeric) = 2.0006125625285948709206270893221
absolute error = 1.7017272521297e-18
relative error = 8.5060310227127103503498195277735e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 2.0006480699870233787690112062878
y[1] (numeric) = 2.0006480699870233805193796818386
absolute error = 1.7503684755508e-18
relative error = 8.7490073932001106796802490491907e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=7.6MB, alloc=4.1MB, time=0.42
x[1] = 0.037
y[1] (analytic) = 2.0006845780936052626844465076978
y[1] (numeric) = 2.0006845780936052644834579422566
absolute error = 1.7990114345588e-18
relative error = 8.9919793167647956018787892484365e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 2.000722086884848630589431973426
y[1] (numeric) = 2.0007220868848486324370881512227
absolute error = 1.8476561777967e-18
relative error = 9.2349466720464193864421076161965e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 2.0007605963982622768530682162631
y[1] (numeric) = 2.0007605963982622787493709701722
absolute error = 1.8963027539091e-18
relative error = 9.4779093376928472092737530447173e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 2.00080010667235571809812772462
y[1] (numeric) = 2.0008001066723557200430789361627
absolute error = 1.9449512115427e-18
relative error = 9.7208671923626534225815747046723e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 2.0008406177466392317105746944272
y[1] (numeric) = 2.000840617746639233704176293773
absolute error = 1.9936015993458e-18
relative error = 9.9638201147226216093158866486414e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 2.0008821296616238953498457076217
y[1] (numeric) = 2.0008821296616238973920996735907
absolute error = 2.0422539659690e-18
relative error = 1.0206767983451242273480718152154e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 2.0009246424588216274599307675074
y[1] (numeric) = 2.000924642458821629550839127572
absolute error = 2.0909083600646e-18
relative error = 1.0449710677235713078186627085854e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 2.0009681561807452287812952020716
y[1] (numeric) = 2.0009681561807452309208600323586
absolute error = 2.1395648302870e-18
relative error = 1.0692648074773937020838381131364e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 2.0010126708709084248636839471835
y[1] (numeric) = 2.0010126708709084270519073724762
absolute error = 2.1882234252927e-18
relative error = 1.0935580054774521342498847344031e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 2.0010581865738259095798507224835
y[1] (numeric) = 2.0010581865738259118167349162237
absolute error = 2.2368841937402e-18
relative error = 1.1178506495956276676811045835179e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 2.0011047033350133896402556136946
y[1] (numeric) = 2.001104703335013391925802797985
absolute error = 2.2855471842904e-18
relative error = 1.1421427277050214864936896140203e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 2.0011522212009876301087755760583
y[1] (numeric) = 2.0011522212009876324429880216645
absolute error = 2.3342124456062e-18
relative error = 1.1664342276797548770283608091576e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 2.0012007402192665009194733746086
y[1] (numeric) = 2.0012007402192665033023534009615
absolute error = 2.3828800263529e-18
relative error = 1.1907251373951689951736186731611e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 2.0012502604383690243944714780576
y[1] (numeric) = 2.0012502604383690268260214532557
absolute error = 2.4315499751981e-18
relative error = 1.2150154447277747586003913848516e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 2.00130078190781542376297842417
y[1] (numeric) = 2.0013007819078154262432007649816
absolute error = 2.4802223408116e-18
relative error = 1.2393051375552027435993327354580e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 2.0013523046781271726815161756566
y[1] (numeric) = 2.0013523046781271752104133475226
absolute error = 2.5288971718660e-18
relative error = 1.2635942037565028506794329280333e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 2.0014048288008270457553979868197
y[1] (numeric) = 2.0014048288008270483329725038558
absolute error = 2.5775745170361e-18
relative error = 1.2878826312118443421517168337705e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 2.001458354328439170061507302431
y[1] (numeric) = 2.0014583543284391726877617274301
absolute error = 2.6262544249991e-18
relative error = 1.3121704078026156322821190891442e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 2.0015128813144890776724292116254
y[1] (numeric) = 2.0015128813144890803473661560605
absolute error = 2.6749369444351e-18
relative error = 1.3364575214116739460258621469225e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 2.0015684098135037591819869809478
y[1] (numeric) = 2.0015684098135037619056091049742
absolute error = 2.7236221240264e-18
relative error = 1.3607439599229954040099261994242e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 2.0016249398810117182322371920918
y[1] (numeric) = 2.0016249398810117210045472045501
absolute error = 2.7723100124583e-18
relative error = 1.3850297112220745538550370782956e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 2.0016824715735430270419780113322
y[1] (numeric) = 2.0016824715735430298629786697509
absolute error = 2.8210006584187e-18
relative error = 1.4093147631957243355715911847133e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 2.0017410049486293829368261191625
y[1] (numeric) = 2.0017410049486293858065202297607
absolute error = 2.8696941105982e-18
relative error = 1.4335991037321258603981749013121e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 2.0018005400648041658809188302198
y[1] (numeric) = 2.0018005400648041687993092479102
absolute error = 2.9183904176904e-18
relative error = 1.4578827207209780882222523908772e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.66
NO POLE
x[1] = 0.061
y[1] (analytic) = 2.001861076981602497010298935204
y[1] (numeric) = 2.0018610769816024999773885635955
absolute error = 2.9670896283915e-18
relative error = 1.4821656020532978003922734868907e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 2.0019226157595612981680407981811
y[1] (numeric) = 2.0019226157595613011838325895817
absolute error = 3.0157917914006e-18
relative error = 1.5064477356215692694539920210575e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 2.0019851564602193524411772444006
y[1] (numeric) = 2.0019851564602193555056741998207
absolute error = 3.0644969554201e-18
relative error = 1.5307291093199438490471581851936e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 2.002048699146117365699487775561
y[1] (numeric) = 2.0020486991461173688126929447161
absolute error = 3.1132051691551e-18
relative error = 1.5550097110439400342404646967206e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 2.0021132438807980291362096513148
y[1] (numeric) = 2.0021132438807980322981261326285
absolute error = 3.1619164813137e-18
relative error = 1.5792895286905931003293764089851e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 2.00217879072880608281073437773
y[1] (numeric) = 2.0021787907288060860213653183374
absolute error = 3.2106309406074e-18
relative error = 1.6035685501586546556316193277513e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 2.0022453397556883801933531454105
y[1] (numeric) = 2.002245339755688383452701741161
absolute error = 3.2593485957505e-18
relative error = 1.6278467633482927119963374342339e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 2.0023128910279939537121157620248
y[1] (numeric) = 2.0023128910279939570201852574856
absolute error = 3.3080694954608e-18
relative error = 1.6521241561614410606347878255316e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 2.0023814446132740813018686261092
y[1] (numeric) = 2.0023814446132740846586623145682
absolute error = 3.3567936884590e-18
relative error = 1.6764007165014993470413665458050e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 2.002451000580082353955538291187
y[1] (numeric) = 2.0024510005800823573610595146565
absolute error = 3.4055212234695e-18
relative error = 1.7006764322737323469338059948241e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 2.0025215589979747442777281714951
y[1] (numeric) = 2.0025215589979747477319803207148
absolute error = 3.4542521492197e-18
relative error = 1.7249512913849200998657101047806e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 2.0025931199375096760406969429182
y[1] (numeric) = 2.0025931199375096795436834573587
absolute error = 3.5029865144405e-18
relative error = 1.7492252817436073357397538576868e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 2.0026656834702480947427881951162
y[1] (numeric) = 2.0026656834702480982945125629828
absolute error = 3.5517243678666e-18
relative error = 1.7734983912602529777709613403106e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 2.0027392496687535391693818932809
y[1] (numeric) = 2.0027392496687535427698476515164
absolute error = 3.6004657582355e-18
relative error = 1.7977706078467304973598228118959e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 2.0028138186065922139564392104767
y[1] (numeric) = 2.0028138186065922176056499447655
absolute error = 3.6492107342888e-18
relative error = 1.8220419194169767597336479244727e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 2.0028893903583330631567132941199
y[1] (numeric) = 2.0028893903583330668546726388912
absolute error = 3.6979593447713e-18
relative error = 1.8463123138865423082704912504005e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 2.0029659649995478448086995328102
y[1] (numeric) = 2.0029659649995478485554111712419
absolute error = 3.7467116384317e-18
relative error = 1.8705817791729405613051468446754e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 2.003043542606811206508399892473
y[1] (numeric) = 2.0030435426068112103038675564953
absolute error = 3.7954676640223e-18
relative error = 1.8948503031954976849750042556055e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 2.003122123257700761983976893582
y[1] (numeric) = 2.0031221232577007658282043638812
absolute error = 3.8442274702992e-18
relative error = 1.9191178738754521067037440577105e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 2.0032017070307971686733738041236
y[1] (numeric) = 2.0032017070307971725663649101457
absolute error = 3.8929911060221e-18
relative error = 1.9433844791358543208344202953833e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 2.0032822940056842063049786259279
y[1] (numeric) = 2.0032822940056842102467372458826
absolute error = 3.9417586199547e-18
relative error = 1.9676501069017662224974255740702e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 2.003363884262948856481410455039
y[1] (numeric) = 2.0033638842629488604719405159034
absolute error = 3.9905300608644e-18
relative error = 1.9919147451001109769269782989192e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 2.0034464778841813832665077999156
y[1] (numeric) = 2.0034464778841813873058132774385
absolute error = 4.0393054775229e-18
relative error = 2.0161783816599721468834910765093e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=15.2MB, alloc=4.1MB, time=0.90
x[1] = 0.084
y[1] (analytic) = 2.0035300749519754147755994444593
y[1] (numeric) = 2.0035300749519754188636843631646
absolute error = 4.0880849187053e-18
relative error = 2.0404410045121440629817123863466e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 2.0036146755499280257691394461449
y[1] (numeric) = 2.0036146755499280299060078793362
absolute error = 4.1368684331913e-18
relative error = 2.0647026015897304078726382262475e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 2.0037002797626398212497888628985
y[1] (numeric) = 2.0037002797626398254354449326628
absolute error = 4.1856560697643e-18
relative error = 2.0889631608276945837711155293052e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 2.0037868876757150210630278058084
y[1] (numeric) = 2.0037868876757150252974756830205
absolute error = 4.2344478772121e-18
relative error = 2.1132226701632086780493037464416e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 2.0038744993757615455013824182913
y[1] (numeric) = 2.0038744993757615497846263226175
absolute error = 4.2832439043262e-18
relative error = 2.1374811175353036875963120096289e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 2.0039631149503911019123523859445
y[1] (numeric) = 2.0039631149503911062443965858474
absolute error = 4.3320441999029e-18
relative error = 2.1617384908854180504647062102692e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 2.0040527344882192723101255850222
y[1] (numeric) = 2.0040527344882192766909743977646
absolute error = 4.3808488127424e-18
relative error = 2.1859947781569480497185761240518e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 2.0041433580788656019911674812549
y[1] (numeric) = 2.0041433580788656064208252729042
absolute error = 4.4296577916493e-18
relative error = 2.2102499672954968851975121035864e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 2.0042349858129536891537738946108
y[1] (numeric) = 2.0042349858129536936322450800435
absolute error = 4.4784711854327e-18
relative error = 2.2345040462489240961797212386323e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 2.0043276177821112755216767495584
y[1] (numeric) = 2.0043276177821112800489657924643
absolute error = 4.5272890429059e-18
relative error = 2.2587570029671953970366347616410e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 2.0044212540789703379717934344438
y[1] (numeric) = 2.0044212540789703425479048473306
absolute error = 4.5761114128868e-18
relative error = 2.2830088254025817775854471003581e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 2.0045158947971671811662113977398
y[1] (numeric) = 2.0045158947971671857911497419375
absolute error = 4.6249383441977e-18
relative error = 2.3072595015095592187719847564973e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 2.0046115400313425311885006131587
y[1] (numeric) = 2.0046115400313425358622704988243
absolute error = 4.6737698856656e-18
relative error = 2.3315090192449578564473615831214e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 2.0047081898771416301844475499503
y[1] (numeric) = 2.0047081898771416349070536360722
absolute error = 4.7226060861219e-18
relative error = 2.3557573665678118019448507255876e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 2.0048058444312143320073052891247
y[1] (numeric) = 2.0048058444312143367787522835277
absolute error = 4.7714469944030e-18
relative error = 2.3800045314396579222066993782900e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 2.0049045037912151988676554308609
y[1] (numeric) = 2.0049045037912152036879480902107
absolute error = 4.8202926593498e-18
relative error = 2.4042505018242858727677950089933e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 2.0050041680558035989879784429683
y[1] (numeric) = 2.0050041680558036038571215727763
absolute error = 4.8691431298080e-18
relative error = 2.4284952656878872004665822609131e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 2.0051048373246438052620301049819
y[1] (numeric) = 2.0051048373246438101800285596098
absolute error = 4.9179984546279e-18
relative error = 2.4527388109989550332342208492950e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 2.0052065116984050949191227072741
y[1] (numeric) = 2.0052065116984050998859813899389
absolute error = 4.9668586826648e-18
relative error = 2.4769811257284830159683854141489e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 2.0053091912787618501934106694736
y[1] (numeric) = 2.0053091912787618552091345322528
absolute error = 5.0157238627792e-18
relative error = 2.5012221978500644454396693346535e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 2.0054128761683936599982812474859
y[1] (numeric) = 2.0054128761683936650628752913219
absolute error = 5.0645940438360e-18
relative error = 2.5254620153394927180323675765884e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 2.0055175664709854226059520035125
y[1] (numeric) = 2.0055175664709854277194212782181
absolute error = 5.1134692747056e-18
relative error = 2.5497005661753092823926364279080e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 2.0056232622912274493323777186775
y[1] (numeric) = 2.0056232622912274544947273229407
absolute error = 5.1623496042632e-18
relative error = 2.5739378383384539387141382657635e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 2.0057299637348155692275704331751
y[1] (numeric) = 2.0057299637348155744388055145641
absolute error = 5.2112350813890e-18
relative error = 2.5981738198123639566142367911301e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=1.15
NO POLE
x[1] = 0.108
y[1] (analytic) = 2.0058376709084512347714373042674
y[1] (numeric) = 2.0058376709084512400315630592361
absolute error = 5.2601257549687e-18
relative error = 2.6224084985832227198061148815000e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 2.0059463839198416285752419779802
y[1] (numeric) = 2.0059463839198416338842636518729
absolute error = 5.3090216738927e-18
relative error = 2.6466418626395602114227671547146e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 2.0060561028776997710887961759647
y[1] (numeric) = 2.0060561028776997764467190630219
absolute error = 5.3579228870572e-18
relative error = 2.6708738999728007553932469641177e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 2.0061668278917446293134892047287
y[1] (numeric) = 2.0061668278917446347203186480919
absolute error = 5.4068294433632e-18
relative error = 2.6951045985767638001029929500415e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 2.0062785590727012265212641002729
y[1] (numeric) = 2.0062785590727012319770054919902
absolute error = 5.4557413917173e-18
relative error = 2.7193339464480620443954594348589e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 2.0063912965323007529796501271196
y[1] (numeric) = 2.0063912965323007584843089081511
absolute error = 5.5046587810315e-18
relative error = 2.7435619315860010180040515438943e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 2.006505040383280677682962356775
y[1] (numeric) = 2.0065050403832806832365440169983
absolute error = 5.5535816602233e-18
relative error = 2.7677885419926282028885046546873e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 2.0066197907393848610897800568335
y[1] (numeric) = 2.006619790739384866692290135049
absolute error = 5.6025100782155e-18
relative error = 2.7920137656726326264864490344727e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 2.0067355477153636688668166282126
y[1] (numeric) = 2.0067355477153636745182607121489
absolute error = 5.6514440839363e-18
relative error = 2.8162375906333939799212871902528e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 2.0068523114269740866392948343964
y[1] (numeric) = 2.0068523114269740923396785607165
absolute error = 5.7003837263201e-18
relative error = 2.8404600048853805185560651403084e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 2.0069700819909798357479420730751
y[1] (numeric) = 2.0069700819909798414972711273814
absolute error = 5.7493290543063e-18
relative error = 2.8646809964415502896956745732354e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 2.0070888595251514900127214471822
y[1] (numeric) = 2.0070888595251514958110015640224
absolute error = 5.7982801168402e-18
relative error = 2.8889005533177988558236436763263e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 2.0072086441482665935034153990723
y[1] (numeric) = 2.0072086441482665993506523619454
absolute error = 5.8472369628731e-18
relative error = 2.9131186635330082901370460236187e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 2.0073294359801097793171796784333
y[1] (numeric) = 2.0073294359801097852133793197949
absolute error = 5.8961996413616e-18
relative error = 2.9373353151086976077388393181233e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 2.0074512351414728893631864214943
y[1] (numeric) = 2.0074512351414728953083546227629
absolute error = 5.9451682012686e-18
relative error = 2.9615504960695201616322535033574e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 2.0075740417541550951544761261857
y[1] (numeric) = 2.0075740417541551011486188177482
absolute error = 5.9941426915625e-18
relative error = 2.9857641944428642469337019860978e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 2.0076978559409630196071393151105
y[1] (numeric) = 2.0076978559409630256502624763282
absolute error = 6.0431231612177e-18
relative error = 3.0099763982591013523535864107025e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 2.0078226778257108598469496855204
y[1] (numeric) = 2.0078226778257108659390593447354
absolute error = 6.0921096592150e-18
relative error = 3.0341870955517845087051066950105e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 2.0079485075332205110235715529401
y[1] (numeric) = 2.0079485075332205171646737874807
absolute error = 6.1411022345406e-18
relative error = 3.0583962743571493268749911671553e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 2.008075345189321691132465402656
y[1] (numeric) = 2.0080753451893216973225663388432
absolute error = 6.1901009361872e-18
relative error = 3.0826039227146609940873950126888e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 2.008203190920852066844616370987
y[1] (numeric) = 2.0082031909208520730837221841406
absolute error = 6.2391058131536e-18
relative error = 3.1068100286668141204419570610255e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 2.0083320448556573803442114860759
y[1] (numeric) = 2.0083320448556573866323284005204
absolute error = 6.2881169144445e-18
relative error = 3.1310145802590322392107515321132e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 2.0084619071225915771743925058882
y[1] (numeric) = 2.0084619071225915835115267949593
absolute error = 6.3371342890711e-18
relative error = 3.1552175655399656540820360483258e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 2.0085927778515169350912121991831
y[1] (numeric) = 2.0085927778515169414773701852339
absolute error = 6.3861579860508e-18
relative error = 3.1794189725613410891568271031674e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.2MB, time=1.40
NO POLE
x[1] = 0.132
y[1] (analytic) = 2.0087246571733041939259229234232
y[1] (numeric) = 2.0087246571733042003611109778305
absolute error = 6.4351880544073e-18
relative error = 3.2036187893780105214593892644384e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 2.0088575452198326864557273619225
y[1] (numeric) = 2.008857545219832692939951905093
absolute error = 6.4842245431705e-18
relative error = 3.2278170040479004282071542550238e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 2.008991442123990470283122290993
y[1] (numeric) = 2.0089914421239904768163897923702
absolute error = 6.5332675013772e-18
relative error = 3.2520136046323592571055472203543e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 2.0091263480196744607239672564477
y[1] (numeric) = 2.0091263480196744673062842345178
absolute error = 6.5823169780701e-18
relative error = 3.2762085791956586112050183744091e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 2.0092622630417905647044110475359
y[1] (numeric) = 2.0092622630417905713357840698347
absolute error = 6.6313730222988e-18
relative error = 3.3004019158054900174009630952166e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 2.0093991873262538156668098652518
y[1] (numeric) = 2.0093991873262538223472455483712
absolute error = 6.6804356831194e-18
relative error = 3.3245936025327647610082466018742e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 2.0095371210099885094847720909438
y[1] (numeric) = 2.0095371210099885162142771005382
absolute error = 6.7295050095944e-18
relative error = 3.3487836274515630821107636428141e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 2.0096760642309283413874655702809
y[1] (numeric) = 2.0096760642309283481660466210742
absolute error = 6.7785810507933e-18
relative error = 3.3729719786394317006834779562431e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 2.0098160171280165438933243368962
y[1] (numeric) = 2.0098160171280165507209881926882
absolute error = 6.8276638557920e-18
relative error = 3.3971586441770841411873961174051e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 2.0099569798412060257532927094232
y[1] (numeric) = 2.0099569798412060326300461830966
absolute error = 6.8767534736734e-18
relative error = 3.4213436121486982022056396844575e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 2.0100989525114595119037457051836
y[1] (numeric) = 2.0100989525114595188295956587107
absolute error = 6.9258499535271e-18
relative error = 3.4455268706417655544801867156497e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 2.0102419352807496844292257234561
y[1] (numeric) = 2.0102419352807496914041790679057
absolute error = 6.9749533444496e-18
relative error = 3.4697084077471901209062903765216e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 2.0103859282920593245351364610762
y[1] (numeric) = 2.0103859282920593315592001566204
absolute error = 7.0240636955442e-18
relative error = 3.4938882115592371819122349277434e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 2.0105309316893814555305360330718
y[1] (numeric) = 2.0105309316893814626037170889932
absolute error = 7.0731810559214e-18
relative error = 3.5180662701757311855120971558831e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 2.0106769456177194868211722811407
y[1] (numeric) = 2.0106769456177194939434777558392
absolute error = 7.1223054746985e-18
relative error = 3.5422425716978555878426760824180e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 2.0108239702230873589129042630159
y[1] (numeric) = 2.0108239702230873660843412640159
absolute error = 7.1714370010000e-18
relative error = 3.5664171042303506196195995608261e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 2.0109720056525096894256549261538
y[1] (numeric) = 2.0109720056525096966462306101111
absolute error = 7.2205756839573e-18
relative error = 3.5905898558813628677461100878513e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 2.0111210520540219201180409797089
y[1] (numeric) = 2.011121052054021927387762552418
absolute error = 7.2697215727091e-18
relative error = 3.6147608147626429798911317715965e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 2.0112711095766704649228269894375
y[1] (numeric) = 2.0112711095766704722417017058388
absolute error = 7.3188747164013e-18
relative error = 3.6389299689894946743160420483026e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 2.0114221783705128589933517309974
y[1] (numeric) = 2.0114221783705128663613868951846
absolute error = 7.3680351641872e-18
relative error = 3.6630973066808729122657725975110e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 2.0115742585866179087610758480819
y[1] (numeric) = 2.0115742585866179161782788133089
absolute error = 7.4172029652270e-18
relative error = 3.6872628159591340315558845783162e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 2.0117273503770658430044008729476
y[1] (numeric) = 2.0117273503770658504707790416362
absolute error = 7.4663781686886e-18
relative error = 3.7114264849504321963427623302219e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 2.0118814538949484649289106781689
y[1] (numeric) = 2.0118814538949484724444715019163
absolute error = 7.5155608237474e-18
relative error = 3.7355883017846186107822622552324e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 2.0120365692943693052591874398729
y[1] (numeric) = 2.0120365692943693128239384194587
absolute error = 7.5647509795858e-18
relative error = 3.7597482545949916670453069294169e-16 %
memory used=26.7MB, alloc=4.2MB, time=1.65
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 2.0121926967304437763423552042824
y[1] (numeric) = 2.0121926967304437839563038896766
absolute error = 7.6139486853942e-18
