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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
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_abserr,
> glob_h,
> glob_not_yet_finished,
> glob_clock_sec,
> sec_in_min,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_initial_pass,
> years_in_century,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_small_float,
> glob_almost_1,
> centuries_in_millinium,
> hours_in_day,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_max_hours,
> glob_last_good_h,
> days_in_year,
> glob_iter,
> glob_warned,
> glob_dump_analytic,
> glob_hmin,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_relerr,
> glob_log10_relerr,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_percent_done,
> glob_max_minutes,
> glob_log10relerr,
> glob_orig_start_sec,
> glob_dump,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_done,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_max_rel_trunc_err,
> glob_hmin_init,
> glob_hmax,
> min_in_hour,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_tmp1_g,
> array_y,
> array_x,
> array_m1,
> array_fact_1,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_fact_2,
> array_real_pole,
> array_y_set_initial,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_abserr, glob_h, glob_not_yet_finished, glob_clock_sec, sec_in_min,
djd_debug, glob_curr_iter_when_opt, glob_start, glob_warned2,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_log10_abserr,
glob_look_poles, glob_initial_pass, years_in_century,
glob_reached_optimal_h, glob_current_iter, glob_small_float, glob_almost_1,
centuries_in_millinium, hours_in_day, glob_unchanged_h_cnt, glob_no_eqs,
glob_max_iter, glob_large_float, glob_not_yet_start_msg, glob_max_hours,
glob_last_good_h, days_in_year, glob_iter, glob_warned, glob_dump_analytic,
glob_hmin, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_max_sec,
glob_relerr, glob_log10_relerr, glob_disp_incr, glob_clock_start_sec,
glob_percent_done, glob_max_minutes, glob_log10relerr, glob_orig_start_sec,
glob_dump, glob_subiter_method, MAX_UNCHANGED, glob_smallish_float,
glob_optimal_start, glob_optimal_done, glob_display_flag, glob_max_opt_iter,
glob_log10normmin, glob_log10abserr, glob_max_rel_trunc_err, glob_hmin_init,
glob_hmax, min_in_hour, glob_html_log, array_const_1, array_const_0D0,
array_type_pole, array_1st_rel_error, array_pole, array_norms, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_tmp1_g,
array_y, array_x, array_m1, array_fact_1, array_y_higher_work,
array_complex_pole, array_y_higher, array_y_higher_work2, array_poles,
array_fact_2, array_real_pole, array_y_set_initial, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_abserr,
> glob_h,
> glob_not_yet_finished,
> glob_clock_sec,
> sec_in_min,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_initial_pass,
> years_in_century,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_small_float,
> glob_almost_1,
> centuries_in_millinium,
> hours_in_day,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_max_hours,
> glob_last_good_h,
> days_in_year,
> glob_iter,
> glob_warned,
> glob_dump_analytic,
> glob_hmin,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_relerr,
> glob_log10_relerr,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_percent_done,
> glob_max_minutes,
> glob_log10relerr,
> glob_orig_start_sec,
> glob_dump,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_done,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_max_rel_trunc_err,
> glob_hmin_init,
> glob_hmax,
> min_in_hour,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_tmp1_g,
> array_y,
> array_x,
> array_m1,
> array_fact_1,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_fact_2,
> array_real_pole,
> array_y_set_initial,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_abserr, glob_h, glob_not_yet_finished, glob_clock_sec, sec_in_min,
djd_debug, glob_curr_iter_when_opt, glob_start, glob_warned2,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_log10_abserr,
glob_look_poles, glob_initial_pass, years_in_century,
glob_reached_optimal_h, glob_current_iter, glob_small_float, glob_almost_1,
centuries_in_millinium, hours_in_day, glob_unchanged_h_cnt, glob_no_eqs,
glob_max_iter, glob_large_float, glob_not_yet_start_msg, glob_max_hours,
glob_last_good_h, days_in_year, glob_iter, glob_warned, glob_dump_analytic,
glob_hmin, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_max_sec,
glob_relerr, glob_log10_relerr, glob_disp_incr, glob_clock_start_sec,
glob_percent_done, glob_max_minutes, glob_log10relerr, glob_orig_start_sec,
glob_dump, glob_subiter_method, MAX_UNCHANGED, glob_smallish_float,
glob_optimal_start, glob_optimal_done, glob_display_flag, glob_max_opt_iter,
glob_log10normmin, glob_log10abserr, glob_max_rel_trunc_err, glob_hmin_init,
glob_hmax, min_in_hour, glob_html_log, array_const_1, array_const_0D0,
array_type_pole, array_1st_rel_error, array_pole, array_norms, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_tmp1_g,
array_y, array_x, array_m1, array_fact_1, array_y_higher_work,
array_complex_pole, array_y_higher, array_y_higher_work2, array_poles,
array_fact_2, array_real_pole, array_y_set_initial, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_abserr,
> glob_h,
> glob_not_yet_finished,
> glob_clock_sec,
> sec_in_min,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_initial_pass,
> years_in_century,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_small_float,
> glob_almost_1,
> centuries_in_millinium,
> hours_in_day,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_max_hours,
> glob_last_good_h,
> days_in_year,
> glob_iter,
> glob_warned,
> glob_dump_analytic,
> glob_hmin,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_relerr,
> glob_log10_relerr,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_percent_done,
> glob_max_minutes,
> glob_log10relerr,
> glob_orig_start_sec,
> glob_dump,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_done,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_max_rel_trunc_err,
> glob_hmin_init,
> glob_hmax,
> min_in_hour,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_tmp1_g,
> array_y,
> array_x,
> array_m1,
> array_fact_1,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_fact_2,
> array_real_pole,
> array_y_set_initial,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_abserr, glob_h, glob_not_yet_finished, glob_clock_sec, sec_in_min,
djd_debug, glob_curr_iter_when_opt, glob_start, glob_warned2,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_log10_abserr,
glob_look_poles, glob_initial_pass, years_in_century,
glob_reached_optimal_h, glob_current_iter, glob_small_float, glob_almost_1,
centuries_in_millinium, hours_in_day, glob_unchanged_h_cnt, glob_no_eqs,
glob_max_iter, glob_large_float, glob_not_yet_start_msg, glob_max_hours,
glob_last_good_h, days_in_year, glob_iter, glob_warned, glob_dump_analytic,
glob_hmin, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_max_sec,
glob_relerr, glob_log10_relerr, glob_disp_incr, glob_clock_start_sec,
glob_percent_done, glob_max_minutes, glob_log10relerr, glob_orig_start_sec,
glob_dump, glob_subiter_method, MAX_UNCHANGED, glob_smallish_float,
glob_optimal_start, glob_optimal_done, glob_display_flag, glob_max_opt_iter,
glob_log10normmin, glob_log10abserr, glob_max_rel_trunc_err, glob_hmin_init,
glob_hmax, min_in_hour, glob_html_log, array_const_1, array_const_0D0,
array_type_pole, array_1st_rel_error, array_pole, array_norms, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_tmp1_g,
array_y, array_x, array_m1, array_fact_1, array_y_higher_work,
array_complex_pole, array_y_higher, array_y_higher_work2, array_poles,
array_fact_2, array_real_pole, array_y_set_initial, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_abserr,
> glob_h,
> glob_not_yet_finished,
> glob_clock_sec,
> sec_in_min,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_initial_pass,
> years_in_century,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_small_float,
> glob_almost_1,
> centuries_in_millinium,
> hours_in_day,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_max_hours,
> glob_last_good_h,
> days_in_year,
> glob_iter,
> glob_warned,
> glob_dump_analytic,
> glob_hmin,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_relerr,
> glob_log10_relerr,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_percent_done,
> glob_max_minutes,
> glob_log10relerr,
> glob_orig_start_sec,
> glob_dump,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_done,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_max_rel_trunc_err,
> glob_hmin_init,
> glob_hmax,
> min_in_hour,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_tmp1_g,
> array_y,
> array_x,
> array_m1,
> array_fact_1,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_fact_2,
> array_real_pole,
> array_y_set_initial,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_abserr, glob_h, glob_not_yet_finished, glob_clock_sec, sec_in_min,
djd_debug, glob_curr_iter_when_opt, glob_start, glob_warned2,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_log10_abserr,
glob_look_poles, glob_initial_pass, years_in_century,
glob_reached_optimal_h, glob_current_iter, glob_small_float, glob_almost_1,
centuries_in_millinium, hours_in_day, glob_unchanged_h_cnt, glob_no_eqs,
glob_max_iter, glob_large_float, glob_not_yet_start_msg, glob_max_hours,
glob_last_good_h, days_in_year, glob_iter, glob_warned, glob_dump_analytic,
glob_hmin, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_max_sec,
glob_relerr, glob_log10_relerr, glob_disp_incr, glob_clock_start_sec,
glob_percent_done, glob_max_minutes, glob_log10relerr, glob_orig_start_sec,
glob_dump, glob_subiter_method, MAX_UNCHANGED, glob_smallish_float,
glob_optimal_start, glob_optimal_done, glob_display_flag, glob_max_opt_iter,
glob_log10normmin, glob_log10abserr, glob_max_rel_trunc_err, glob_hmin_init,
glob_hmax, min_in_hour, glob_html_log, array_const_1, array_const_0D0,
array_type_pole, array_1st_rel_error, array_pole, array_norms, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_tmp1_g,
array_y, array_x, array_m1, array_fact_1, array_y_higher_work,
array_complex_pole, array_y_higher, array_y_higher_work2, array_poles,
array_fact_2, array_real_pole, array_y_set_initial, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_abserr,
> glob_h,
> glob_not_yet_finished,
> glob_clock_sec,
> sec_in_min,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_initial_pass,
> years_in_century,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_small_float,
> glob_almost_1,
> centuries_in_millinium,
> hours_in_day,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_max_hours,
> glob_last_good_h,
> days_in_year,
> glob_iter,
> glob_warned,
> glob_dump_analytic,
> glob_hmin,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_relerr,
> glob_log10_relerr,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_percent_done,
> glob_max_minutes,
> glob_log10relerr,
> glob_orig_start_sec,
> glob_dump,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_done,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_max_rel_trunc_err,
> glob_hmin_init,
> glob_hmax,
> min_in_hour,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_tmp1_g,
> array_y,
> array_x,
> array_m1,
> array_fact_1,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_fact_2,
> array_real_pole,
> array_y_set_initial,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_abserr, glob_h, glob_not_yet_finished, glob_clock_sec, sec_in_min,
djd_debug, glob_curr_iter_when_opt, glob_start, glob_warned2,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_log10_abserr,
glob_look_poles, glob_initial_pass, years_in_century,
glob_reached_optimal_h, glob_current_iter, glob_small_float, glob_almost_1,
centuries_in_millinium, hours_in_day, glob_unchanged_h_cnt, glob_no_eqs,
glob_max_iter, glob_large_float, glob_not_yet_start_msg, glob_max_hours,
glob_last_good_h, days_in_year, glob_iter, glob_warned, glob_dump_analytic,
glob_hmin, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_max_sec,
glob_relerr, glob_log10_relerr, glob_disp_incr, glob_clock_start_sec,
glob_percent_done, glob_max_minutes, glob_log10relerr, glob_orig_start_sec,
glob_dump, glob_subiter_method, MAX_UNCHANGED, glob_smallish_float,
glob_optimal_start, glob_optimal_done, glob_display_flag, glob_max_opt_iter,
glob_log10normmin, glob_log10abserr, glob_max_rel_trunc_err, glob_hmin_init,
glob_hmax, min_in_hour, glob_html_log, array_const_1, array_const_0D0,
array_type_pole, array_1st_rel_error, array_pole, array_norms, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_tmp1_g,
array_y, array_x, array_m1, array_fact_1, array_y_higher_work,
array_complex_pole, array_y_higher, array_y_higher_work2, array_poles,
array_fact_2, array_real_pole, array_y_set_initial, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_abserr,
> glob_h,
> glob_not_yet_finished,
> glob_clock_sec,
> sec_in_min,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_initial_pass,
> years_in_century,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_small_float,
> glob_almost_1,
> centuries_in_millinium,
> hours_in_day,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_max_hours,
> glob_last_good_h,
> days_in_year,
> glob_iter,
> glob_warned,
> glob_dump_analytic,
> glob_hmin,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_relerr,
> glob_log10_relerr,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_percent_done,
> glob_max_minutes,
> glob_log10relerr,
> glob_orig_start_sec,
> glob_dump,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_done,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_max_rel_trunc_err,
> glob_hmin_init,
> glob_hmax,
> min_in_hour,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_tmp1_g,
> array_y,
> array_x,
> array_m1,
> array_fact_1,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_fact_2,
> array_real_pole,
> array_y_set_initial,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cosh $eq_no = 1
> array_tmp1_g[1] := sinh(array_x[1]);
> array_tmp1[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 cosh $eq_no = 1
> array_tmp1_g[2] := att(1,array_tmp1,array_x,1);
> array_tmp1[2] := att(1,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[3] := att(2,array_tmp1,array_x,1);
> array_tmp1[3] := att(2,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[4] := att(3,array_tmp1,array_x,1);
> array_tmp1[4] := att(3,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[5] := att(4,array_tmp1,array_x,1);
> array_tmp1[5] := att(4,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[kkk] := att(kkk-1,array_tmp1,array_x,1);
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,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 INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_abserr, glob_h, glob_not_yet_finished, glob_clock_sec, sec_in_min,
djd_debug, glob_curr_iter_when_opt, glob_start, glob_warned2,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_log10_abserr,
glob_look_poles, glob_initial_pass, years_in_century,
glob_reached_optimal_h, glob_current_iter, glob_small_float, glob_almost_1,
centuries_in_millinium, hours_in_day, glob_unchanged_h_cnt, glob_no_eqs,
glob_max_iter, glob_large_float, glob_not_yet_start_msg, glob_max_hours,
glob_last_good_h, days_in_year, glob_iter, glob_warned, glob_dump_analytic,
glob_hmin, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_max_sec,
glob_relerr, glob_log10_relerr, glob_disp_incr, glob_clock_start_sec,
glob_percent_done, glob_max_minutes, glob_log10relerr, glob_orig_start_sec,
glob_dump, glob_subiter_method, MAX_UNCHANGED, glob_smallish_float,
glob_optimal_start, glob_optimal_done, glob_display_flag, glob_max_opt_iter,
glob_log10normmin, glob_log10abserr, glob_max_rel_trunc_err, glob_hmin_init,
glob_hmax, min_in_hour, glob_html_log, array_const_1, array_const_0D0,
array_type_pole, array_1st_rel_error, array_pole, array_norms, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_tmp1_g,
array_y, array_x, array_m1, array_fact_1, array_y_higher_work,
array_complex_pole, array_y_higher, array_y_higher_work2, array_poles,
array_fact_2, array_real_pole, array_y_set_initial, glob_last;
array_tmp1_g[1] := sinh(array_x[1]);
array_tmp1[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_g[2] := att(1, array_tmp1, array_x, 1);
array_tmp1[2] := att(1, array_tmp1_g, 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_g[3] := att(2, array_tmp1, array_x, 1);
array_tmp1[3] := att(2, array_tmp1_g, 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_g[4] := att(3, array_tmp1, array_x, 1);
array_tmp1[4] := att(3, array_tmp1_g, 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_g[5] := att(4, array_tmp1, array_x, 1);
array_tmp1[5] := att(4, array_tmp1_g, 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_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, 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 + sinh(x);
> end;
exact_soln_y := proc(x) 1.0 + sinh(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
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_abserr,
> glob_h,
> glob_not_yet_finished,
> glob_clock_sec,
> sec_in_min,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_start,
> glob_warned2,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_initial_pass,
> years_in_century,
> glob_reached_optimal_h,
> glob_current_iter,
> glob_small_float,
> glob_almost_1,
> centuries_in_millinium,
> hours_in_day,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_iter,
> glob_large_float,
> glob_not_yet_start_msg,
> glob_max_hours,
> glob_last_good_h,
> days_in_year,
> glob_iter,
> glob_warned,
> glob_dump_analytic,
> glob_hmin,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_max_sec,
> glob_relerr,
> glob_log10_relerr,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_percent_done,
> glob_max_minutes,
> glob_log10relerr,
> glob_orig_start_sec,
> glob_dump,
> glob_subiter_method,
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_done,
> glob_display_flag,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10abserr,
> glob_max_rel_trunc_err,
> glob_hmin_init,
> glob_hmax,
> min_in_hour,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_tmp1_g,
> array_y,
> array_x,
> array_m1,
> array_fact_1,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_fact_2,
> array_real_pole,
> array_y_set_initial,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGL := 3;
> glob_abserr := 0.1e-10;
> glob_h := 0.1;
> glob_not_yet_finished := true;
> glob_clock_sec := 0.0;
> sec_in_min := 60.0;
> djd_debug := true;
> glob_curr_iter_when_opt := 0;
> glob_start := 0;
> glob_warned2 := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_initial_pass := true;
> years_in_century := 100.0;
> glob_reached_optimal_h := false;
> glob_current_iter := 0;
> glob_small_float := 0.1e-50;
> glob_almost_1 := 0.9990;
> centuries_in_millinium := 10.0;
> hours_in_day := 24.0;
> glob_unchanged_h_cnt := 0;
> glob_no_eqs := 0;
> glob_max_iter := 1000;
> glob_large_float := 9.0e100;
> glob_not_yet_start_msg := true;
> glob_max_hours := 0.0;
> glob_last_good_h := 0.1;
> days_in_year := 365.0;
> glob_iter := 0;
> glob_warned := false;
> glob_dump_analytic := false;
> glob_hmin := 0.00000000001;
> djd_debug2 := true;
> glob_optimal_expect_sec := 0.1;
> glob_normmax := 0.0;
> glob_max_sec := 10000.0;
> glob_relerr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_disp_incr := 0.1;
> glob_clock_start_sec := 0.0;
> glob_percent_done := 0.0;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> glob_orig_start_sec := 0.0;
> glob_dump := false;
> glob_subiter_method := 3;
> MAX_UNCHANGED := 10;
> glob_smallish_float := 0.1e-100;
> glob_optimal_start := 0.0;
> glob_optimal_done := false;
> glob_display_flag := true;
> glob_max_opt_iter := 10;
> glob_log10normmin := 0.1;
> glob_log10abserr := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_hmax := 1.0;
> min_in_hour := 60.0;
> glob_html_log := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/coshpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cosh ( 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 := 0.1;");
> omniout_str(ALWAYS,"x_end := 2.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> 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 + sinh(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_type_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 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_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[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
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #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_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #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 := 0.1;
> x_end := 2.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> 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 ) = cosh ( 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,"2012-06-17T19:43:19-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cosh")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cosh ( 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,"cosh diffeq.mxt")
> ;
> logitem_str(html_log_file,"cosh 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 INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL,
glob_abserr, glob_h, glob_not_yet_finished, glob_clock_sec, sec_in_min,
djd_debug, glob_curr_iter_when_opt, glob_start, glob_warned2,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_log10_abserr,
glob_look_poles, glob_initial_pass, years_in_century,
glob_reached_optimal_h, glob_current_iter, glob_small_float, glob_almost_1,
centuries_in_millinium, hours_in_day, glob_unchanged_h_cnt, glob_no_eqs,
glob_max_iter, glob_large_float, glob_not_yet_start_msg, glob_max_hours,
glob_last_good_h, days_in_year, glob_iter, glob_warned, glob_dump_analytic,
glob_hmin, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_max_sec,
glob_relerr, glob_log10_relerr, glob_disp_incr, glob_clock_start_sec,
glob_percent_done, glob_max_minutes, glob_log10relerr, glob_orig_start_sec,
glob_dump, glob_subiter_method, MAX_UNCHANGED, glob_smallish_float,
glob_optimal_start, glob_optimal_done, glob_display_flag, glob_max_opt_iter,
glob_log10normmin, glob_log10abserr, glob_max_rel_trunc_err, glob_hmin_init,
glob_hmax, min_in_hour, glob_html_log, array_const_1, array_const_0D0,
array_type_pole, array_1st_rel_error, array_pole, array_norms, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_tmp1_g,
array_y, array_x, array_m1, array_fact_1, array_y_higher_work,
array_complex_pole, array_y_higher, array_y_higher_work2, array_poles,
array_fact_2, array_real_pole, array_y_set_initial, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGL := 3;
glob_abserr := 0.1*10^(-10);
glob_h := 0.1;
glob_not_yet_finished := true;
glob_clock_sec := 0.;
sec_in_min := 60.0;
djd_debug := true;
glob_curr_iter_when_opt := 0;
glob_start := 0;
glob_warned2 := false;
glob_optimal_clock_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_initial_pass := true;
years_in_century := 100.0;
glob_reached_optimal_h := false;
glob_current_iter := 0;
glob_small_float := 0.1*10^(-50);
glob_almost_1 := 0.9990;
centuries_in_millinium := 10.0;
hours_in_day := 24.0;
glob_unchanged_h_cnt := 0;
glob_no_eqs := 0;
glob_max_iter := 1000;
glob_large_float := 0.90*10^101;
glob_not_yet_start_msg := true;
glob_max_hours := 0.;
glob_last_good_h := 0.1;