relative error = 3.7839063315187926563667763417872e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 2.0123498363592993272635051611252
y[1] (numeric) = 2.0123498363592993349266591514953
absolute error = 7.6631539903701e-18
relative error = 3.8080625206967570712870262012996e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 2.0125079883380755999731577393461
y[1] (numeric) = 2.012507988338075607685524683065
absolute error = 7.7123669437189e-18
relative error = 3.8322168102735108262534568512786e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 2.0126671528249245864269176525981
y[1] (numeric) = 2.0126671528249245941885052472516
absolute error = 7.7615875946535e-18
relative error = 3.8563691883973700596032738445720e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 2.0128273299790107867374790341803
y[1] (numeric) = 2.0128273299790107945482950265749
absolute error = 7.8108159923946e-18
relative error = 3.8805196432204887909391396279470e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 2.0129885199605113683391388134405
y[1] (numeric) = 2.0129885199605113761991909996112
absolute error = 7.8600521861707e-18
relative error = 3.9046681628988574673255486365631e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 2.0131507229306163261649774981705
y[1] (numeric) = 2.0131507229306163340742737233882
absolute error = 7.9092962252177e-18
relative error = 3.9288147355921028075812645610452e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 2.0133139390515286438368675401857
y[1] (numeric) = 2.0133139390515286517954156989656
absolute error = 7.9585481587799e-18
relative error = 3.9529593494639831059053998860422e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 2.0134781684864644558684704741142
y[1] (numeric) = 2.0134781684864644638762785102234
absolute error = 8.0078080361092e-18
relative error = 3.9771019926819893103487310465044e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 2.0136434113996532108813850324027
y[1] (numeric) = 2.0136434113996532189384609388682
absolute error = 8.0570759064655e-18
relative error = 4.0012426534175422214544849197988e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 2.0138096679563378358346094527036
y[1] (numeric) = 2.0138096679563378439409612718202
absolute error = 8.1063518191166e-18
relative error = 4.0253813198459412997591239905252e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 2.0139769383227749012674822071171
y[1] (numeric) = 2.0139769383227749094231180304555
absolute error = 8.1556358233384e-18
relative error = 4.0495179801464624486069123054480e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 2.0141452226662347875562663962447
y[1] (numeric) = 2.0141452226662347957611943646597
absolute error = 8.2049279684150e-18
relative error = 4.0736526225024060903931593506058e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 2.0143145211550018521845440646509
y[1] (numeric) = 2.0143145211550018604387723682894
absolute error = 8.2542283036385e-18
relative error = 4.0977852351009962752012887995989e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 2.0144848339583745980275877081423
y[1] (numeric) = 2.0144848339583746063311245864516
absolute error = 8.3035368783093e-18
relative error = 4.1219158061335280334638389041476e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 2.0146561612466658426508772572493
y[1] (numeric) = 2.0146561612466658510037309989852
absolute error = 8.3528537417359e-18
relative error = 4.1460443237952664634385490082025e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 2.0148285031912028886229318354409
y[1] (numeric) = 2.014828503191202897025110778676
absolute error = 8.4021789432351e-18
relative error = 4.1701707762855443888482998418384e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 2.0150018599643276948426266049198
y[1] (numeric) = 2.0150018599643277032941391370521
absolute error = 8.4515125321323e-18
relative error = 4.1942951518079095850439480587569e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 2.0151762317393970488811660273279
y[1] (numeric) = 2.0151762317393970573820205850888
absolute error = 8.5008545577609e-18
relative error = 4.2184174385698253082326196260409e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 2.0153516186907827403388858813502
y[1] (numeric) = 2.0153516186907827488890909508132
absolute error = 8.5502050694630e-18
relative error = 4.2425376247830160193721392524459e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 2.0155280209938717352170573940335
y[1] (numeric) = 2.0155280209938717438166215106227
absolute error = 8.5995641165892e-18
relative error = 4.2666556986633663853483384976524e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 2.0157054388250663513048678576385
y[1] (numeric) = 2.015705438825066359953799606137
absolute error = 8.6489317484985e-18
relative error = 4.2907716484308699333611506128471e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 2.0158838723617844345817531190212
y[1] (numeric) = 2.0158838723617844432800611335796
absolute error = 8.6983080145584e-18
relative error = 4.3148854623096769349684380635998e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.3MB, time=1.90
x[1] = 0.179
y[1] (analytic) = 2.016063321782459536635258343889
y[1] (numeric) = 2.0160633217824595453829513080344
absolute error = 8.7476929641454e-18
relative error = 4.3389971285283406618506691600439e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 2.0162437872665410930946044738096
y[1] (numeric) = 2.016243787266541101891691120454
absolute error = 8.7970866466444e-18
relative error = 4.3631066353195179309602077791991e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 2.016425268994494603080138809552
y[1] (numeric) = 2.016425268994494611926627921001
absolute error = 8.8464891114490e-18
relative error = 4.3872139709201161346298698807507e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 2.0166077671478018096688491702255
y[1] (numeric) = 2.0166077671478018185647495781872
absolute error = 8.8959004079617e-18
relative error = 4.4113191235713905938305090313508e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 2.0167912819089608813761220937471
y[1] (numeric) = 2.0167912819089608903214426793408
absolute error = 8.9453205855937e-18
relative error = 4.4354220815188435136375016596425e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 2.0169758134614865946539265604088
y[1] (numeric) = 2.0169758134614866036486762541742
absolute error = 8.9947496937654e-18
relative error = 4.4595228330124700379893172350029e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 2.0171613619899105174056057377456
y[1] (numeric) = 2.0171613619899105264497935196513
absolute error = 9.0441877819057e-18
relative error = 4.4836213663064092637201736848481e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 2.0173479276797811935174602615094
y[1] (numeric) = 2.0173479276797812026110951609623
absolute error = 9.0936348994529e-18
relative error = 4.5077176696593885574598734939027e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 2.0175355107176643284073075843492
y[1] (numeric) = 2.0175355107176643375503986802032
absolute error = 9.1430910958540e-18
relative error = 4.5318117313343745693792315171449e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 2.0177241112911429755902029407709
y[1] (numeric) = 2.017724111291142984782759361336
absolute error = 9.1925564205651e-18
relative error = 4.5559035395987695995665664350595e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 2.0179137295888177242615084941142
y[1] (numeric) = 2.0179137295888177335035394171659
absolute error = 9.2420309230517e-18
relative error = 4.5799930827245582885355723626787e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 2.0181043658003068878974982486313
y[1] (numeric) = 2.0181043658003068971890129014195
absolute error = 9.2915146527882e-18
relative error = 4.6040803489880578025861114522002e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 2.0182960201162466938736873272872
y[1] (numeric) = 2.0182960201162467032146949865457
absolute error = 9.3410076592585e-18
relative error = 4.6281653266702131643076587068444e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 2.018488692728291474101075233628
y[1] (numeric) = 2.0184886927282914834915852255834
absolute error = 9.3905099919554e-18
relative error = 4.6522480040562979003511077233544e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 2.018682383829113856680493733975
y[1] (numeric) = 2.0186823838291138661205154343563
absolute error = 9.4400217003813e-18
relative error = 4.6763283694362588344400778070061e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 2.0188770936124049585752510143094
y[1] (numeric) = 2.0188770936124049680647938483574
absolute error = 9.4895428340480e-18
relative error = 4.7004064111046148793569148865205e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 2.0190728222728745793022647845074
y[1] (numeric) = 2.019072822272874588841338226984
absolute error = 9.5390734424766e-18
relative error = 4.7244821173604054038444217219242e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 2.0192695700062513956418780210754
y[1] (numeric) = 2.019269570006251405230491596273
absolute error = 9.5886135751976e-18
relative error = 4.7485554765072376646516525501705e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 2.0194673370092831573665520582161
y[1] (numeric) = 2.0194673370092831670047153399674
absolute error = 9.6381632817513e-18
relative error = 4.7726264768534827544792303790582e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 2.0196661234797368839886327559364
y[1] (numeric) = 2.0196661234797368936763553676237
absolute error = 9.6877226116873e-18
relative error = 4.7966951067120258054961941146152e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 2.0198659296163990625273864929789
y[1] (numeric) = 2.0198659296163990722646781075439
absolute error = 9.7372916145650e-18
relative error = 4.8207613544005114116063050684688e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 2.0200667556190758462955037516294
y[1] (numeric) = 2.0200667556190758560823740915827
absolute error = 9.7868703399533e-18
relative error = 4.8448252082411928679328685492927e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 2.0202686016885932547052690809203
y[1] (numeric) = 2.0202686016885932645417279183514
absolute error = 9.8364588374311e-18
relative error = 4.8688866565611774760080445037546e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 2.0204714680267973740945972444179
y[1] (numeric) = 2.0204714680267973839806544010047
absolute error = 9.8860571565868e-18
relative error = 4.8929456876921767568273160902815e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.3MB, time=2.15
NO POLE
x[1] = 0.203
y[1] (analytic) = 2.0206753548365545595731363786447
y[1] (numeric) = 2.0206753548365545695088017256634
absolute error = 9.9356653470187e-18
relative error = 4.9170022899707021986538547215949e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 2.0208802623217516378886400082574
y[1] (numeric) = 2.0208802623217516478739234665925
absolute error = 9.9852834583351e-18
relative error = 4.9410564517381124254619645474793e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 2.0210861906872961113138107843703
y[1] (numeric) = 2.0210861906872961213487223245244
absolute error = 1.00349115401541e-17
relative error = 4.9651081613405118900239485306877e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 2.0212931401391163625538198328837
y[1] (numeric) = 2.0212931401391163726383694749873
absolute error = 1.00845496421036e-17
relative error = 4.9891574071287485640562760296655e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 2.0215011108841618606747066203537
y[1] (numeric) = 2.0215011108841618708089044341756
absolute error = 1.01341978138219e-17
relative error = 5.0132041774587084280729859383164e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 2.0217101031304033680528652658218
y[1] (numeric) = 2.0217101031304033782367213707789
absolute error = 1.01838561049571e-17
relative error = 5.0372484606910162109462339664952e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 2.0219201170868331483458242481064
y[1] (numeric) = 2.0219201170868331585793488132738
absolute error = 1.02335245651674e-17
relative error = 5.0612902451911814245617107936291e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 2.0221311529634651754845274793535
y[1] (numeric) = 2.022131152963465185767730723475
absolute error = 1.02832032441215e-17
relative error = 5.0853295193297937493335607783078e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 2.0223432109713353436873257371461
y[1] (numeric) = 2.022343210971335354020217928644
absolute error = 1.03328921914979e-17
relative error = 5.1093662714821743618213211737579e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 2.0225562913225016784958884691798
y[1] (numeric) = 2.0225562913225016888784799261654
absolute error = 1.03825914569856e-17
relative error = 5.1334004900287196632462584596239e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 2.0227703942300445488332470064351
y[1] (numeric) = 2.022770394230044559265548096719
absolute error = 1.04323010902839e-17
relative error = 5.1574321633547998452873183563873e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 2.0229855199080668800841812429068
y[1] (numeric) = 2.0229855199080668905662023840092
absolute error = 1.04820211411024e-17
relative error = 5.1814612798507563717903879593796e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 2.0232016685716943681981628622947
y[1] (numeric) = 2.0232016685716943787299145214558
absolute error = 1.05317516591611e-17
relative error = 5.2054878279119488769908681488400e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 2.0234188404370756948150692146173
y[1] (numeric) = 2.023418840437075705396561908808
absolute error = 1.05814926941907e-17
relative error = 5.2295117959389008645616863242593e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 2.0236370357213827434138829684801
y[1] (numeric) = 2.0236370357213827540451272644122
absolute error = 1.06312442959321e-17
relative error = 5.2535331723370499727603864819298e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 2.0238562546428108164845936877157
y[1] (numeric) = 2.0238562546428108271656002018526
absolute error = 1.06810065141369e-17
relative error = 5.2775519455169924952893251048293e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 2.0240764974205788537235185043155
y[1] (numeric) = 2.0240764974205788644542979028829
absolute error = 1.07307793985674e-17
relative error = 5.3015681038944807054527504089751e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 2.0242977642749296512522600829931
y[1] (numeric) = 2.0242977642749296620328230819895
absolute error = 1.07805629989964e-17
relative error = 5.3255816358903213698008279803972e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 2.0245200554271300818605210963532
y[1] (numeric) = 2.0245200554271300926908784615608
absolute error = 1.08303573652076e-17
relative error = 5.3495925299305706827242682913373e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 2.0247433710994713162729954535016
y[1] (numeric) = 2.0247433710994713271531580004969
absolute error = 1.08801625469953e-17
relative error = 5.3736007744463833376542169687175e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 2.0249677115152690454405575490035
y[1] (numeric) = 2.0249677115152690563705361431682
absolute error = 1.09299785941647e-17
relative error = 5.3976063578741579866674220547707e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 2.0251930768988637038559718233995
y[1] (numeric) = 2.0251930768988637148357773799314
absolute error = 1.09798055565319e-17
relative error = 5.4216092686555344572570618915424e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 2.0254194674756206938943459510072
y[1] (numeric) = 2.0254194674756207049239894349309
absolute error = 1.10296434839237e-17
relative error = 5.4456094952372922133060549255756e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 2.0256468834719306111785519954791
y[1] (numeric) = 2.0256468834719306222580444216574
absolute error = 1.10794924261783e-17
relative error = 5.4696070260716931744117237937190e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=2.40
NO POLE
x[1] = 0.227
y[1] (analytic) = 2.025875325115209470969840898559
y[1] (numeric) = 2.0258753251152094820991933317034
absolute error = 1.11293524331444e-17
relative error = 5.4936018496160345095208646200868e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 2.0261047926338989355838766926674
y[1] (numeric) = 2.0261047926338989467631002473496
absolute error = 1.11792235546822e-17
relative error = 5.5175939543331394802624748635003e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 2.026335286257466542832417853372
y[1] (numeric) = 2.0263352862574665540615236940347
absolute error = 1.12291058406627e-17
relative error = 5.5415833286910089856393901987381e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 2.0265668062164059354908742334413
y[1] (numeric) = 2.0265668062164059467698735744096
absolute error = 1.12789993409683e-17
relative error = 5.5655699611631148102475076085038e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 2.0267993527422370917919690460588
y[1] (numeric) = 2.0267993527422371031208731515512
absolute error = 1.13289041054924e-17
relative error = 5.5895538402281992703214506330119e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 2.0270329260675065569457363908782
y[1] (numeric) = 2.027032926067506568324556575018
absolute error = 1.13788201841398e-17
relative error = 5.6135349543704696501490909467353e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 2.0272675264257876756860858429371
y[1] (numeric) = 2.0272675264257876871148334697636
absolute error = 1.14287476268265e-17
relative error = 5.6375132920794965265556457198051e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 2.0275031540516808258441666510125
y[1] (numeric) = 2.0275031540516808373228531344926
absolute error = 1.14786864834801e-17
relative error = 5.6614888418504080813605660651905e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 2.0277398091808136529487651188023
y[1] (numeric) = 2.0277398091808136644774019228416
absolute error = 1.15286368040393e-17
relative error = 5.6854615921836404213028761807060e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 2.0279774920498413058539697693492
y[1] (numeric) = 2.0279774920498413174325684078038
absolute error = 1.15785986384546e-17
relative error = 5.7094315315852797821791401858040e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 2.0282162028964466733943399203925
y[1] (numeric) = 2.0282162028964466850229119570802
absolute error = 1.16285720366877e-17
relative error = 5.7333986485667635221112983967630e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 2.0284559419593406220678143258353
y[1] (numeric) = 2.0284559419593406337463713745474
absolute error = 1.16785570487121e-17
relative error = 5.7573629316451728954192476914204e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 2.0286967094782622347465975662562
y[1] (numeric) = 2.0286967094782622464751512907691
absolute error = 1.17285537245129e-17
relative error = 5.7813243693431312641435305967001e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 2.0289385056939790504162628993717
y[1] (numeric) = 2.0289385056939790621948250134582
absolute error = 1.17785621140865e-17
relative error = 5.8052829501886530813462763383798e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 2.0291813308482873049433113095711
y[1] (numeric) = 2.0291813308482873167718935770126
absolute error = 1.18285822674415e-17
relative error = 5.8292386627155843410670671229776e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 2.0294251851840121728714275241051
y[1] (numeric) = 2.0294251851840121847500417587031
absolute error = 1.18786142345980e-17
relative error = 5.8531914954632542981313431652362e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 2.0296700689450080102466747922021
y[1] (numeric) = 2.02967006894500802217533285779
absolute error = 1.19286580655879e-17
relative error = 5.8771414369766201157302779740255e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 2.0299159823761585984718712523284
y[1] (numeric) = 2.0299159823761586104505850627836
absolute error = 1.19787138104552e-17
relative error = 5.9010884758064113953471742068069e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 2.030162925723377389190391741989
y[1] (numeric) = 2.0301629257233774012191732612446
absolute error = 1.20287815192556e-17
relative error = 5.9250326005089297877784331130862e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 2.0304108992336077501996399338908
y[1] (numeric) = 2.0304108992336077622785011759475
absolute error = 1.20788612420567e-17
relative error = 5.9489737996461442431747214094801e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 2.0306599031548232123944367119608
y[1] (numeric) = 2.030659903154823224523389740899
absolute error = 1.21289530289382e-17
relative error = 5.9729120617857861781224358638829e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 2.0309099377360277177405717306283
y[1] (numeric) = 2.0309099377360277299196286606205
absolute error = 1.21790569299922e-17
relative error = 5.9968473755014937979355103970949e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 2.0311610032272558682787661309445
y[1] (numeric) = 2.0311610032272558805079391262668
absolute error = 1.22291729953223e-17
relative error = 6.0207797293723655026702422919899e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 2.0314130998795731761592954175204
y[1] (numeric) = 2.0314130998795731884385966925651
absolute error = 1.22793012750447e-17
relative error = 6.0447091119834981468796959911580e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=2.65
NO POLE
x[1] = 0.251
y[1] (analytic) = 2.0316662279450763147075225309294
y[1] (numeric) = 2.0316662279450763270369643502171
absolute error = 1.23294418192877e-17
relative error = 6.0686355119257373544389901120549e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 2.0319203876768933705205921811271
y[1] (numeric) = 2.0319203876768933829001868593188
absolute error = 1.23795946781917e-17
relative error = 6.0925589177956740777747778296260e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 2.0321755793291840965955385386037
y[1] (numeric) = 2.0321755793291841090252984405134
absolute error = 1.24297599019097e-17
relative error = 6.1164793181958871878040570482648e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 2.0324318031571401664890594113985
y[1] (numeric) = 2.0324318031571401789689969520053
absolute error = 1.24799375406068e-17
relative error = 6.1403967017346938454596397222690e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 2.0326890594169854295092110677709
y[1] (numeric) = 2.0326890594169854420393387122318
absolute error = 1.25301276444609e-17
relative error = 6.1643110570264903985284991989445e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 2.0329473483659761669392788962454
y[1] (numeric) = 2.0329473483659761795196091599072
absolute error = 1.25803302636618e-17
relative error = 6.1882223726913059707410317344592e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 2.0332066702624013492940801269205
y[1] (numeric) = 2.0332066702624013619246255753328
absolute error = 1.26305454484123e-17
relative error = 6.2121306373553400445842845939843e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 2.0334670253655828946089558703679
y[1] (numeric) = 2.0334670253655829072897291192955
absolute error = 1.26807732489276e-17
relative error = 6.2360358396506636083047964924219e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 2.0337284139358759277617107631341
y[1] (numeric) = 2.0337284139358759404927244785696
absolute error = 1.27310137154355e-17
relative error = 6.2599379682153138833418729725393e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 2.0339908362346690408277595418062
y[1] (numeric) = 2.0339908362346690536090264399825
absolute error = 1.27812668981763e-17
relative error = 6.2838370116932414712944027265318e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 2.0342542925243845544687409008098
y[1] (numeric) = 2.0342542925243845673002737482132
absolute error = 1.28315328474034e-17
relative error = 6.3077329587346016339269756785552e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 2.0345187830684787803548600225756
y[1] (numeric) = 2.0345187830684787932366716359582
absolute error = 1.28818116133826e-17
relative error = 6.3316257979954063602714388177892e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 2.0347843081314422846212222024373
y[1] (numeric) = 2.0347843081314422975533254488301
absolute error = 1.29321032463928e-17
relative error = 6.3555155181378647236699292876775e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 2.0350508679788001523584210246188
y[1] (numeric) = 2.0350508679788001653408288213444
absolute error = 1.29824077967256e-17
relative error = 6.3794021078301824309633756228077e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 2.0353184628771122531376455799187
y[1] (numeric) = 2.0353184628771122661703708946042
absolute error = 1.30327253146855e-17
relative error = 6.4032855557466563081346968269428e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 2.0355870930939735075705722502224
y[1] (numeric) = 2.0355870930939735206536281008124
absolute error = 1.30830558505900e-17
relative error = 6.4271658505677195710556369542693e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 2.0358567588980141549043076197562
y[1] (numeric) = 2.0358567588980141680377070745259
absolute error = 1.31333994547697e-17
relative error = 6.4510429809799870454264501448758e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 2.0361274605589000216516501080476
y[1] (numeric) = 2.0361274605589000348354062856159
absolute error = 1.31837561775683e-17
relative error = 6.4749169356762512227293998685537e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 2.0363991983473327912569389548773
y[1] (numeric) = 2.0363991983473328044910650242197
absolute error = 1.32341260693424e-17
relative error = 6.4987877033553800914467380611797e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 2.0366719725350502747977602230921
y[1] (numeric) = 2.0366719725350502880822694035539
absolute error = 1.32845091804618e-17
relative error = 6.5226552727224605337274155015254e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 2.0369457833948266827227805210095
y[1] (numeric) = 2.0369457833948266960576860823194
absolute error = 1.33349055613099e-17
relative error = 6.5465196324889906851903753078282e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 2.0372206312004728976259801822697
y[1] (numeric) = 2.0372206312004729110112954445525
absolute error = 1.33853152622828e-17
relative error = 6.5703807713724339993967719333167e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 2.0374965162268367480575586773896
y[1] (numeric) = 2.03749651622683676149329701118
absolute error = 1.34357383337904e-17
relative error = 6.5942386780967552546947067034742e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=4.3MB, time=2.89
x[1] = 0.274
y[1] (analytic) = 2.0377734387498032833717860679493
y[1] (numeric) = 2.037773438749803296857960894205
absolute error = 1.34861748262557e-17
relative error = 6.6180933413920727937976337133500e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 2.0380513990462950496120753512833
y[1] (numeric) = 2.0380513990462950631487001413986
absolute error = 1.35366247901153e-17
relative error = 6.6419447499948998284700879109838e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 2.0383303973942723664335515807735
y[1] (numeric) = 2.0383303973942723800206398565924
absolute error = 1.35870882758189e-17
relative error = 6.6657928926478949340123908350523e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 2.0386104340727336050633946843345
y[1] (numeric) = 2.0386104340727336187009600181647
absolute error = 1.36375653338302e-17
relative error = 6.6896377581002994755030081404852e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 2.0388915093617154672992339414589