days_in_year := 365.0;
glob_iter := 0;
glob_warned := false;
glob_dump_analytic := false;
glob_hmin := 0.1*10^(-10);
djd_debug2 := true;
glob_optimal_expect_sec := 0.1;
glob_normmax := 0.;
glob_max_sec := 10000.0;
glob_relerr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_clock_start_sec := 0.;
glob_percent_done := 0.;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
glob_orig_start_sec := 0.;
glob_dump := false;
glob_subiter_method := 3;
MAX_UNCHANGED := 10;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_start := 0.;
glob_optimal_done := false;
glob_display_flag := true;
glob_max_opt_iter := 10;
glob_log10normmin := 0.1;
glob_log10abserr := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_hmax := 1.0;
min_in_hour := 60.0;
glob_html_log := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/coshpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh ( 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 := 0.1;");
omniout_str(ALWAYS, "x_end := 2.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
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\tsinh(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_type_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_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_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
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_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
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 := 0.1;
x_end := 2.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.001;
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 ) = cosh ( 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, "2012-06-17T19:43:19-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "cosh");
logitem_str(html_log_file, "diff ( y , x , 1 ) = cosh ( 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,
"cosh diffeq.mxt");
logitem_str(html_log_file,
"cosh 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/coshpostode.ode#################
diff ( y , x , 1 ) = cosh ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 2.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
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 + sinh(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y[1] (analytic) = 1.1001667500198440258237293835219
y[1] (numeric) = 1.1001667500198440258237293835219
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.1011718044387797160104557541879
y[1] (numeric) = 1.1011718044387797160153345428277
absolute error = 4.8787886398e-21
relative error = 4.4305426456923408076573865963412e-19 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.1021769600295282759608823997477
y[1] (numeric) = 1.1021769600295282759706888347998
absolute error = 9.8064350521e-21
relative error = 8.8973326495931080851182424632278e-19 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.1031822177972453801865379584404
y[1] (numeric) = 1.1031822177972453802013209026046
absolute error = 1.47829441642e-20
relative error = 1.3400274157534478580769748735792e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.1041875787471888801760100913961
y[1] (numeric) = 1.104187578747188880195818412349
absolute error = 1.98083209529e-20
relative error = 1.7939271672820771116854412522424e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.1051930438847198096528807427147
y[1] (numeric) = 1.1051930438847198096777633131582
absolute error = 2.48825704435e-20
relative error = 2.2514230053456113433592379475555e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.1061986142153033899368436431364
y[1] (numeric) = 1.1061986142153033899668493408467
absolute error = 3.00056977103e-20
relative error = 2.7125054510744382302774303321792e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.1072042907445100354090094185068
y[1] (numeric) = 1.1072042907445100354441871263831
absolute error = 3.51777078763e-20
relative error = 3.1771650607175381592361045728689e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.1082100744780163590824037684248
y[1] (numeric) = 1.1082100744780163591228023745383
absolute error = 4.03986061135e-20
relative error = 3.6453924254865082424276594809983e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.1092159664216061782786642856553
y[1] (numeric) = 1.1092159664216061783243326832983
absolute error = 4.56683976430e-20
relative error = 4.1171781713825170867321228957132e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.1102219675811715204119415930882
y[1] (numeric) = 1.1102219675811715204629286808227
absolute error = 5.09870877345e-20
relative error = 4.5925129589702689256226039608625e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.1112280789627136288810105822271
y[1] (numeric) = 1.1112280789627136289373652639337
absolute error = 5.63546817066e-20
relative error = 5.0713874832252989134445154852880e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.1122343015723439690705976454038
y[1] (numeric) = 1.1122343015723439691323688303308
absolute error = 6.17711849270e-20
relative error = 5.5537924733732163259323557564323e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.11324063641628523446292990313
y[1] (numeric) = 1.1132406364162852345301665059421
absolute error = 6.72366028121e-20
relative error = 6.0397186926760318942662254626599e-18 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.48
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.1142470845008723528605125382179
y[1] (numeric) = 1.1142470845008723529332634790453
absolute error = 7.27509408274e-20
relative error = 6.5291569382915484498789784194714e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.1152536468325534927211404595326
y[1] (numeric) = 1.1152536468325534927994546640198
absolute error = 7.83142044872e-20
relative error = 7.0220980410708540733846495880995e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.1162603244178910696061506304702
y[1] (numeric) = 1.116260324417891069690077029825
absolute error = 8.39263993548e-20
relative error = 7.5185328654018094967319122222086e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 1.117267118263562752742921510499
y[1] (numeric) = 1.1172671182635627528325090415413
absolute error = 8.95875310423e-20
relative error = 8.0184523090176852736280597773156e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.1182740293763624717026261723463
y[1] (numeric) = 1.1182740293763624717979237775573
absolute error = 9.52976052110e-20
relative error = 8.5218473028605911455205847369478e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.1192810587632014231942457726687
y[1] (numeric) = 1.1192810587632014232953024002396
absolute error = 1.010566275709e-19
relative error = 9.0287088108653372618239629149820e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.1202882074311090779758501703025
y[1] (numeric) = 1.1202882074311090780827147741834
absolute error = 1.068646038809e-19
relative error = 9.5390278298070475961958498867528e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 1.1212954763872341878841526034584
y[1] (numeric) = 1.1212954763872341879968741434076
absolute error = 1.127215399492e-19
relative error = 1.0052795389167532806054197093438e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.1223028666388457929833454555008
y[1] (numeric) = 1.1223028666388457931019728971334
absolute error = 1.186274416326e-19
relative error = 1.0570002550904470681919695942222e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.1233103791933342288342242582293
y[1] (numeric) = 1.1233103791933342289588065730662
absolute error = 1.245823148369e-19
relative error = 1.1090640409319853341430277019107e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.1243180150582121338846072018716
y[1] (numeric) = 1.1243180150582121340151933673888
absolute error = 1.305861655172e-19
relative error = 1.1614700090920346520710855413914e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.1253257752411154569820575422914
y[1] (numeric) = 1.1253257752411154571186965419686
absolute error = 1.366389996772e-19
relative error = 1.2142172754189634079623278988132e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 1.1263336607498044650099164182164
y[1] (numeric) = 1.1263336607498044651526572415863
absolute error = 1.427408233699e-19
relative error = 1.2673049589486379047316249674926e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.127341672592164750647653714605
y[1] (numeric) = 1.1273416725921647507965453573019
absolute error = 1.488916426969e-19
relative error = 1.3207321818818642560066689521912e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.1283498117762082402565447325845
y[1] (numeric) = 1.1283498117762082404116361963936
absolute error = 1.550914638091e-19
relative error = 1.3744980695743682560688281332535e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.1293580793100742018916805517234
y[1] (numeric) = 1.1293580793100742020530208446297
absolute error = 1.613402929063e-19
relative error = 1.4286017505170983528133533583363e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.1303664762020302534413200967308
y[1] (numeric) = 1.1303664762020302536089582329683
absolute error = 1.676381362375e-19
relative error = 1.4830423563228361143363250928496e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.1313750034604733708945920480198
y[1] (numeric) = 1.1313750034604733710685770481201
absolute error = 1.739850001003e-19
relative error = 1.5378190217049326935232860442466e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.1323836620939308967385548639201
y[1] (numeric) = 1.1323836620939308969189357547618
absolute error = 1.803808908417e-19
relative error = 1.5929308844685314557102215626528e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.1333924531110615484856233116846
y[1] (numeric) = 1.1333924531110615486724491265422
absolute error = 1.868258148576e-19
relative error = 1.6483770854903766404356144870583e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.1344013775206564273323700348
y[1] (numeric) = 1.1344013775206564275256898133929
absolute error = 1.933197785929e-19
relative error = 1.7041567687040279616940951019645e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.1354104363316400269507108154875
y[1] (numeric) = 1.1354104363316400271505736040291
absolute error = 1.998627885416e-19
relative error = 1.7602690810851630348308808123008e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.1364196305530712424124823236624
y[1] (numeric) = 1.136419630553071242618937174909
absolute error = 2.064548512466e-19
relative error = 1.8167131726343271529936615040548e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=7.6MB, alloc=4.1MB, time=1.06
x[1] = 0.137
y[1] (analytic) = 1.1374289611941443792484212770148
y[1] (numeric) = 1.1374289611941443794615172503149
absolute error = 2.130959733001e-19
relative error = 1.8734881963650587907682625583811e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.1384384292641901626425540712747
y[1] (numeric) = 1.1384384292641901628623402326178
absolute error = 2.197861613431e-19
relative error = 1.9305933082841814714318428588564e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.1394480357726767467630060751348
y[1] (numeric) = 1.1394480357726767469895314972007
absolute error = 2.265254220659e-19
relative error = 1.9880276673809852587908607698953e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.140457781729210724230239920725
y[1] (numeric) = 1.1404577817292107244635536829327
absolute error = 2.333137622077e-19
relative error = 2.0457904356085827563191200323233e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.1414676681435381357237322579606
y[1] (numeric) = 1.1414676681435381359638834465174
absolute error = 2.401511885568e-19
relative error = 2.1038807778706289868908089458882e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 1.1424776960255454797280985795249
y[1] (numeric) = 1.1424776960255454799751362874757
absolute error = 2.470377079508e-19
relative error = 2.1622978620081201688509467991919e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 1.1434878663852607224196758626961
y[1] (numeric) = 1.1434878663852607226736491899721
absolute error = 2.539733272760e-19
relative error = 2.2210408587792747021795501510905e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.1444981802328543076945729146838
y[1] (numeric) = 1.1444981802328543079555309681519
absolute error = 2.609580534681e-19
relative error = 2.2801089418508877059787952938042e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.1455086385786401673391984496111
y[1] (numeric) = 1.145508638578640167607190343123
absolute error = 2.679918935119e-19
relative error = 2.3395012877810098044394897157048e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.1465192424330767313442770677541
y[1] (numeric) = 1.1465192424330767316193519221953
absolute error = 2.750748544412e-19
relative error = 2.3992170760034700847515677466558e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.147529992806767938363363451138
y[1] (numeric) = 1.1475299928067679386455703944769
absolute error = 2.822069433389e-19
relative error = 2.4592554888142318108410334039166e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.1485408907104642463168652340899
y[1] (numeric) = 1.148540890710464246606253401427
absolute error = 2.893881673371e-19
relative error = 2.5196157113578282116033573008008e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.1495519371550636431425851528534
y[1] (numeric) = 1.1495519371550636434392036864706
absolute error = 2.966185336172e-19
relative error = 2.5802969316138777968013794987584e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.1505631331516126576937932248942
y[1] (numeric) = 1.1505631331516126579976912743035
absolute error = 3.038980494093e-19
relative error = 2.6412983403775946807198346009482e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.1515744797113073707858398560492
y[1] (numeric) = 1.1515744797113073710970665780423
absolute error = 3.112267219931e-19
relative error = 2.7026191312534350559470921357823e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.1525859778454944263923209222205
y[1] (numeric) = 1.1525859778454944267109254809177
absolute error = 3.186045586972e-19
relative error = 2.7642585006349030434244087384982e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.153597628565672042991806021861
y[1] (numeric) = 1.1535976285656720433178375887604
absolute error = 3.260315668994e-19
relative error = 2.8262156476931389985781175469135e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.1546094328834910250661412460648
y[1] (numeric) = 1.1546094328834910253996490000915
absolute error = 3.335077540267e-19
relative error = 2.8884897743629771494496039100947e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.1556213918107557747513379646497
y[1] (numeric) = 1.1556213918107557750923710922052
absolute error = 3.410331275555e-19
relative error = 2.9510800853308147002484577380229e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 1.1566335063594253036420592792055
y[1] (numeric) = 1.1566335063594253039906669742165
absolute error = 3.486076950110e-19
relative error = 3.0139857880156354756072827340810e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.1576457775416142447507159476769
y[1] (numeric) = 1.1576457775416142451069474116446
absolute error = 3.562314639677e-19
relative error = 3.0772060925596425738406226436621e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.1586582063695938646221837396634
y[1] (numeric) = 1.1586582063695938649860881817129
absolute error = 3.639044420495e-19
relative error = 3.1407402118154952137289874582615e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 1.1596707938557930756051543372368
y[1] (numeric) = 1.1596707938557930759767809741662
absolute error = 3.716266369294e-19
relative error = 3.2045873613301704719244812271428e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.1606835410127994482811320527117
y[1] (numeric) = 1.1606835410127994486605301090412
absolute error = 3.793980563295e-19
relative error = 3.2687467593315014061268733427700e-17 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=1.66
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.1616964488533602240520887924501
y[1] (numeric) = 1.1616964488533602244393075004714
absolute error = 3.872187080213e-19
relative error = 3.3332176267173751909845635003442e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.1627095183903833278877898544397
y[1] (numeric) = 1.1627095183903833282828784542651
absolute error = 3.950885998254e-19
relative error = 3.3979991870398344577784603111806e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.1637227506369383812338033070557
y[1] (numeric) = 1.1637227506369383816368110466673
absolute error = 4.030077396116e-19
relative error = 3.4630906664927059618094111040764e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 1.1647361466062577150812058570999
y[1] (numeric) = 1.1647361466062577154921819923992
absolute error = 4.109761352993e-19
relative error = 3.5284912939018764945886042437526e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.1657497073117373831989982769083
y[1] (numeric) = 1.165749707311737383617992071765
absolute error = 4.189937948567e-19
relative error = 3.5942003007053326272592980252235e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.1667634337669381755302436230255
y[1] (numeric) = 1.1667634337669381759573043493269
absolute error = 4.270607263014e-19
relative error = 3.6602169209453103529044843848081e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.1677773269855866317529416426697
y[1] (numeric) = 1.1677773269855866321881185803701
absolute error = 4.351769377004e-19
relative error = 3.7265403912553544541858538355636e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.168791387981576055006652928947
y[1] (numeric) = 1.168791387981576055449995366117
absolute error = 4.433424371700e-19
relative error = 3.7931699508465963769787929896347e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 1.1698056177689675257858865515234
y[1] (numeric) = 1.1698056177689675262374437843991
absolute error = 4.515572328757e-19
relative error = 3.8601048414941101541677349718792e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.1708200173619909160012650562269
y[1] (numeric) = 1.1708200173619909164610863892591
absolute error = 4.598213330322e-19
relative error = 3.9273443075241999698976455485029e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.1718345877750459032094808948285
y[1] (numeric) = 1.1718345877750459036776156407321
absolute error = 4.681347459036e-19
relative error = 3.9948875958034670426485288977834e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.1728493300227029850130585150442
y[1] (numeric) = 1.1728493300227029854895559948475
absolute error = 4.764974798033e-19
relative error = 4.0627339557253818884742192063027e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.1738642451197044936309365106035
y[1] (numeric) = 1.1738642451197044941158460536977
absolute error = 4.849095430942e-19
relative error = 4.1308826391994883406861060362475e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.1748793340809656106408844020522
y[1] (numeric) = 1.1748793340809656111342553462404
absolute error = 4.933709441882e-19
relative error = 4.1993329006347118600485607077974e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.1758945979215753818947687907895
y[1] (numeric) = 1.1758945979215753823966504823363
absolute error = 5.018816915468e-19
relative error = 4.2680839969321152179495342387046e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 1.1769100376567977326076838016915
y[1] (numeric) = 1.1769100376567977331181255953722
absolute error = 5.104417936807e-19
relative error = 4.3371351874692011338987561682527e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.1779256543020724826219609035351
y[1] (numeric) = 1.1779256543020724831410121626851
absolute error = 5.190512591500e-19
relative error = 4.4064857340893960313265766451738e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.1789414488730163618470733713173
y[1] (numeric) = 1.1789414488730163623747834678814
absolute error = 5.277100965641e-19
relative error = 4.4761349010890496688301421395383e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.1799574223854240258764508304587
y[1] (numeric) = 1.1799574223854240264128691450407
absolute error = 5.364183145820e-19
relative error = 4.5460819552078979938476838857042e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 1.1809735758552690717822194997908
y[1] (numeric) = 1.1809735758552690723273954217027
absolute error = 5.451759219119e-19
relative error = 4.6163261656136539763742280809064e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.1819899102987050540888839281515
y[1] (numeric) = 1.1819899102987050546428668554627
absolute error = 5.539829273112e-19
relative error = 4.6868668038900680614410851251606e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.1830064267320665009269661983549
y[1] (numeric) = 1.183006426732066501489805537942
absolute error = 5.628393395871e-19
relative error = 4.7577031440301279537602768169712e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.1840231261718699303676187522608
y[1] (numeric) = 1.1840231261718699309393639198566
absolute error = 5.717451675958e-19
relative error = 4.8288344624174752454856619066018e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.1850400096348148669392271716391
memory used=15.2MB, alloc=4.2MB, time=2.27
y[1] (numeric) = 1.1850400096348148675199275918826
absolute error = 5.807004202435e-19
relative error = 4.9002600378231129208412306557260e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.1860570781377848583270194315195
y[1] (numeric) = 1.1860570781377848589167245380046
absolute error = 5.897051064851e-19
relative error = 4.9719791513827436195459678974391e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.1870743326978484922566983257171
y[1] (numeric) = 1.1870743326978484928554575610426
absolute error = 5.987592353255e-19
relative error = 5.0439910865961327392787592411705e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.1880917743322604135631139482542
y[1] (numeric) = 1.1880917743322604141709767640729
absolute error = 6.078628158187e-19
relative error = 5.1162951293079634304623933165178e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.1891094040584623414449932994332
y[1] (numeric) = 1.1891094040584623420620091565016
absolute error = 6.170158570684e-19
relative error = 5.1888905677014100108069913537141e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.190127222894084086906744271377
y[1] (numeric) = 1.1901272228940840875329626396044
absolute error = 6.262183682274e-19
relative error = 5.2617766922816670019620445510682e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.191145231856944570388351454923
y[1] (numeric) = 1.1911452318569445710238218134215
absolute error = 6.354703584985e-19
relative error = 5.3349527958721610902366921026895e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 1.1921634319650528395843813978548
y[1] (numeric) = 1.1921634319650528402291532349885
absolute error = 6.447718371337e-19
relative error = 5.4084181735965282128427378638348e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.1931818242366090874531151335586
y[1] (numeric) = 1.1931818242366090881072379469928
absolute error = 6.541228134342e-19
relative error = 5.4821721228673931398635176774722e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 1.1942004096900056704168259893228
y[1] (numeric) = 1.194200409690005671080349286074
absolute error = 6.635232967512e-19
relative error = 5.5562139433819109276636063441826e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.1952191893438281267542208746443