y[1] (numeric) = 2.0388915093617154809872899560852
absolute error = 1.36880560146263e-17
relative error = 6.7134793351076389641768771496013e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 2.0391736235422932655458731172394
y[1] (numeric) = 2.0391736235422932792844334859371
absolute error = 1.37385603686977e-17
relative error = 6.7373176124317188811218151047378e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 2.0394567768965812038906262901154
y[1] (numeric) = 2.0394567768965812176797047366643
absolute error = 1.37890784465489e-17
relative error = 6.7611525788409146853988535462580e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 2.0397409697077326602175454487053
y[1] (numeric) = 2.0397409697077326740571557474034
absolute error = 1.38396102986981e-17
relative error = 6.7849842231100203323142005293920e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 2.0400262022599404693608219719743
y[1] (numeric) = 2.0400262022599404832509779476512
absolute error = 1.38901559756769e-17
relative error = 6.8088125340200969017342887984187e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 2.0403124748384372072976451461622
y[1] (numeric) = 2.0403124748384372212383606741933
absolute error = 1.39407155280311e-17
relative error = 6.8326375003588604711544561881627e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 2.0405997877294954763808019113554
y[1] (numeric) = 2.0405997877294954903720909176756
absolute error = 1.39912890063202e-17
relative error = 6.8564591109204325789697877210990e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 2.0408881412204281916113030703244
y[1] (numeric) = 2.0408881412204282056531795314421
absolute error = 1.40418764611177e-17
relative error = 6.8802773545054828680893178066210e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 2.0411775355995888679513222322786
y[1] (numeric) = 2.0411775355995888820438001752897
absolute error = 1.40924779430111e-17
relative error = 6.9040922199212246188207738035075e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 2.0414679711563719086777348045
y[1] (numeric) = 2.041467971156371922820828307102
absolute error = 1.41430935026020e-17
relative error = 6.9279036959814592535303831259131e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 2.0417594481812128947765453854202
y[1] (numeric) = 2.0417594481812129089702685759259
absolute error = 1.41937231905057e-17
relative error = 6.9517117715063759000825954237287e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 2.0420519669655888753784929535903
y[1] (numeric) = 2.0420519669655888896228600109424
absolute error = 1.42443670573521e-17
relative error = 6.9755164353229877255887043385785e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 2.0423455278020186592361242881752
y[1] (numeric) = 2.0423455278020186735311494419601
absolute error = 1.42950251537849e-17
relative error = 6.9993176762647355026691581943761e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 2.0426401309840631072426270980681
y[1] (numeric) = 2.0426401309840631215883246285305
absolute error = 1.43456975304624e-17
relative error = 7.0231154831718748006317101679561e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 2.0429357768063254259927153784849
y[1] (numeric) = 2.0429357768063254403890996165417
absolute error = 1.43963842380568e-17
relative error = 7.0469098448911285879727532309626e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 2.0432324655644514623858605559455
y[1] (numeric) = 2.0432324655644514768329458832004
absolute error = 1.44470853272549e-17
relative error = 7.0707007502760253084633206866469e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 2.0435301975551299992721630249001
y[1] (numeric) = 2.0435301975551300137699638736579
absolute error = 1.44978008487578e-17
relative error = 7.0944881881867472973072596076825e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 2.043828973076093052141159721896
y[1] (numeric) = 2.043828973076093066689690575177
absolute error = 1.45485308532810e-17
relative error = 7.1182721474901750237230173200559e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 2.0441287924261161668538644261162
y[1] (numeric) = 2.0441287924261161814531398176708
absolute error = 1.45992753915546e-17
relative error = 7.1420526170599801988160589376831e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 2.0444296559050187184183385183567
y[1] (numeric) = 2.0444296559050187330683730326797
absolute error = 1.46500345143230e-17
relative error = 7.1658295857764742176352170636487e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=49.5MB, alloc=4.3MB, time=3.14
x[1] = 0.298
y[1] (analytic) = 2.044731563813664210809090974036
y[1] (numeric) = 2.0447315638136642255098992463814
absolute error = 1.47008082723454e-17
relative error = 7.1896030425268479676575290954197e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 2.045034516453960577830607409664
y[1] (numeric) = 2.0450345164539605925822041260596
absolute error = 1.47515967163956e-17
relative error = 7.2133729762050691156228184225136e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 2.0453385141288604850253090463229
y[1] (numeric) = 2.0453385141288604998277089435848
absolute error = 1.48023998972619e-17
relative error = 7.2371393757118283598946650850589e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 2.0456435571423616326262434981446
y[1] (numeric) = 2.0456435571423616474794613638922
absolute error = 1.48532178657476e-17
relative error = 7.2609022299547790202846690560080e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 2.0459496457995070595548103385009
y[1] (numeric) = 2.0459496457995070744588610111716
absolute error = 1.49040506726707e-17
relative error = 7.2846615278483853799920306830494e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 2.0462567804063854484638254416571
y[1] (numeric) = 2.0462567804063854634187238105211
absolute error = 1.49548983688640e-17
relative error = 7.3084172583139666249117166447831e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 2.0465649612701314318262291429792
y[1] (numeric) = 2.0465649612701314468319901481543
absolute error = 1.50057610051751e-17
relative error = 7.3321694102796918640339551276505e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 2.0468741886989258990697443064274
y[1] (numeric) = 2.0468741886989259141263829388941
absolute error = 1.50566386324667e-17
relative error = 7.3559179726807217022079305966479e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 2.0471844630019963047577914340209
y[1] (numeric) = 2.0471844630019963198653227356374
absolute error = 1.51075313016165e-17
relative error = 7.3796629344591542768918728818946e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 2.0474957844896169778169689982138
y[1] (numeric) = 2.0474957844896169929754080617308
absolute error = 1.51584390635170e-17
relative error = 7.4034042845639224860228638826830e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 2.0478081534731094318114082246882
y[1] (numeric) = 2.0478081534731094470207701937644
absolute error = 1.52093619690762e-17
relative error = 7.4271420119511307867828189075650e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 2.0481215702648426762643125999463
y[1] (numeric) = 2.0481215702648426915246126691631
absolute error = 1.52603000692168e-17
relative error = 7.4508761055836592901481940334139e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 2.0484360351782335290269934252649
y[1] (numeric) = 2.048436035178233544338246840142
absolute error = 1.53112534148771e-17
relative error = 7.4746065544315981024593528241058e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 2.0487515485277469296957137860763
y[1] (numeric) = 2.0487515485277469450579358430866
absolute error = 1.53622220570103e-17
relative error = 7.4983333474719002862892386342616e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 2.0490681106288962540766543536436
y[1] (numeric) = 2.0490681106288962694898604002286
absolute error = 1.54132060465850e-17
relative error = 7.5220564736886207558733508702858e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 2.0493857217982436296993154840235
y[1] (numeric) = 2.0493857217982436451635209186089
absolute error = 1.54642054345854e-17
relative error = 7.5457759220730085486268216816168e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 2.049704382353400252378671127745
y[1] (numeric) = 2.0497043823534002678938913997558
absolute error = 1.55152202720108e-17
relative error = 7.5694916816232574797393827721556e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 2.0500240926130267038263911123841
y[1] (numeric) = 2.05002409261302671939264172226
absolute error = 1.55662506098759e-17
relative error = 7.5932037413446472505949798481202e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 2.0503448528968332703114494092822
y[1] (numeric) = 2.0503448528968332859287459084934
absolute error = 1.56172964992112e-17
relative error = 7.6169120902497331802145612450846e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 2.0506666635255802623704370450457
y[1] (numeric) = 2.0506666635255802780387950361083
absolute error = 1.56683579910626e-17
relative error = 7.6406167173581456232113909370230e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 2.0509895248210783355678993681634
y[1] (numeric) = 2.0509895248210783512873345046549
absolute error = 1.57194351364915e-17
relative error = 7.6643176116966333427865868712810e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 2.0513134371061888123070184311073
y[1] (numeric) = 2.0513134371061888280775464176824
absolute error = 1.57705279865751e-17
relative error = 7.6880147622992043235919303704545e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 2.0516384007048240046909622986259
y[1] (numeric) = 2.0516384007048240205125988910321
absolute error = 1.58216365924062e-17
relative error = 7.7117081582070227253128822245183e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 2.0519644159419475384352241436057
y[1] (numeric) = 2.0519644159419475543079851486992
absolute error = 1.58727610050935e-17
relative error = 7.7353977884685495846353519977519e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=3.38
NO POLE
x[1] = 0.322
y[1] (analytic) = 2.0522914831435746778312750428676
y[1] (numeric) = 2.0522914831435746937551763186291
absolute error = 1.59239012757615e-17
relative error = 7.7590836421394884606719906014837e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 2.0526196026367726517618554365776
y[1] (numeric) = 2.0526196026367726677369128921278
absolute error = 1.59750574555502e-17
relative error = 7.7827657082826336771462013591727e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 2.0529487747496609807682312665902
y[1] (numeric) = 2.0529487747496609967944608622062
absolute error = 1.60262295956160e-17
relative error = 7.8064439759683032172255024898220e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 2.053278999811411805169741861009
y[1] (numeric) = 2.05327899981141182124715960814
absolute error = 1.60774177471310e-17
relative error = 7.8301184342739919420725870185423e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 2.0536102781522502142359676845385
y[1] (numeric) = 2.0536102781522502303645896458218
absolute error = 1.61286219612833e-17
relative error = 7.8537890722845120719543755350832e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 2.0539426101034545764118471268228
y[1] (numeric) = 2.0539426101034545925916894161001
absolute error = 1.61798422892773e-17
relative error = 7.8774558790921335133241665851444e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 2.054275995997356870596072553916
y[1] (numeric) = 2.0542759959973568868271513362491
absolute error = 1.62310787823331e-17
relative error = 7.9011188437962859200638603914196e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 2.0546104361673430184730969013066
y[1] (numeric) = 2.0546104361673430347554283929939
absolute error = 1.62823314916873e-17
relative error = 7.9247779555039424204486580687124e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 2.0549459309478532178990831405318
y[1] (numeric) = 2.0549459309478532342326836091243
absolute error = 1.63336004685925e-17
relative error = 7.9484332033293703309110127946311e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 2.0552824806743822773421300053576
y[1] (numeric) = 2.0552824806743822937270157696755
absolute error = 1.63848857643179e-17
relative error = 7.9720845763944173008311067156785e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 2.0556200856834799513771084177797
y[1] (numeric) = 2.0556200856834799678132958479283
absolute error = 1.64361874301486e-17
relative error = 7.9957320638281647446494663046291e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 2.0559587463127512772354441087076
y[1] (numeric) = 2.055958746312751293722949626094
absolute error = 1.64875055173864e-17
relative error = 8.0193756547673111828775466763527e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 2.0562984629008569124101829831449
y[1] (numeric) = 2.0562984629008569289490230604942
absolute error = 1.65388400773493e-17
relative error = 8.0430153383559229816809248971982e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 2.0566392357875134733166768349572
y[1] (numeric) = 2.0566392357875134899068679963291
absolute error = 1.65901911613719e-17
relative error = 8.0666511037456229270348815648964e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 2.0569810653134938750092280719431
y[1] (numeric) = 2.0569810653134938916507868927485
absolute error = 1.66415588208054e-17
relative error = 8.0902829400955841327534946204395e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 2.0573239518206276719540331678806
y[1] (numeric) = 2.0573239518206276886469762748979
absolute error = 1.66929431070173e-17
relative error = 8.1139108365723781143794245681970e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 2.0576678956518013998587656145203
y[1] (numeric) = 2.0576678956518014166031096859122
absolute error = 1.67443440713919e-17
relative error = 8.1375347823502117854955094161210e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 2.0580128971509589185591402031382
y[1] (numeric) = 2.0580128971509589353549019684685
absolute error = 1.67957617653303e-17
relative error = 8.1611547666109212445030868375075e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 2.0583589566631017559628015222396
y[1] (numeric) = 2.0583589566631017728099977624897
absolute error = 1.68471962402501e-17
relative error = 8.1847707785438198003956735431474e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 2.0587060745342894530508806153321
y[1] (numeric) = 2.0587060745342894699495281629179
absolute error = 1.68986475475858e-17
relative error = 8.2083828073458861517066250896412e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 2.0590542511116399099375648003526
y[1] (numeric) = 2.0590542511116399268876805391412
absolute error = 1.69501157387886e-17
relative error = 8.2319908422216609599022729013640e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 2.0594034867433297329880267103471
y[1] (numeric) = 2.059403486743329749989627575674
absolute error = 1.70016008653269e-17
relative error = 8.2555948723834834121737826514891e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 2.0597537817785945829950596733617
y[1] (numeric) = 2.0597537817785946000481626520475
absolute error = 1.70531029786858e-17
relative error = 8.2791948870512420287099878565868e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 2.0601051365677295244147676082088
y[1] (numeric) = 2.0601051365677295415193897385761
absolute error = 1.71046221303673e-17
relative error = 8.3027908754524654925010097972236e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=3.63
NO POLE
x[1] = 0.346
y[1] (analytic) = 2.0604575514620893756616586718269
y[1] (numeric) = 2.0604575514620893928178170437175
absolute error = 1.71561583718906e-17
relative error = 8.3263828268224618998878137734573e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 2.0608110268140890604634929533583
y[1] (numeric) = 2.0608110268140890776712047081503
absolute error = 1.72077117547920e-17
relative error = 8.3499707304042637498910232002848e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 2.0611655629772039602762355698204
y[1] (numeric) = 2.0611655629772039775355179004452
absolute error = 1.72592823306248e-17
relative error = 8.3735545754485729697450000855608e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 2.0615211603059702677594675783534
y[1] (numeric) = 2.061521160305970285070337729313
absolute error = 1.73108701509596e-17
relative error = 8.3971343512139000087425054368053e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 2.0618778191559853413126081804854
y[1] (numeric) = 2.0618778191559853586750834478696
absolute error = 1.73624752673842e-17
relative error = 8.4207100469665087702412595126312e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 2.0622355398839080606723027546654
y[1] (numeric) = 2.0622355398839080780864004861693
absolute error = 1.74140977315039e-17
relative error = 8.4442816519805555446919093052116e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 2.0625943228474591835713323144834
y[1] (numeric) = 2.0625943228474592010370699094243
absolute error = 1.74657375949409e-17
relative error = 8.4678491555377914339292685636745e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 2.0629541684054217034594010515152
y[1] (numeric) = 2.0629541684054217209767959608504
absolute error = 1.75173949093352e-17
relative error = 8.4914125469279921784708898776299e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 2.0633150769176412082861596836105
y[1] (numeric) = 2.0633150769176412258552294099547
absolute error = 1.75690697263442e-17
relative error = 8.5149718154487574610001092730482e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 2.063677048745026240346823391677
y[1] (numeric) = 2.0636770487450262579675854893196
absolute error = 1.76207620976426e-17
relative error = 8.5385269504054557707322991629163e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 2.0640400842495486571907441906084
y[1] (numeric) = 2.0640400842495486748632162655313
absolute error = 1.76724720749229e-17
relative error = 8.5620779411114599977086217495470e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 2.0644041837942439935932986429589
y[1] (numeric) = 2.0644041837942440113174983528539
absolute error = 1.77241997098950e-17
relative error = 8.5856247768879467968559834551603e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 2.064769347743211824591452887282
y[1] (numeric) = 2.0647693477432118423673979415685
absolute error = 1.77759450542865e-17
relative error = 8.6091674470640351643375099160906e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 2.0651355764616161295833680167288
y[1] (numeric) = 2.0651355764616161474110761765716
absolute error = 1.78277081598428e-17
relative error = 8.6327059409768280006110986854979e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 2.0655028703156856574924099075419
y[1] (numeric) = 2.0655028703156856753718989858688
absolute error = 1.78794890783269e-17
relative error = 8.6562402479713083651667432161102e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 2.0658712296727142929959286614845
y[1] (numeric) = 2.0658712296727143109272165230044
absolute error = 1.79312878615199e-17
relative error = 8.6797703574005746612071402163635e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 2.0662406549010614238191738910155
y[1] (numeric) = 2.066240654901061441802278452236
absolute error = 1.79831045612205e-17
relative error = 8.7032962586255915770413136825907e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 2.0666111463701523090947131411555
y[1] (numeric) = 2.0666111463701523271296523704009
absolute error = 1.80349392292454e-17
relative error = 8.7268179410153767689415085275000e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 2.0669827044504784487877218074939
y[1] (numeric) = 2.0669827044504784668745137249232
absolute error = 1.80867919174293e-17
relative error = 8.7503353939469938038545191543491e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 2.0673553295135979541875139756568
y[1] (numeric) = 2.0673553295135979723261766532817
absolute error = 1.81386626776249e-17
relative error = 8.7738486068055450883710675034543e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 2.0677290219321359194656846737981
y[1] (numeric) = 2.067729021932135937656236235501
absolute error = 1.81905515617029e-17
relative error = 8.7973575689841647841177855542181e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 2.0681037820797847943012350962868
y[1] (numeric) = 2.0681037820797848125436937178391
absolute error = 1.82424586215523e-17
relative error = 8.8208622698841567701546647299871e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 2.0684796103313047575730534237467
y[1] (numeric) = 2.0684796103313047758674373328267
absolute error = 1.82943839090800e-17
relative error = 8.8443626989147940211737826497788e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 2.0688565070625240921201249319604
y[1] (numeric) = 2.0688565070625241104664524081718
absolute error = 1.83463274762114e-17
relative error = 8.8678588454936015418086670287082e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=3.87
NO POLE
x[1] = 0.37
y[1] (analytic) = 2.0692344726503395605698461498793
y[1] (numeric) = 2.0692344726503395789681355247694
absolute error = 1.83982893748901e-17
relative error = 8.8913506990462040270465285822390e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 2.0696135074727167822348188950849
y[1] (numeric) = 2.0696135074727168006850885521628
absolute error = 1.84502696570779e-17
relative error = 8.9148382490063186221686394781388e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 2.0699936119086906110785010835261
y[1] (numeric) = 2.0699936119086906295807694582813
absolute error = 1.85022683747552e-17
relative error = 8.9383214848159409067598844455727e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 2.0703747863383655147500922792166
y[1] (numeric) = 2.0703747863383655333043778591373
absolute error = 1.85542855799207e-17
relative error = 8.9618003959251925491451533899697e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 2.0707570311429159546890330188074
y[1] (numeric) = 2.0707570311429159732953543433989
absolute error = 1.86063213245915e-17
relative error = 8.9852749717923622731685030396924e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.375
y[1] (analytic) = 2.071140346704586767299498015567
y[1] (numeric) = 2.0711403467045867859578736763705
absolute error = 1.86583756608035e-17
relative error = 9.0087452018840916060159760297926e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 2.0715247334066935461952644172937
y[1] (numeric) = 2.0715247334066935649057130579047
absolute error = 1.87104486406110e-17
relative error = 9.0322110756751742088176746013695e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 2.0719101916336230255153373630596
y[1] (numeric) = 2.0719101916336230442778776791465
absolute error = 1.87625403160869e-17
relative error = 9.0556725826486449962665764096535e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 2.072296721770833464310716154445
y[1] (numeric) = 2.0722967217708334831253668937679
absolute error = 1.88146507393229e-17
relative error = 9.0791297122958691353083598937122e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 2.07268432420485503200268542806
y[1] (numeric) = 2.0726843242048550508694653904895
absolute error = 1.88667799624295e-17
relative error = 9.1025824541165344289325915109739e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 2.0730729993232901949130167876779
y[1] (numeric) = 2.0730729993232902138319448252138
absolute error = 1.89189280375359e-17
relative error = 9.1260307976185954485318585813800e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 2.0734627475148141038664674262136
y[1] (numeric) = 2.0734627475148141228375624430037
absolute error = 1.89710950167901e-17
relative error = 9.1494747323183141639692358363291e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 2.0738535691691749828659633400772
y[1] (numeric) = 2.0738535691691750018892442924364
absolute error = 1.90232809523592e-17
relative error = 9.1729142477403969447312349495912e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 2.0742454646771945188408558111204
y[1] (numeric) = 2.0742454646771945379163417075495
absolute error = 1.90754858964291e-17
relative error = 9.1963493334178421219214387702514e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 2.0746384344307682524686409044622
y[1] (numeric) = 2.074638434430768271596350805667
absolute error = 1.91277099012048e-17
relative error = 9.2197799788920769074826158868238e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 2.0750324788228659700705328039483
y[1] (numeric) = 2.0750324788228659892504858228584
absolute error = 1.91799530189101e-17
relative error = 9.2432061737128049835304192173238e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 2.075427598247532096581282880848
y[1] (numeric) = 2.0754275982475321158134981826364
absolute error = 1.92322153017884e-17
relative error = 9.2666279074383842542664071237361e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 2.0758237930998860895936374656428
y[1] (numeric) = 2.0758237930998861088781342677445
absolute error = 1.92844968021017e-17
relative error = 9.2900451696353370181535758892086e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 2.0762210637761228344778283673944
y[1] (numeric) = 2.0762210637761228538146259395262
absolute error = 1.93367975721318e-17
relative error = 9.3134579498789202954685119753232e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 2.0766194106735130405764912602189
y[1] (numeric) = 2.0766194106735130599656089243982
absolute error = 1.93891176641793e-17
relative error = 9.3368662377526360647641435327380e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 2.0770188341904036384754081318156
y[1] (numeric) = 2.0770188341904036579168652623799
absolute error = 1.94414571305643e-17
relative error = 9.3602700228485605203411181340361e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 2.0774193347262181783504710648275
y[1] (numeric) = 2.0774193347262181978442870884539
absolute error = 1.94938160236264e-17
relative error = 9.3836692947673359713281727680609e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 2.0778209126814572293912656980308
y[1] (numeric) = 2.0778209126814572489374600937552
absolute error = 1.95461943957244e-17
relative error = 9.4070640431180183446294033735505e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 2.0782235684576987803016737909688
y[1] (numeric) = 2.0782235684576987999002660902054
absolute error = 1.95985922992366e-17
relative error = 9.4304542575182135498923313836711e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=4.12
NO POLE
x[1] = 0.394
y[1] (analytic) = 2.078627302457598640877895392667
y[1] (numeric) = 2.078627302457598660528905179228
absolute error = 1.96510097865610e-17
relative error = 9.4538399275941655547713617276232e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 2.0790321150848908446642921924854
y[1] (numeric) = 2.0790321150848908643677391026005
absolute error = 1.97034469101151e-17
relative error = 9.4772210429806519369669132004198e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 2.0794380067443880526874547089841
y[1] (numeric) = 2.07943800674438807244335843132
absolute error = 1.97559037223359e-17
relative error = 9.5005975933209757146954253193096e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 2.079844977841981958268897050903
y[1] (numeric) = 2.0798449778419819780772773265834
absolute error = 1.98083802756804e-17
relative error = 9.5239695682671975664352617738601e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 2.0802530287846436929167840629853
y[1] (numeric) = 2.0802530287846437127776606856104
absolute error = 1.98608766226251e-17
relative error = 9.5473369574798870438957428824695e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 2.080662159980424233297096748404
y[1] (numeric) = 2.0806621599804242532104895640704
absolute error = 1.99133928156664e-17
relative error = 9.5706997506283066086528117846450e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 2.0810723718384548092846429389925
y[1] (numeric) = 2.0810723718384548292505718463128
absolute error = 1.99659289073203e-17
relative error = 9.5940579373902590636237107249481e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 2.0814836647689473130943212643223
y[1] (numeric) = 2.0814836647689473331128062144454
absolute error = 2.00184849501231e-17
relative error = 9.6174115074524155681396974733254e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 2.0818960391831947094930475509275
y[1] (numeric) = 2.0818960391831947295641085475582
absolute error = 2.00710609966307e-17
relative error = 9.6407604505099707766804409933194e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 2.0823094954935714470927538636352
y[1] (numeric) = 2.0823094954935714672164109630545
absolute error = 2.01236570994193e-17
relative error = 9.6641047562669706938032983908734e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 2.0827240341135338707248714820363
y[1] (numeric) = 2.0827240341135338909011447931212
absolute error = 2.01762733110849e-17
relative error = 9.6874444144360639467211514411922e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 2.0831396554576206348967101866133
y[1] (numeric) = 2.083139655457620655125619870857
absolute error = 2.02289096842437e-17
relative error = 9.7107794147386853709937075894455e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 2.0835563599414531183301473109388
y[1] (numeric) = 2.083556359941453138611713582471
absolute error = 2.02815662715322e-17
relative error = 9.7341097469050953685329694304100e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 2.0839741479817358395830410986696
y[1] (numeric) = 2.0839741479817358599172842242765
absolute error = 2.03342431256069e-17
relative error = 9.7574354006742272531377043449270e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 2.0843930199962568737537839867819
y[1] (numeric) = 2.0843930199962568941407242859265
absolute error = 2.03869402991446e-17
relative error = 9.7807563657938226092604393804252e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 2.084812976403888270269412519638
y[1] (numeric) = 2.0848129764038882907090703644806
absolute error = 2.04396578448426e-17
relative error = 9.8040726320205184980859147668690e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 2.0852340176245864717576916820286
y[1] (numeric) = 2.085234017624586492250087497447
absolute error = 2.04923958154184e-17
relative error = 9.8273841891196947525676232058616e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 2.0856561440793927340035925233085
y[1] (numeric) = 2.0856561440793927545487467869185
absolute error = 2.05451542636100e-17
relative error = 9.8506910268656091123870718954301e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 2.0860793561904335469905830291406
y[1] (numeric) = 2.0860793561904335675885162713164
absolute error = 2.05979332421758e-17
relative error = 9.8739931350413404236446557582968e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 2.0865036543809210570271532821724
y[1] (numeric) = 2.0865036543809210776778860860672
absolute error = 2.06507328038948e-17
relative error = 9.8972905034388756645452092868407e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 2.0869290390751534899589970382061
y[1] (numeric) = 2.0869290390751535106625500397727
absolute error = 2.07035530015666e-17
relative error = 9.9205831218591010060519679039511e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 2.087355510698515575467272930079
y[1] (numeric) = 2.0873555106985155962236668180904
absolute error = 2.07563938880114e-17
relative error = 9.9438709801117928588766825435005e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 2.0877830696774789724533695975508
y[1] (numeric) = 2.0877830696774789932626251136209
absolute error = 2.08092555160701e-17
relative error = 9.9671540680156568046755867812436e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.3MB, time=4.37
x[1] = 0.417
y[1] (analytic) = 2.0882117164396026955106001279986
y[1] (numeric) = 2.0882117164396027163727380666028
absolute error = 2.08621379386042e-17
relative error = 9.9904323753982706792066252641605e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 2.0886414514135335424832522796486
y[1] (numeric) = 2.0886414514135335633982934881448
absolute error = 2.09150412084962e-17
relative error = 1.0013705892096267091204068354339e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 2.0890722750290065231134220464317
y[1] (numeric) = 2.0890722750290065440813874250812
absolute error = 2.09679653786495e-17
relative error = 1.0036974607955276350621002374629e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 2.0895041877168452887760592113318
y[1] (numeric) = 2.08950418771684530979696971332
absolute error = 2.10209105019882e-17
relative error = 1.0060238512829821583944246045003e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 2.0899371899089625633026546233074
y[1] (numeric) = 2.0899371899089625843765312547647
absolute error = 2.10738766314573e-17
relative error = 1.0083497596583405348242449340270e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 2.0903712820383605748940000215105
y[1] (numeric) = 2.0903712820383605960208638415336
absolute error = 2.11268638200231e-17
relative error = 1.0106751849088691789996548582292e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 2.0908064645391314891224523195991
y[1] (numeric) = 2.0908064645391315103023244402718
absolute error = 2.11798721206727e-17
relative error = 1.0130001260227258095831752561748e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 2.0912427378464578430241353524419
y[1] (numeric) = 2.0912427378464578642570369388564
absolute error = 2.12329015864145e-17
relative error = 1.0153245819889824412861662248799e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 2.0916801023966129802815131774552
y[1] (numeric) = 2.091680102396613001567465447733
absolute error = 2.12859522702778e-17
relative error = 1.0176485517976053180393958352047e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 2.0921185586269614874967701131797
y[1] (numeric) = 2.0921185586269615088357943384932
absolute error = 2.13390242253135e-17
relative error = 1.0199720344394874470984507731998e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 2.0925581069759596315564337885153
y[1] (numeric) = 2.0925581069759596529485512931087
absolute error = 2.13921175045934e-17
relative error = 1.0222950289064141859707680593372e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 2.0929987478831557980876785672719
y[1] (numeric) = 2.0929987478831558195329107284829
absolute error = 2.14452321612110e-17
relative error = 1.0246175341911005376520797901711e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 2.0934404817891909310067478043776
y[1] (numeric) = 2.0934404817891909525051160526582
absolute error = 2.14983682482806e-17
relative error = 1.0269395492871471902192696422930e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 2.0938833091357989731599344822012
y[1] (numeric) = 2.0938833091357989947114603011398
absolute error = 2.15515258189386e-17
relative error = 1.0292610731891016774647912438264e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 2.0943272303658073080575608680088
y[1] (numeric) = 2.0943272303658073296622657943513
absolute error = 2.16047049263425e-17
relative error = 1.0315821048924096389507169989678e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 2.0947722459231372027013989265695
y[1] (numeric) = 2.0947722459231372243593045502408
absolute error = 2.16579056236713e-17
relative error = 1.0339026433934329724290405119454e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 2.0952183562528042515059743153667
y[1] (numeric) = 2.0952183562528042732171022794925
absolute error = 2.17111279641258e-17
relative error = 1.0362226876894631878860631140935e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 2.0956655618009188213141978837586
y[1] (numeric) = 2.095665561800918843078569884687
absolute error = 2.17643720009284e-17
relative error = 1.0385422367787108831694850133400e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 2.096113863014686497507769691754
y[1] (numeric) = 2.096113863014686519325407479077
absolute error = 2.18176377873230e-17
relative error = 1.0408612896603000012044050189099e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 2.0965632603424085312128016588456
y[1] (numeric) = 2.096563260342408553083727035421
absolute error = 2.18709253765754e-17
relative error = 1.0431798453342859405865433059188e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 2.0970137542334822876011060485606
y[1] (numeric) = 2.0970137542334823095253408705339
absolute error = 2.19242348219733e-17
relative error = 1.0454979028016545655769270035573e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 2.0974653451384016952875980900551
y[1] (numeric) = 2.0974653451384017172651642668813
absolute error = 2.19775661768262e-17
relative error = 1.0478154610643164470687082433665e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 2.0979180335087576968242621341911
y[1] (numeric) = 2.0979180335087577188551816286563
absolute error = 2.20309194944652e-17
relative error = 1.0501325191250963417452332743250e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 2.0983718197972387002911318381003
y[1] (numeric) = 2.0983718197972387223754266663442
absolute error = 2.20842948282439e-17
relative error = 1.0524490759877751039015948232547e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=72.4MB, alloc=4.3MB, time=4.62
x[1] = 0.441
y[1] (analytic) = 2.0988267044576310319847359692537
y[1] (numeric) = 2.0988267044576310541224282007911
absolute error = 2.21376922315374e-17
relative error = 1.0547651306570410134994658664827e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 2.0992826879448193902044625175181
y[1] (numeric) = 2.0992826879448194123955742752615
absolute error = 2.21911117577434e-17
relative error = 1.0570806821385411990038225049095e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 2.0997397707147873001372949016042
y[1] (numeric) = 2.0997397707147873223818483618853
absolute error = 2.22445534602811e-17
relative error = 1.0593957294388282157352479122104e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 2.1001979532246175698413751546778
y[1] (numeric) = 2.1001979532246175921393925472703
absolute error = 2.22980173925925e-17
relative error = 1.0617102715654209662613401633648e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 2.1006572359324927473288500727377
y[1] (numeric) = 2.1006572359324927696803536808789
absolute error = 2.23515036081412e-17
relative error = 1.0640243075267465280930074644572e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 2.101117619297695578748457408642
y[1] (numeric) = 2.1011176192976956011534695690558
absolute error = 2.24050121604138e-17
relative error = 1.0663378363322057986472513326912e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 2.1015791037806094676683102944102
y[1] (numeric) = 2.1015791037806094901268533973288
absolute error = 2.24585431029186e-17
relative error = 1.0686508569921105764821192033090e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 2.1020416898427189354593391746206
y[1] (numeric) = 2.1020416898427189579714356638073
absolute error = 2.25120964891867e-17
relative error = 1.0709633685177348973913649573266e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 2.1025053779466100827798516343857
y[1] (numeric) = 2.1025053779466101053455240071571
absolute error = 2.25656723727714e-17
relative error = 1.0732753699212854442242104671290e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 2.1029701685559710521616716065027
y[1] (numeric) = 2.1029701685559710747809424137513
absolute error = 2.26192708072486e-17
relative error = 1.0755868602159195449102948986029e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 2.1034360621355924916983205439575
y[1] (numeric) = 2.1034360621355925143712123901742
absolute error = 2.26728918462167e-17
relative error = 1.0778978384157393733477676774317e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 2.1039030591513680198357042460012
y[1] (numeric) = 2.103903059151368042562239789298
absolute error = 2.27265355432968e-17
relative error = 1.0802083035358004145017503536254e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 2.1043711600702946912657701285254
y[1] (numeric) = 2.104371160070294714045972080658
absolute error = 2.27802019521326e-17
relative error = 1.0825182545921056594901669275741e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 2.1048403653604734639236008324323
y[1] (numeric) = 2.1048403653604734867574919588228
absolute error = 2.28338911263905e-17
relative error = 1.0848276906016093076058989306911e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 2.1053106754911096670884111671317
y[1] (numeric) = 2.1053106754911096899760142868914
absolute error = 2.28876031197597e-17
relative error = 1.0871366105822204606915518617489e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 2.1057820909325134705889164902013
y[1] (numeric) = 2.1057820909325134935302544761535
absolute error = 2.29413379859522e-17
relative error = 1.0894450135528020610129167677615e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 2.1062546121561003551135417286173
y[1] (numeric) = 2.1062546121561003781086375073202
absolute error = 2.29950957787029e-17
relative error = 1.0917528985331745755924464454778e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 2.1067282396343915836259413518044
y[1] (numeric) = 2.1067282396343916066748179035739
absolute error = 2.30488765517695e-17
relative error = 1.0940602645441101794590059648326e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 2.1072029738410146738863017120632
y[1] (numeric) = 2.107202973841014696988982070996
absolute error = 2.31026803589328e-17
relative error = 1.0963671106073459265249888611583e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 2.1076788152507038720788982737177
y[1] (numeric) = 2.1076788152507038952354055277143
absolute error = 2.31565072539966e-17
relative error = 1.0986734357455779217045254453018e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 2.1081557643393006275463813585793
y[1] (numeric) = 2.1081557643393006507567386493672
absolute error = 2.32103572907879e-17
relative error = 1.1009792389824697285972037153112e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 2.1086338215837540686312651420527
y[1] (numeric) = 2.1086338215837540918954956652094
absolute error = 2.32642305231567e-17
relative error = 1.1032845193426417933641988702739e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 2.1091129874621214796250957414119
y[1] (numeric) = 2.1091129874621215029432227463881
absolute error = 2.33181270049762e-17
relative error = 1.1055892758516798455358350022151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 2.1095932624535687788257753454548
y[1] (numeric) = 2.1095932624535688021978221355977
absolute error = 2.33720467901429e-17
relative error = 1.1078935075361385443777686400646e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=4.87
NO POLE
x[1] = 0.465
y[1] (analytic) = 2.1100746470383709977035204428998
y[1] (numeric) = 2.1100746470383710211295103754763
absolute error = 2.34259899325765e-17
relative error = 1.1101972134235356391509075929705e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 2.1105571416979127611759333155229
y[1] (numeric) = 2.1105571416979127846558898017433
absolute error = 2.34799564862204e-17
relative error = 1.1125003925423745630924103355492e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 2.1110407469146887689926670711471
y[1] (numeric) = 2.111040746914688792526613576188
absolute error = 2.35339465050409e-17
relative error = 1.1148030439221054125904641537769e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 2.1115254631723042782301656011879
y[1] (numeric) = 2.111525463172304301818125644216
absolute error = 2.35879600430281e-17
relative error = 1.1171051665931664876934404017391e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 2.1120112909554755868969609575369
y[1] (numeric) = 2.1120112909554756105389581117325
absolute error = 2.36419971541956e-17
relative error = 1.1194067595869689547953200387488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 2.1124982307500305186500117541203
y[1] (numeric) = 2.1124982307500305423460696467008
absolute error = 2.36960578925805e-17
relative error = 1.1217078219358957287929396725660e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 2.1129862830429089086225673095104
y[1] (numeric) = 2.1129862830429089323727096217539
absolute error = 2.37501423122435e-17
relative error = 1.1240083526733050866209237677248e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 2.113475448322163090364043358496
y[1] (numeric) = 2.1134754483221631141682938257651
absolute error = 2.38042504672691e-17
relative error = 1.1263083508335390045149168555330e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 2.1139657270769583838923962725276
y[1] (numeric) = 2.1139657270769584077507786842929
absolute error = 2.38583824117653e-17
relative error = 1.1286078154519078286241739772488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 2.1144571197975735848594838414512
y[1] (numeric) = 2.1144571197975736087720220413154
absolute error = 2.39125381998642e-17
relative error = 1.1309067455647175282338634473191e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 2.1149496269754014548299017819344
y[1] (numeric) = 2.1149496269754014787966196676559
absolute error = 2.39667178857215e-17
relative error = 1.1332051402092448974570421743092e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 2.1154432491029492126737862514597
y[1] (numeric) = 2.1154432491029492366947077749767
absolute error = 2.40209215235170e-17
relative error = 1.1355029984237600600948810189079e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 2.1159379866738390270740737607307
y[1] (numeric) = 2.1159379866738390511492229281849
absolute error = 2.40751491674542e-17
relative error = 1.1378003192475064058298397421521e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 2.1164338401828085101487109917904
y[1] (numeric) = 2.1164338401828085342781118635514
absolute error = 2.41294008717610e-17
relative error = 1.1400971017207325259028978104493e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 2.1169308101257112121883081441041
y[1] (numeric) = 2.1169308101257112363719848347928
absolute error = 2.41836766906887e-17
relative error = 1.1423933448846437960901969477184e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 2.1174288969995171175097305462993
y[1] (numeric) = 2.1174288969995171417477072248128
absolute error = 2.42379766785135e-17
relative error = 1.1446890477814720927075252279038e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 2.1179281013023131414261243871986
y[1] (numeric) = 2.1179281013023131657184252767338
absolute error = 2.42923008895352e-17
relative error = 1.1469842094544132027046920536602e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 2.1184284235333036283338735362098
y[1] (numeric) = 2.1184284235333036526805229142879
absolute error = 2.43466493780781e-17
relative error = 1.1492788289476681698369109146786e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 2.1189298641928108509169855400733
y[1] (numeric) = 2.118929864192810875318007738564
absolute error = 2.44010221984907e-17
relative error = 1.1515729053064279470813680572833e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 2.1194324237822755104694060003938
y[1] (numeric) = 2.1194324237822755349248254055395
absolute error = 2.44554194051457e-17
relative error = 1.1538664375768722226115709886921e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 2.1199361028042572383357616543121
y[1] (numeric) = 2.1199361028042572628456027067526
absolute error = 2.45098410524405e-17
relative error = 1.1561594248061918301769217533908e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 2.1204409017624350984710335991031
y[1] (numeric) = 2.1204409017624351230353207938997
absolute error = 2.45642871947966e-17
relative error = 1.1584518660425592485965204060529e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 2.120946821161608091119663220413
y[1] (numeric) = 2.1209468211616081157384211070732
absolute error = 2.46187578866602e-17
relative error = 1.1607437603351557189340654513465e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 2.1214538615076956576145945032859
y[1] (numeric) = 2.1214538615076956822878476857879
absolute error = 2.46732531825020e-17
relative error = 1.1630351067341606099901600551661e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=5.12
NO POLE
x[1] = 0.489
y[1] (analytic) = 2.1219620233077381862967575250624
y[1] (numeric) = 2.1219620233077382110245306618796
absolute error = 2.47277731368172e-17
relative error = 1.1653259042907502212959895555449e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 2.1224713070698975195554990496768
y[1] (numeric) = 2.1224713070698975443378168538027
absolute error = 2.47823178041259e-17
relative error = 1.1676161520571154308557497131958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 2.1229817133034574619904672638255
y[1] (numeric) = 2.1229817133034574868273545027982
absolute error = 2.48368872389727e-17
relative error = 1.1699058490864416316658238721493e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 2.1234932425188242896954588169337
y[1] (numeric) = 2.1234932425188243145869403128608
absolute error = 2.48914814959271e-17
relative error = 1.1721949944329263679515701867792e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 2.1240058952275272606647374488098
y[1] (numeric) = 2.1240058952275272856108380783931
absolute error = 2.49461006295833e-17
relative error = 1.1744835871517686944647880280023e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 2.1245196719422191263223346113487
y[1] (numeric) = 2.1245196719422191513230793059092
absolute error = 2.50007446945605e-17
relative error = 1.1767716262991820829262031429320e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 2.1250345731766766441748436136273
y[1] (numeric) = 2.12503457317667666923025735913
absolute error = 2.50554137455027e-17
relative error = 1.1790591109323837777375736689220e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 2.1255505994458010915882199432289
y[1] (numeric) = 2.1255505994458011166983277803079
absolute error = 2.51101078370790e-17
relative error = 1.1813460401096076874788694845335e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 2.1260677512656187806891015406401
y[1] (numeric) = 2.1260677512656188058539285646236
absolute error = 2.51648270239835e-17
relative error = 1.1836324128900984405665973806790e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 2.1265860291532815743911639280829
y[1] (numeric) = 2.1265860291532815996107352890182
absolute error = 2.52195713609353e-17
relative error = 1.1859182283341101489300566480409e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 2.1271054336270674035470262191799
y[1] (numeric) = 2.1271054336270674288213671218587
absolute error = 2.52743409026788e-17
relative error = 1.1882034855029192741759866500857e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 2.1276259652063807852262251614027
y[1] (numeric) = 2.1276259652063808105553608653863
absolute error = 2.53291357039836e-17
relative error = 1.1904881834588186715869612946438e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 2.1281476244117533421197754893198
y[1] (numeric) = 2.1281476244117533675037313089643
absolute error = 2.53839558196445e-17
relative error = 1.1927723212651163387202718748455e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 2.128670411764844323071835993248
y[1] (numeric) = 2.1286704117648443485106372977296
absolute error = 2.54388013044816e-17
relative error = 1.1950558979861388605884025379872e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 2.1291943277884411247390018350168
y[1] (numeric) = 2.1291943277884411502326740483571
absolute error = 2.54936722133403e-17
relative error = 1.1973389126872301501238720642039e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 2.1297193730064598143777447701809
y[1] (numeric) = 2.1297193730064598399263133712726
absolute error = 2.55485686010917e-17
relative error = 1.1996213644347689692834354851469e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 2.1302455479439456537605240641665
y[1] (numeric) = 2.1302455479439456793640145867985
absolute error = 2.56034905226320e-17
relative error = 1.2019032522961394782131285096815e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 2.1307728531270736242210920185032
y[1] (numeric) = 2.1307728531270736498795300513865
absolute error = 2.56584380328833e-17
relative error = 1.2041845753397675288387199620384e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 2.1313012890831489528295191524932
y[1] (numeric) = 2.1313012890831489785429303392861
absolute error = 2.57134111867929e-17
relative error = 1.2064653326350865220005387314465e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.508
y[1] (analytic) = 2.1318308563406076396974652153853
y[1] (numeric) = 2.1318308563406076654658752547194
absolute error = 2.57684100393341e-17
relative error = 1.2087455232525736743206531969789e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 2.1323615554290169864142233343697
y[1] (numeric) = 2.1323615554290170122376579798755
absolute error = 2.58234346455058e-17
relative error = 1.2110251462637299523429508372641e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 2.1328933868790761256140657344809
y[1] (numeric) = 2.1328933868790761514925507948134
absolute error = 2.58784850603325e-17
relative error = 1.2133042007410787873394726707306e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 2.1334263512226165516754205977991
y[1] (numeric) = 2.1334263512226165776089819366638
absolute error = 2.59335613388647e-17
relative error = 1.2155826857581835381671287777298e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 2.1339604489926026525524107611713
y[1] (numeric) = 2.13396044899260267854107429735
absolute error = 2.59886635361787e-17
relative error = 1.2178606003896368081205294062137e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=5.36
NO POLE
x[1] = 0.513
y[1] (analytic) = 2.1344956807231322427392860840343
y[1] (numeric) = 2.1344956807231322687830777914109
absolute error = 2.60437917073766e-17
relative error = 1.2201379437110591445717617934947e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 2.1350320469494370973682824508175
y[1] (numeric) = 2.1350320469494371234672283584041
absolute error = 2.60989459075866e-17
relative error = 1.2224147147991117887889793659763e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.515
y[1] (analytic) = 2.1355695482078834874414415058279
y[1] (numeric) = 2.1355695482078835135955676977909
absolute error = 2.61541261919630e-17
relative error = 1.2246909127314953556471740109556e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 2.136108185035972716196926352483
y[1] (numeric) = 2.1361081850359727424062589681689
absolute error = 2.62093326156859e-17
relative error = 1.2269665365869344679264138264635e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 2.1366479579723416566103695832499
y[1] (numeric) = 2.1366479579723416828749348172119
absolute error = 2.62645652339620e-17
relative error = 1.2292415854452138932468244470582e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 2.1371888675567632900317911416864
y[1] (numeric) = 2.1371888675567633163516152437101
absolute error = 2.63198241020237e-17
relative error = 1.2315160583871350793469182328691e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 2.1377309143301472459586246535433
y[1] (numeric) = 2.1377309143301472723337339286733
absolute error = 2.63751092751300e-17
relative error = 1.2337899544945569535943031165814e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 2.1382740988345403429453920000028
y[1] (numeric) = 2.1382740988345403693758128085688