y[1] (numeric) = 1.1952191893438281274271941711294
absolute error = 6.729732964851e-19
relative error = 5.6305429371039498674969315867600e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 1.1962381642168561951860634420663
y[1] (numeric) = 1.1962381642168561958685362641522
absolute error = 6.824728220859e-19
relative error = 5.7051584082564022381848524732940e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.197257335328064833654997706256
y[1] (numeric) = 1.1972573353280648343470195893092
absolute error = 6.920218830532e-19
relative error = 5.7800596633101986283008887461263e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.198276703696625238300590901232
y[1] (numeric) = 1.1982767036966252390022113901679
absolute error = 7.016204889359e-19
relative error = 5.8552460109708799473328544469307e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.1992962703419058626306145508665
y[1] (numeric) = 1.1992962703419058633418832001994
absolute error = 7.112686493329e-19
relative error = 5.9307167621735813198278323653276e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.2003160362834734368895829240317
y[1] (numeric) = 1.2003160362834734376105492979238
absolute error = 7.209663738921e-19
relative error = 6.0064712300638837393949389316804e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.2013360025410939876255682430103
y[1] (numeric) = 1.2013360025410939883562819153216
absolute error = 7.307136723113e-19
relative error = 6.0825087299945840601885996946493e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.2023561701347338574563122120732
y[1] (numeric) = 1.2023561701347338581968227664109
absolute error = 7.405105543377e-19
relative error = 6.1588285795108426715773615572181e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.203376540084560725035653632419
y[1] (numeric) = 1.2033765400845607257860106621874
absolute error = 7.503570297684e-19
relative error = 6.2354300983437216666820826205956e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.2043971134109446252212920699892
y[1] (numeric) = 1.2043971134109446259815451784389
absolute error = 7.602531084497e-19
relative error = 6.3123126083937973212859855003220e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.2054178911344589694449077440064
y[1] (numeric) = 1.2054178911344589702151065442843
absolute error = 7.701988002779e-19
relative error = 6.3894754337273045484335454439216e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 1.2064388742758815662856580064423
y[1] (numeric) = 1.2064388742758815670658521216406
absolute error = 7.801941151983e-19
relative error = 6.4669179005573858527319546922879e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.2074600638561956422480709859943
y[1] (numeric) = 1.2074600638561956430383100492009
absolute error = 7.902390632066e-19
relative error = 6.5446393372453166754263544070712e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.208481460896590862745357174553
y[1] (numeric) = 1.2084814608965908635456908289005
absolute error = 8.003336543475e-19
relative error = 6.6226390742785597378891295096897e-17 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=2.88
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.2095030664184643532891599395536
y[1] (numeric) = 1.2095030664184643540996378382693
absolute error = 8.104778987157e-19
relative error = 6.7009164442687781774538871552499e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 1.2105248814434217208867661520495
y[1] (numeric) = 1.210524881443421721707437958505
absolute error = 8.206718064555e-19
relative error = 6.7794707819382982175740753339038e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.2115469069932780756467983278028
y[1] (numeric) = 1.2115469069932780764777137155635
absolute error = 8.309153877607e-19
relative error = 6.8583014241091211694738921170270e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.2125691440900590525944098871684
y[1] (numeric) = 1.2125691440900590534356185400434
absolute error = 8.412086528750e-19
relative error = 6.9374077096961190975214297322054e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.2135915937560018336970053490536
y[1] (numeric) = 1.2135915937560018345485569611451
absolute error = 8.515516120915e-19
relative error = 7.0167889796928534463630414795753e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.2146142570135561701015074847568
y[1] (numeric) = 1.2146142570135561709634517605101
absolute error = 8.619442757533e-19
relative error = 7.0964445771665262037147405332397e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.2156371348853854045841936690395
y[1] (numeric) = 1.2156371348853854054565803232926
absolute error = 8.723866542531e-19
relative error = 7.1763738472447349060741952705861e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.2166602283943674942141238783517
y[1] (numeric) = 1.2166602283943674950970026363848
absolute error = 8.828787580331e-19
relative error = 7.2565761371047646773541012903899e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.2176835385635960332311829997242
y[1] (numeric) = 1.2176835385635960341246035973096
absolute error = 8.934205975854e-19
relative error = 7.3370507959670448265329835845184e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.2187070664163812761397603284558
y[1] (numeric) = 1.2187070664163812770437725119079
absolute error = 9.040121834521e-19
relative error = 7.4177971750861811661078091316165e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 1.2197308129762511610190893483606
y[1] (numeric) = 1.2197308129762511619337428745852
absolute error = 9.146535262246e-19
relative error = 7.4988146277354789930536807226444e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.2207547792669523330512711049985
y[1] (numeric) = 1.2207547792669523339766157415427
absolute error = 9.253446365442e-19
relative error = 7.5801025092021973975828926116701e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.2217789663124511682680046999996
y[1] (numeric) = 1.2217789663124511692040902251018
absolute error = 9.360855251022e-19
relative error = 7.6616601767787393115859513719530e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 1.2228033751369347975170486532981
y[1] (numeric) = 1.2228033751369347984639248559373
absolute error = 9.468762026392e-19
relative error = 7.7434869897473477099153789464918e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.2238280067648121306494370998203
y[1] (numeric) = 1.2238280067648121316071537797664
absolute error = 9.577166799461e-19
relative error = 7.8255823093787737035913832711884e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.2248528622207148809284750079315
y[1] (numeric) = 1.2248528622207148818970819757948
absolute error = 9.686069678633e-19
relative error = 7.9079454989162598297605380635486e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.2258779425294985896615368287195
y[1] (numeric) = 1.2258779425294985906410839060007
absolute error = 9.795470772812e-19
relative error = 7.9905759235702124395400373512164e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.2269032487162436510556932080006
y[1] (numeric) = 1.2269032487162436520462302271404
absolute error = 9.905370191398e-19
relative error = 8.0734729505055693333941774001208e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 1.2279287818062563372981906167592
y[1] (numeric) = 1.2279287818062563382997674211882
absolute error = 1.0015768044290e-18
relative error = 8.1566359488349353831275604542610e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.228954542825069823862808980586
y[1] (numeric) = 1.2289545428250698248754754247748
absolute error = 1.0126664441888e-18
relative error = 8.2400642896109428333537801335042e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.2299805327984452150431226145598
y[1] (numeric) = 1.2299805327984452160669285640683
absolute error = 1.0238059495085e-18
relative error = 8.3237573458105235896998286501716e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.2310067527523725697136899969154
y[1] (numeric) = 1.2310067527523725707486853284434
absolute error = 1.0349953315280e-18
relative error = 8.4077144923363233039211533859346e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.2320332037130719273201981427777
y[1] (numeric) = 1.2320332037130719283664327442141
absolute error = 1.0462346014364e-18
relative error = 8.4919351059961973015829837874583e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.2330598867069943340995875681872
y[1] (numeric) = 1.2330598867069943351571113386603
absolute error = 1.0575237704731e-18
relative error = 8.5764185655030875502204153073829e-17 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.2MB, time=3.48
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.2340868027608228695311840646311
y[1] (numeric) = 1.2340868027608228706000469145584
absolute error = 1.0688628499273e-18
relative error = 8.6611642514619390287603267572311e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.2351139529014736730198637352953
y[1] (numeric) = 1.2351139529014736741001155864332
absolute error = 1.0802518511379e-18
relative error = 8.7461715463599237289168749829241e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.236141338156096970812277976288
y[1] (numeric) = 1.236141338156096971903968761782
absolute error = 1.0916907854940e-18
relative error = 8.8314398345615709794457609305690e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.2371689595520781031471653191461
y[1] (numeric) = 1.2371689595520781042503449835807
absolute error = 1.1031796644346e-18
relative error = 8.9169685022974593912589419907179e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.238196818117038551640777285022
y[1] (numeric) = 1.2381968181170385527554957844705
absolute error = 1.1147184994485e-18
relative error = 9.0027569376545840608378529969607e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.2392249148788369669084456360611
y[1] (numeric) = 1.2392249148788369680347529381356
absolute error = 1.1263073020745e-18
relative error = 9.0888045305691962496574116666642e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.240253250865570196423318645624
y[1] (numeric) = 1.2402532508655701975612647295255
absolute error = 1.1379460839015e-18
relative error = 9.1751106728188760261039252927719e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.2412818271055743126132942461751
y[1] (numeric) = 1.2412818271055743137629291027434
absolute error = 1.1496348565683e-18
relative error = 9.2616747580122310561910453069281e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.2423106446274256411971781518561
y[1] (numeric) = 1.2423106446274256423585517836196
absolute error = 1.1613736317635e-18
relative error = 9.3484961815794550892080570457587e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 1.2433397044599417897610952919879
y[1] (numeric) = 1.243339704459941790934257713214
absolute error = 1.1731624212261e-18
relative error = 9.4355743407685668584448570912845e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.2443690076321826765761831319997
y[1] (numeric) = 1.2443690076321826777611843687445
absolute error = 1.1850012367448e-18
relative error = 9.5229086346312240887950588113137e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.2453985551734515596585956995622
y[1] (numeric) = 1.2453985551734515608554857897205
absolute error = 1.1968900901583e-18
relative error = 9.6104984640166408835441239754415e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.2464283481132960660728473760157
y[1] (numeric) = 1.2464283481132960672816763693714
absolute error = 1.2088289933557e-18
relative error = 9.6983432315663409995223469441024e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.2474583874815092214795257565236
y[1] (numeric) = 1.2474583874815092227003437147992
absolute error = 1.2208179582756e-18
relative error = 9.7864423416985193326488725364634e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.2484886743081304799284031267476
y[1] (numeric) = 1.2484886743081304811612601236548
absolute error = 1.2328569969072e-18
relative error = 9.8747952006085035703269903777796e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 1.2495192096234467538979763492446
y[1] (numeric) = 1.2495192096234467551429224705341
absolute error = 1.2449461212895e-18
relative error = 9.9634012162540110689433085182849e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.2505499944579934445824651992088
y[1] (numeric) = 1.2505499944579934458395505427203
absolute error = 1.2570853435115e-18
relative error = 1.0052259798348478428857233952587e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.2515810298425554724272994366444
y[1] (numeric) = 1.251581029842555473696574112357
absolute error = 1.2692746757126e-18
relative error = 1.0141370358356025310651403385415e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.2526123168081683079141251505421
y[1] (numeric) = 1.2526123168081683091956392806241
absolute error = 1.2815141300820e-18
relative error = 1.0230732309478463071990440762671e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.2536438563861190025963611601497
y[1] (numeric) = 1.253643856386119003890164879009
absolute error = 1.2938037188593e-18
relative error = 1.0320345066651942859610740504114e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.2546756496079472203863365089824
y[1] (numeric) = 1.2546756496079472216924799633163
absolute error = 1.3061434543339e-18
relative error = 1.0410208046534059221600581670677e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.2557076975054462690950403387926
y[1] (numeric) = 1.2557076975054462704135736876383
absolute error = 1.3185333488457e-18
relative error = 1.0500320667501373207167565308306e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.256740001110664132225515683338
y[1] (numeric) = 1.2567400011106641335564890981225
absolute error = 1.3309734147845e-18
relative error = 1.0590682349636606599984700771925e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.2577725614559045010209289754259
y[1] (numeric) = 1.2577725614559045023643926400163
absolute error = 1.3434636645904e-18
relative error = 1.0681292514723852896816563788691e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.2MB, time=4.09
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.2588053795737278067683473153903
y[1] (numeric) = 1.2588053795737278081243514261439
absolute error = 1.3560041107536e-18
relative error = 1.0772150586239048530454924208882e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.2598384564969522533592558048642
y[1] (numeric) = 1.2598384564969522547278505706788
absolute error = 1.3685947658146e-18
relative error = 1.0863255989343669040435476201380e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.2608717932586548501078475064515
y[1] (numeric) = 1.2608717932586548514890831488156
absolute error = 1.3812356423641e-18
relative error = 1.0954608150876079968540420028195e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.2619053908921724448281188476736
y[1] (numeric) = 1.2619053908921724462220456007165
absolute error = 1.3939267530429e-18
relative error = 1.1046206499342933261743940280927e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.2629392504311027571708035463726
y[1] (numeric) = 1.2629392504311027585774716569148
absolute error = 1.4066681105422e-18
relative error = 1.1138050464913776125865215469212e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.2639733729093054122211783945914
y[1] (numeric) = 1.2639733729093054136406381221946
absolute error = 1.4194597276032e-18
relative error = 1.1230139479410151206392362765056e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.265007759360902974358774498822
y[1] (numeric) = 1.2650077593609029757910761158395
absolute error = 1.4323016170175e-18
relative error = 1.1322472976301077237705776900306e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.2660424108202819813800278364195
y[1] (numeric) = 1.2660424108202819828252216280468
absolute error = 1.4451937916273e-18
relative error = 1.1415050390696975031007234937937e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.26707732832209397888490325092
y[1] (numeric) = 1.2670773283220939803430395152445
absolute error = 1.4581362643245e-18
relative error = 1.1507871159334944701808272925329e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.2681125129012565549285262729694
y[1] (numeric) = 1.2681125129012565563996553210211
absolute error = 1.4711290480517e-18
relative error = 1.1600934720579100744477280340526e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.2691479655929543749388574185849
y[1] (numeric) = 1.2691479655929543764230295743865
absolute error = 1.4841721558016e-18
relative error = 1.1694240514408301419286728470510e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.2701836874326402169014438825068
y[1] (numeric) = 1.2701836874326402183987094831242
absolute error = 1.4972656006174e-18
relative error = 1.1787787982411813835947272164921e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.2712196794560360068122838114804
y[1] (numeric) = 1.2712196794560360083226932070728
absolute error = 1.5104093955924e-18
relative error = 1.1881576567778709841224694076895e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.2722559426991338543998386104168
y[1] (numeric) = 1.2722559426991338559234421642874
absolute error = 1.5236035538706e-18
relative error = 1.1975605715295176524703507292065e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.2732924781981970891172290035342
y[1] (numeric) = 1.2732924781981970906540770921801
absolute error = 1.5368480886459e-18
relative error = 1.2069874871330847471238290839372e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.2743292869897612964056508427576
y[1] (numeric) = 1.2743292869897612979557938559207
absolute error = 1.5501430131631e-18
relative error = 1.2164383483839328505442272909388e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.275366370110635354230046926884
y[1] (numeric) = 1.275366370110635355793535267601
absolute error = 1.5634883407170e-18
relative error = 1.2259131002343825875699655292910e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 1.2764037285979024698880713672675
y[1] (numeric) = 1.2764037285979024714649554519204
absolute error = 1.5768840846529e-18
relative error = 1.2354116877933815471743484788447e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.2774413634889212170933833090769
y[1] (numeric) = 1.2774413634889212186837135674435
absolute error = 1.5903302583666e-18
relative error = 1.2449340563257816836327040155500e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.2784792758213265733343070915056
y[1] (numeric) = 1.2784792758213265749381339668099
absolute error = 1.6038268753043e-18
relative error = 1.2544801512515422794449816231416e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.2795174666330309575088962056802
y[1] (numeric) = 1.2795174666330309591262701546428
absolute error = 1.6173739489626e-18
relative error = 1.2640499181450152005800123682430e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 1.2805559369622252678374386854187
y[1] (numeric) = 1.2805559369622252694684101783072
absolute error = 1.6309714928885e-18
relative error = 1.2736433027342338850375621520646e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.2815946878473799200534418434292
y[1] (numeric) = 1.2815946878473799216980613641088
absolute error = 1.6446195206796e-18
relative error = 1.2832602509003620980088312772560e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.3MB, time=4.70
x[1] = 0.279
y[1] (analytic) = 1.2826337203272458858741345440218
y[1] (numeric) = 1.2826337203272458875324525900057
absolute error = 1.6583180459839e-18
relative error = 1.2929007086768337590888793926799e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.283673035440855731751525482921
y[1] (numeric) = 1.283673035440855733423592565421
absolute error = 1.6720670825000e-18
relative error = 1.3025646222488088022390000774912e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.2847126342275246579050562253248
y[1] (numeric) = 1.2847126342275246595909228693016
absolute error = 1.6858666439768e-18
relative error = 1.3122519379522427322312523505005e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.2857525177268515376368880349488
y[1] (numeric) = 1.2857525177268515393366047791628
absolute error = 1.6997167442140e-18
relative error = 1.3219626022735831438695011579303e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.2867926869787199569308618094302
y[1] (numeric) = 1.2867926869787199586444792064918
absolute error = 1.7136173970616e-18
relative error = 1.3316965618486908297071814109743e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.2878331430232992543361707211367
y[1] (numeric) = 1.2878331430232992560637393375571
absolute error = 1.7275686164204e-18
relative error = 1.3414537634625428548897602144592e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.2888738869010455611367854471412
y[1] (numeric) = 1.2888738869010455628783558633827
absolute error = 1.7415704162415e-18
relative error = 1.3512341540481614377579877418223e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.2899149196527028418076721578725
y[1] (numeric) = 1.2899149196527028435632949683992
absolute error = 1.7556228105267e-18
relative error = 1.3610376806862459724824410559672e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.2909562423193039347588437207484
y[1] (numeric) = 1.2909562423193039365285695340769
absolute error = 1.7697258133285e-18
relative error = 1.3708642906044972188837311814903e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 1.2919978559421715933682848629279
y[1] (numeric) = 1.2919978559421715951521643016777
absolute error = 1.7838794387498e-18
relative error = 1.3807139311767127937510763914713e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.2930397615629195273047923261949
y[1] (numeric) = 1.2930397615629195291028760271392
absolute error = 1.7980837009443e-18
relative error = 1.3905865499224286240964746968103e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.2940819602234534441417713369004
y[1] (numeric) = 1.2940819602234534459541099510166
absolute error = 1.8123386141162e-18
relative error = 1.4004820945060214366358586842542e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 1.2951244529659720912630300048461
y[1] (numeric) = 1.2951244529659720930896741973665
absolute error = 1.8266441925204e-18
relative error = 1.4104005127362018698059152192777e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.2961672408329682980616135569912
y[1] (numeric) = 1.2961672408329682999026140074537
absolute error = 1.8410004504625e-18
relative error = 1.4203417525653559549150355080349e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.2972103248672300184327206049028
y[1] (numeric) = 1.2972103248672300202881280072016
absolute error = 1.8554074022988e-18
relative error = 1.4303057620888899952813090911117e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 1.2982537061118413735617439389537
y[1] (numeric) = 1.2982537061118413754316090013899
absolute error = 1.8698650624362e-18
relative error = 1.4402924895445017968149587536175e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.2992973856101836950084786373948
y[1] (numeric) = 1.2992973856101836968928520827272
absolute error = 1.8843734453324e-18
relative error = 1.4503018833116865219913605056228e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.3003413644059365680885405745973
y[1] (numeric) = 1.3003413644059365699874731400931
absolute error = 1.8989325654958e-18
relative error = 1.4603338919110144308646794986079e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.3013856435430788755530387099704