absolute error = 2.64304208085660e-17
relative error = 1.2360632728503711839721530348215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 2.1388184216131271306505670427694
y[1] (numeric) = 2.1388184216131271571363258004127
absolute error = 2.64857587576433e-17
relative error = 1.2383360125385195538536989689901e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 2.1393638832102304330211705479249
y[1] (numeric) = 2.1393638832102304595622937256247
absolute error = 2.65411231776998e-17
relative error = 1.2406081726439832613811833194064e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 2.1399104841713118926156394931857
y[1] (numeric) = 2.1399104841713119192121536172857
absolute error = 2.65965141241000e-17
relative error = 1.2428797522527955974759907121140e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 2.1404582250429725160655150814786
y[1] (numeric) = 2.1404582250429725427174467337133
absolute error = 2.66519316522347e-17
relative error = 1.2451507504520265698585227600624e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 2.1410071063729532206764949225669
y[1] (numeric) = 2.1410071063729532473838707400884
absolute error = 2.67073758175215e-17
relative error = 1.2474211663298049130703210241349e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 2.141557128710135382169395983826
y[1] (numeric) = 2.1415571287101354089322426592307
absolute error = 2.67628466754047e-17
relative error = 1.2496909989753120444653450012866e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 2.1421082926045413835615760511772
y[1] (numeric) = 2.1421082926045414103799203325322
absolute error = 2.68183442813550e-17
relative error = 1.2519602474787666896464696707765e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 2.1426605986073351651893625816447
y[1] (numeric) = 2.1426605986073351920632312725148
absolute error = 2.68738686908701e-17
relative error = 1.2542289109314515322945106751793e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 2.1432140472708227758720389700136
y[1] (numeric) = 2.1432140472708228028014589294879
absolute error = 2.69294199594743e-17
relative error = 1.2564969884256931606979601684690e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 2.1437686391484529252179393936186
y[1] (numeric) = 2.1437686391484529522029375363376
absolute error = 2.69849981427190e-17
relative error = 1.2587644790548840242288229797141e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 2.1443243747948175370732045414055
y[1] (numeric) = 2.1443243747948175641138078375879
absolute error = 2.70406032961824e-17
relative error = 1.2610313819134670447277761309297e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 2.1448812547656523041137516760674
y[1] (numeric) = 2.1448812547656523312099871515369
absolute error = 2.70962354754695e-17
relative error = 1.2632976960969342353167809750880e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 2.1454392796178372435810136212707
y[1] (numeric) = 2.1454392796178372707329083574834
absolute error = 2.71518947362127e-17
relative error = 1.2655634207018532844604493025732e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 2.1459984499093972541620024097582
y[1] (numeric) = 2.1459984499093972813695835438293
absolute error = 2.72075811340711e-17
relative error = 1.2678285548258335174095958864155e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 2.146558766199502674014254472437
y[1] (numeric) = 2.1465587661995027012775491971681
absolute error = 2.72632947247311e-17
relative error = 1.2700930975675524696015827034793e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 2.147120229048469839936215393445
y[1] (numeric) = 2.1471202290484698672552509573514
absolute error = 2.73190355639064e-17
relative error = 1.2723570480267544708323958922495e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.3MB, time=5.61
NO POLE
x[1] = 0.537
y[1] (analytic) = 2.1476828390177616476836234016259
y[1] (numeric) = 2.1476828390177616750584271089637
absolute error = 2.73748037073378e-17
relative error = 1.2746204053042399159527990369874e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 2.148246596669988113432451914844
y[1] (numeric) = 2.1482465966699881408630511256374
absolute error = 2.74305992107934e-17
relative error = 1.2768831685018731689691821521715e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.539
y[1] (analytic) = 2.1488115025689069363889726001267
y[1] (numeric) = 2.1488115025689069638753947301955
absolute error = 2.74864221300688e-17
relative error = 1.2791453367225904514396583385022e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 2.1493775572794240625475015597464
y[1] (numeric) = 2.1493775572794240900897740807332
absolute error = 2.75422725209868e-17
relative error = 1.2814069090703844525585675178698e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 2.1499447613675942495963924010334
y[1] (numeric) = 2.1499447613675942771945428404313
absolute error = 2.75981504393979e-17
relative error = 1.2836678846503261705015382727284e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.542
y[1] (analytic) = 2.1505131154006216329728410959611
y[1] (numeric) = 2.1505131154006216606268970371411
absolute error = 2.76540559411800e-17
relative error = 1.2859282625685495154787090526307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 2.1510826199468602930670686853548
y[1] (numeric) = 2.1510826199468603207770577675934
absolute error = 2.77099890822386e-17
relative error = 1.2881880419322591779495605278528e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 2.151653275575814823576449031954
y[1] (numeric) = 2.1516532755758148513423989504609
absolute error = 2.77659499185069e-17
relative error = 1.2904472218497338334476202855096e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 2.1522250828581409010101499765046
y[1] (numeric) = 2.1522250828581409288320884824503
absolute error = 2.78219385059457e-17
relative error = 1.2927058014303200462466950904551e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 2.1527980423656458553448574015677
y[1] (numeric) = 2.1527980423656458832228123021111
absolute error = 2.78779549005434e-17
relative error = 1.2949637797844308245148953137431e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 2.1533721546712892418321528588176
y[1] (numeric) = 2.1533721546712892697661520171343
absolute error = 2.79339991583167e-17
relative error = 1.2972211560235766816200337741464e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 2.1539474203491834139581165672551
y[1] (numeric) = 2.1539474203491834419481879025649
absolute error = 2.79900713353098e-17
relative error = 1.2994779292603270047778859514449e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 2.1545238399745940975557287419852
y[1] (numeric) = 2.15452383997459412560190022958
absolute error = 2.80461714875948e-17
relative error = 1.3017340986083271789267481683012e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 2.1551014141239409660706433660095
y[1] (numeric) = 2.1551014141239409941729430372813
absolute error = 2.81022996712718e-17
relative error = 1.3039896631823017593728202466815e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 2.1556801433747982169809096708541
y[1] (numeric) = 2.1556801433747982451393656133232
absolute error = 2.81584559424691e-17
relative error = 1.3062446220980622748616857765469e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 2.1562600283058951493712177458042
y[1] (numeric) = 2.1562600283058951775858581031472
absolute error = 2.82146403573430e-17
relative error = 1.3084989744724964640264854262947e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 2.1568410694971167426622458500373
y[1] (numeric) = 2.156841069497116770933098822115
absolute error = 2.82708529720777e-17
relative error = 1.3107527194235621621893727539340e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 2.1574232675295042364956881570507
y[1] (numeric) = 2.1574232675295042648227819999368
absolute error = 2.83270938428861e-17
relative error = 1.3130058560703229111263294128915e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 2.1580066229852557117755428164614
y[1] (numeric) = 2.1580066229852557401589058424704
absolute error = 2.83833630260090e-17
relative error = 1.3152583835329093652630754069528e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 2.1585911364477266728662413745122
y[1] (numeric) = 2.1585911364477267013059019522277
absolute error = 2.84396605777155e-17
relative error = 1.3175103009325363487902671856535e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 2.1591768085014306309482017514636
y[1] (numeric) = 2.1591768085014306594441883057668
absolute error = 2.84959865543032e-17
relative error = 1.3197616073915106189416155983690e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 2.1597636397320396885313881314727
y[1] (numeric) = 2.1597636397320397170837291435707
absolute error = 2.85523410120980e-17
relative error = 1.3220123020332200926478039251690e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 2.1603516307263851251274622785674
y[1] (numeric) = 2.1603516307263851537361862860219
absolute error = 2.86087240074545e-17
relative error = 1.3242623839821508605566834730984e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 2.1609407820724579840811119509166
y[1] (numeric) = 2.1609407820724580127462475476723
absolute error = 2.86651355967557e-17
relative error = 1.3265118523638717765279383081119e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.3MB, time=5.85
NO POLE
x[1] = 0.561
y[1] (analytic) = 2.1615310943594096605611432447731
y[1] (numeric) = 2.1615310943594096892827190811862
absolute error = 2.87215758364131e-17
relative error = 1.3287607063050375742500984327217e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 2.1621225681775524907119248592309
y[1] (numeric) = 2.1621225681775525194899696420979
absolute error = 2.87780447828670e-17
relative error = 1.3310089449334012255068526589125e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.563
y[1] (analytic) = 2.1627152041183603419657734332904
y[1] (numeric) = 2.1627152041183603708003159258767
absolute error = 2.88345424925863e-17
relative error = 1.3332565673778031556100578327176e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 2.1633090027744692045168702676655
y[1] (numeric) = 2.1633090027744692334079392897342
absolute error = 2.88910690220687e-17
relative error = 1.3355035727681789632606494708559e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 2.1639039647396777839573009052987
y[1] (numeric) = 2.1639039647396778129049253331396
absolute error = 2.89476244278409e-17
relative error = 1.3377499602355671242367520815725e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.566
y[1] (analytic) = 2.1645000906089480950758102066747
y[1] (numeric) = 2.1645000906089481240800189731328
absolute error = 2.90042087664581e-17
relative error = 1.3399957289120843388226721978296e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 2.1650973809784060568198667187338
y[1] (numeric) = 2.1650973809784060858806888132386
absolute error = 2.90608220945048e-17
relative error = 1.3422408779309609599736028605432e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 2.1656958364453420884216312995027
y[1] (numeric) = 2.1656958364453421175390957680969
absolute error = 2.91174644685942e-17
relative error = 1.3444854064265117150318109237927e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 2.1662954576082117066884261244582
y[1] (numeric) = 2.166295457608211735862562069827
absolute error = 2.91741359453688e-17
relative error = 1.3467293135341618665306811285376e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 2.1668962450666361244583013651443
y[1] (numeric) = 2.1668962450666361536891379466444
absolute error = 2.92308365815001e-17
relative error = 1.3489725983904317920135659302457e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 2.1674981994214028502212979956586
y[1] (numeric) = 2.1674981994214028795088644293472
absolute error = 2.92875664336886e-17
relative error = 1.3512152601329354267747045096947e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 2.1681013212744662889070063483202
y[1] (numeric) = 2.1681013212744663182513319069845
absolute error = 2.93443255586643e-17
relative error = 1.3534572979004017673633307895702e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 2.1687056112289483438390212061293
y[1] (numeric) = 2.1687056112289483732401352193155
absolute error = 2.94011140131862e-17
relative error = 1.3556987108326502252085373578762e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 2.1693110698891390198568953865219
y[1] (numeric) = 2.1693110698891390493148272405647
absolute error = 2.94579318540428e-17
relative error = 1.3579394980706121154543057650635e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 2.1699176978604970276061949384248
y[1] (numeric) = 2.1699176978604970571209740764767
absolute error = 2.95147791380519e-17
relative error = 1.3601796587563198470148143271704e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 2.1705254957496503889972602427159
y[1] (numeric) = 2.1705254957496504185689161647768
absolute error = 2.95716559220609e-17
relative error = 1.3624191920329191630689365141528e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 2.1711344641643970438332784749014
y[1] (numeric) = 2.171134464164397073461840737848
absolute error = 2.96285622629466e-17
relative error = 1.3646580970446583279895422055564e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 2.1717446037137054576082740581332
y[1] (numeric) = 2.1717446037137054872937722757484
absolute error = 2.96854982176152e-17
relative error = 1.3668963729368865380576195484551e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 2.1723559150077152304756249046068
y[1] (numeric) = 2.1723559150077152602180887476095
absolute error = 2.97424638430027e-17
relative error = 1.3691340188560707445089663588563e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 2.1729683986577377073877134139076
y[1] (numeric) = 2.1729683986577377371871726099825
absolute error = 2.97994591960749e-17
relative error = 1.3713710339497940366051951998680e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 2.1735820552762565894073223680074
y[1] (numeric) = 2.1735820552762566192638067018344
absolute error = 2.98564843338270e-17
relative error = 1.3736074173667356209810377871051e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.582
y[1] (analytic) = 2.1741968854769285461913870343572
y[1] (numeric) = 2.1741968854769285761049263476413
absolute error = 2.99135393132841e-17
relative error = 1.3758431682566922259094230457488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 2.1748128898745838296477159608796
y[1] (numeric) = 2.174812889874583859618340152381
absolute error = 2.99706241915014e-17
relative error = 1.3780782857705856714169959413388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 2.175430069085226888765294119634
y[1] (numeric) = 2.1754300690852269187930331451975
absolute error = 3.00277390255635e-17
relative error = 1.3803127690604290517278731714353e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.3MB, time=6.10
NO POLE
x[1] = 0.585
y[1] (analytic) = 2.1760484237260369856187832295067
y[1] (numeric) = 2.1760484237260370157036671020922
absolute error = 3.00848838725855e-17
relative error = 1.3825466172793756903970498225802e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 2.1766679544153688125478352624802
y[1] (numeric) = 2.1766679544153688426898940521922
absolute error = 3.01420587897120e-17
relative error = 1.3847798295816715306621670499948e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.587
y[1] (analytic) = 2.1772886617727531105118363128439
y[1] (numeric) = 2.1772886617727531407111001469621
absolute error = 3.01992638341182e-17
relative error = 1.3870124051227040536279756043072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 2.1779105464188972886206991841443
y[1] (numeric) = 2.1779105464188973188771982471532
absolute error = 3.02564990630089e-17
relative error = 1.3892443430589546864983863425386e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 2.1785336089756860448423242247164
y[1] (numeric) = 2.1785336089756860751560887583358
absolute error = 3.03137645336194e-17
relative error = 1.3914756425480385032590567181989e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 2.1791578500661819878873491193109
y[1] (numeric) = 2.1791578500661820182584094225262
absolute error = 3.03710603032153e-17
relative error = 1.3937063027486933754491276758299e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 2.1797832703146262602718095216178
y[1] (numeric) = 2.17978327031462629070019595071
absolute error = 3.04283864290922e-17
relative error = 1.3959363228207645502175642512889e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 2.1804098703464391625583335903986
y[1] (numeric) = 2.180409870346439193044076558975
absolute error = 3.04857429685764e-17
relative error = 1.3981657019252351142160427314750e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 2.1810376507882207787764946704749
y[1] (numeric) = 2.1810376507882208093196246494993
absolute error = 3.05431299790244e-17
relative error = 1.4003944392242013816315493003623e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 2.1816666122677516030229475389772
y[1] (numeric) = 2.1816666122677516336234950568003
absolute error = 3.06005475178231e-17
relative error = 1.4026225338808804065418248811843e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 2.1822967554139931672419748170421
y[1] (numeric) = 2.1822967554139931978999704594323
absolute error = 3.06579956423902e-17
relative error = 1.4048499850596266433000878306288e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 2.1829280808570886701870713275584
y[1] (numeric) = 2.1829280808570887009025457377321
absolute error = 3.07154744101737e-17
relative error = 1.4070767919259073453107688327607e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 2.1835605892283636075641953605963
y[1] (numeric) = 2.1835605892283636383371792392487
absolute error = 3.07729838786524e-17
relative error = 1.4093029536463237995153472275510e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 2.1841942811603264033573169898256
y[1] (numeric) = 2.1841942811603264341878410951614
absolute error = 3.08305241053358e-17
relative error = 1.4115284693886050502237654377298e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 2.184829157286669042336894765523
y[1] (numeric) = 2.1848291572866690732249899132872
absolute error = 3.08880951477642e-17
relative error = 1.4137533383216107841436848094899e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 2.1854652182422677037519132926977
y[1] (numeric) = 2.1854652182422677346976103562062
absolute error = 3.09456970635085e-17
relative error = 1.4159775596153204795903360812784e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 2.1861024646631833962061153864261
y[1] (numeric) = 2.1861024646631834272094452965968
absolute error = 3.10033299101707e-17
relative error = 1.4182011324408545913813650083798e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 2.1867408971866625937190636806802
y[1] (numeric) = 2.1867408971866626247800574260639
absolute error = 3.10609937453837e-17
relative error = 1.4204240559704636838516130644933e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 2.1873805164511378729726677517652
y[1] (numeric) = 2.1873805164511379040913563785764
absolute error = 3.11186886268112e-17
relative error = 1.4226463293775221507789325876541e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 2.1880213230962285517438140029452
y[1] (numeric) = 2.1880213230962285829202286150935
absolute error = 3.11764146121483e-17
relative error = 1.4248679518365539349767085844254e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 2.1886633177627413285237367429417
y[1] (numeric) = 2.1886633177627413597579085020625
absolute error = 3.12341717591208e-17
relative error = 1.4270889225231988019439845762384e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 2.1893065010926709233247700777273
y[1] (numeric) = 2.1893065010926709546167302032132
absolute error = 3.12919601254859e-17
relative error = 1.4293092406142426162537815332761e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 2.1899508737292007196751214224219
y[1] (numeric) = 2.1899508737292007510249011914539
absolute error = 3.13497797690320e-17
relative error = 1.4315289052876064640508210312941e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 2.1905964363167034078023086281173
y[1] (numeric) = 2.190596436316703439209939375696
absolute error = 3.14076307475787e-17
relative error = 1.4337479157223449208429535554173e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.3MB, time=6.34
NO POLE
x[1] = 0.609
y[1] (analytic) = 2.1912431895007416290059039071208
y[1] (numeric) = 2.1912431895007416604714170260978
absolute error = 3.14655131189770e-17
relative error = 1.4359662710986534458145562054925e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 2.1918911339280686212202289294161
y[1] (numeric) = 2.1918911339280686527436558705254
absolute error = 3.15234269411093e-17
relative error = 1.4381839705978666347140169076230e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 2.1925402702466288657676466530899
y[1] (numeric) = 2.1925402702466288973490189249794
absolute error = 3.15813722718895e-17
relative error = 1.4404010134024610329341783219311e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 2.1931905991055587353030966420702
y[1] (numeric) = 2.1931905991055587669424458113329
absolute error = 3.16393491692627e-17
relative error = 1.4426173986960397015031172446963e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.613
y[1] (analytic) = 2.193842121155187142950521815765
y[1] (numeric) = 2.1938421211551871746478795069711
absolute error = 3.16973576912061e-17
relative error = 1.4448331256633715052953115927188e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 2.1944948370470361926318357670838
y[1] (numeric) = 2.1944948370470362243872336628118
absolute error = 3.17553978957280e-17
relative error = 1.4470481934903437471260900651747e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 2.195148747433821830589080977861
y[1] (numeric) = 2.1951487474338218624025508187298
absolute error = 3.18134698408688e-17
relative error = 1.4492626013640059924704379925223e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 2.1958038529694544981004294538961
y[1] (numeric) = 2.1958038529694545299720030385964
absolute error = 3.18715735847003e-17
relative error = 1.4514763484725363916917444175180e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 2.1964601543090397853906784956642
y[1] (numeric) = 2.1964601543090398173203876809905
absolute error = 3.19297091853263e-17
relative error = 1.4536894340052672447844074664530e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 2.1971176521088790867368955152475
y[1] (numeric) = 2.1971176521088791187247722161299
absolute error = 3.19878767008824e-17
relative error = 1.4559018571526741051437634764403e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 2.1977763470264702567698670051877
y[1] (numeric) = 2.1977763470264702888159431947238
absolute error = 3.20460761895361e-17
relative error = 1.4581136171063785491525060156387e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 2.198436239720508267972007960762
y[1] (numeric) = 2.1984362397205083000763156702488
absolute error = 3.21043077094868e-17
relative error = 1.4603247130591463882419356902338e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 2.1990973308508858693723892536474
y[1] (numeric) = 2.1990973308508859015349605726137
absolute error = 3.21625713189663e-17
relative error = 1.4625351442049086169076171115416e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 2.1997596210786942464395416520563
y[1] (numeric) = 2.1997596210786942786604087282943
absolute error = 3.22208670762380e-17
relative error = 1.4647449097387232216596618406613e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 2.2004231110662236821726963802011
y[1] (numeric) = 2.2004231110662237144518914197988
absolute error = 3.22791950395977e-17
relative error = 1.4669540088568097683261897893767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 2.2010878014769642193921233083838
y[1] (numeric) = 2.2010878014769642517296785757572
absolute error = 3.23375552673734e-17
relative error = 1.4691624407565384908897284887213e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 2.2017536929756063242292290641051
y[1] (numeric) = 2.2017536929756063566251768820304
absolute error = 3.23959478179253e-17
relative error = 1.4713702046364284797912106507239e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 2.2024207862280415508170785543448
y[1] (numeric) = 2.2024207862280415832714513039908
absolute error = 3.24543727496460e-17
relative error = 1.4735772996961549505319851654767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 2.2030890819013632071820045895915
y[1] (numeric) = 2.2030890819013632396948347105519
absolute error = 3.25128301209604e-17
relative error = 1.4757837251365428779064062673088e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 2.2037585806638670223369715012861
y[1] (numeric) = 2.203758580663867054908291491612
absolute error = 3.25713199903259e-17
relative error = 1.4779894801595742509876444919817e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 2.2044292831850518145773598460989
y[1] (numeric) = 2.2044292831850518472072022623313
absolute error = 3.26298424162324e-17
relative error = 1.4801945639683862383214885747354e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 2.2051011901356201609798404928803
y[1] (numeric) = 2.2051011901356201936682379500825
absolute error = 3.26883974572022e-17
relative error = 1.4823989757672648175706135642771e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 2.2057743021874790681050075912146
y[1] (numeric) = 2.2057743021874791008519927630051
absolute error = 3.27469851717905e-17
relative error = 1.4846027147616656142049471267861e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
memory used=102.9MB, alloc=4.3MB, time=6.60
y[1] (analytic) = 2.206448620013740643904441124267
y[1] (numeric) = 2.2064486200137406767100467428519
absolute error = 3.28056056185849e-17
relative error = 1.4868057801581893763833855079208e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 2.2071241442887227708328709530407
y[1] (numeric) = 2.2071241442887228036971298092466
absolute error = 3.28642588562059e-17
relative error = 1.4890081711646027986310543025922e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 2.2078008756879497801661154642659
y[1] (numeric) = 2.2078008756879498130890604075726
absolute error = 3.29229449433067e-17
relative error = 1.4912098869898275975924731977032e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 2.2084788148881531275254691399139
y[1] (numeric) = 2.2084788148881531605071330784874
absolute error = 3.29816639385735e-17
relative error = 1.4934109268439522438827589397424e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 2.2091579625672720696092145727818
y[1] (numeric) = 2.2091579625672721026496304735071
absolute error = 3.30404159007253e-17
relative error = 1.4956112899382210352895707862852e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 2.209838319404454342131935659715
y[1] (numeric) = 2.209838319404454375231136548229
absolute error = 3.30992008885140e-17
relative error = 1.4978109754850367617651066021249e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 2.2105198860800568389723099118374
y[1] (numeric) = 2.210519886080056872130328872562
absolute error = 3.31580189607246e-17
relative error = 1.5000099826979678853512432993516e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 2.2112026632756462925300590296388
y[1] (numeric) = 2.2112026632756463257469292058139
absolute error = 3.32168701761751e-17
relative error = 1.5022083107917421355431922327527e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 2.2118866516739999552927380999261
y[1] (numeric) = 2.2118866516739999885684926936429
absolute error = 3.32757545937168e-17