y[1] (numeric) = 1.3013856435430788774665811474559
absolute error = 1.9135424374855e-18
relative error = 1.4703884640034891535550967924154e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.3024302240658898415675448373133
y[1] (numeric) = 1.3024302240658898434957479132246
absolute error = 1.9282030759113e-18
relative error = 1.4804655483899092620952418053738e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 1.3034751070189500759914047736586
y[1] (numeric) = 1.3034751070189500779343192690925
absolute error = 1.9429144954339e-18
relative error = 1.4905650940103865583053039265217e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.3045202934471426189584352670051
y[1] (numeric) = 1.3045202934471426209161119777698
absolute error = 1.9576767107647e-18
relative error = 1.5006870499435602587833628435883e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.3055657843956539857600512037242
y[1] (numeric) = 1.3055657843956539877325409403902
absolute error = 1.9724897366660e-18
relative error = 1.5108313654061215412993449519579e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.3066115809099752120318679988541
y[1] (numeric) = 1.3066115809099752140192215868048
absolute error = 1.9873535879507e-18
relative error = 1.5209979897519579091556934708986e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.3MB, time=5.32
x[1] = 0.303
y[1] (analytic) = 1.3076576840359028992448243559707
y[1] (numeric) = 1.3076576840359029012470926354535
absolute error = 2.0022682794828e-18
relative error = 1.5311868724719136449418387420612e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.3087040948195402605018708878464
y[1] (numeric) = 1.3087040948195402625191047140233
absolute error = 2.0172338261769e-18
relative error = 1.5413979631927874993779378658556e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.3097508143072981666412703946711
y[1] (numeric) = 1.3097508143072981686735206376697
absolute error = 2.0322502429986e-18
relative error = 1.5516312116770225373177573229937e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.3107978435458961926475559032242
y[1] (numeric) = 1.3107978435458961946948734481884
absolute error = 2.0473175449642e-18
relative error = 1.5618865678218636413171806208885e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.3118451835823636643711928780411
y[1] (numeric) = 1.3118451835823636664336286251822
absolute error = 2.0624357471411e-18
relative error = 1.5721639816590528446896992672742e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.3128928354640407055579923243261
y[1] (numeric) = 1.3128928354640407076355971889736
absolute error = 2.0776048646475e-18
relative error = 1.5824634033539931427746052288138e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.3139408002385792851893218121097
y[1] (numeric) = 1.3139408002385792872821467247621
absolute error = 2.0928249126524e-18
relative error = 1.5927847832051448169982145617078e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.3149890789539442651341617619494
y[1] (numeric) = 1.3149890789539442672422576683255
absolute error = 2.1080959063761e-18
relative error = 1.6031280716438050672385923395537e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 1.3160376726584144481140546443191
y[1] (numeric) = 1.3160376726584144502374725054085
absolute error = 2.1234178610894e-18
relative error = 1.6134932192329010719405911216565e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.3170865824005836259819950577205
y[1] (numeric) = 1.3170865824005836281207858498348
absolute error = 2.1387907921143e-18
relative error = 1.6238801766669278775406120608281e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.3181358092293616283163089644971
y[1] (numeric) = 1.3181358092293616304705236793208
absolute error = 2.1542147148237e-18
relative error = 1.6342888947711281227745123327954e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.3191853541939753713305706783153
y[1] (numeric) = 1.3191853541939753735002603229569
absolute error = 2.1696896446416e-18
relative error = 1.6447193245010548823113620669971e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.3202352183439699071006065133182
y[1] (numeric) = 1.3202352183439699092858221103611
absolute error = 2.1852155970429e-18
relative error = 1.6551714169418338009211765913407e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.3212854027292094731096343220422
y[1] (numeric) = 1.3212854027292094753104269095958
absolute error = 2.2007925875536e-18
relative error = 1.6656451233077316608733236461598e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.3223359083998785421125884673247
y[1] (numeric) = 1.3223359083998785443290090990752
absolute error = 2.2164206317505e-18
relative error = 1.6761403949413490649116026896266e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.3233867364064828723206800926134
y[1] (numeric) = 1.3233867364064828745527798378753
absolute error = 2.2320997452619e-18
relative error = 1.6866571833135727782497519899308e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.3244378877998505579072428753276
y[1] (numeric) = 1.3244378877998505601550728190944
absolute error = 2.2478299437668e-18
relative error = 1.6971954400223959165707995656708e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.3254893636311330798359147692023
y[1] (numeric) = 1.3254893636311330820995260121977
absolute error = 2.2636112429954e-18
relative error = 1.7077551167927246908680513769957e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.3265411649518063570122065638857
y[1] (numeric) = 1.3265411649518063592916502226147
absolute error = 2.2794436587290e-18
relative error = 1.7183361654757339397695596325315e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.3275932928136717977595084134466
y[1] (numeric) = 1.3275932928136718000548356202465
absolute error = 2.2953272067999e-18
relative error = 1.7289385380482258956236152757439e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 1.3286457482688573516205858098841
y[1] (numeric) = 1.328645748268857353931847712976
absolute error = 2.3112619030919e-18
relative error = 1.7395621866124437539148043096461e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.3296985323698185614856168032261
y[1] (numeric) = 1.3296985323698185638128645667656
absolute error = 2.3272477635395e-18
relative error = 1.7502070633949086299460012915449e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.3307516461693396160478225963379
y[1] (numeric) = 1.3307516461693396183911074004666
absolute error = 2.3432848041287e-18
relative error = 1.7608731207464645298840851771496e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.3318050907205344025877439701627
y[1] (numeric) = 1.3318050907205344049471170110592
absolute error = 2.3593730408965e-18
relative error = 1.7715603111413471543074006422695e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=5.93
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.3328588670768475600872163237558
y[1] (numeric) = 1.3328588670768475624627288136868
absolute error = 2.3755124899310e-18
relative error = 1.7822685871767074402899852038580e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 1.3339129762920555326740964431758
y[1] (numeric) = 1.3339129762920555350657996105476
absolute error = 2.3917031673718e-18
relative error = 1.7929979015723624258174594345947e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.3349674194202676233987944440484
y[1] (numeric) = 1.334967419420267625806739533458
absolute error = 2.4079450894096e-18
relative error = 1.8037482071699481886477781928865e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.3360221975159270483436646644214
y[1] (numeric) = 1.3360221975159270507679029367075
absolute error = 2.4242382722861e-18
relative error = 1.8145194569323015015915699866064e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.3370773116338119910663096173894
y[1] (numeric) = 1.3370773116338119935068923496842
absolute error = 2.4405827322948e-18
relative error = 1.8253116039435176818942520313404e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.338132762829036657377851446882
y[1] (numeric) = 1.338132762829036659834829932662
absolute error = 2.4569784857800e-18
relative error = 1.8361246014076631642322431224095e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.3391885521570523304572256649722
y[1] (numeric) = 1.3391885521570523329306512141095
absolute error = 2.4734255491373e-18
relative error = 1.8469584026486143966129723560491e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.3402446806736484263025522850884
y[1] (numeric) = 1.3402446806736484287924762239024
absolute error = 2.4899239388140e-18
relative error = 1.8578129611098230379723521384773e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.3413011494349535495206398025889
y[1] (numeric) = 1.3413011494349535520271134738973
absolute error = 2.5064736713084e-18
relative error = 1.8686882303532623166793436932194e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.3423579594974365494556778122904
y[1] (numeric) = 1.3423579594974365519787525754606
absolute error = 2.5230747631702e-18
relative error = 1.8795841640591979676405061873477e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.343415111917907576658174391731
y[1] (numeric) = 1.3434151119179075791979016227317
absolute error = 2.5397272310007e-18
relative error = 1.8905007160258115252674151516014e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.3444726077535191396951947191943
y[1] (numeric) = 1.3444726077535191422516258106464
absolute error = 2.5564310914521e-18
relative error = 1.9014378401681561329814448425554e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.3455304480617671623029577368192
y[1] (numeric) = 1.3455304480617671648761440980476
absolute error = 2.5731863612284e-18
relative error = 1.9123954905183065447432455917003e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.3465886339004920408828480114826
y[1] (numeric) = 1.3465886339004920434728410685675
absolute error = 2.5899930570849e-18
relative error = 1.9233736212244689001792161462015e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 1.3476471663278797023419002895533
y[1] (numeric) = 1.3476471663278797049487514853815
absolute error = 2.6068511958282e-18
relative error = 1.9343721865504658533562949201163e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.3487060464024626622788145860899
y[1] (numeric) = 1.3487060464024626649025753804063
absolute error = 2.6237607943164e-18
relative error = 1.9453911408753725585876680529858e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.3497652751831210835165599945868
y[1] (numeric) = 1.3497652751831210861572818640461
absolute error = 2.6407218694593e-18
relative error = 1.9564304386931545103216044319727e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 1.3508248537290838349826257499603
y[1] (numeric) = 1.350824853729083837640360188178
absolute error = 2.6577344382177e-18
relative error = 1.9674900346116409662143266270815e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 1.3518847830999295509379784251124
y[1] (numeric) = 1.3518847830999295536127769427168
absolute error = 2.6747985176044e-18
relative error = 1.9785698833527608395730793982033e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.3529450643555876905557844901204
y[1] (numeric) = 1.3529450643555876932476986148039
absolute error = 2.6919141246835e-18
relative error = 1.9896699397515211017876848135324e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 1.3540056985563395978509578128612
y[1] (numeric) = 1.3540056985563396005600390894317
absolute error = 2.7090812765705e-18
relative error = 2.0007901587555809589316558772105e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.3550666867628195619615920307066
y[1] (numeric) = 1.355066686762819564687892021139
absolute error = 2.7262999904324e-18
relative error = 2.0119304954248281628723206184417e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.3561280300360158777833380748105
y[1] (numeric) = 1.3561280300360158805269083582987
absolute error = 2.7435702834882e-18
relative error = 2.0230909049312524019014732594250e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.3571897294372719069577874814545
y[1] (numeric) = 1.3571897294372719097186796544626
absolute error = 2.7608921730081e-18
relative error = 2.0342713425578615550885482251824e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=6.55
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.3582517860282871392159224789222
y[1] (numeric) = 1.3582517860282871419941881552361
absolute error = 2.7782656763139e-18
relative error = 2.0454717636984866482318193839715e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.3593142008711182540776941934418
y[1] (numeric) = 1.359314200871118256873385004221
absolute error = 2.7956908107792e-18
relative error = 2.0566921238574407211297884318281e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.3603769750281801829087906738637
y[1] (numeric) = 1.3603769750281801857219582676928
absolute error = 2.8131675938291e-18
relative error = 2.0679323786488118760806473568486e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.3614401095622471713356567919288
y[1] (numeric) = 1.3614401095622471741663528348693
absolute error = 2.8306960429405e-18
relative error = 2.0791924837962004741577860065399e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.3625036055364538420198284332374
y[1] (numeric) = 1.362503605536453844868104608879
absolute error = 2.8482761756416e-18
relative error = 2.0904723951318705332857560868257e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.363567464014296257792643753339
y[1] (numeric) = 1.3635674640142962606585517628518
absolute error = 2.8659080095128e-18
relative error = 2.1017720685969319407917173142870e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.3646316860596329851513946337461
y[1] (numeric) = 1.3646316860596329880349861959319
absolute error = 2.8835915621858e-18
relative error = 2.1130914602402028999405464313510e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.3656962727366861581179818341094
y[1] (numeric) = 1.3656962727366861610193086854535
absolute error = 2.9013268513441e-18
relative error = 2.1244305262181029351538152757964e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.3667612251100425424611376992989
y[1] (numeric) = 1.3667612251100425453802515940221
absolute error = 2.9191138947232e-18
relative error = 2.1357892227943270220902081729185e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.3678265442446546002832806437037
y[1] (numeric) = 1.3678265442446546032202333538136
absolute error = 2.9369527101099e-18
relative error = 2.1471675063388633814927756816590e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 1.3688922312058415549730659996915
y[1] (numeric) = 1.3688922312058415579279093150346
absolute error = 2.9548433153431e-18
relative error = 2.1585653333281117549689614320685e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 1.3699582870592904565246981828687
y[1] (numeric) = 1.3699582870592904594974839111822
absolute error = 2.9727857283135e-18
relative error = 2.1699826603441983028914758533286e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.3710247128710572472250694935423
y[1] (numeric) = 1.3710247128710572502158494605057
absolute error = 2.9907799669634e-18
relative error = 2.1814194440743667529176823936446e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.3720915097075678277097912416102
y[1] (numeric) = 1.3720915097075678307186172908973
absolute error = 3.0088260492871e-18
relative error = 2.1928756413108097923809795687992e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.3731586786356191233891832510004
y[1] (numeric) = 1.373158678635619126416107244331
absolute error = 3.0269239933306e-18
relative error = 2.2043512089499915878806542605618e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.3742262207223801512452881697377
y[1] (numeric) = 1.3742262207223801542903619869297
absolute error = 3.0450738171920e-18
relative error = 2.2158461039924829525240957974314e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.3752941370353930870009773827408
y[1] (numeric) = 1.3752941370353930900642529217618
absolute error = 3.0632755390210e-18
relative error = 2.2273602835421429879200243268131e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.3763624286425743326622156965444
y[1] (numeric) = 1.3763624286425743357437448735639
absolute error = 3.0815291770195e-18
relative error = 2.2388937048061038554683520257593e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.3774310966122155844345523383009
y[1] (numeric) = 1.3774310966122155875343870877417
absolute error = 3.0998347494408e-18
relative error = 2.2504463250937393443629254321386e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.3785001420129849010149061856399
y[1] (numeric) = 1.3785001420129849041330984602307
absolute error = 3.1181922745908e-18
relative error = 2.2620181018170891990042167981846e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 1.3795695659139277722597135192623
y[1] (numeric) = 1.3795695659139277753963152900892
absolute error = 3.1366017708269e-18
relative error = 2.2736089924896143954178309156819e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.3806393693844681882305069665034
y[1] (numeric) = 1.380639369384468191385570223062
absolute error = 3.1550632565586e-18
relative error = 2.2852189547261896229227467078555e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.3817095534944097086179946815344
y[1] (numeric) = 1.3817095534944097117915714317817
absolute error = 3.1735767502473e-18
relative error = 2.2968479462425169149557133443519e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.3827801193139365325457091863699
y[1] (numeric) = 1.3827801193139365357378514567766
absolute error = 3.1921422704067e-18
relative error = 2.3084959248549760165846937473357e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=7.17
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.3838510679136145687542956764205
y[1] (numeric) = 1.3838510679136145719650555120227
absolute error = 3.2107598356022e-18
relative error = 2.3201628484797529297612141560966e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.3849224003643925061675099749663
y[1] (numeric) = 1.3849224003643925093969394394176
absolute error = 3.2294294644513e-18
relative error = 2.3318486751326946674160296594313e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.38599411773760288484099670264
y[1] (numeric) = 1.3859941177376028880891478782636
absolute error = 3.2481511756236e-18
relative error = 2.3435533629288761827586037221501e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 1.3870662211049631672949186107858
y[1] (numeric) = 1.3870662211049631705618435986269
absolute error = 3.2669249878411e-18
relative error = 2.3552768700823856915622273410964e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 1.3881387115385768102315084114142
y[1] (numeric) = 1.3881387115385768135172593312916
absolute error = 3.2857509198774e-18
relative error = 2.3670191549053186614822477772730e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 1.3892115901109343366386148213921
y[1] (numeric) = 1.3892115901109343399432438119505
absolute error = 3.3046289905584e-18
relative error = 2.3787801758078563102022982111312e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.3902848578949144082803149245047
y[1] (numeric) = 1.3902848578949144116038741432669
absolute error = 3.3235592187622e-18
relative error = 2.3905598912977684179873100704014e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.3913585159637848985756653420909
y[1] (numeric) = 1.39135851596378490191820696551
absolute error = 3.3425416234191e-18
relative error = 2.4023582599799904110715655986539e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.3924325653912039658666650910922
y[1] (numeric) = 1.3924325653912039692282413146036
absolute error = 3.3615762235114e-18
relative error = 2.4141752405560588649385398153867e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.3935070072512211270765033975679
y[1] (numeric) = 1.3935070072512211304571664356418
absolute error = 3.3806630380739e-18
relative error = 2.4260107918240520440943869553611e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.3945818426182783317591661240139
y[1] (numeric) = 1.3945818426182783351589682102072
absolute error = 3.3998020861933e-18
relative error = 2.4378648726777420449638506919057e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.3956570725672110365414748601806
y[1] (numeric) = 1.3956570725672110399604682471891
absolute error = 3.4189933870085e-18
relative error = 2.4497374421063958082450571872540e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.3967326981732492799586331195186
y[1] (numeric) = 1.3967326981732492833968700792296
absolute error = 3.4382369597110e-18
relative error = 2.4616284591946487400976186040332e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.3978087205120187576843544768887
y[1] (numeric) = 1.3978087205120187611418873004331
absolute error = 3.4575328235444e-18
relative error = 2.4735378831217351441324684022217e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.3988851406595418981566478777532
y[1] (numeric) = 1.3988851406595419016335288755576
absolute error = 3.4768809978044e-18
relative error = 2.4854656731610797239008135408744e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.3999619596922389386003357447232
y[1] (numeric) = 1.3999619596922389420966172465624
absolute error = 3.4962815018392e-18
relative error = 2.4974117886801767834007755604798e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 1.4010391786869290014473809040705
y[1] (numeric) = 1.40103917868692900496311525912
absolute error = 3.5157343550495e-18
relative error = 2.5093761891401845724389150340722e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.4021167987208311711560987526206
y[1] (numeric) = 1.4021167987208311746913383295086
absolute error = 3.5352395768880e-18
relative error = 2.5213588340951649869003327696693e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.403194820871565571430331484328
y[1] (numeric) = 1.4031948208715655749851286711878
absolute error = 3.5547971868598e-18
relative error = 2.5333596831919682543299501725614e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.4042732462171544428396615957979
y[1] (numeric) = 1.4042732462171544464140688003207
absolute error = 3.5744072045228e-18
relative error = 2.5453786961701182388097947846548e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 1.4053520758360232208417422910593
y[1] (numeric) = 1.4053520758360232244358119405461
absolute error = 3.5940696494868e-18
relative error = 2.5574158328607733249905148578571e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 1.4064313108070016142078228080065
y[1] (numeric) = 1.4064313108070016178216073494209
absolute error = 3.6137845414144e-18
relative error = 2.5694710531869720053500793142503e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.407510952209324683852547092128
y[1] (numeric) = 1.4075109522093246874860989921483
absolute error = 3.6335519000203e-18
relative error = 2.5815443171627406647408948546109e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
memory used=49.5MB, alloc=4.3MB, time=7.77
y[1] (analytic) = 1.4085910011226339220691046474076
y[1] (numeric) = 1.4085910011226339257224763924796
absolute error = 3.6533717450720e-18
relative error = 2.5936355848931994531509510384370e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.4096714586269783321708127996421
y[1] (numeric) = 1.4096714586269783358440568960314
absolute error = 3.6732440963893e-18
relative error = 2.6057448165738164933760104638773e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.4107523258028155085402100138447
y[1] (numeric) = 1.4107523258028155122333789876893
absolute error = 3.6931689738446e-18
relative error = 2.6178719724902326715017756063507e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.4118336037310127170867403149195
y[1] (numeric) = 1.4118336037310127207998867122823
absolute error = 3.7131463973628e-18
relative error = 2.6300170130178039949439439913443e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.4129152934928479761141092693808
y[1] (numeric) = 1.412915293492847979847285656302
absolute error = 3.7331763869212e-18
relative error = 2.6421798986211461329516416521442e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.4139973961700111375983923955628
y[1] (numeric) = 1.4139973961700111413516513581127
absolute error = 3.7532589625499e-18
relative error = 2.6543605898540347358055358812542e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.4150799128446049688779772805197
y[1] (numeric) = 1.4150799128446049726513714248511
absolute error = 3.7733941443314e-18
relative error = 2.6665590473587409520051768305832e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.4161628445991462347564210936465
y[1] (numeric) = 1.4161628445991462385500030460474
absolute error = 3.7935819524009e-18
relative error = 2.6787752318658643652910360369968e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.4172461925165667800193055999695
y[1] (numeric) = 1.4172461925165667838331280069158
absolute error = 3.8138224069463e-18
relative error = 2.6910091041939550979889968011199e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.418329957680214612366172190052
y[1] (numeric) = 1.4183299576802146162002877182599
absolute error = 3.8341155282079e-18
relative error = 2.7032606252489262071417739879012e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.4194141411738549857586198585386
y[1] (numeric) = 1.4194141411738549896130811950176
absolute error = 3.8544613364790e-18
relative error = 2.7155297560241029139777473365890e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.4204987440816714841856494795291
y[1] (numeric) = 1.4204987440816714880605093316344
absolute error = 3.8748598521053e-18
relative error = 2.7278164575994269103850851564534e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.4215837674882671058473381442138
y[1] (numeric) = 1.4215837674882671097426492396992
absolute error = 3.8953110954854e-18
relative error = 2.7401206911414381678599753305208e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.4226692124786653477579277445372
y[1] (numeric) = 1.4226692124786653516737428316077
absolute error = 3.9158150870705e-18
relative error = 2.7524424179026945814379057583566e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 1.4237550801383112907694124060675
y[1] (numeric) = 1.4237550801383112947057842534319
absolute error = 3.9363718473644e-18
relative error = 2.7647815992214050525573311450872e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 1.4248413715530726850167097937502
y[1] (numeric) = 1.4248413715530726889736911906744
absolute error = 3.9569813969242e-18
relative error = 2.7771381965215556061976250505880e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.4259280878092410357855017358085
y[1] (numeric) = 1.4259280878092410397631454921678
absolute error = 3.9776437563593e-18
relative error = 2.7895121713118427978278124581918e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.4270152299935326898038300337198
y[1] (numeric) = 1.4270152299935326938021889800519
absolute error = 3.9983589463321e-18
relative error = 2.8019034851858033631346921995764e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.4281027991930899219585337499566
y[1] (numeric) = 1.4281027991930899259776607375142
absolute error = 4.0191269875576e-18
relative error = 2.8143120998211730948918702051995e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.4291907964954820224376146900174
y[1] (numeric) = 1.4291907964954820264775625908214
absolute error = 4.0399479008040e-18
relative error = 2.8267379769799484142946885047482e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.4302792229887063842996182212062
y[1] (numeric) = 1.4302792229887063883604399280985
absolute error = 4.0608217068923e-18
relative error = 2.8391810785077485670813397398533e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.4313680797611895914711169976305
y[1] (numeric) = 1.4313680797611895955528654243267
absolute error = 4.0817484266962e-18
relative error = 2.8516413663333903880767964799853e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.4324573679017885071733855889919
y[1] (numeric) = 1.4324573679017885112761136701343
absolute error = 4.1027280811424e-18
relative error = 2.8641188024687443146463194005979e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.4335470884997913627793544399356
y[1] (numeric) = 1.4335470884997913669031151311462
absolute error = 4.1237606912106e-18
relative error = 2.8766133490083818538019436849810e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.3MB, time=8.39
x[1] = 0.422
y[1] (analytic) = 1.4346372426449188471019320170035
y[1] (numeric) = 1.4346372426449188512467782949369
absolute error = 4.1448462779334e-18
relative error = 2.8891249681291550191199757399078e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.435727831427325196114784431603
y[1] (numeric) = 1.4357278314273252002807692939994
absolute error = 4.1659848623964e-18
relative error = 2.9016536220899170525888145189535e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.4368188559375992831066622598621
y[1] (numeric) = 1.4368188559375992872938387256003
absolute error = 4.1871764657382e-18
relative error = 2.9141992732311748864045177449235e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.4379103172667657092703647137897
y[1] (numeric) = 1.4379103172667657134787858229401
absolute error = 4.2084211091504e-18
relative error = 2.9267618839747432524722671831764e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.4390022165062858947274317527941
y[1] (numeric) = 1.4390022165062858989571505666717
absolute error = 4.2297188138776e-18
relative error = 2.9393414168234004310068190984409e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.4400945547480591699896551603447
y[1] (numeric) = 1.4400945547480591742407247615622
absolute error = 4.2510696012175e-18
relative error = 2.9519378343606150695623963410548e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.4411873330844238678585000473774
y[1] (numeric) = 1.4411873330844238721309735398984
absolute error = 4.2724734925210e-18
relative error = 2.9645510992502743081888604019064e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.4422805526081584157635286819574
y[1] (numeric) = 1.4422805526081584200574591911492
absolute error = 4.2939305091918e-18
relative error = 2.9771811742360665303040096218277e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 1.4433742144124824285409189837133
y[1] (numeric) = 1.4433742144124824328563596564003
absolute error = 4.3154406726870e-18
relative error = 2.9898280221415598023890961085086e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.4444683195910578016531704616525
y[1] (numeric) = 1.4444683195910578059901744661694
absolute error = 4.3370040045169e-18
relative error = 3.0024916058697261825875615633589e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.4455628692379898048510908151554
y[1] (numeric) = 1.4455628692379898092097113414002
absolute error = 4.3586205262448e-18
relative error = 3.0151718884024682503702311183562e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.4466578644478281762791568602251
y[1] (numeric) = 1.4466578644478281806594471197122
absolute error = 4.3802902594871e-18
relative error = 3.0278688328003552210977491998383e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.4477533063155682170253438864454
y[1] (numeric) = 1.4477533063155682214273571123589
absolute error = 4.4020132259135e-18
relative error = 3.0405824022024293913913136723039e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.4488491959366518861165179945673
y[1] (numeric) = 1.4488491959366518905403074418145
absolute error = 4.4237894472472e-18
relative error = 3.0533125598260135223636651474679e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.4499455344069688959604864102087
y[1] (numeric) = 1.4499455344069689004061053554729
absolute error = 4.4456189452642e-18
relative error = 3.0660592689658984420579844053765e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.4510423228228578082358012158069
y[1] (numeric) = 1.451042322822857812703302957601
absolute error = 4.4675017417941e-18
relative error = 3.0788224929945681291213256743747e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.4521395622811071302304123907205
y[1] (numeric) = 1.4521395622811071347198502494402
absolute error = 4.4894378587197e-18
relative error = 3.0916021953615974681694255572645e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.453237253878956411630266498225
y[1] (numeric) = 1.4532372538789564161416938162021
absolute error = 4.5114273179771e-18
relative error = 3.1043983395933968499498893831882e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.4543353987140973417589478080914
y[1] (numeric) = 1.4543353987140973462924179496471
absolute error = 4.5334701415557e-18
relative error = 3.1172108892928892254425495748790e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 1.4554339978846748472694590944808
y[1] (numeric) = 1.4554339978846748518250254459792
absolute error = 4.5555663514984e-18
relative error = 3.1300398081393260946253783572737e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.4565330524892881902892398010276
y[1] (numeric) = 1.4565330524892881948669557709291
absolute error = 4.5777159699015e-18
relative error = 3.1428850598878984153394695035593e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.4576325636269920670195197182209
y[1] (numeric) = 1.4576325636269920716194387371353
absolute error = 4.5999190189144e-18
relative error = 3.1557466083692121188079885876529e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.4587325323972977067901067725278
y[1] (numeric) = 1.4587325323972977114122822932681
absolute error = 4.6221755207403e-18
relative error = 3.1686244174894515790865374328784e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 1.4598329599001739715707079821408
y[1] (numeric) = 1.4598329599001739762151934797766
absolute error = 4.6444854976358e-18
relative error = 3.1815184512297888871893822808819e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=9.00
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.4609338472360484559398830907598
y[1] (numeric) = 1.4609338472360484606067320626704
absolute error = 4.6668489719106e-18
relative error = 3.1944286736458642976294908310156e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 1.462035195505808587512730848454
y[1] (numeric) = 1.4620351955058085922019968143823
absolute error = 4.6892659659283e-18
relative error = 3.2073550488680214521650008872019e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.4631370058108027278284083673828
y[1] (numeric) = 1.4631370058108027325401448694888
absolute error = 4.7117365021060e-18
relative error = 3.2202975411007214387667127913770e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.4642392792528412736985844399864
y[1] (numeric) = 1.4642392792528412784328450429006
absolute error = 4.7342606029142e-18
relative error = 3.2332561146221644323101071643588e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.4653420169341977590179281681905
y[1] (numeric) = 1.4653420169341977637747664590674
absolute error = 4.7568382908769e-18
relative error = 3.2462307337840495820764183423912e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.4664452199576099570377347142061
y[1] (numeric) = 1.466445219957609961817204302778
absolute error = 4.7794695885719e-18
relative error = 3.2592213630114724187253234994045e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.4675488894262809831037904466425
y[1] (numeric) = 1.467548889426280987905944965273
absolute error = 4.8021545186305e-18
relative error = 3.2722279668024139299196795759970e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.4686530264438803978595802198896
y[1] (numeric) = 1.4686530264438804026844733236271
absolute error = 4.8248931037375e-18
relative error = 3.2852505097274362587762079592231e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.4697576321145453109159399900689
y[1] (numeric) = 1.4697576321145453157636253567006
absolute error = 4.8476853666317e-18
relative error = 3.2982889564297200165823983103432e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.4708627075428814849882584372989
y[1] (numeric) = 1.470862707542881489858789767404
absolute error = 4.8705313301051e-18
relative error = 3.3113432716242176418133679075581e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.4719682538339644405023317315665
y[1] (numeric) = 1.4719682538339644453957627485703
absolute error = 4.8934310170038e-18
relative error = 3.3244134200979655381939525261215e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.4730742720933405606699760481533
y[1] (numeric) = 1.4730742720933405655863604983808
absolute error = 4.9163844502275e-18
relative error = 3.3374993667094444630118761996214e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.4741807634270281970355029083199
y[1] (numeric) = 1.4741807634270282019748945610496
absolute error = 4.9393916527297e-18
relative error = 3.3506010763884176823738939554873e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.4752877289415187754941628918166
y[1] (numeric) = 1.4752877289415187804566155393341
absolute error = 4.9624526475175e-18
relative error = 3.3637185141354987692706545353572e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.4763951697437779027836637397559
y[1] (numeric) = 1.4763951697437779077692311974079
absolute error = 4.9855674576520e-18
relative error = 3.3768516450221277887789382633419e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.4775030869412464734498693394572
y[1] (numeric) = 1.477503086941246478458605445705
absolute error = 5.0087361062478e-18
relative error = 3.3900004341899385016412713720414e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.4786114816418417772877865570546
y[1] (numeric) = 1.4786114816418417823197451735284
absolute error = 5.0319586164738e-18
relative error = 3.4031648468510076625692258460500e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.4797203549539586072589473589483
y[1] (numeric) = 1.4797203549539586123141823705007
absolute error = 5.0552350115524e-18
relative error = 3.4163448482870219588882080892158e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 1.480829707986470367886294139572
y[1] (numeric) = 1.480829707986470372964859454332
absolute error = 5.0785653147600e-18
relative error = 3.4295404038493266235736348525208e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.4819395418487301841276766504554
y[1] (numeric) = 1.4819395418487301892296261998823
absolute error = 5.1019495494269e-18
relative error = 3.4427514789585690009992537382612e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.483049857650572010729069404171
y[1] (numeric) = 1.4830498576505720158544571431083
absolute error = 5.1253877389373e-18
relative error = 3.4559780391044111864031127881342e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.4841606565023117420586189064743
y[1] (numeric) = 1.4841606565023117472074988132037
absolute error = 5.1488799067294e-18
relative error = 3.4692200498453113779196643288354e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.4852719395147483224226305507782
y[1] (numeric) = 1.4852719395147483275950566270736
absolute error = 5.1724260762954e-18
relative error = 3.4824774768082389260963232423397e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.48638370779916485686460549104
y[1] (numeric) = 1.4863837077991648620606317622215
absolute error = 5.1960262711815e-18
relative error = 3.4957502856883907052295437256651e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=9.61
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.4874959624673297224484382921912
y[1] (numeric) = 1.4874959624673297276681188071791
absolute error = 5.2196805149879e-18
relative error = 3.5090384422489087998767402297492e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.4886087046314976800268866413996
y[1] (numeric) = 1.4886087046314976852702754727685
absolute error = 5.2433888313689e-18
relative error = 3.5223419123206666767602291499763e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.4897219354044109864964248887274
y[1] (numeric) = 1.48972193540441099176357613276
absolute error = 5.2671512440326e-18
relative error = 3.5356606618017878509952506593141e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.4908356558993005075395936721294
y[1] (numeric) = 1.490835655899300512830561448871
absolute error = 5.2909677767416e-18
relative error = 3.5489946566578375159750930005805e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.4919498672298868308559583692358
y[1] (numeric) = 1.4919498672298868361707968225482
absolute error = 5.3148384533124e-18
relative error = 3.5623438629211420137710874429209e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.4930645705103813798827896069699
y[1] (numeric) = 1.4930645705103813852215529045855
absolute error = 5.3387632976156e-18
relative error = 3.5757082466906472042235636304536e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.4941797668554875280065795497733
y[1] (numeric) = 1.4941797668554875333693218833495
absolute error = 5.3627423335762e-18
relative error = 3.5890877741318444358517109485754e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.4952954573804017132665081780494
y[1] (numeric) = 1.4952954573804017186532837632225
absolute error = 5.3867755851731e-18
relative error = 3.6024824114761618771252684541118e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.4964116432008145535509742603827
y[1] (numeric) = 1.4964116432008145589618373368223
absolute error = 5.4108630764396e-18
relative error = 3.6158921250210268761089951523894e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.4975283254329119622883062161587
y[1] (numeric) = 1.4975283254329119677233110476219
absolute error = 5.4350048314632e-18
relative error = 3.6293168811294606445752335262946e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.4986455051933762646327685593887
y[1] (numeric) = 1.4986455051933762700919694337744
absolute error = 5.4592008743857e-18
relative error = 3.6427566462298749741926962354350e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 1.4997631835993873141469801098373
y[1] (numeric) = 1.4997631835993873196304313392404
absolute error = 5.4834512294031e-18
relative error = 3.6562113868157365461230356842712e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 1.500881361768623609981860653966
y[1] (numeric) = 1.5008813617686236154896165747316
absolute error = 5.5077559207656e-18
relative error = 3.6696810694452994069268469562066e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.5020000408192634145552232357302
y[1] (numeric) = 1.5020000408192634200873382085085
absolute error = 5.5321149727783e-18
relative error = 3.6831656607418047235259222321961e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.5031192218699858717301297559184
y[1] (numeric) = 1.5031192218699858772866581657182
absolute error = 5.5565284097998e-18
relative error = 3.6966651273922825890410550913446e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.504238906039972125494128058478
y[1] (numeric) = 1.5042389060399721310751243147218
absolute error = 5.5809962562438e-18
relative error = 3.7101794361483535793964796778040e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.5053590944489064391404891831623
y[1] (numeric) = 1.5053590944489064447460077197404
absolute error = 5.6055185365781e-18
relative error = 3.7237085538252996083506598536853e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.5064797882169773149525639658265
y[1] (numeric) = 1.5064797882169773205826592411515
absolute error = 5.6300952753250e-18
relative error = 3.7372524473020682828334758015680e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.5076009884648786143923786708234
y[1] (numeric) = 1.5076009884648786200471051678845
absolute error = 5.6547264970611e-18
relative error = 3.7508110835208792929268345151690e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.5087226963138106787945898441876
y[1] (numeric) = 1.5087226963138106844740020706055
absolute error = 5.6794122264179e-18
relative error = 3.7643844294873628433430723948027e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.5098449128854814505669190816577
y[1] (numeric) = 1.5098449128854814562710715697386
absolute error = 5.7041524880809e-18
relative error = 3.7779724522697040242517054071882e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.5109676393021075948981889120622
y[1] (numeric) = 1.5109676393021076006271362188526
absolute error = 5.7289473067904e-18
relative error = 3.7915751189989161375569493754983e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.5120908766864156219750815042008
y[1] (numeric) = 1.5120908766864156277288782115421
absolute error = 5.7537967073413e-18
relative error = 3.8051923968684515058000328005590e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.5132146261616430097087424140723
y[1] (numeric) = 1.5132146261616430154874431286552
absolute error = 5.7787007145829e-18
relative error = 3.8188242531338140490420490406907e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=10.22
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.5143388888515393269723520991462
y[1] (numeric) = 1.5143388888515393327760114525655
absolute error = 5.8036593534193e-18
relative error = 3.8324706551125698343052476261528e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.5154636658803673573507884373441
y[1] (numeric) = 1.5154636658803673631794610861531
absolute error = 5.8286726488090e-18
relative error = 3.8461315701838297215353053948603e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.5165889583729042234035040004854
y[1] (numeric) = 1.5165889583729042292572446262509
absolute error = 5.8537406257655e-18
relative error = 3.8598069657883937204132300595810e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.5177147674544425114417423451704
y[1] (numeric) = 1.5177147674544425173206056545271
absolute error = 5.8788633093567e-18
relative error = 3.8734968094281040765955177300161e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 1.5188410942507913968212180984089
y[1] (numeric) = 1.5188410942507914027252588231142
absolute error = 5.9040407247053e-18
relative error = 3.8872010686658596651483261271930e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.5199679398882777697513861307696
y[1] (numeric) = 1.5199679398882777756806590277581
absolute error = 5.9292728969885e-18
relative error = 3.9009197111251698178237118107346e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 1.5210953054937473616224256264115
y[1] (numeric) = 1.5210953054937473675769854778503
absolute error = 5.9545598514388e-18
relative error = 3.9146527044904333298759051339333e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 1.5222231921945658718510653770781
y[1] (numeric) = 1.5222231921945658778309669904211
absolute error = 5.9799016133430e-18
relative error = 3.9284000165060337786581062153063e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 1.5233516011186200952463771459702
y[1] (numeric) = 1.5233516011186201012516753540132
absolute error = 6.0052982080430e-18
relative error = 3.9421616149766204983657356763127e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 1.5244805333943190498966644673877
y[1] (numeric) = 1.5244805333943190559274141283228