relative error = 1.5044059589822581966040488517513e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 2.2125718519591062826130449814848
y[1] (numeric) = 2.2125718519591063159477172537189
absolute error = 3.33346722722341e-17
relative error = 1.5066029264865747710371312073891e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 2.2132582648161656166973326568164
y[1] (numeric) = 2.2132582648161656500909559274612
absolute error = 3.33936232706448e-17
relative error = 1.5087992125229222504503791085223e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 2.2139458909315908718060085385224
y[1] (numeric) = 2.2139458909315909052586161864221
absolute error = 3.34526076478997e-17
relative error = 1.5109948163106827429186949701423e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 2.214634730993008220666505930789
y[1] (numeric) = 2.2146347309930082541781313937724
absolute error = 3.35116254629834e-17
relative error = 1.5131897370704243185335037162728e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 2.2153247856892577820995140590041
y[1] (numeric) = 2.2153247856892578156701908339176
absolute error = 3.35706767749135e-17
relative error = 1.5153839740238629628454974329880e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 2.2160160557103943098591542937911
y[1] (numeric) = 2.2160160557103943434889159365326
absolute error = 3.36297616427415e-17
relative error = 1.5175775263939013115496773636892e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 2.2167085417476878826877914096955
y[1] (numeric) = 2.2167085417476879163766715352477
absolute error = 3.36888801255522e-17
relative error = 1.5197703934045996407715032592733e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 2.2174022444936245955861699333913
y[1] (numeric) = 2.2174022444936246293342022158553
absolute error = 3.37480322824640e-17
relative error = 1.5219625742811874956202861611089e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 2.2180971646419072522995668516017
y[1] (numeric) = 2.2180971646419072861067850242309
absolute error = 3.38072181726292e-17
relative error = 1.5241540682500752929001931154174e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 2.2187933028874560590206531649455
y[1] (numeric) = 2.2187933028874560928870910201792
absolute error = 3.38664378552337e-17
relative error = 1.5263448745388388561736287293905e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 2.2194906599264093193097579906269
y[1] (numeric) = 2.2194906599264093532354493801241
absolute error = 3.39256913894972e-17
relative error = 1.5285349923762265034932926407363e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 2.2201892364561241302332301342922
y[1] (numeric) = 2.2201892364561241642182089689652
absolute error = 3.39849788346730e-17
relative error = 1.5307244209921481012207698354174e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 2.2208890331751770797205932694713
y[1] (numeric) = 2.2208890331751771137648935195201
absolute error = 3.40443002500488e-17
relative error = 1.5329131596177091614432327411661e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 2.2215900507833649451411920818197
y[1] (numeric) = 2.2215900507833649792448477767656
absolute error = 3.41036556949459e-17
relative error = 1.5351012074851728503250182663093e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 2.2222922899817053931010279548629
y[1] (numeric) = 2.2222922899817054272640731835827
absolute error = 3.41630452287198e-17
relative error = 1.5372885638279850622014794834559e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.3MB, time=6.85
x[1] = 0.656
y[1] (analytic) = 2.2229957514724376804604839941385
y[1] (numeric) = 2.2229957514724377146829529048985
absolute error = 3.42224689107600e-17
relative error = 1.5394752278807634546007897857956e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 2.2237004359590233565736404075195
y[1] (numeric) = 2.2237004359590233908555672080098
absolute error = 3.42819268004903e-17
relative error = 1.5416611988793089849584089773774e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 2.2244063441461469667498824810923
y[1] (numeric) = 2.2244063441461470010913014384608
absolute error = 3.43414189573685e-17
relative error = 1.5438464760605904477658914858753e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.659
y[1] (analytic) = 2.225113476739716756938504612256
y[1] (numeric) = 2.2251134767397167913394500531427
absolute error = 3.44009454408867e-17
relative error = 1.5460310586627560019144763621926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 2.2258218344468653796370150847057
y[1] (numeric) = 2.2258218344468654140975213952772
absolute error = 3.44605063105715e-17
relative error = 1.5482149459251401792249026223100e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 2.2265314179759506010238474936642
y[1] (numeric) = 2.2265314179759506355439491196479
absolute error = 3.45201016259837e-17
relative error = 1.5503981370882484189453817420542e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 2.2272422280365560093161859541311
y[1] (numeric) = 2.2272422280365560438959174008498
absolute error = 3.45797314467187e-17
relative error = 1.5525806313937730566298509320896e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 2.2279542653394917243536124500346
y[1] (numeric) = 2.2279542653394917589930082824408
absolute error = 3.46393958324062e-17
relative error = 1.5547624280845778592898347908056e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 2.2286675305967951084082859079922
y[1] (numeric) = 2.2286675305967951431073807507029
absolute error = 3.46990948427107e-17
relative error = 1.5569435264047184818875685241942e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 2.2293820245217314782223638059184
y[1] (numeric) = 2.2293820245217315129811923432497
absolute error = 3.47588285373313e-17
relative error = 1.5591239255994314815400852299963e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.666
y[1] (analytic) = 2.2300977478287948182733783539607
y[1] (numeric) = 2.2300977478287948530919753299622
absolute error = 3.48185969760015e-17
relative error = 1.5613036249151233485905599920976e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 2.230814701233708495268280513199
y[1] (numeric) = 2.2308147012337085301466807316888
absolute error = 3.48784002184898e-17
relative error = 1.5634826235993954159711635743728e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.668
y[1] (analytic) = 2.2315328854534259738668663462125
y[1] (numeric) = 2.231532885453426008805104670812
absolute error = 3.49382383245995e-17
relative error = 1.5656609209010328665603125870429e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 2.2322523012061315336353014229997
y[1] (numeric) = 2.2322523012061315686334127771684
absolute error = 3.49981113541687e-17
relative error = 1.5678385160700027170405390319404e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 2.2329729492112409872304602358361
y[1] (numeric) = 2.2329729492112410222884796029066
absolute error = 3.50580193670705e-17
relative error = 1.5700154083574607581023301592035e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 2.2336948301894023998157988074685
y[1] (numeric) = 2.2336948301894024349337612306812
absolute error = 3.51179624232127e-17
relative error = 1.5721915970157360925417848208765e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 2.234417944862496809709479908578
y[1] (numeric) = 2.2344179448624968448874204911166
absolute error = 3.51779405825386e-17
relative error = 1.5743670812983649289331588266953e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 2.2351422939536389502654715326986
y[1] (numeric) = 2.2351422939536389855034254377248
absolute error = 3.52379539050262e-17
relative error = 1.5765418604600527216373073307209e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 2.2358678781871779729883405097476
y[1] (numeric) = 2.2358678781871780082863429604366
absolute error = 3.52980024506890e-17
relative error = 1.5787159337567079406804842318824e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 2.2365946982886981718824643730246
y[1] (numeric) = 2.2365946982886982072405506525999
absolute error = 3.53580862795753e-17
relative error = 1.5808893004454087054322716346059e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 2.2373227549850197090363858289479
y[1] (numeric) = 2.2373227549850197444545912807171
absolute error = 3.54182054517692e-17
relative error = 1.5830619597844454627070559914018e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 2.2380520490041993414430354139469
y[1] (numeric) = 2.2380520490041993769213954413366
absolute error = 3.54783600273897e-17
relative error = 1.5852339110332786820457421982364e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 2.2387825810755311490565491587907
y[1] (numeric) = 2.2387825810755311845950992253821
absolute error = 3.55385500665914e-17
relative error = 1.5874051534525680967594770599849e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 2.2395143519295472640864093172327
y[1] (numeric) = 2.2395143519295472996851849467971
absolute error = 3.55987756295644e-17
relative error = 1.5895756863041661614865382584215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.3MB, time=7.09
x[1] = 0.68
y[1] (analytic) = 2.2402473622980186015296374531729
y[1] (numeric) = 2.2402473622980186371886742297071
absolute error = 3.56590367765342e-17
relative error = 1.5917455088511115182204198888987e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 2.2409816129139555909417704185907
y[1] (numeric) = 2.2409816129139556266611039863529
absolute error = 3.57193335677622e-17
relative error = 1.5939146203576492448436462379165e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 2.2417171045116089094473509932868
y[1] (numeric) = 2.2417171045116089452270170568317
absolute error = 3.57796660635449e-17
relative error = 1.5960830200891930682725136254506e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.683
y[1] (analytic) = 2.2424538378264702159906661969838
y[1] (numeric) = 2.2424538378264702518307005211987
absolute error = 3.58400343242149e-17
relative error = 1.5982507073123679168608509757042e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 2.2431918135952728868274675245872
y[1] (numeric) = 2.2431918135952729227279059347277
absolute error = 3.59004384101405e-17
relative error = 1.6004176812949899736130186402475e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.685
y[1] (analytic) = 2.2439310325559927522584085963871
y[1] (numeric) = 2.2439310325559927882192869781127
absolute error = 3.59608783817256e-17
relative error = 1.6025839413060601337359265528003e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 2.2446714954478488346049369566992
y[1] (numeric) = 2.2446714954478488706262912561097
absolute error = 3.60213542994105e-17
relative error = 1.6047494866157975657753181311235e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 2.2454132030113040874283779969003
y[1] (numeric) = 2.2454132030113041235102442205712
absolute error = 3.60818662236709e-17
relative error = 1.6069143164955930385506072688238e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 2.2461561559880661359929502220013
y[1] (numeric) = 2.24615615598806617213536443702
absolute error = 3.61424142150187e-17
relative error = 1.6090784302180424730732297558636e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 2.2469003551210880189734523238367
y[1] (numeric) = 2.2469003551210880551764506578388
absolute error = 3.62029983340021e-17
relative error = 1.6112418270569492695970080698156e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 2.2476458011545689314083637686188
y[1] (numeric) = 2.2476458011545689676719824098238
absolute error = 3.62636186412050e-17
relative error = 1.6134045062872954818977431996136e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 2.2483924948339549688991018520184
y[1] (numeric) = 2.2483924948339550052233770492663
absolute error = 3.63242751972479e-17
relative error = 1.6155664671852797588569374426698e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.692
y[1] (analytic) = 2.2491404369059398730561794210927
y[1] (numeric) = 2.2491404369059399094411474838799
absolute error = 3.63849680627872e-17
relative error = 1.6177277090282840678266354249150e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 2.249889628118465778193008709278
y[1] (numeric) = 2.2498896281184658146387060077939
absolute error = 3.64456972985159e-17
relative error = 1.6198882310949027052084556845359e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 2.2506400692207239592680979783159
y[1] (numeric) = 2.2506400692207239957745609434791
absolute error = 3.65064629651632e-17
relative error = 1.6220480326649223697381747875719e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 2.2513917609631555810763889093694
y[1] (numeric) = 2.2513917609631556176436540328641
absolute error = 3.65672651234947e-17
relative error = 1.6242071130193289213563898708447e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 2.2521447040974524486904839347305
y[1] (numeric) = 2.2521447040974524853185877690432
absolute error = 3.66281038343127e-17
relative error = 1.6263654714403185623824319061898e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 2.2528988993765577591525139514087
y[1] (numeric) = 2.2528988993765577958414931098645
absolute error = 3.66889791584558e-17
relative error = 1.6285231072112779207410105590355e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 2.25365434755466685441739810853
y[1] (numeric) = 2.2536543475546668911672892653294
absolute error = 3.67498911567994e-17
relative error = 1.6306800196168041038805522852261e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 2.2544110493872279755482486118705
y[1] (numeric) = 2.2544110493872280123590885021259
absolute error = 3.68108398902554e-17
relative error = 1.6328362079426892219762507702753e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 2.2551690056309430181646747409903
y[1] (numeric) = 2.255169005630943055036500160763
absolute error = 3.68718254197727e-17
relative error = 1.6349916714759404118915973714845e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 2.2559282170437682891447415273365
y[1] (numeric) = 2.2559282170437683260775893336732
absolute error = 3.69328478063367e-17
relative error = 1.6371464095047554886701080006538e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 2.2566886843849152645813397953357
y[1] (numeric) = 2.2566886843849153015752469063056
absolute error = 3.69939071109699e-17
relative error = 1.6393004213185473856879895328612e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 2.2574504084148513489937255229102
y[1] (numeric) = 2.2574504084148513860487289176417
absolute error = 3.70550033947315e-17
relative error = 1.6414537062079242432106141827980e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=114.4MB, alloc=4.3MB, time=7.33
x[1] = 0.704
y[1] (analytic) = 2.2582133898953006357949877330194
y[1] (numeric) = 2.2582133898953006729111244517373
absolute error = 3.71161367187179e-17
relative error = 1.6436062634647093872683710175805e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 2.2589776295892446690162053837593
y[1] (numeric) = 2.2589776295892447061935125278216
absolute error = 3.71773071440623e-17
relative error = 1.6457580923819214225488344348381e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 2.2597431282609232062880549812383
y[1] (numeric) = 2.2597431282609232435265697131735
absolute error = 3.72385147319352e-17
relative error = 1.6479091922537941887196575216924e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 2.2605098866758349830806318969027
y[1] (numeric) = 2.2605098866758350203803914404468
absolute error = 3.72997595435441e-17
relative error = 1.6500595623757612814880396865456e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 2.2612779056007384782022496291953
y[1] (numeric) = 2.2612779056007385155632912693293
absolute error = 3.73610416401340e-17
relative error = 1.6522092020444759788567643187083e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.709
y[1] (analytic) = 2.2620471858036526805579825084111
y[1] (numeric) = 2.2620471858036527179803435913979
absolute error = 3.74223610829868e-17
relative error = 1.6543581105577824937579270326738e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 2.2628177280538578571687186033559
y[1] (numeric) = 2.262817728053857894652436536778
absolute error = 3.74837179334221e-17
relative error = 1.6565062872147491505706038399610e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 2.2635895331218963224514908489257
y[1] (numeric) = 2.2635895331218963599966031017225
absolute error = 3.75451122527968e-17
relative error = 1.6586537313156484762434971236791e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 2.2643626017795732087618556750013
y[1] (numeric) = 2.2643626017795732463683997775064
absolute error = 3.76065441025051e-17
relative error = 1.6608004421619549925567314424105e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 2.265136934799957238199089679101
y[1] (numeric) = 2.2651369347999572758671032230798
absolute error = 3.76680135439788e-17
relative error = 1.6629464190563562526496736805468e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 2.2659125329573814956749761480529
y[1] (numeric) = 2.2659125329573815334044967867404
absolute error = 3.77295206386875e-17
relative error = 1.6650916613027594371705577233266e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 2.2666893970274442032469544975378
y[1] (numeric) = 2.266689397027444241038019945676
absolute error = 3.77910654481382e-17
relative error = 1.6672361682062714619646996433753e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 2.2674675277870094957164069627153
y[1] (numeric) = 2.2674675277870095335690549965911
absolute error = 3.78526480338758e-17
relative error = 1.6693799390732188139472746157840e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 2.2682469260142081974928581382867
y[1] (numeric) = 2.2682469260142082354071265957695
absolute error = 3.79142684574828e-17
relative error = 1.6715229732111320720832167512641e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 2.2690275924884386007248642322568
y[1] (numeric) = 2.2690275924884386387007910128365
absolute error = 3.79759267805797e-17
relative error = 1.6736652699287613059022658359410e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 2.2698095279903672446983701643499
y[1] (numeric) = 2.2698095279903672827359932291747
absolute error = 3.80376230648248e-17
relative error = 1.6758068285360650037380970325708e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 2.2705927333019296965033139075021
y[1] (numeric) = 2.2705927333019297346026712794165
absolute error = 3.80993573719144e-17
relative error = 1.6779476483442166357831734416670e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 2.2713772092063313329692587390984
y[1] (numeric) = 2.2713772092063313711303885026812
absolute error = 3.81611297635828e-17
relative error = 1.6800877286656023937586017937597e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 2.2721629564880481238708353376532
y[1] (numeric) = 2.2721629564880481620937756392556
absolute error = 3.82229403016024e-17
relative error = 1.6822270688138233317543263868808e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 2.2729499759328274164037769304403
y[1] (numeric) = 2.2729499759328274546885659782241
absolute error = 3.82847890477838e-17
relative error = 1.6843656681036974980250527703170e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 2.2737382683276887209323319681743
y[1] (numeric) = 2.2737382683276887592790080321499
absolute error = 3.83466760639756e-17
relative error = 1.6865035258512488636031243495325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 2.2745278344609244980088400742199
y[1] (numeric) = 2.2745278344609245364174414862849
absolute error = 3.84086014120650e-17
relative error = 1.6886406413737314414669357246277e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 2.2753186751221009466662582879727
y[1] (numeric) = 2.2753186751221009851368234419499
absolute error = 3.84705651539772e-17
relative error = 1.6907770139896006109958730649239e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 2.2761107911020587939844258950013
y[1] (numeric) = 2.2761107911020588325169932466773
absolute error = 3.85325673516760e-17
relative error = 1.6929126430185372190577787964254e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=118.2MB, alloc=4.3MB, time=7.58
x[1] = 0.728
y[1] (analytic) = 2.2769041831929140859308574102828
y[1] (numeric) = 2.2769041831929141245254654774464
absolute error = 3.85946080671636e-17
relative error = 1.6950475277814364907636890872987e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 2.2776988521880589794768545553899
y[1] (numeric) = 2.2776988521880590181335419178707
absolute error = 3.86566873624808e-17
relative error = 1.6971816676004145202968385461594e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 2.2784947988821625359897293458082
y[1] (numeric) = 2.278494798882162574708534645515
absolute error = 3.87188052997068e-17
relative error = 1.6993150617987971880539836230073e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 2.2792920240711715159019316806719
y[1] (numeric) = 2.2792920240711715546828936216315
absolute error = 3.87809619409596e-17
relative error = 1.7014477097011354203171205422205e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 2.2800905285523111746578761041129
y[1] (numeric) = 2.2800905285523112135010334525087
absolute error = 3.88431573483958e-17
relative error = 1.7035796106331940975143480651056e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 2.2808903131240860599392636851151
y[1] (numeric) = 2.2808903131240860988446552693259
absolute error = 3.89053915842108e-17
relative error = 1.7057107639219585180942160483744e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 2.2816913785862808101696962412638
y[1] (numeric) = 2.2816913785862808491373609519027
absolute error = 3.89676647106389e-17
relative error = 1.7078411688956364614262504448541e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 2.2824937257399609542993814110692
y[1] (numeric) = 2.2824937257399609933293582010224
absolute error = 3.90299767899532e-17
relative error = 1.7099708248836514793025303208362e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 2.2832973553874737128707283596373
y[1] (numeric) = 2.2832973553874737519630562441031
absolute error = 3.90923278844658e-17
relative error = 1.7120997312166493357762895561041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 2.2841022683324488003656351833496
y[1] (numeric) = 2.2841022683324488395203532398774
absolute error = 3.91547180565278e-17
relative error = 1.7142278872264956725388769490991e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 2.2849084653797992288352703609061
y[1] (numeric) = 2.2849084653797992680524177294355
absolute error = 3.92171473685294e-17
relative error = 1.7163552922462780510542370921360e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 2.2857159473357221128131518805808
y[1] (numeric) = 2.2857159473357221520927677634806
absolute error = 3.92796158828998e-17
relative error = 1.7184819456102992356593355761521e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 2.2865247150076994755123289568342
y[1] (numeric) = 2.2865247150076995148544526189419
absolute error = 3.93421236621077e-17
relative error = 1.7206078466540967268829043579381e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 2.287334769204499056307472533534
y[1] (numeric) = 2.2873347692044990957121433021947
absolute error = 3.94046707686607e-17
relative error = 1.7227329947144141576729366966902e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 2.2881461107361751195026820559393
y[1] (numeric) = 2.2881461107361751589699393210454
absolute error = 3.94672572651061e-17
relative error = 1.7248573891292339305345767653973e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 2.2889587404140692643858172793247
y[1] (numeric) = 2.2889587404140693039157004933551
absolute error = 3.95298832140304e-17
relative error = 1.7269810292377529861526739524646e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 2.2897726590508112365701651686424
y[1] (numeric) = 2.2897726590508112761627138467017
absolute error = 3.95925486780593e-17
relative error = 1.7291039143803804550327718233038e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 2.2905878674603197406242532309562
y[1] (numeric) = 2.2905878674603197802795069508147
absolute error = 3.96552537198585e-17
relative error = 1.7312260438987702349994880365294e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 2.2914043664578032539906219105309
y[1] (numeric) = 2.2914043664578032937086203126638
absolute error = 3.97179984021329e-17
relative error = 1.7333474171357836681973915572168e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 2.292222156859760842194369965414
y[1] (numeric) = 2.2922221568597608819751527530413
absolute error = 3.97807827876273e-17
relative error = 1.7354680334355177317167822806077e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 2.2930412394839829753422880341259
y[1] (numeric) = 2.293041239483983015185894973252
absolute error = 3.98436069391261e-17
relative error = 1.7375878921432895529541569017338e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 2.2938616151495523459133968916587
y[1] (numeric) = 2.2938616151495523858198678111121
absolute error = 3.99064709194534e-17
relative error = 1.7397069926056383911607004936682e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 2.2946832846768446878417081853902
y[1] (numeric) = 2.2946832846768447278110829768634
absolute error = 3.99693747914732e-17
relative error = 1.7418253341703319678772291144754e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.751
y[1] (analytic) = 2.2955062488875295968920267337422
y[1] (numeric) = 2.2955062488875296369243453518315
absolute error = 4.00323186180893e-17
relative error = 1.7439429161863597099625122007282e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=122.0MB, alloc=4.3MB, time=7.83
x[1] = 0.752
y[1] (analytic) = 2.296330508604571352329614763454
y[1] (numeric) = 2.2963305086045713924249172256997
absolute error = 4.00953024622457e-17
relative error = 1.7460597380039477762086416717508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 2.2971560646522297398845397552037
y[1] (numeric) = 2.2971560646522297800428661421299
absolute error = 4.01583263869262e-17
relative error = 1.7481757989745392211029110222860e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 2.2979829178560608760115288619932
y[1] (numeric) = 2.2979829178560609162329193171478
absolute error = 4.02213904551546e-17
relative error = 1.7502910984508003063562490279024e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 2.2988110690429180334461541602208
y[1] (numeric) = 2.2988110690429180737306488902159
absolute error = 4.02844947299951e-17
relative error = 1.7524056357866354941899229788774e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 2.2996405190409524680581742896949
y[1] (numeric) = 2.2996405190409525084058135642468
absolute error = 4.03476392745519e-17
relative error = 1.7545194103371676153227148601875e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 2.3004712686796142470028593359996
y[1] (numeric) = 2.3004712686796142874136834879692
absolute error = 4.04108241519696e-17
relative error = 1.7566324214587528504744186344887e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 2.3013033187896530781711271066062
y[1] (numeric) = 2.3013033187896531186451765320393
absolute error = 4.04740494254331e-17
relative error = 1.7587446685089739477770266549170e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 2.3021366702031191409393202509354
y[1] (numeric) = 2.302136670203119181476635409103
absolute error = 4.05373151581676e-17
relative error = 1.7608561508466377938032292487469e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 2.3029713237533639182194549742173
y[1] (numeric) = 2.3029713237533639588200763876562
absolute error = 4.06006214134389e-17
relative error = 1.7629668678317860116746081066079e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 2.3038072802750410298107733954668
y[1] (numeric) = 2.3038072802750410704747416500201
absolute error = 4.06639682545533e-17
relative error = 1.7650768188256881686974523445335e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 2.3046445406041070670534329011966
y[1] (numeric) = 2.3046445406041071077807886460541
absolute error = 4.07273557448575e-17
relative error = 1.7671860031908349938748064616788e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 2.3054831055778224287851671486257
y[1] (numeric) = 2.3054831055778224695759510963648
absolute error = 4.07907839477391e-17
relative error = 1.7692944202909576302583377814776e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 2.3063229760347521586017546751156
y[1] (numeric) = 2.3063229760347521994560076017421
absolute error = 4.08542529266265e-17
relative error = 1.7714020694910208249746767418422e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 2.3071641528147667834221323743718
y[1] (numeric) = 2.3071641528147668243398951193601
absolute error = 4.09177627449883e-17
relative error = 1.7735089501571944575316285442320e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 2.3080066367590431533589924045926
y[1] (numeric) = 2.3080066367590431943403058709272
absolute error = 4.09813134663346e-17
relative error = 1.7756150616569074476648165261516e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 2.3088504287100652828957023992357
y[1] (numeric) = 2.3088504287100653239406075534516
absolute error = 4.10449051542159e-17
relative error = 1.7777204033587975924439455330026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 2.3096955295116251933703901573883
y[1] (numeric) = 2.3096955295116252344789280296124
absolute error = 4.11085378722241e-17
relative error = 1.7798249746327524294168853983613e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 2.3105419400088237567680352978996
y[1] (numeric) = 2.3105419400088237979402469818915
absolute error = 4.11722116839919e-17
relative error = 1.7819287748498807573745064840243e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
y[1] (analytic) = 2.3113896610480715408214116694355
y[1] (numeric) = 2.3113896610480715820573383226285
absolute error = 4.12359266531930e-17
relative error = 1.7840318033825188259060057156746e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 2.3122386934770896554217256174682
y[1] (numeric) = 2.3122386934770896967214084610108
absolute error = 4.12996828435426e-17
relative error = 1.7861340596042494809018407380553e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 2.3130890381449106003397965189116
y[1] (numeric) = 2.3130890381449106417032768377081
absolute error = 4.13634803187965e-17
relative error = 1.7882355428898607377909627766358e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 2.3139406959018791142586273056503
y[1] (numeric) = 2.3139406959018791556859464484029
absolute error = 4.14273191427526e-17
relative error = 1.7903362526154081603487705912767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 2.3147936675996530251182140096074
y[1] (numeric) = 2.3147936675996530666094133888569
absolute error = 4.14911993792495e-17
relative error = 1.7924361881581518157141234379099e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 2.3156479540912041017734446742281
y[1] (numeric) = 2.3156479540912041433285657663955
absolute error = 4.15551210921674e-17
relative error = 1.7945353488965926879415415291641e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=125.8MB, alloc=4.3MB, time=8.08
x[1] = 0.776
y[1] (analytic) = 2.3165035562308189069659392903508
y[1] (numeric) = 2.316503556230818948585023635779
absolute error = 4.16190843454282e-17
relative error = 1.7966337342104744713162893994479e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 2.3173604748740996516106837283765
y[1] (numeric) = 2.3173604748740996932937729313716
absolute error = 4.16830892029951e-17
relative error = 1.7987313434807637783685816386847e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 2.3182187108779650503983119534413
y[1] (numeric) = 2.3182187108779650921454476823142
absolute error = 4.17471357288729e-17
relative error = 1.8008281760896605823791064794219e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 2.3190782651006511787138921259457
y[1] (numeric) = 2.3190782651006512205251161130538
absolute error = 4.18112239871081e-17
relative error = 1.8029242314206000076395345731363e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 2.3199391384017123308730735062978
y[1] (numeric) = 2.3199391384017123727484275480869
absolute error = 4.18753540417891e-17
relative error = 1.8050195088582584211850038017458e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 2.3208013316420218796764524000898
y[1] (numeric) = 2.3208013316420219216159783571356
absolute error = 4.19395259570458e-17
relative error = 1.8071140077885336527885498622103e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 2.3216648456837731372830166981443
y[1] (numeric) = 2.3216648456837731792867564951945
absolute error = 4.20037397970502e-17
relative error = 1.8092077275985683265593184537872e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 2.3225296813904802174035298849471
y[1] (numeric) = 2.3225296813904802594715255109633
absolute error = 4.20679956260162e-17
relative error = 1.8113006676767386902998327022574e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 2.3233958396269788988147167089229
y[1] (numeric) = 2.3233958396269789409470102171225
absolute error = 4.21322935081996e-17
relative error = 1.8133928274126520728224088791571e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
y[1] (analytic) = 2.3242633212594274901951140288106
y[1] (numeric) = 2.3242633212594275323917475367088
absolute error = 4.21966335078982e-17
relative error = 1.8154842061971486443714373119949e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 2.3251321271553076962834516720611
y[1] (numeric) = 2.3251321271553077385444673615133
absolute error = 4.22610156894522e-17
relative error = 1.8175748034223160705815805705256e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 2.3260022581834254853604294637126
y[1] (numeric) = 2.3260022581834255276858695809561
absolute error = 4.23254401172435e-17
relative error = 1.8196646184814568370732158049252e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 2.3268737152139119580547579075891
y[1] (numeric) = 2.3268737152139120004446647632859
absolute error = 4.23899068556968e-17
relative error = 1.8217536507691329993259093289869e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 2.3277464991182242174743313259392
y[1] (numeric) = 2.327746499118224259928747295218
absolute error = 4.24544159692788e-17
relative error = 1.8238418996811292029842724741317e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 2.3286206107691462406634035887577
y[1] (numeric) = 2.3286206107691462831823711112562
absolute error = 4.25189675224985e-17
relative error = 1.8259293646144630204444804879155e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 2.3294960510407897513866378900402
y[1] (numeric) = 2.3294960510407897939701994699477
absolute error = 4.25835615799075e-17
relative error = 1.8280160449673952591710123820571e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 2.330372820808595094240903355092
y[1] (numeric) = 2.3303728208085951368891015611919
absolute error = 4.26481982060999e-17
relative error = 1.8301019401394230770518955530753e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.793
y[1] (analytic) = 2.3312509209493321100956925907621
y[1] (numeric) = 2.3312509209493321528085700564744
absolute error = 4.27128774657123e-17
relative error = 1.8321870495312773977064944993178e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 2.3321303523411010128630356190915
y[1] (numeric) = 2.3321303523411010556406350425155
absolute error = 4.27775994234240e-17
relative error = 1.8342713725449289023957843529402e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 2.3330111158633332675977869643636
y[1] (numeric) = 2.3330111158633333104401511083205
absolute error = 4.28423641439569e-17
relative error = 1.8363549085835811443630012546173e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 2.3338932123967924699291639939162
y[1] (numeric) = 2.333893212396792512836335685992
absolute error = 4.29071716920758e-17
relative error = 1.8384376570516808123985744013794e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.797
y[1] (analytic) = 2.3347766428235752268244159443281
y[1] (numeric) = 2.3347766428235752697964380769163
absolute error = 4.29720221325882e-17
relative error = 1.8405196173549065506978571172908e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 2.3356614080271120386855043967211
y[1] (numeric) = 2.3356614080271120817224199270657
absolute error = 4.30369155303446e-17
relative error = 1.8426007889001792061674537977222e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 2.3365475088921681827796772979326
y[1] (numeric) = 2.3365475088921682258815292481709
absolute error = 4.31018519502383e-17
relative error = 1.8446811710956506482365546585876e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.3MB, time=8.33
x[1] = 0.8
y[1] (analytic) = 2.3374349463048445980048199582053
y[1] (numeric) = 2.3374349463048446411716514154112
absolute error = 4.31668314572059e-17
relative error = 1.8467607633507225563167714099948e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 2.3383237211525787709904677908206
y[1] (numeric) = 2.3383237211525788142223219070473
absolute error = 4.32318541162267e-17
relative error = 1.8488395650760181170835200023167e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 2.3392138343241456235353668947597
y[1] (numeric) = 2.3392138343241456668322868870833
absolute error = 4.32969199923236e-17
relative error = 1.8509175756834179052300905883707e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 2.3401052867096584013824699180295
y[1] (numeric) = 2.3401052867096584447444990685917
absolute error = 4.33620291505622e-17
relative error = 1.8529947945860187575782638116508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 2.340998079200569564332255976721
y[1] (numeric) = 2.340998079200569607759437632773
absolute error = 4.34271816560520e-17
relative error = 1.8550712211981824412932269175395e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 2.3418922126896716776952647431966
y[1] (numeric) = 2.3418922126896717211876423171418
absolute error = 4.34923775739452e-17
relative error = 1.8571468549354817243955042714657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 2.3427876880710983050847361560118
y[1] (numeric) = 2.3427876880710983486423531254497
absolute error = 4.35576169694379e-17
relative error = 1.8592216952147490066088572662003e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 2.3436845062403249025502485442888
y[1] (numeric) = 2.3436845062403249461731484520582
absolute error = 4.36228999077694e-17
relative error = 1.8612957414540437646763468950135e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 2.3445826680941697140532493002512
y[1] (numeric) = 2.344582668094169757741475754474
absolute error = 4.36882264542228e-17
relative error = 1.8633689930726755140999170222611e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 2.3454821745307946682853735755283
y[1] (numeric) = 2.3454821745307947120389702496528
absolute error = 4.37535966741245e-17
relative error = 1.8654414494911798142753835080622e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 2.3463830264497062768304478196196
y[1] (numeric) = 2.3463830264497063206494584524643
absolute error = 4.38190106328447e-17
relative error = 1.8675131101313369423900641541365e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 2.3472852247517565336710763225998
y[1] (numeric) = 2.3472852247517565775555447183973
absolute error = 4.38844683957975e-17
relative error = 1.8695839744161734781941877842126e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 2.3481887703391438160407102687252
y[1] (numeric) = 2.3481887703391438599906802971658
absolute error = 4.39499700284406e-17
relative error = 1.8716540417699468454429757338965e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 2.3490936641154137866221001530857
y[1] (numeric) = 2.3490936641154138306376157493613
absolute error = 4.40155155962756e-17
relative error = 1.8737233116181554255488585477718e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 2.3499999069854602970930337598291
y[1] (numeric) = 2.3499999069854603411741389246772
absolute error = 4.40811051648481e-17
relative error = 1.8757917833875401320370278657868e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 2.3509074998555262930202632477729
y[1] (numeric) = 2.3509074998555263371670020475207
absolute error = 4.41467387997478e-17
relative error = 1.8778594565060859761042865266195e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 2.3518164436332047201025262374043
y[1] (numeric) = 2.3518164436332047643149428040125
absolute error = 4.42124165666082e-17
relative error = 1.8799263304030066151484063485831e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 2.3527267392274394317635671423658
y[1] (numeric) = 2.3527267392274394760417056734729
absolute error = 4.42781385311071e-17
relative error = 1.8819924045087629349781354107736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 2.3536383875485260980960663385231
y[1] (numeric) = 2.3536383875485261424399710974896
absolute error = 4.43439047589665e-17
relative error = 1.8840576782550560912307299612333e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 2.3545513895081131161573861146209
y[1] (numeric) = 2.3545513895081131605671014305734
absolute error = 4.44097153159525e-17
relative error = 1.8861221510748205616521800782917e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 2.3554657460192025216180437003469
y[1] (numeric) = 2.3554657460192025660936139682228
absolute error = 4.44755702678759e-17
relative error = 1.8881858224022469274008441599767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.821
y[1] (analytic) = 2.3563814579961509017638230203552
y[1] (numeric) = 2.3563814579961509463052927009466
absolute error = 4.45414696805914e-17
relative error = 1.8902486916727451828833111650273e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 2.3572985263546703098524381764344
y[1] (numeric) = 2.3572985263546703544598517964331
absolute error = 4.46074136199987e-17
relative error = 1.8923107583229887265489612131032e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 2.3582169520118291808256630145627
y[1] (numeric) = 2.3582169520118292254990651666041
absolute error = 4.46734021520414e-17
relative error = 1.8943720217908649529558462023560e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.3MB, time=8.58
x[1] = 0.824
y[1] (analytic) = 2.359136735886053248377842489053
y[1] (numeric) = 2.3591367358860532931172778317614
absolute error = 4.47394353427084e-17
relative error = 1.8964324815155319258864027673597e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 2.3600578788971264633817028923793
y[1] (numeric) = 2.3600578788971265081872161504119
absolute error = 4.48055132580326e-17
relative error = 1.8984921369373605096948449386940e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 2.360980381966191913672379376567
y[1] (numeric) = 2.3609803819661919585440153406591
absolute error = 4.48716359640921e-17
relative error = 1.9005509874979825189650290017607e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.827
y[1] (analytic) = 2.3619042460157527451905805502554
y[1] (numeric) = 2.3619042460157527901283840772649
absolute error = 4.49378035270095e-17
relative error = 1.9026090326402583065221861910323e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 2.3628294719696730844858112946707
y[1] (numeric) = 2.3628294719696731294898273076232
absolute error = 4.50040160129525e-17
relative error = 1.9046662718082994408780825795555e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 2.3637560607531789625805763018108
y[1] (numeric) = 2.3637560607531790076508497899442
absolute error = 4.50702734881334e-17
relative error = 1.9067227044474447890089989801803e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 2.3646840132928592401964881991215
y[1] (numeric) = 2.3646840132928592853330642179314
absolute error = 4.51365760188099e-17
relative error = 1.9087783300042916256529965135719e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 2.3656133305166665343432054868507
y[1] (numeric) = 2.3656133305166665795461291581351
absolute error = 4.52029236712844e-17
relative error = 1.9108331479266632555509877807227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 2.3665440133539181462711268770934
y[1] (numeric) = 2.3665440133539181915404433889981
absolute error = 4.52693165119047e-17
relative error = 1.9128871576636358645799845438579e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 2.3674760627352969907887699873024
y[1] (numeric) = 2.3674760627352970361245245943658
absolute error = 4.53357546070634e-17
relative error = 1.9149403586655103914344382122733e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 2.3684094795928525269457637057171
y[1] (numeric) = 2.3684094795928525723480017289159
absolute error = 4.54022380231988e-17
relative error = 1.9169927503838477939980522254500e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 2.3693442648600016900823849117839
y[1] (numeric) = 2.3693442648600017355511517385782
absolute error = 4.54687668267943e-17
relative error = 1.9190443322714409183483430559257e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.836
y[1] (analytic) = 2.3702804194715298252465716011802
y[1] (numeric) = 2.3702804194715298707819126855588
absolute error = 4.55353410843786e-17
relative error = 1.9210951037823201801640830378029e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 2.3712179443635916219793458325333
y[1] (numeric) = 2.3712179443635916675813066950594
absolute error = 4.56019608625261e-17
relative error = 1.9231450643717676618355986703213e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 2.3721568404737120504695812813365
y[1] (numeric) = 2.3721568404737120961382075091929
absolute error = 4.56686262278564e-17
relative error = 1.9251942134962932305827207027105e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 2.3730971087407872990790515559056
y[1] (numeric) = 2.3730971087407873448143888029407
absolute error = 4.57353372470351e-17
relative error = 1.9272425506136654885935162616117e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 2.3740387501050857132386968005047
y[1] (numeric) = 2.3740387501050857590407907872778
absolute error = 4.58020939867731e-17
relative error = 1.9292900751828794607523015950275e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 2.374981765508248735717047481984
y[1] (numeric) = 2.3749817655082487815859439958112
absolute error = 4.58688965138272e-17
relative error = 1.9313367866641790910483499764558e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 2.3759261558932918482617456284335
y[1] (numeric) = 2.3759261558932918941974905234332
absolute error = 4.59357448949997e-17
relative error = 1.9333826845190375911951411020255e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 2.3768719222046055146151051614505
y[1] (numeric) = 2.3768719222046055606177443585898
absolute error = 4.60026391971393e-17
relative error = 1.9354277682101925244102358026271e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.844
y[1] (analytic) = 2.3778190653879561249046543376622
y[1] (numeric) = 2.3778190653879561709742338248024
absolute error = 4.60695794871402e-17
relative error = 1.9374720372016051004015896373999e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 2.378767586390486941409604690122
y[1] (numeric) = 2.3787675863904869875461705220646
absolute error = 4.61365658319426e-17
relative error = 1.9395154909584784161083133085951e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 2.3797174861607190457041922361288
y[1] (numeric) = 2.3797174861607190919077905346618
absolute error = 4.62035982985330e-17
relative error = 1.9415581289472672431068475970053e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 2.3806687656485522871788380948894
y[1] (numeric) = 2.3806687656485523334495150488332
absolute error = 4.62706769539438e-17
relative error = 1.9435999506356583825950969452982e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=8.83
NO POLE
x[1] = 0.848
y[1] (analytic) = 2.381621425805266232940077036263
y[1] (numeric) = 2.3816214258052662792778789015166
absolute error = 4.63378018652536e-17
relative error = 1.9456409554925804537203294814181e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 2.3825754675835211190902038605954
y[1] (numeric) = 2.3825754675835211654951769601828
absolute error = 4.64049730995874e-17
relative error = 1.9476811429882094558697278218042e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 2.3835308919373588033875888893701
y[1] (numeric) = 2.3835308919373588498597796134866
absolute error = 4.64721907241165e-17
relative error = 1.9497205125939617257407248780958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 2.3844876998222037192886152270691
y[1] (numeric) = 2.3844876998222037658280700331275
absolute error = 4.65394548060584e-17
relative error = 1.9517590637824869058394642083546e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 2.3854458921948638313721918362615
y[1] (numeric) = 2.3854458921948638779789572489387
absolute error = 4.66067654126772e-17
relative error = 1.9537967960276818848940519622840e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.853
y[1] (analytic) = 2.386405470013531592147797850512
y[1] (numeric) = 2.3864054700135316388219204617956
absolute error = 4.66741226112836e-17
relative error = 1.9558337088046879376049788123477e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 2.3873664342377849002480149332341
y[1] (numeric) = 2.3873664342377849469895414024688
absolute error = 4.67415264692347e-17
relative error = 1.9578698015898794883242250178736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 2.3883287858285880600065058750989
y[1] (numeric) = 2.3883287858285881068154829290334
absolute error = 4.68089770539345e-17
relative error = 1.9599050738608822055681517089715e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 2.3892925257482927424223990080597
y[1] (numeric) = 2.3892925257482927892988734408931
absolute error = 4.68764744328334e-17
relative error = 1.9619395250965491939077673545557e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 2.3902576549606389475120394004551
y[1] (numeric) = 2.3902576549606389944560580738841
absolute error = 4.69440186734290e-17
relative error = 1.9639731547769916253777765785945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 2.3912241744307559680490691850239
y[1] (numeric) = 2.3912241744307560150606790282892
absolute error = 4.70116098432653e-17
relative error = 1.9660059623835423798635599209054e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 2.3921920851251633546938007599905
y[1] (numeric) = 2.3921920851251634017730487699242
absolute error = 4.70792480099337e-17
relative error = 1.9680379473987950128757595220597e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 2.3931613880117718825128479926762
y[1] (numeric) = 2.3931613880117719296597812337485
absolute error = 4.71469332410723e-17
relative error = 1.9700691093065715875167930585490e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 2.3941320840598845188899819453471
y[1] (numeric) = 2.3941320840598845661046475497134
absolute error = 4.72146656043663e-17
relative error = 1.9720994475919365246590788003275e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 2.3951041742401973928291790342347
y[1] (numeric) = 2.3951041742401974401116242017828
absolute error = 4.72824451675481e-17
relative error = 1.9741289617411978884059972175130e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 2.3960776595248007656508309248595
y[1] (numeric) = 2.3960776595248008130011029232568
absolute error = 4.73502719983973e-17
relative error = 1.9761576512419044893659270215239e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 2.3970525408871800030820868599469
y[1] (numeric) = 2.3970525408871800505002330246876
absolute error = 4.74181461647407e-17
relative error = 1.9781855155828429894107676807699e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 2.3980288193022165487423005103599
y[1] (numeric) = 2.3980288193022165962283682448123
absolute error = 4.74860677344524e-17
relative error = 1.9802125542540391780325675789614e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 2.3990064957461888990245548345755
y[1] (numeric) = 2.3990064957461889465785916100295
absolute error = 4.75540367754540e-17
relative error = 1.9822387667467634084239697964836e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 2.3999855711967735793742398283117
y[1] (numeric) = 2.3999855711967736269962931840264
absolute error = 4.76220533557147e-17
relative error = 1.9842641525535318479954514999052e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 2.4009660466330461219656594429643
y[1] (numeric) = 2.4009660466330461696557769862153
absolute error = 4.76901175432510e-17
relative error = 1.9862887111680910602477016973786e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 2.4019479230354820447776453495411
y[1] (numeric) = 2.4019479230354820925358747556681
absolute error = 4.77582294061270e-17
relative error = 1.9883124420854275985474708737751e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 2.4029312013859578320691566237894
y[1] (numeric) = 2.4029312013859578798955456362441
absolute error = 4.78263890124547e-17
relative error = 1.9903353448017775708384455682790e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 2.4039158826677519162558458281983
y[1] (numeric) = 2.4039158826677519641504422585918
absolute error = 4.78945964303935e-17
relative error = 1.9923574188146028962089939440708e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=9.08
NO POLE
x[1] = 0.872
y[1] (analytic) = 2.404901967865545661188573367523
y[1] (numeric) = 2.4049019678655457091514250956741
absolute error = 4.79628517281511e-17
relative error = 1.9943786636226258286121527264329e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 2.4058894579654243468348533964289
y[1] (numeric) = 2.4058894579654243948660083704115
absolute error = 4.80311549739826e-17
relative error = 1.9963990787257885736682258969766e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 2.4068783539548781553642159607811
y[1] (numeric) = 2.4068783539548782034637221969725
absolute error = 4.80995062361914e-17
relative error = 1.9984186636252877848837687456700e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.875
y[1] (analytic) = 2.4078686568228031586384714580263
y[1] (numeric) = 2.407868656822803206806377041155
absolute error = 4.81679055831287e-17
relative error = 2.0004374178235508265847016774591e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 2.4088603675595023071078649070117
y[1] (numeric) = 2.4088603675595023553442179902055
absolute error = 4.82363530831938e-17
relative error = 2.0024553408242453004451664066645e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.877
y[1] (analytic) = 2.4098534871566864201141089234785
y[1] (numeric) = 2.4098534871566864684189577283127
absolute error = 4.83048488048342e-17
relative error = 2.0044724321322802436378041312910e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 2.4108480166074751776012857043457
y[1] (numeric) = 2.4108480166074752259746785208914
absolute error = 4.83733928165457e-17
relative error = 2.0064886912538073183646190002590e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 2.4118439569063981132356097317683
y[1] (numeric) = 2.4118439569063981616775949186407
absolute error = 4.84419851868724e-17
relative error = 2.0085041176962178465637828852190e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 2.4128413090493956089350443168161
y[1] (numeric) = 2.4128413090493956574456703012226
absolute error = 4.85106259844065e-17
relative error = 2.0105187109681315572985445677149e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 2.4138400740338198908097665124707