absolute error = 6.0307496609351e-18
relative error = 3.9559374677664043980676627643436e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 1.5256099901505951055785747691203
y[1] (numeric) = 1.5256099901505951116348307665913
absolute error = 6.0562559974710e-18
relative error = 3.9697275427995712466289778147121e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 1.5267399725169051126895632267963
y[1] (numeric) = 1.5267399725169051187713804699533
absolute error = 6.0818172431570e-18
relative error = 3.9835318080595141723665680487313e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 1.5278704816232315317048372827447
y[1] (numeric) = 1.527870481623231537812270706299
absolute error = 6.1074334235543e-18
relative error = 3.9973502315887895555240016758083e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 1.529001518600083563159911286411
y[1] (numeric) = 1.52900151860008356929301585069
absolute error = 6.1331045642790e-18
relative error = 4.0111827814888769417156791085208e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.508
y[1] (analytic) = 1.5301330845784982781599012389744
y[1] (numeric) = 1.5301330845784982843187319299769
absolute error = 6.1588306910025e-18
relative error = 4.0250294259202014663204469959735e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 1.5312651806900417494166901515569
y[1] (numeric) = 1.5312651806900417556013019810076
absolute error = 6.1846118294507e-18
relative error = 4.0388901331013725440115606584524e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 1.5323978080668101828150950542814
y[1] (numeric) = 1.5323978080668101890255430596862
absolute error = 6.2104480054048e-18
relative error = 4.0527648713094700785693235101244e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 1.5335309678414310495091672224427
y[1] (numeric) = 1.5335309678414310557455064671437
absolute error = 6.2363392447010e-18
relative error = 4.0666536088796121362511654600394e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 1.5346646611470642185497577161848
y[1] (numeric) = 1.5346646611470642248120432894153
absolute error = 6.2622855732305e-18
relative error = 4.0805563142047200462663180034132e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 1.5357988891174030900444808613435
y[1] (numeric) = 1.5357988891174030963327678782833
absolute error = 6.2882870169398e-18
relative error = 4.0944729557354799095007652087010e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 1.5369336528866757288512088315148
y[1] (numeric) = 1.5369336528866757351655524333449
absolute error = 6.3143436018301e-18
relative error = 4.1084035019797187253384924345868e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.515
y[1] (analytic) = 1.5380689535896459988062310249348
y[1] (numeric) = 1.5380689535896460051466863788928
absolute error = 6.3404553539580e-18
relative error = 4.1223479215026285251327039521771e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 1.5392047923616146974882124644279
y[1] (numeric) = 1.5392047923616147038548347638633
absolute error = 6.3666222994354e-18
relative error = 4.1363061829264697942432223254670e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 1.5403411703384206915190859844748
y[1] (numeric) = 1.5403411703384206979119304489041
absolute error = 6.3928444644293e-18
relative error = 4.1502782549302113134909537324822e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=10.83
NO POLE
x[1] = 0.518
y[1] (analytic) = 1.5414780886564420524030135063876
y[1] (numeric) = 1.5414780886564420588221353815493
absolute error = 6.4191218751617e-18
relative error = 4.1642641062492364947230767856281e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 1.542615548452597192904552240647
y[1] (numeric) = 1.542615548452597199350006798557
absolute error = 6.4454545579100e-18
relative error = 4.1782637056753751684579500544660e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 1.5437535508643460039671621946639
y[1] (numeric) = 1.543753550864346010439004733671
absolute error = 6.4718425390071e-18
relative error = 4.1922770220567409276318109809066e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 1.5448920970296909921731919045672
y[1] (numeric) = 1.544892097029690998671477749408
absolute error = 6.4982858448408e-18
relative error = 4.2063040242971161112338376566642e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 1.5460311880871784177464798510972
y[1] (numeric) = 1.5460311880871784242712643529516
absolute error = 6.5247845018544e-18
relative error = 4.2203446813561157139700613526496e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 1.5471708251758994330987095623025
y[1] (numeric) = 1.5471708251758994396500480988492
absolute error = 6.5513385365467e-18
relative error = 4.2343989622489627950595845622497e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 1.5483110094354912219206569494894
y[1] (numeric) = 1.548311009435491228498604924961
absolute error = 6.5779479754716e-18
relative error = 4.2484668360460065593197220972720e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 1.5494517420061381388194689677663
y[1] (numeric) = 1.5494517420061381454240818130049
absolute error = 6.6046128452386e-18
relative error = 4.2625482718728234434955103357124e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 1.5505930240285728495031132385565
y[1] (numeric) = 1.5505930240285728561344464110691
absolute error = 6.6313331725126e-18
relative error = 4.2766432389098663430825041776341e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 1.5517348566440774715131388186248
y[1] (numeric) = 1.5517348566440774781712478026387
absolute error = 6.6581089840139e-18
relative error = 4.2907517063922443010819352858015e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 1.5528772409944847155068888484726
y[1] (numeric) = 1.5528772409944847221918291549909
absolute error = 6.6849403065183e-18
relative error = 4.3048736436095675916029493473433e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 1.5540201782221790270903063624102
y[1] (numeric) = 1.5540201782221790338021335292673
absolute error = 6.7118271668571e-18
relative error = 4.3190090199057291635521398415922e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 1.5551636694700977292024750932068
y[1] (numeric) = 1.5551636694700977359412446851239
absolute error = 6.7387695919171e-18
relative error = 4.3331578046786870737684183268673e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 1.5563077158817321650530376559541
y[1] (numeric) = 1.5563077158817321718188052645951
absolute error = 6.7657676086410e-18
relative error = 4.3473199673805049234645003056405e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 1.5574523186011288416136340486579
y[1] (numeric) = 1.5574523186011288484064552926845
absolute error = 6.7928212440266e-18
relative error = 4.3614954775166216522959578271007e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 1.5585974787728905736645039610897
y[1] (numeric) = 1.5585974787728905804844344862172
absolute error = 6.8199305251275e-18
relative error = 4.3756843046460869787236494680707e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 1.5597431975421776283973969385975
y[1] (numeric) = 1.5597431975421776352444924176506
absolute error = 6.8470954790531e-18
relative error = 4.3898864183813470370584717738938e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 1.5608894760547088705759350038811
y[1] (numeric) = 1.5608894760547088774502511368494
absolute error = 6.8743161329683e-18
relative error = 4.4041017883878387845930007652668e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 1.5620363154567629082545728971892
y[1] (numeric) = 1.5620363154567629151561654112829
absolute error = 6.9015925140937e-18
relative error = 4.4183303843839063139830151752483e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 1.5631837168951792390573016539944
y[1] (numeric) = 1.5631837168951792459862263037003
absolute error = 6.9289246497059e-18
relative error = 4.4325721761407815306948396559070e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 1.564331681517359397017241798946
y[1] (numeric) = 1.5643316815173594039735543660829
absolute error = 6.9563125671369e-18
relative error = 4.4468271334819896136731427890366e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.539
y[1] (analytic) = 1.5654802104712680999782729957881
y[1] (numeric) = 1.5654802104712681069620292895626
absolute error = 6.9837562937745e-18
relative error = 4.4610952262833958973440361719309e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 1.5666293049054343975598475549686
y[1] (numeric) = 1.5666293049054344045711034120312
absolute error = 7.0112558570626e-18
relative error = 4.4753764244731887405404831883804e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 1.5677789659689528196861357638494
y[1] (numeric) = 1.56777896596895282672494704835
absolute error = 7.0388112845006e-18
relative error = 4.4896706980312884333668564614663e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=11.44
NO POLE
x[1] = 0.542
y[1] (analytic) = 1.5689291948114845256806515687567
y[1] (numeric) = 1.5689291948114845327470741724009
absolute error = 7.0664226036442e-18
relative error = 4.5039780169896510544548330848704e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 1.5700799925832584539275077035954
y[1] (numeric) = 1.5700799925832584610215975456999
absolute error = 7.0940898421045e-18
relative error = 4.5182983514314882685040058066861e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 1.5712313604350724721004499263762
y[1] (numeric) = 1.571231360435072479222262953925
absolute error = 7.1218130275488e-18
relative error = 4.5326316714915725291807866505861e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 1.572383299518294527960820592787
y[1] (numeric) = 1.5723832995182945351104127804872
absolute error = 7.1495921877002e-18
relative error = 4.5469779473557777918925709741122e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 1.5735358109848638007256023648672
y[1] (numeric) = 1.5735358109848638079030297152052
absolute error = 7.1774273503380e-18
relative error = 4.5613371492611306753722996798502e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 1.5746888959872918530066934229254
y[1] (numeric) = 1.5746888959872918602120119662228
absolute error = 7.2053185432974e-18
relative error = 4.5757092474954168888200529880870e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 1.575842555678663783322566120071
y[1] (numeric) = 1.5758425556786637905558319145405
absolute error = 7.2332657944695e-18
relative error = 4.5900942123969797833056052491450e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 1.5769967912126393791834615911146
y[1] (numeric) = 1.5769967912126393864447307229161
absolute error = 7.2612691318015e-18
relative error = 4.6044920143546466332742343690084e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 1.5781516037434542707512734011279
y[1] (numeric) = 1.5781516037434542780406019844247
absolute error = 7.2893285832968e-18
relative error = 4.6189026238075918984736369849227e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 1.5793069944259210850752738936428
y[1] (numeric) = 1.5793069944259210923927180706577
absolute error = 7.3174441770149e-18
relative error = 4.6333260112450744695321770933968e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 1.5804629644154306009048374743131
y[1] (numeric) = 1.5804629644154306082504534153844
absolute error = 7.3456159410713e-18
relative error = 4.6477621472061760874792511631337e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 1.5816195148679529040803156428564
y[1] (numeric) = 1.5816195148679529114541595464943
absolute error = 7.3738439036379e-18
relative error = 4.6622110022798570637362526667997e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 1.5827766469400385435032191642498
y[1] (numeric) = 1.5827766469400385509053472571923
absolute error = 7.4021280929425e-18
relative error = 4.6766725471044431561434910987742e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 1.5839343617888196876868633494558
y[1] (numeric) = 1.5839343617888196951173318867252
absolute error = 7.4304685372694e-18
relative error = 4.6911467523678091884667318458141e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 1.5850926605720112818886329964219
y[1] (numeric) = 1.585092660572011289347498261381
absolute error = 7.4588652649591e-18
relative error = 4.7056335888069940963377514908872e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 1.5862515444479122058250241237141
y[1] (numeric) = 1.5862515444479122133123424281223
absolute error = 7.4873183044082e-18
relative error = 4.7201330272079437635496109567640e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 1.5874110145754064319706202119222
y[1] (numeric) = 1.5874110145754064394864478959921
absolute error = 7.5158276840699e-18
relative error = 4.7346450384056329798172955263581e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 1.5885710721139641844421612519118
y[1] (numeric) = 1.5885710721139641919865546843652
absolute error = 7.5443934324534e-18
relative error = 4.7491695932834944387832437519722e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 1.5897317182236430984688644840853
y[1] (numeric) = 1.5897317182236431060418800622098
absolute error = 7.5730155781245e-18
relative error = 4.7637066627736051006692796047507e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.561
y[1] (analytic) = 1.5908929540650893804501562990724
y[1] (numeric) = 1.5908929540650893880518504487779
absolute error = 7.6016941497055e-18
relative error = 4.7782562178564317553370833478359e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 1.5920547807995389686019753576771
y[1] (numeric) = 1.5920547807995389762324045335518
absolute error = 7.6304291758747e-18
relative error = 4.7928182295603264707013354225484e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.563
y[1] (analytic) = 1.5932171995888186941928075764805
y[1] (numeric) = 1.5932171995888187018520282618479
absolute error = 7.6592206853674e-18
relative error = 4.8073926689619657603192490113480e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 1.5943802115953474433706142152332
y[1] (numeric) = 1.5943802115953474510586829222081
absolute error = 7.6880687069749e-18
relative error = 4.8219795071855334438866780357104e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 1.5955438179821373195818148930598
y[1] (numeric) = 1.5955438179821373272987881626052
absolute error = 7.7169732695454e-18
relative error = 4.8365787154030979172460695131031e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=12.06
NO POLE
x[1] = 0.566
y[1] (analytic) = 1.5967080199127948065834879525575
y[1] (numeric) = 1.5967080199127948143294223545408
absolute error = 7.7459344019833e-18
relative error = 4.8511902648339857310575467820192e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 1.5978728185515219320499511840842
y[1] (numeric) = 1.597872818551521939824903317334
absolute error = 7.7749521332498e-18
relative error = 4.8658141267449715086283339385975e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 1.5990382150631174317748865169153
y[1] (numeric) = 1.599038215063117439578913009278
absolute error = 7.8040264923627e-18
relative error = 4.8804502724499667526069180966653e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 1.6002042106129779144701728794904
y[1] (numeric) = 1.6002042106129779223033303878868
absolute error = 7.8331575083964e-18
relative error = 4.8950986733098350141878624470681e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 1.6013708063670990271625920276795
y[1] (numeric) = 1.6013708063670990350249372381612
absolute error = 7.8623452104817e-18
relative error = 4.9097593007320829958347349966748e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 1.6025380034920766211895727378715
y[1] (numeric) = 1.602538003492076629081162365678
absolute error = 7.8915896278065e-18
relative error = 4.9244321261711146316424261195116e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 1.6037058031551079187951393607276
y[1] (numeric) = 1.6037058031551079267160301503427
absolute error = 7.9208907896151e-18
relative error = 4.9391171211276110987898295956349e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 1.6048742065239926803272313316439
y[1] (numeric) = 1.6048742065239926882774800568526
absolute error = 7.9502487252087e-18
relative error = 4.9538142571486612761682211144000e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 1.6060432147671343720375608353407
y[1] (numeric) = 1.6060432147671343800172242992861
absolute error = 7.9796634639454e-18
relative error = 4.9685235058275803283603917591939e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 1.6072128290535413344851764245339
y[1] (numeric) = 1.6072128290535413424943114597735
absolute error = 8.0091350352396e-18
relative error = 4.9832448388033557821134717026835e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 1.6083830505528279515449009963477
y[1] (numeric) = 1.6083830505528279595835644649109
absolute error = 8.0386634685632e-18
relative error = 4.9979782277612151747562577096533e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 1.6095538804352158200218131350068
y[1] (numeric) = 1.6095538804352158280900619284513
absolute error = 8.0682487934445e-18
relative error = 5.0127236444317622772254750048283e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 1.6107253198715349198729414353844
y[1] (numeric) = 1.6107253198715349279708324748532
absolute error = 8.0978910394688e-18
relative error = 5.0274810605911725267261052015563e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 1.611897370033224785037342029199
y[1] (numeric) = 1.6118973700332247931649322654773
absolute error = 8.1275902362783e-18
relative error = 5.0422504480609533550878200728264e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 1.6130700320923356748757301440347
y[1] (numeric) = 1.6130700320923356830330765576071
absolute error = 8.1573464135724e-18
relative error = 5.0570317787079535539006201632069e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 1.6142433072215297462208371349153
y[1] (numeric) = 1.6142433072215297544079967360224
absolute error = 8.1871596011071e-18
relative error = 5.0718250244438150793946395758547e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.582
y[1] (analytic) = 1.6154171965940822260396650388846
y[1] (numeric) = 1.6154171965940822342566948675803
absolute error = 8.2170298286957e-18
relative error = 5.0866301572252320094499865664929e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 1.6165917013838825847088113149478
y[1] (numeric) = 1.6165917013838825929557684411561
absolute error = 8.2469571262083e-18
relative error = 5.1014471490534660877032170427051e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 1.6177668227654357099040370447943
y[1] (numeric) = 1.6177668227654357181809785683666
absolute error = 8.2769415235723e-18
relative error = 5.1162759719744825310348371230804e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 1.6189425619138630811052524839698
y[1] (numeric) = 1.6189425619138630894122355347419
absolute error = 8.3069830507721e-18
relative error = 5.1311165980785911132579071640161e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 1.6201189200049039447180944685794
y[1] (numeric) = 1.6201189200049039530551762064287
absolute error = 8.3370817378493e-18
relative error = 5.1459689995003974476795951181883e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.587
y[1] (analytic) = 1.6212958982149164898132707991985
y[1] (numeric) = 1.621295898214916498180508414101
absolute error = 8.3672376149025e-18
relative error = 5.1608331484185077826120075125222e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 1.6224734977208790244848473414329
y[1] (numeric) = 1.6224734977208790328822980535204
absolute error = 8.3974507120875e-18
relative error = 5.1757090170554816358689748677819e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
memory used=80.1MB, alloc=4.3MB, time=12.67
y[1] (analytic) = 1.6236517197003911528286542015135
y[1] (numeric) = 1.6236517197003911612563752611309
absolute error = 8.4277210596174e-18
relative error = 5.1905965776777230629051133328555e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 1.62483056533167495254198795543
y[1] (numeric) = 1.6248305653316749610000366431927
absolute error = 8.4580486877627e-18
relative error = 5.2054958025953724145487516428732e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 1.6260100357935761531457875314041
y[1] (numeric) = 1.626010035793576161634221158255
absolute error = 8.4884336268509e-18
relative error = 5.2204066641618910805785853016435e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 1.6271901322655653148304619679756
y[1] (numeric) = 1.6271901322655653233493378752427
absolute error = 8.5188759072671e-18
relative error = 5.2353291347742626121595622447019e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 1.6283708559277390079265488936282
y[1] (numeric) = 1.6283708559277390164759244530817
absolute error = 8.5493755594535e-18
relative error = 5.2502631868725174644922084808796e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 1.6295522079608209930013831987114
y[1] (numeric) = 1.6295522079608210015813158126211
absolute error = 8.5799326139097e-18
relative error = 5.2652087929397507539984047049025e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 1.630734189546163401582955996425
y[1] (numeric) = 1.6307341895461634101935030976178
absolute error = 8.6105471011928e-18
relative error = 5.2801659255020173108085864782084e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 1.6319168018657479175121445968248
y[1] (numeric) = 1.631916801865747926153363648742
absolute error = 8.6412190519172e-18
relative error = 5.2951345571280433702819659842446e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 1.6331000461021869589244948461766
y[1] (numeric) = 1.6331000461021869675964433429316
absolute error = 8.6719484967550e-18
relative error = 5.3101146604293069325590800420195e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 1.6342839234387248608627378135404
y[1] (numeric) = 1.634283923438724869565473279976
absolute error = 8.7027354664356e-18
relative error = 5.3251062080596282778153097118558e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 1.6354684350592390585212234371991
y[1] (numeric) = 1.6354684350592390672548034289452
absolute error = 8.7335799917461e-18
relative error = 5.3401091727152514320509029848143e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 1.6366535821482412711234543754652
y[1] (numeric) = 1.6366535821482412798879364789959
absolute error = 8.7644821035307e-18
relative error = 5.3551235271343142921215277864715e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 1.6378393658908786864339039394957
y[1] (numeric) = 1.6378393658908786952293457721875
absolute error = 8.7954418326918e-18
relative error = 5.3701492440973590199821107777040e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 1.6390257874729351459053026200354
y[1] (numeric) = 1.6390257874729351547317618302244
absolute error = 8.8264592101890e-18
relative error = 5.3851862964265589880998431659076e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 1.64021284808083233046257835547
y[1] (numeric) = 1.6402128480808323393201126225098
absolute error = 8.8575342670398e-18
relative error = 5.4002346569859855454754006074169e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 1.6414005489016309469246363252315
y[1] (numeric) = 1.6414005489016309558133033595505
absolute error = 8.8886670343190e-18
relative error = 5.4152942986810816354160203389776e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 1.6425888911230319150651646904314