y[1] (numeric) = 2.4138400740338199393890817902597
absolute error = 4.85793152777890e-17
relative error = 2.0125324705794226413998520309880e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 2.414840252858436026514476336492
y[1] (numeric) = 2.4148402528584360751625294722009
absolute error = 4.86480531357089e-17
relative error = 2.0145453960411836198717521899121e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 2.415841846523422924013547656542
y[1] (numeric) = 2.4158418465234229727303872834464
absolute error = 4.87168396269044e-17
relative error = 2.0165574868657720832373173291101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 2.4168448560303743317600195028051
y[1] (numeric) = 2.4168448560303743805456943229669
absolute error = 4.87856748201618e-17
relative error = 2.0185687425667621435990394266948e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 2.4178492823822998402894279871747
y[1] (numeric) = 2.4178492823822998891439867714909
absolute error = 4.88545587843162e-17
relative error = 2.0205791626589704481105573987333e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 2.4188551265836258852294804229247
y[1] (numeric) = 2.4188551265836259341529720111766
absolute error = 4.89234915882519e-17
relative error = 2.0225887466584697194784642493871e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 2.4198623896401967517265746546231
y[1] (numeric) = 2.4198623896401968007190479555246
absolute error = 4.89924733009015e-17
relative error = 2.0245974940825485348433957899660e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 2.4208710725592755802901680248894
y[1] (numeric) = 2.4208710725592756293516720161361
absolute error = 4.90615039912467e-17
relative error = 2.0266054044497414220029889298953e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 2.4218811763495453740560018224496
y[1] (numeric) = 2.4218811763495454231865855507679
absolute error = 4.91305837283183e-17
relative error = 2.0286124772798258426261250966562e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 2.4228927020211100074691884747977
y[1] (numeric) = 2.4228927020211100566689010559936
absolute error = 4.91997125811959e-17
relative error = 2.0306187120938067953372480204329e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 2.4239056505854952363881701686333
y[1] (numeric) = 2.4239056505854952856570607876417
absolute error = 4.92688906190084e-17
relative error = 2.0326241084139344562177532846368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 2.4249200230556497096105590021199
y[1] (numeric) = 2.4249200230556497589486769130538
absolute error = 4.93381179109339e-17
relative error = 2.0346286657636970263018571931966e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 2.4259358204459459818218701948871
y[1] (numeric) = 2.4259358204459460312292647210868
absolute error = 4.94073945261997e-17
relative error = 2.0366323836678177133536200465563e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 2.426953043772181527968161304595
y[1] (numeric) = 2.4269530437721815774448818386774
absolute error = 4.94767205340824e-17
relative error = 2.0386352616522558358734544214855e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 2.4279716940515797590535918227839
y[1] (numeric) = 2.4279716940515798085996878266919
absolute error = 4.95460960039080e-17
relative error = 2.0406372992442079185908381520472e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=9.32
NO POLE
x[1] = 0.896
y[1] (analytic) = 2.4289917723027910393639189476544
y[1] (numeric) = 2.4289917723027910889794399527064
absolute error = 4.96155210050520e-17
relative error = 2.0426384959721087794445822502187e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 2.4300132795458937051169467573578
y[1] (numeric) = 2.4300132795458937548019423642971
absolute error = 4.96849956069393e-17
relative error = 2.0446388513656243776443828705573e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 2.4310362168023950845409474343307
y[1] (numeric) = 2.4310362168023951342954673133754
absolute error = 4.97545198790447e-17
relative error = 2.0466383649556693548355798164814e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 2.4320605850952325193820746191814
y[1] (numeric) = 2.4320605850952325692061685100737
absolute error = 4.98240938908923e-17
relative error = 2.0486370362743792970667974823100e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 2.433086385448774387841790401624
y[1] (numeric) = 2.4330863854487744377355081136803
absolute error = 4.98937177120563e-17
relative error = 2.0506348648551406011166355223612e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 2.4341136188888211289453288859756
y[1] (numeric) = 2.434113618888821178908720298136
absolute error = 4.99633914121604e-17
relative error = 2.0526318502325627437359640701388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 2.4351422864426062683422206997627
y[1] (numeric) = 2.4351422864426063183753357606409
absolute error = 5.00331150608782e-17
relative error = 2.0546279919424916806092797887006e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 2.4361723891387974455399042460485
y[1] (numeric) = 2.4361723891387974956427929739821
absolute error = 5.01028887279336e-17
relative error = 2.0566232895220232056313927221398e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 2.437203928007497442571450933178
y[1] (numeric) = 2.437203928007497492744163416278
absolute error = 5.01727124831000e-17
relative error = 2.0586177425094670336913084551906e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 2.4382369040802452140984330497498
y[1] (numeric) = 2.4382369040802452643410194459513
absolute error = 5.02425863962015e-17
relative error = 2.0606113504443929952960503748569e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 2.4392713183900169189499643877719
y[1] (numeric) = 2.4392713183900169692624749248837
absolute error = 5.03125105371118e-17
relative error = 2.0626041128675828175690707457767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 2.4403071719712269530989451531242
y[1] (numeric) = 2.4403071719712270034814301288792
absolute error = 5.03824849757550e-17
relative error = 2.0645960293210598810563945118736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 2.4413444658597289840765441396612
y[1] (numeric) = 2.4413444658597290345290539217669
absolute error = 5.04525097821057e-17
relative error = 2.0665870993480902223159951331462e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 2.4423832010928169868259525815233
y[1] (numeric) = 2.4423832010928170373485376077119
absolute error = 5.05225850261886e-17
relative error = 2.0685773224931630562380730278859e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 2.4434233787092262809964455374948
y[1] (numeric) = 2.4434233787092263315891563155738
absolute error = 5.05927107780790e-17
relative error = 2.0705666983020081757637081420955e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 2.4444649997491345696787881015588
y[1] (numeric) = 2.4444649997491346203416752094615
absolute error = 5.06628871079027e-17
relative error = 2.0725552263215887561145862511661e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 2.4455080652541629795830251751404
y[1] (numeric) = 2.4455080652541630303161392609764
absolute error = 5.07331140858360e-17
relative error = 2.0745429061000982606502960000318e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 2.4465525762673771026596949789151
y[1] (numeric) = 2.446552576267377153463086761021
absolute error = 5.08033917821059e-17
relative error = 2.0765297371869655235580971569307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 2.4475985338332880391655079254826
y[1] (numeric) = 2.4475985338332880900392281924725
absolute error = 5.08737202669899e-17
relative error = 2.0785157191328434711188426989880e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 2.4486459389978534421745339186714
y[1] (numeric) = 2.4486459389978534931186335294882
absolute error = 5.09440996108168e-17
relative error = 2.0805008514896387049216648424031e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 2.4496947928084785635359425907501
y[1] (numeric) = 2.4496947928084786145504724747159
absolute error = 5.10145298839658e-17
relative error = 2.0824851338104716068776108673322e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 2.4507450963140173012793424353703
y[1] (numeric) = 2.4507450963140173523643535922374
absolute error = 5.10850111568671e-17
relative error = 2.0844685656496977466207526286769e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 2.4517968505647732484687662416698
y[1] (numeric) = 2.4517968505647732996243097416719
absolute error = 5.11555435000021e-17
relative error = 2.0864511465629129135165834702374e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 2.4528500566125007435063516836075
y[1] (numeric) = 2.4528500566125007947324786675107
absolute error = 5.12261269839032e-17
relative error = 2.0884328761069418222201307210743e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=9.57
NO POLE
x[1] = 0.92
y[1] (analytic) = 2.4539047155104059218867673682993
y[1] (numeric) = 2.4539047155104059731835290474531
absolute error = 5.12967616791538e-17
relative error = 2.0904137538398349916559824660700e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 2.4549608283131477694034360978672
y[1] (numeric) = 2.4549608283131478207708837542557
absolute error = 5.13674476563885e-17
relative error = 2.0923937793208737729366502386178e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 2.4560183960768391768076085511139
y[1] (numeric) = 2.4560183960768392282457935374073
absolute error = 5.14381849862934e-17
relative error = 2.0943729521105794300539522955454e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 2.4570774198590479959213420441841
y[1] (numeric) = 2.45707741985904804743031578379
absolute error = 5.15089737396059e-17
relative error = 2.0963512717707018417876811381857e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 2.458137900718798097205440483279
y[1] (numeric) = 2.4581379007187981487852544703936
absolute error = 5.15798139871146e-17
relative error = 2.0983287378642122949699895550964e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 2.4591998397165704287834130774524
y[1] (numeric) = 2.4591998397165704804341188771122
absolute error = 5.16507057996598e-17
relative error = 2.1003053499553206886845519980671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 2.4602632379143040769225108355351
y[1] (numeric) = 2.4602632379143041286441600836685
absolute error = 5.17216492481334e-17
relative error = 2.1022811076094683003530534060831e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 2.4613280963753973279729013283127
y[1] (numeric) = 2.4613280963753973797655457317916
absolute error = 5.17926444034789e-17
relative error = 2.1042560103933246274240020086295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 2.4623944161647087317660436552204
y[1] (numeric) = 2.4623944161647087836297349919116
absolute error = 5.18636913366912e-17
relative error = 2.1062300578747761091251292448867e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 2.4634621983485581664733270140167
y[1] (numeric) = 2.4634621983485582184081171328343
absolute error = 5.19347901188176e-17
relative error = 2.1082032496229635835306250040357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 2.4645314439947279049260377321664
y[1] (numeric) = 2.464531443994727956931978553123
absolute error = 5.20059408209566e-17
relative error = 2.1101755852082303748070871670027e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 2.4656021541724636823977210799852
y[1] (numeric) = 2.4656021541724637344748645942442
absolute error = 5.20771435142590e-17
relative error = 2.1121470642021637930245574519505e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 2.4666743299524757658500056479996
y[1] (numeric) = 2.4666743299524758179984039179271
absolute error = 5.21483982699275e-17
relative error = 2.1141176861775757093716329329765e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 2.4677479724069400246429595344339
y[1] (numeric) = 2.4677479724069400768626646936508
absolute error = 5.22197051592169e-17
relative error = 2.1160874507085074896222111222304e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 2.4688230826094990027110490532703
y[1] (numeric) = 2.4688230826094990550021133067044
absolute error = 5.22910642534341e-17
relative error = 2.1180563573702268077292099169114e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 2.4698996616352629922057721389306
y[1] (numeric) = 2.4698996616352630445682477628687
absolute error = 5.23624756239381e-17
relative error = 2.1200244057392244617425518728875e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 2.4709777105608111086060400903009
y[1] (numeric) = 2.4709777105608111610399794324413
absolute error = 5.24339393421404e-17
relative error = 2.1219915953932273799972175707072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 2.4720572304641923672973827645726
y[1] (numeric) = 2.4720572304641924198028382440773
absolute error = 5.25054554795047e-17
relative error = 2.1239579259111832707575498670526e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.938
y[1] (analytic) = 2.4731382224249267616210538001932
y[1] (numeric) = 2.4731382224249268141980779077402
absolute error = 5.25770241075470e-17
relative error = 2.1259233968732614798075021086838e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 2.4742206875240063423941139181219
y[1] (numeric) = 2.474220687524006395042759215958
absolute error = 5.26486452978361e-17
relative error = 2.1278880078608700065308798312693e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 2.4753046268438962989015718215649
y[1] (numeric) = 2.475304626843896351621890943558
absolute error = 5.27203191219931e-17
relative error = 2.1298517584566320702337037012618e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 2.4763900414685360413616636864191
y[1] (numeric) = 2.4763900414685360941537093381109
absolute error = 5.27920456516918e-17
relative error = 2.1318146482443990751757193455967e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 2.4774769324833402848653537077954
y[1] (numeric) = 2.4774769324833403377291786664544
absolute error = 5.28638249586590e-17
relative error = 2.1337766768092594991685536069233e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 2.4785653009752001347911396422128
y[1] (numeric) = 2.4785653009752001877267967568865
absolute error = 5.29356571146737e-17
relative error = 2.1357378437375033721760926682358e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=9.82
NO POLE
x[1] = 0.944
y[1] (analytic) = 2.479655148032484173696248760357
y[1] (numeric) = 2.4796551480324842267037909519253
absolute error = 5.30075421915683e-17
relative error = 2.1376981486166674988106800955426e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 2.4807464747450395496853111016935
y[1] (numeric) = 2.4807464747450396027647913629212
absolute error = 5.30794802612277e-17
relative error = 2.1396575910354959036794166931755e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 2.4818392822041930662575983996958
y[1] (numeric) = 2.4818392822041931194090697952858
absolute error = 5.31514713955900e-17
relative error = 2.1416161705839648432889959833860e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 2.4829335715027522736339185250206
y[1] (numeric) = 2.4829335715027523268574341916669
absolute error = 5.32235156666463e-17
relative error = 2.1435738868532714984513058243397e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 2.4840293437350065615642567736144
y[1] (numeric) = 2.4840293437350066148598699200554
absolute error = 5.32956131464410e-17
relative error = 2.1455307394358428190583752845398e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 2.4851265999967282536172568074846
y[1] (numeric) = 2.4851265999967283069850207145562
absolute error = 5.33677639070716e-17
relative error = 2.1474867279253242196731863454944e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 2.4862253413851737029526355377064
y[1] (numeric) = 2.4862253413851737563926035583952
absolute error = 5.34399680206888e-17
relative error = 2.1494418519165803654383716826151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 2.4873255689990843895776277221722
y[1] (numeric) = 2.4873255689990844430898532816689
absolute error = 5.35122255594967e-17
relative error = 2.1513961110056999702325208577732e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 2.4884272839386880190885575346191
y[1] (numeric) = 2.488427283938688072673094130372
absolute error = 5.35845365957529e-17
relative error = 2.1533495047899965574133081055708e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 2.4895304873056996228986358465988
y[1] (numeric) = 2.4895304873056996765555370483672
absolute error = 5.36569012017684e-17
relative error = 2.1553020328680011787779278546226e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 2.4906351802033226599530834502771
y[1] (numeric) = 2.4906351802033227136824029001849
absolute error = 5.37293194499078e-17
relative error = 2.1572536948394671918878228315242e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 2.4917413637362501199326819372795
y[1] (numeric) = 2.4917413637362501737344733498689
absolute error = 5.38017914125894e-17
relative error = 2.1592044903053710053347479884422e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 2.4928490390106656279468554372248
y[1] (numeric) = 2.49284903901066568182117259951
absolute error = 5.38743171622852e-17
relative error = 2.1611544188679088044178403657577e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 2.4939582071342445507173879091215
y[1] (numeric) = 2.4939582071342446046642846806423
absolute error = 5.39468967715208e-17
relative error = 2.1631034801304892697244241526625e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 2.4950688692161551042538821694347
y[1] (numeric) = 2.4950688692161551582734124823107
absolute error = 5.40195303128760e-17
relative error = 2.1650516736977543643733466119992e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 2.4961810263670594630220683323775
y[1] (numeric) = 2.4961810263670595171142861913617
absolute error = 5.40922178589842e-17
relative error = 2.1669989991755519861856615166205e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 2.4972946796991148706060708308246
y[1] (numeric) = 2.4972946796991149247710303133577
absolute error = 5.41649594825331e-17
relative error = 2.1689454561709607430983572394337e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 2.4984098303259747518657446802108
y[1] (numeric) = 2.498409830325974806103499936475
absolute error = 5.42377552562642e-17
relative error = 2.1708910442922666256517494740101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 2.4995264793627898265901931428407
y[1] (numeric) = 2.499526479362789880900798395814
absolute error = 5.43106052529733e-17
relative error = 2.1728357631489797433261004709331e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 2.5006446279262092246485804462218
y[1] (numeric) = 2.5006446279262092790320899917323
absolute error = 5.43835095455105e-17
relative error = 2.1747796123518310150761259085272e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 2.5017642771343816026393547063264
y[1] (numeric) = 2.5017642771343816570958229131064
absolute error = 5.44564682067800e-17
relative error = 2.1767225915127608681779997124168e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 2.5028854281069562620389977050968
y[1] (numeric) = 2.5028854281069563165684790148374
absolute error = 5.45294813097406e-17
relative error = 2.1786647002449359289751269609942e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 2.5040080819650842688514196710394
y[1] (numeric) = 2.5040080819650843234539685984446
absolute error = 5.46025489274052e-17
relative error = 2.1806059381627257266487878345930e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 2.5051322398314195747591187123931
y[1] (numeric) = 2.5051322398314196294347898452346
absolute error = 5.46756711328415e-17
relative error = 2.1825463048817273551135471141598e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=10.06
NO POLE
x[1] = 0.968
y[1] (analytic) = 2.5062579028301201397772260541264
y[1] (numeric) = 2.5062579028301201945260740532982
absolute error = 5.47488479991718e-17
relative error = 2.1844858000187541522800019971204e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 2.5073850720868490564115597329022
y[1] (numeric) = 2.5073850720868491112336393324751
absolute error = 5.48220795995729e-17
relative error = 2.1864244231918283917782696863884e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 2.5085137487287756753218109081564
y[1] (numeric) = 2.5085137487287757302171769154328
absolute error = 5.48953660072764e-17
relative error = 2.1883621740201899339081197647442e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 2.5096439338845767324909884525713
y[1] (numeric) = 2.50964393388457678745969574814
absolute error = 5.49687072955687e-17
relative error = 2.1902990521242928931838171612314e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 2.5107756286844374779022489914824
y[1] (numeric) = 2.5107756286844375329443525292736
absolute error = 5.50421035377912e-17
relative error = 2.1922350571258102743268773177987e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.973
y[1] (analytic) = 2.5119088342600528057242410681426
y[1] (numeric) = 2.5119088342600528608397958754826
absolute error = 5.51155548073400e-17
relative error = 2.1941701886476186843195358751063e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 2.5130435517446283860060936202811
y[1] (numeric) = 2.5130435517446284411951547979476
absolute error = 5.51890611776665e-17
relative error = 2.1961044463138188927632059018749e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 2.514179782272881797883180463042
y[1] (numeric) = 2.514179782272881853145803185319
absolute error = 5.52626227222770e-17
relative error = 2.1980378297497165559509909453680e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 2.515317526981043664294793984159
y[1] (numeric) = 2.5153175269810437196310334988921
absolute error = 5.53362395147331e-17
relative error = 2.1999703385818347920571115245414e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 2.5164567870068587882148627691366
y[1] (numeric) = 2.5164567870068588436247743977882
absolute error = 5.54099116286516e-17
relative error = 2.2019019724379068467990186865103e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 2.5175975634895872903968493872484
y[1] (numeric) = 2.517597563489587345880488524953
absolute error = 5.54836391377046e-17
relative error = 2.2038327309468767168360298517519e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 2.5187398575700057486339660833466
y[1] (numeric) = 2.5187398575700058041913881989662
absolute error = 5.55574221156196e-17
relative error = 2.2057626137388997652435785779488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 2.5198836703904083385358476357918
y[1] (numeric) = 2.5198836703904083941671082719714
absolute error = 5.56312606361796e-17
relative error = 2.2076916204453433290682106589810e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 2.5210290030946079758228221572727
y[1] (numeric) = 2.5210290030946080315279769304958
absolute error = 5.57051547732231e-17
relative error = 2.2096197506987833523342687152932e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 2.52217585682793746013892213288
y[1] (numeric) = 2.5221758568279375159180267335243
absolute error = 5.57791046006443e-17
relative error = 2.2115470041330089516249315169306e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 2.5233242327372506203847795085422
y[1] (numeric) = 2.5233242327372506762378897009352
absolute error = 5.58531101923930e-17
relative error = 2.2134733803830150738660314580801e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 2.5244741319709234615715501628133
y[1] (numeric) = 2.5244741319709235174987217852881
absolute error = 5.59271716224748e-17
relative error = 2.2153988790850070515367276901896e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 2.5256255556788553131970146160318
y[1] (numeric) = 2.525625555678855369198303580983
absolute error = 5.60012889649512e-17
relative error = 2.2173234998764011797593270225896e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 2.5267785050124699791450033530492
y[1] (numeric) = 2.5267785050124700352204656469886
absolute error = 5.60754622939394e-17
relative error = 2.2192472423958134126875984350133e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 2.5279329811247168891092966590468
y[1] (numeric) = 2.5279329811247169452589883426596
absolute error = 5.61496916836128e-17
relative error = 2.2211701062830757751650256127493e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 2.5290889851700722515431503924384
y[1] (numeric) = 2.5290889851700723077671276006393
absolute error = 5.62239772082009e-17
relative error = 2.2230920911792289991984516661485e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 2.5302465183045402081356006444805
y[1] (numeric) = 2.5302465183045402644339195864696
absolute error = 5.62983189419891e-17
relative error = 2.2250131967265112220834010173939e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 2.5314055816856539898157017619896
y[1] (numeric) = 2.5314055816856540461884187213088
absolute error = 5.63727169593192e-17
relative error = 2.2269334225683743618806764323511e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 2.5325661764724770742858537375025
y[1] (numeric) = 2.5325661764724771307330250720917
absolute error = 5.64471713345892e-17
relative error = 2.2288527683494728016916843585921e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=10.31
NO POLE
x[1] = 0.992
y[1] (analytic) = 2.5337283038256043450853765003026
y[1] (numeric) = 2.5337283038256044016070586425561
absolute error = 5.65216821422535e-17
relative error = 2.2307712337156678857026126285793e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 2.5348919649071632521854901719835
y[1] (numeric) = 2.5348919649071633087817396288065
absolute error = 5.65962494568230e-17
relative error = 2.2326888183140284516125701677911e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 2.5360571608808149741168618816266
y[1] (numeric) = 2.5360571608808150307877352344914
absolute error = 5.66708733528648e-17
relative error = 2.2346055217928155827373640518160e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 2.5372238929117555816308812682357
y[1] (numeric) = 2.5372238929117556383764351732387
absolute error = 5.67455539050030e-17
relative error = 2.2365213438015107502985682098291e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 2.5383921621667172028958283318034
y[1] (numeric) = 2.5383921621667172597161195197214
absolute error = 5.68202911879180e-17
relative error = 2.2384362839907847792481973184110e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.997
y[1] (analytic) = 2.5395619698139691902290988292709
y[1] (numeric) = 2.5395619698139692471241841056181
absolute error = 5.68950852763472e-17
relative error = 2.2403503420125220209905351753224e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 2.5407333170233192883666539477067
y[1] (numeric) = 2.5407333170233193453365901927914
absolute error = 5.69699362450847e-17
relative error = 2.2422635175198050943025941548688e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 2.5419062049661148042708625242498
y[1] (numeric) = 2.5419062049661148613157066932312
absolute error = 5.70448441689814e-17
relative error = 2.2441758101669153982721803836911e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 2.5430806348152437784779056207571
y[1] (numeric) = 2.5430806348152438355977147437024
absolute error = 5.71198091229453e-17
relative error = 2.2460872196093414819715649878145e-15 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = sinh ( x ) ;
Iterations = 1000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Expected Time Remaining = 1 Minutes 33 Seconds
Optimized Time Remaining = 1 Minutes 33 Seconds
Time to Timeout = 14 Minutes 49 Seconds
Percent Done = 10.01 %
> quit
memory used=161.6MB, alloc=4.4MB, time=10.40