y[1] (numeric) = 1.642588891123031923985022233591
absolute error = 8.9198575431596e-18
relative error = 5.4303651944590509047966570664418e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 1.6437778759333775553136533426294
y[1] (numeric) = 1.6437778759333775642647591673815
absolute error = 8.9511058247521e-18
relative error = 5.4454473173082717732659063547789e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 1.6449675045216527770978133618533
y[1] (numeric) = 1.644967504521652786080225272198
absolute error = 8.9824119103447e-18
relative error = 5.4605406402582611811605770299132e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 1.6461577780774862678285855263887
y[1] (numeric) = 1.6461577780774862768423613576323
absolute error = 9.0137758312436e-18
relative error = 5.4756451363796992577391879275197e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.609
y[1] (analytic) = 1.6473486977911516825289268594476
y[1] (numeric) = 1.6473486977911516915741244782602
absolute error = 9.0451976188126e-18
relative error = 5.4907607787840289720405046153584e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 1.6485402648535688341075648415995
y[1] (numeric) = 1.6485402648535688431842421460731
absolute error = 9.0766773044736e-18
relative error = 5.5058875406236034713086893890660e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 1.6497324804563048842789095628203
y[1] (numeric) = 1.6497324804563048933871244825265
absolute error = 9.1082149197062e-18
relative error = 5.5210253950912872528229238848624e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 1.650925345791575535130314734169
y[1] (numeric) = 1.650925345791575544270125230217
absolute error = 9.1398104960480e-18
relative error = 5.5361743154204830828957485472919e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=83.9MB, alloc=4.3MB, time=13.28
x[1] = 0.613
y[1] (analytic) = 1.6521188620522462213378791264532
y[1] (numeric) = 1.6521188620522462305093431915478
absolute error = 9.1714640650946e-18
relative error = 5.5513342748849772291709388853021e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 1.653313030431833303031980651784
y[1] (numeric) = 1.6533130304318333122351563102837
absolute error = 9.2031756584997e-18
relative error = 5.5665052467988458621958624186180e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 1.6545078521245052593137359536544
y[1] (numeric) = 1.6545078521245052685486812616291
absolute error = 9.2349453079747e-18
relative error = 5.5816872045160596718603944484551e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 1.6557033283250838824235790220985
y[1] (numeric) = 1.6557033283250838916903520673879
absolute error = 9.2667730452894e-18
relative error = 5.5968801214307545806092248780623e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 1.656899460229045472563153002612
y[1] (numeric) = 1.6568994602290454818618119048834
absolute error = 9.2986589022714e-18
relative error = 5.6120839709767167012074116331690e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 1.6580962490325220333717100208232
y[1] (numeric) = 1.65809624903252204270231293163
absolute error = 9.3306029108068e-18
relative error = 5.6272987266276535693556316253700e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 1.6592936959323024680582144994161
y[1] (numeric) = 1.6592936959323024774208196022555
absolute error = 9.3626051028394e-18
relative error = 5.6425243618965602176444327519780e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 1.6604918021258337761903460995061
y[1] (numeric) = 1.6604918021258337855850116098775
absolute error = 9.3946655103714e-18
relative error = 5.6577608503359913531330512582273e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 1.6616905688112222511415990755734
y[1] (numeric) = 1.6616905688112222605683832410366
absolute error = 9.4267841654632e-18
relative error = 5.6730081655377907550401164978923e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 1.6628899971872346781976754911513
y[1] (numeric) = 1.6628899971872346876566365913849
absolute error = 9.4589611002336e-18
relative error = 5.6882662811330624014508175282433e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 1.664090088453299533323370401764
y[1] (numeric) = 1.6640900884532995428145667486235
absolute error = 9.4911963468595e-18
relative error = 5.7035351707918412700662806017596e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 1.665290843809508182591147772098
y[1] (numeric) = 1.6652908438095081921146377096741
absolute error = 9.5234899375761e-18
relative error = 5.7188148082230658239558954336129e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 1.666492264456616082272606556083
y[1] (numeric) = 1.66649226445661609182844846076
absolute error = 9.5558419046770e-18
relative error = 5.7341051671744906241134968863140e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 1.6676943515960439795940370314491
y[1] (numeric) = 1.6676943515960439891822893119632
absolute error = 9.5882522805141e-18
relative error = 5.7494062214324794072979801619918e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 1.6688971064298791141572681444159
y[1] (numeric) = 1.6688971064298791237779892419137
absolute error = 9.6207210974978e-18
relative error = 5.7647179448219788311583424592934e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 1.6701005301608764200270072854613
y[1] (numeric) = 1.6701005301608764296802556735584
absolute error = 9.6532483880971e-18
relative error = 5.7800403112064324697396030792434e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 1.6713046239924597284858745836106
y[1] (numeric) = 1.6713046239924597381717087684496
absolute error = 9.6858341848390e-18
relative error = 5.7953732944872763591217980008173e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 1.6725093891287229714583344743783
y[1] (numeric) = 1.6725093891287229811768129946879
absolute error = 9.7184785203096e-18
relative error = 5.8107168686044531725915269597693e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 1.673714826774431385604727965398
y[1] (numeric) = 1.6737148267744313953559093925511
absolute error = 9.7511814271531e-18
relative error = 5.8260710075356694946326644833808e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
y[1] (analytic) = 1.6749209381350227170866096938689
y[1] (numeric) = 1.6749209381350227268705526319413
absolute error = 9.7839429380724e-18
relative error = 5.8414356852966115837549877214618e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 1.6761277244166084270045945412598
y[1] (numeric) = 1.6761277244166084368213576270888
absolute error = 9.8167630858290e-18
relative error = 5.8568108759407425884872039296798e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 1.6773351868259748975099192432156
y[1] (numeric) = 1.6773351868259749073595611464586
absolute error = 9.8496419032430e-18
relative error = 5.8721965535591602700188461854401e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 1.678543326570584638590925106329
y[1] (numeric) = 1.6785433265705846484735045295224
absolute error = 9.8825794231934e-18
relative error = 5.8875926922806340784941303756399e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 1.6797521448585774955356686183615
y[1] (numeric) = 1.6797521448585775054512442969791
absolute error = 9.9155756786176e-18
relative error = 5.9029992662711658213641863327255e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=87.7MB, alloc=4.3MB, time=13.90
x[1] = 0.637
y[1] (analytic) = 1.6809616428987718570718674146234
y[1] (numeric) = 1.6809616428987718670204981171352
absolute error = 9.9486307025118e-18
relative error = 5.9184162497340876480881513260572e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 1.6821718219006658641853897405604
y[1] (numeric) = 1.6821718219006658741671342684915
absolute error = 9.9817445279311e-18
relative error = 5.9338436169099812847446414139443e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 1.6833826830744386196184962291372
y[1] (numeric) = 1.6833826830744386296334134171265
absolute error = 1.00149171879893e-17
relative error = 5.9492813420764194169708924527325e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 1.6845942276309513980490434913598
y[1] (numeric) = 1.684594227630951408097192207219
absolute error = 1.00481487158592e-17
relative error = 5.9647293995480050083128739803783e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 1.685806456781748856951859699242
y[1] (numeric) = 1.6858064567817488670332988440142
absolute error = 1.00814391447722e-17
relative error = 5.9801877636759952302548262681131e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 1.6870193717390602481435030226915
y[1] (numeric) = 1.6870193717390602582582915307102
absolute error = 1.01147885080187e-17
relative error = 5.9956564088484012355145128744273e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 1.6882329737158006300116144651759
y[1] (numeric) = 1.688232973715800640159811304124
absolute error = 1.01481968389481e-17
relative error = 6.0111353094898505802268226722688e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 1.6894472639255720804300773276217
y[1] (numeric) = 1.6894472639255720906117414985905
absolute error = 1.01816641709688e-17
relative error = 6.0266244400614502514018832852033e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 1.6906622435826649103611962158077
y[1] (numeric) = 1.6906622435826649205763867533558
absolute error = 1.02151905375481e-17
relative error = 6.0421237750605911486088993890516e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 1.6918779139020588781461091935322
y[1] (numeric) = 1.6918779139020588883948851657446
absolute error = 1.02487759722124e-17
relative error = 6.0576332890209307384493609055029e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 1.6930942760994244044846473720676
y[1] (numeric) = 1.6930942760994244147670678806146
absolute error = 1.02824205085470e-17
relative error = 6.0731529565121395425204337449912e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 1.6943113313911237881058569158632
y[1] (numeric) = 1.6943113313911237984219810960597
absolute error = 1.03161241801965e-17
relative error = 6.0886827521400028560679016073894e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 1.6955290809942124221303991351197
y[1] (numeric) = 1.6955290809942124324802861559844
absolute error = 1.03498870208647e-17
relative error = 6.1042226505462271477981318552296e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 1.6967475261264400111260450277366
y[1] (numeric) = 1.696747526126440021509754092051
absolute error = 1.03837090643144e-17
relative error = 6.1197726264081883688734978368916e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 1.6979666680062517888574813262288
y[1] (numeric) = 1.6979666680062517992750716705964
absolute error = 1.04175903443676e-17
relative error = 6.1353326544389169338358516299196e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 1.6991865078527897367316457995195
y[1] (numeric) = 1.6991865078527897471831766944249
absolute error = 1.04515308949054e-17
relative error = 6.1509027093869062237085980986140e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 1.700407046885893802939810255046
y[1] (numeric) = 1.7004070468858938134253410049147
absolute error = 1.04855307498687e-17
relative error = 6.1664827660363924013246062049905e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 1.7016282863261031222976303833647
y[1] (numeric) = 1.7016282863261031328172203266218
absolute error = 1.05195899432571e-17
relative error = 6.1820727992065752237427745717394e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 1.7028502273946572367843822854041
y[1] (numeric) = 1.702850227394657247338090794534
absolute error = 1.05537085091299e-17
relative error = 6.1976727837520754458405081170858e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.656
y[1] (analytic) = 1.7040728713134973167826062217065
y[1] (numeric) = 1.7040728713134973273704927033122
absolute error = 1.05878864816057e-17
relative error = 6.2132826945625687076869339011316e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 1.7052962193052673830193788234023
y[1] (numeric) = 1.7052962193052673936415027182647
absolute error = 1.06221238948624e-17
relative error = 6.2289025065626555715354981423800e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 1.7065202725933155292104357062918
y[1] (numeric) = 1.7065202725933155398668564894294
absolute error = 1.06564207831376e-17
relative error = 6.2445321947119665251904291680282e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.659
y[1] (analytic) = 1.7077450324016951454083671322591
y[1] (numeric) = 1.7077450324016951560991443129869
absolute error = 1.06907771807278e-17
relative error = 6.2601717340045638645591954556476e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 1.708970499955166142056110066314
y[1] (numeric) = 1.7089704999551661527813031883037
absolute error = 1.07251931219897e-17
relative error = 6.2758210994695749702261601715591e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=91.5MB, alloc=4.3MB, time=14.51
x[1] = 0.661
y[1] (analytic) = 1.7101966764791961747469606828591
y[1] (numeric) = 1.7101966764791961855066293241984
absolute error = 1.07596686413393e-17
relative error = 6.2914802661705364716514563588380e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 1.7114235631999618696923320812939
y[1] (numeric) = 1.7114235631999618804865358545458
absolute error = 1.07942037732519e-17
relative error = 6.3071492092052671193114810720518e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 1.7126511613443500498984826788163
y[1] (numeric) = 1.7126511613443500607272812310791
absolute error = 1.08287985522628e-17
relative error = 6.3228279037061499389946512489413e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 1.7138794721399589620534414572535
y[1] (numeric) = 1.7138794721399589729168944702202
absolute error = 1.08634530129667e-17
relative error = 6.3385163248396546721790991650426e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 1.7151084968150995041253569509481
y[1] (numeric) = 1.7151084968150995150235241409662
absolute error = 1.08981671900181e-17
relative error = 6.3542144478064453331742970807831e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.666
y[1] (analytic) = 1.7163382365987964536734975741516
y[1] (numeric) = 1.7163382365987964646064386922828
absolute error = 1.09329411181312e-17
relative error = 6.3699222478411959982791980097198e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 1.7175686927207896968731315990278
y[1] (numeric) = 1.7175686927207897078409064311076
absolute error = 1.09677748320798e-17
relative error = 6.3856397002124073976441950271425e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.668
y[1] (analytic) = 1.7187998664115354582555158092478
y[1] (numeric) = 1.7187998664115354692581841759456
absolute error = 1.10026683666978e-17
relative error = 6.4013667802225733875170476106431e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 1.7200317589022075311642225692698
y[1] (numeric) = 1.7200317589022075422018443261484
absolute error = 1.10376217568786e-17
relative error = 6.4171034632077071958539918613872e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 1.7212643714246985089290357657301
y[1] (numeric) = 1.7212643714246985200016708033058
absolute error = 1.10726350375757e-17
relative error = 6.4328497245375668754979050736207e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 1.7224977052116210167586467949473
y[1] (numeric) = 1.7224977052116210278663550387495
absolute error = 1.11077082438022e-17
relative error = 6.4486055396152411936195761056254e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 1.7237317614963089443533824893352
y[1] (numeric) = 1.7237317614963089554962238999667
absolute error = 1.11428414106315e-17
relative error = 6.4643708838774334742411518934926e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 1.7249665415128186792391975955576
y[1] (numeric) = 1.7249665415128186904172321687544
absolute error = 1.11780345731968e-17
relative error = 6.4801457327940485681751167114722e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 1.7262020464959303408241651385189
y[1] (numeric) = 1.7262020464959303520374529052099
absolute error = 1.12132877666910e-17
relative error = 6.4959300618680133289842341059210e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 1.7274382776811490151786987277833
y[1] (numeric) = 1.7274382776811490264272997541509
absolute error = 1.12486010263676e-17
relative error = 6.5117238466356767633142245937046e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 1.7286752363047059905407415867496
y[1] (numeric) = 1.7286752363047060018247159742893
absolute error = 1.12839743875397e-17
relative error = 6.5275270626661093678030948343025e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 1.7299129236035599935471578098714
y[1] (numeric) = 1.7299129236035600048665656954521
absolute error = 1.13194078855807e-17
relative error = 6.5433396855613881911012852354490e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 1.731151340815398426192562079419
y[1] (numeric) = 1.731151340815398437547463635343
absolute error = 1.13549015559240e-17
relative error = 6.5591616909563030347489355010583e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 1.7323904891786386035168248007138
y[1] (numeric) = 1.7323904891786386149072802347772
absolute error = 1.13904554340634e-17
relative error = 6.5749930545184679910858126197413e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.68
y[1] (analytic) = 1.7336303699324289920224903434455
y[1] (numeric) = 1.7336303699324290034485598989983
absolute error = 1.14260695555528e-17
relative error = 6.5908337519480287369627241536476e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 1.7348709843166504488233468065919
y[1] (numeric) = 1.7348709843166504602850907625983
absolute error = 1.14617439560064e-17
relative error = 6.6066837589776592992380165289502e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 1.7361123335719174615253864556155
y[1] (numeric) = 1.7361123335719174730228651267138
absolute error = 1.14974786710983e-17
relative error = 6.6225430513722132456141113155126e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.683
y[1] (analytic) = 1.7373544189395793888413967129993
y[1] (numeric) = 1.7373544189395794003746704495628
absolute error = 1.15332737365635e-17
relative error = 6.6384116049291822052183042230343e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 1.7385972416617217019404223168181
y[1] (numeric) = 1.738597241661721713509551505015
absolute error = 1.15691291881969e-17
relative error = 6.6542893954780020820360846897950e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=95.3MB, alloc=4.3MB, time=15.14
x[1] = 0.685
y[1] (analytic) = 1.739840802981167226533339996909
y[1] (numeric) = 1.739840802981167238138385058763
absolute error = 1.16050450618540e-17
relative error = 6.6701763988803393531533214789882e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 1.7410851041414773856957877543204
y[1] (numeric) = 1.7410851041414773973368091477711
absolute error = 1.16410213934507e-17
relative error = 6.6860725910298592326873607124408e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 1.7423301463869534434296915670721
y[1] (numeric) = 1.7423301463869534551067497860355
absolute error = 1.16770582189634e-17
relative error = 6.7019779478521670228213718277781e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 1.7435759309626377489646330838569
y[1] (numeric) = 1.7435759309626377606777886582858
absolute error = 1.17131555744289e-17
relative error = 6.7178924453046350202055333854341e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 1.7448224591143149818003026071546
y[1] (numeric) = 1.744822459114314993549616103099
absolute error = 1.17493134959444e-17
relative error = 6.7338160593762874872106482185249e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 1.7460697320885133974912824083156
y[1] (numeric) = 1.7460697320885134092768144279836
absolute error = 1.17855320196680e-17
relative error = 6.7497487660879724845381847127867e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 1.7473177511325060741754061595017
y[1] (numeric) = 1.7473177511325060859972173413198
absolute error = 1.18218111818181e-17
relative error = 6.7656905414919034421583175330727e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.692
y[1] (analytic) = 1.7485665174943121598469410109458
y[1] (numeric) = 1.7485665174943121717050920296198
absolute error = 1.18581510186740e-17
relative error = 6.7816413616718889803633466909066e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 1.7498160324226981203758395868189
y[1] (numeric) = 1.7498160324226981322703911533944
absolute error = 1.18945515665755e-17
relative error = 6.7976012027429902691256125962068e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 1.7510662971671789882743099190578
y[1] (numeric) = 1.7510662971671790002053227809809
absolute error = 1.19310128619231e-17
relative error = 6.8135700408515225132188664137028e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 1.7523173129780196122119520858294
y[1] (numeric) = 1.7523173129780196241794870270075
absolute error = 1.19675349411781e-17
relative error = 6.8295478521749993747895112063060e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 1.7535690811062359072807110698719
y[1] (numeric) = 1.7535690811062359192848289107346
absolute error = 1.20041178408627e-17
relative error = 6.8455346129220776444419481732866e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 1.7548216028035961060108961017694
y[1] (numeric) = 1.754821602803596118051657699329
absolute error = 1.20407615975596e-17
relative error = 6.8615302993322172302394827146641e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 1.7560748793226220101395175042836
y[1] (numeric) = 1.7560748793226220222169837521964
absolute error = 1.20774662479128e-17
relative error = 6.8775348876760259547755308300303e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 1.7573289119165902431321928061852
y[1] (numeric) = 1.7573289119165902552464246348119
absolute error = 1.21142318286267e-17
relative error = 6.8935483542546355102503722777829e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 1.7585837018395335034598746475928
y[1] (numeric) = 1.7585837018395335156109330240598
absolute error = 1.21510583764670e-17
relative error = 6.9095706754001036448123765939193e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 1.7598392503462418186316537536541
y[1] (numeric) = 1.7598392503462418308195996819144
absolute error = 1.21879459282603e-17
relative error = 6.9256018274750759355641857446604e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 1.761095558692263799984891009476
y[1] (numeric) = 1.7610955586922638122097855303702
absolute error = 1.22248945208942e-17
relative error = 6.9416417868727329323520859075630e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 1.7623526281339078982339334265398
y[1] (numeric) = 1.7623526281339079104958376178569
absolute error = 1.22619041913171e-17
relative error = 6.9576905300165673112744035807580e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 1.7636104599282436597786695494222
y[1] (numeric) = 1.763610459928243672077644525961
absolute error = 1.22989749765388e-17
relative error = 6.9737480333606156069746028102732e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 1.7648690553331029837741806114835
y[1] (numeric) = 1.7648690553331029961102875251136
absolute error = 1.23361069136301e-17
relative error = 6.9898142733891223502169270779482e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 1.7661284156070813799627445092769
y[1] (numeric) = 1.7661284156070813923360445489997
absolute error = 1.23733000397228e-17
relative error = 7.0058892266164321355078653720595e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 1.7673885420095392272694504277888
y[1] (numeric) = 1.7673885420095392396800048197991
absolute error = 1.24105543920103e-17
relative error = 7.0219728695872216449602243165373e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 1.7686494358006030331626827122305
y[1] (numeric) = 1.7686494358006030456105527199772
absolute error = 1.24478700077467e-17
relative error = 7.0380651788758825856268737276591e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=99.1MB, alloc=4.3MB, time=15.76
x[1] = 0.709
y[1] (analytic) = 1.7699110982411666937807333469674
y[1] (numeric) = 1.7699110982411667062659802712151
absolute error = 1.24852469242477e-17
relative error = 7.0541661310869242748743639119774e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 1.7711735305928927548258031683066
y[1] (numeric) = 1.7711735305928927673484883471968
absolute error = 1.25226851788902e-17
relative error = 7.0702757028546405394600552960279e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 1.7724367341182136732266527052461
y[1] (numeric) = 1.7724367341182136857868375143587
absolute error = 1.25601848091126e-17
relative error = 7.0863938708431729843604057087199e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 1.7737007100803330795711643109443
y[1] (numeric) = 1.7737007100803330921689101633586
absolute error = 1.25977458524143e-17
relative error = 7.1025206117461229671271677421623e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 1.7749654597432270413100780175742
y[1] (numeric) = 1.7749654597432270539454463639307
absolute error = 1.26353683463565e-17
relative error = 7.1186559022868976492228095899664e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 1.7762309843716453267331643184066
y[1] (numeric) = 1.7762309843716453394062166469683
absolute error = 1.26730523285617e-17
relative error = 7.1347997192183226926388406163580e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 1.7774972852311126697190978533979
y[1] (numeric) = 1.7774972852311126824298956901117
absolute error = 1.27107978367138e-17
relative error = 7.1509520393225941738408495218892e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 1.7787643635879300352602967482626
y[1] (numeric) = 1.778764363587930048008901656821
absolute error = 1.27486049085584e-17
relative error = 7.1671128394113431513639805673865e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 1.7800322207091758857639931319756
y[1] (numeric) = 1.7800322207091758985504667138782
absolute error = 1.27864735819026e-17
relative error = 7.1832820963254190739568677546718e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 1.7813008578627074481308011338795
y[1] (numeric) = 1.7813008578627074609552050284945
absolute error = 1.28244038946150e-17
relative error = 7.1994597869347864010448680641254e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 1.7825702763171619816120494390714
y[1] (numeric) = 1.7825702763171619944744453236973
absolute error = 1.28623958846259e-17
relative error = 7.2156458881385338725950719129792e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 1.7838404773419580464471462595065
y[1] (numeric) = 1.7838404773419580593475958494338
absolute error = 1.29004495899273e-17
relative error = 7.2318403768647716319925891627945e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 1.7851114622072967732822453582898
y[1] (numeric) = 1.7851114622072967862208104068628
absolute error = 1.29385650485730e-17
relative error = 7.2480432300705848169586984853781e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 1.786383232184163133371482545928
y[1] (numeric) = 1.7863832321841631463482248446064
absolute error = 1.29767422986784e-17
relative error = 7.2642544247418194213837594346978e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 1.7876557885443272095620528498828
y[1] (numeric) = 1.7876557885443272225770342283034
absolute error = 1.30149813784206e-17
relative error = 7.2804739378930368988335872851120e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 1.7889291325603454680643993426095
y[1] (numeric) = 1.7889291325603454811176816686485
absolute error = 1.30532823260390e-17
relative error = 7.2967017465677484671277491364507e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 1.7902032655055620310087853983764
y[1] (numeric) = 1.7902032655055620441004305782107
absolute error = 1.30916451798343e-17
relative error = 7.3129378278377546692259939202083e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 1.7914781886541099497895229355413
y[1] (numeric) = 1.7914781886541099629195929137108
absolute error = 1.31300699781695e-17
relative error = 7.3291821588036041587053401342319e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 1.7927539032809124791981299886216
y[1] (numeric) = 1.7927539032809124923666867480909
absolute error = 1.31685567594693e-17
relative error = 7.3454347165941580566027760736005e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 1.7940304106616843523466917434203
y[1] (numeric) = 1.7940304106616843655537973056408
absolute error = 1.32071055622205e-17
relative error = 7.3616954783667135805258463072406e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 1.7953077120729330563826999586758
y[1] (numeric) = 1.7953077120729330696284163836477
absolute error = 1.32457164249719e-17
relative error = 7.3779644213068486528460216043860e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 1.796585808791960108996646489181
y[1] (numeric) = 1.7965858087919601222810358755156
absolute error = 1.32843893863346e-17
relative error = 7.3942415226284898259597138595854e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 1.7978647020968623357236474180725
y[1] (numeric) = 1.7978647020968623490467719030537
absolute error = 1.33231244849812e-17
relative error = 7.4105267595733680904788859950704e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 1.7991443932665331480403751000181
y[1] (numeric) = 1.7991443932665331614022968596651
absolute error = 1.33619217596470e-17
relative error = 7.4268201094115886541347580675246e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=103.0MB, alloc=4.3MB, time=16.37
x[1] = 0.733
y[1] (analytic) = 1.8004248835806638222585762123443
y[1] (numeric) = 1.8004248835806638356593574614735
absolute error = 1.34007812491292e-17
relative error = 7.4431215494410874522257766517892e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 1.801706174319744779216454707726
y[1] (numeric) = 1.8017061743197447926561577000133
absolute error = 1.34397029922873e-17
relative error = 7.4594310569877560199796954108918e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 1.8029882667650668647691993599291
y[1] (numeric) = 1.8029882667650668782478863879722
absolute error = 1.34786870280431e-17
relative error = 7.4757486094053439888551950921348e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 1.8042711621987226310799363932401
y[1] (numeric) = 1.8042711621987226445976697886207
absolute error = 1.35177333953806e-17
relative error = 7.4920741840753065840413223793051e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 1.8055548619036076187123884866415
y[1] (numeric) = 1.8055548619036076322692306199878
absolute error = 1.35568421333463e-17
relative error = 7.5084077584068743204498739295710e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 1.8068393671634216395265222455005
y[1] (numeric) = 1.8068393671634216531225355265493
absolute error = 1.35960132810488e-17
relative error = 7.5247493098367349944730388649712e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 1.8081246792626700603784670365228
y[1] (numeric) = 1.808124679262670074013713914182
absolute error = 1.36352468776592e-17
relative error = 7.5410988158291594883574775910080e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 1.8094107994866650876259888859995
y[1] (numeric) = 1.8094107994866651013005318484108
absolute error = 1.36745429624113e-17
relative error = 7.5574562538760165153506695269755e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 1.8106977291215270524408039469279
y[1] (numeric) = 1.8106977291215270661547055215289
absolute error = 1.37139015746010e-17
relative error = 7.5738216014963454924936617558746e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 1.8119854694541856969290168474245
y[1] (numeric) = 1.8119854694541857106823396010115
absolute error = 1.37533227535870e-17
relative error = 7.5901948362366486883106637190664e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 1.8132740217723814610609700409793
y[1] (numeric) = 1.8132740217723814748537765797697
absolute error = 1.37928065387904e-17
relative error = 7.6065759356705754982718884028086e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 1.8145633873646667704117910885045
y[1] (numeric) = 1.8145633873646667842441440581996
absolute error = 1.38323529696951e-17
relative error = 7.6229648773990489521523525664805e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 1.8158535675204073247139256128348
y[1] (numeric) = 1.8158535675204073385858876986822
absolute error = 1.38719620858474e-17
relative error = 7.6393616390499511279699047953777e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 1.8171445635297833872229444783179
y[1] (numeric) = 1.8171445635297834011345784051746
absolute error = 1.39116339268567e-17
relative error = 7.6557661982784152609486891951057e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 1.8184363766837910748979145614115
y[1] (numeric) = 1.818436376683791088849283093806
absolute error = 1.39513685323945e-17
relative error = 7.6721785327661817485942700746600e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 1.8197290082742436493976232927628
y[1] (numeric) = 1.8197290082742436633887892349584
absolute error = 1.39911659421956e-17
relative error = 7.6885986202221658795674603756165e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 1.8210224595937728088939479671051
y[1] (numeric) = 1.8210224595937728229249741631626
absolute error = 1.40310261960575e-17
relative error = 7.7050264383820346990458328877269e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 1.8223167319358299807036616344469
y[1] (numeric) = 1.8223167319358299947746109682871
absolute error = 1.40709493338402e-17
relative error = 7.7214619650080051853963367144729e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.751
y[1] (analytic) = 1.8236118265946876147399682044671
y[1] (numeric) = 1.8236118265946876288509035999341
absolute error = 1.41109353954670e-17
relative error = 7.7379051778891916588596564931383e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 1.8249077448654404777850602157604
y[1] (numeric) = 1.8249077448654404919360446366843
absolute error = 1.41509844209239e-17
relative error = 7.7543560548411845585235078266673e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 1.826204488044006948584993542597
y[1] (numeric) = 1.826204488044006962776089992857
absolute error = 1.41910964502600e-17
relative error = 7.7708145737061786054439888576677e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 1.8275020574271303137681741341806
y[1] (numeric) = 1.8275020574271303279994456577679
absolute error = 1.42312715235873e-17
relative error = 7.7872807123527721128753344337150e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 1.8288004543123800645887527049984
y[1] (numeric) = 1.8288004543123800788602623860793
absolute error = 1.42715096810809e-17
relative error = 7.8037544486759858827593167657204e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 1.8300996799981531944962241197663
y[1] (numeric) = 1.8300996799981532088080350827452
absolute error = 1.43118109629789e-17
relative error = 7.8202357605971181058528438815056e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.3MB, time=16.98
x[1] = 0.757
y[1] (analytic) = 1.8313997357836754975325290426768
y[1] (numeric) = 1.8313997357836755118847044522594
absolute error = 1.43521754095826e-17
relative error = 7.8367246260637636980132343239798e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 1.8327006229690028675579562481595
y[1] (numeric) = 1.8327006229690028819505593094161
absolute error = 1.43926030612566e-17
relative error = 7.8532210230497789993647622213286e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 1.8340023428550225983071448191648
y[1] (numeric) = 1.8340023428550226127402387775931
absolute error = 1.44330939584283e-17
relative error = 7.8697249295549194793609704794538e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 1.8353048967434546842764862890807
y[1] (numeric) = 1.8353048967434546987501344306695
absolute error = 1.44736481415888e-17
relative error = 7.8862363236052418093175004497908e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 1.8366082859368531224442276147945
y[1] (numeric) = 1.8366082859368531369584932660868
absolute error = 1.45142656512923e-17
relative error = 7.9027551832526875106944295992623e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 1.8379125117386072148245767011098
y[1] (numeric) = 1.8379125117386072293795232292658
absolute error = 1.45549465281560e-17
relative error = 7.9192814865749404313125380550023e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 1.8392175754529428718571130307326
y[1] (numeric) = 1.8392175754529428864528038435938
absolute error = 1.45956908128612e-17
relative error = 7.9358152116759372895271173205553e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 1.840523478384923916632806789348
y[1] (numeric) = 1.8405234783849239312693053354999
absolute error = 1.46364985461519e-17
relative error = 7.9523563366850177460346873279592e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 1.8418302218404533899579507119114
y[1] (numeric) = 1.8418302218404534046353204807475
absolute error = 1.46773697688361e-17
relative error = 7.9689048397575440332474879694899e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 1.8431378071262748562573097141995
y[1] (numeric) = 1.8431378071262748709756142359841
absolute error = 1.47183045217846e-17
relative error = 7.9854606990741615762841407025643e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 1.8444462355499737103177942128746
y[1] (numeric) = 1.8444462355499737250770970588072
absolute error = 1.47593028459326e-17
relative error = 8.0020238928415808388159801575252e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 1.8457555084199784848739638778494
y[1] (numeric) = 1.8457555084199784996743286601275
absolute error = 1.48003647822781e-17
relative error = 8.0185943992916221455299333184020e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 1.8470656270455621590366694025604
y[1] (numeric) = 1.8470656270455621738781597744437
absolute error = 1.48414903718833e-17
relative error = 8.0351721966818887732394337645108e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
y[1] (analytic) = 1.8483765927368434675661407209046
y[1] (numeric) = 1.8483765927368434824488203767782
absolute error = 1.48826796558736e-17
relative error = 8.0517572632951387528244300853665e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 1.8496884068047882109908309440337
y[1] (numeric) = 1.8496884068047882259147636194721
absolute error = 1.49239326754384e-17
relative error = 8.0683495774396324879833470493893e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 1.8510010705612105665733261359612
y[1] (numeric) = 1.851001070561210581538575607792
absolute error = 1.49652494718308e-17
relative error = 8.0849491174488846325086124031097e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 1.8523145853187744001246318940003
y[1] (numeric) = 1.8523145853187744151312619803677
absolute error = 1.50066300863674e-17
relative error = 8.1015558616814710175789572125316e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 1.8536289523909945786681485484284
y[1] (numeric) = 1.8536289523909945937162231088573
absolute error = 1.50480745604289e-17
relative error = 8.1181697885212679953763660333825e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 1.8549441730922382839546476454634
y[1] (numeric) = 1.8549441730922382990442305809231
absolute error = 1.50895829354597e-17
relative error = 8.1347908763771516746520690639830e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.776
y[1] (analytic) = 1.8562602487377263268295632286373
y[1] (numeric) = 1.8562602487377263419607184816057
absolute error = 1.51311552529684e-17
relative error = 8.1514191036831832893894275617257e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 1.8575771806435344624539122859684
y[1] (numeric) = 1.8575771806435344776267038404956
absolute error = 1.51727915545272e-17
relative error = 8.1680544488982016192371662648133e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 1.8588949701265947063801595839614
y[1] (numeric) = 1.8588949701265947215946514657337
absolute error = 1.52144918817723e-17
relative error = 8.1846968905059551053257158780989e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 1.8602136185046966514843429644102
y[1] (numeric) = 1.8602136185046966667405992408143
absolute error = 1.52562562764041e-17
relative error = 8.2013464070151258997590666068974e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 1.8615331270964887857557760362392
y[1] (numeric) = 1.8615331270964888010538608164263
absolute error = 1.52980847801871e-17
relative error = 8.2180029769591926641098419676584e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.3MB, time=17.60
x[1] = 0.781
y[1] (analytic) = 1.8628534972214798109456460521944
y[1] (numeric) = 1.8628534972214798262856234871441
absolute error = 1.53399774349497e-17
relative error = 8.2346665788962402784729725592259e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 1.8641747302000399620758256190927
y[1] (numeric) = 1.8641747302000399774577599016773
absolute error = 1.53819342825846e-17
relative error = 8.2513371914090922266474858360760e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 1.8654968273534023278092177505514
y[1] (numeric) = 1.8654968273534023432331731156
absolute error = 1.54239553650486e-17
relative error = 8.2680147931051207978042851005276e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 1.8668197900036641716829546326518
y[1] (numeric) = 1.8668197900036641871489953570146
absolute error = 1.54660407243628e-17
relative error = 8.2846993626162723715253249810588e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
y[1] (analytic) = 1.8681436194737882542057713358476
y[1] (numeric) = 1.8681436194737882697139617384601
absolute error = 1.55081904026125e-17
relative error = 8.3013908785989320172010274884670e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 1.8694683170876041558208765705996
y[1] (numeric) = 1.8694683170876041713712810125472
absolute error = 1.55504044419476e-17
relative error = 8.3180893197340561332990210569026e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 1.8707938841698096007356434497207
y[1] (numeric) = 1.8707938841698096163283263343026
absolute error = 1.55926828845819e-17
relative error = 8.3347946647267165460592157110810e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 1.872120322045971781619444087229
y[1] (numeric) = 1.872120322045971797254469860023
absolute error = 1.56350257727940e-17
relative error = 8.3515068923065011998484162483616e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 1.8734476320425286851709527316565
y[1] (numeric) = 1.8734476320425287008483858805833
absolute error = 1.56774331489268e-17
relative error = 8.3682259812271658692432577473265e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 1.8747758154867904185562430012262
y[1] (numeric) = 1.8747758154867904342761480566138
absolute error = 1.57199050553876e-17
relative error = 8.3849519102666073970168795238380e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 1.8761048737069405367190056591047
y[1] (numeric) = 1.8761048737069405524814471937529
absolute error = 1.57624415346482e-17
relative error = 8.4016846582268370550569345423981e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 1.8774348080320373705642142390595
y[1] (numeric) = 1.8774348080320373863692568683048
absolute error = 1.58050426292453e-17
relative error = 8.4184242039341138199520441263840e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.793
y[1] (analytic) = 1.8787656197920153560165667052975
y[1] (numeric) = 1.8787656197920153718642750870774
absolute error = 1.58477083817799e-17
relative error = 8.4351705262385448264905302134352e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 1.880097310317686363955032205036
y[1] (numeric) = 1.8800973103176863798454710399538
absolute error = 1.58904388349178e-17
relative error = 8.4519236040142726026319320144348e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 1.8814298809407410310248328484649
y[1] (numeric) = 1.8814298809407410469580668798543
absolute error = 1.59332340313894e-17
relative error = 8.4686834161592894610876523552280e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 1.8827633329937500913281913281922
y[1] (numeric) = 1.8827633329937501073042853421822
absolute error = 1.59760940139900e-17
relative error = 8.4854499415955182547493218135980e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.797
y[1] (analytic) = 1.8840976678101657089951760690317
y[1] (numeric) = 1.8840976678101657250141948946111
absolute error = 1.60190188255794e-17
relative error = 8.5022231592685212672342917792844e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 1.8854328867243228116359764790885
y[1] (numeric) = 1.8854328867243228276979849881711
absolute error = 1.60620085090826e-17
relative error = 8.5190030481477937686879489966160e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 1.8867689910714404246759417545299
y[1] (numeric) = 1.886768991071440440781004862019
absolute error = 1.61050631074891e-17
relative error = 8.5357895872263143246369319469078e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 1.8881059821876230065747175731898
y[1] (numeric) = 1.8881059821876230227229002370435
absolute error = 1.61481826638537e-17
relative error = 8.5525827555208914694440535070267e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 1.8894438614098617849308158962568
y[1] (numeric) = 1.8894438614098618011221831175527
absolute error = 1.61913672212959e-17
relative error = 8.5693825320717679579949745258636e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 1.8907826300760360934729539827254
y[1] (numeric) = 1.8907826300760361097075708057256
absolute error = 1.62346168230002e-17
relative error = 8.5861888959427026990044123158348e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 1.8921222895249147099394996080613
y[1] (numeric) = 1.8921222895249147262174311202776
absolute error = 1.62779315122163e-17
relative error = 8.6030018262209994989283795887072e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 1.8934628410961571948473603666377
y[1] (numeric) = 1.8934628410961572111686716988966
absolute error = 1.63213113322589e-17
relative error = 8.6198213020173244390131090001824e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=114.4MB, alloc=4.3MB, time=18.21
x[1] = 0.805
y[1] (analytic) = 1.8948042861303152311516558269437
y[1] (numeric) = 1.8948042861303152475164121534514
absolute error = 1.63647563265077e-17
relative error = 8.6366473024656295876691228478918e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 1.8961466259688339647975121993473
y[1] (numeric) = 1.896146625968833981205778737755
absolute error = 1.64082665384077e-17
relative error = 8.6534798067232352611745510020062e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 1.8974898619540533461653200683212
y[1] (numeric) = 1.8974898619540533626171620797904
absolute error = 1.64518420114692e-17
relative error = 8.6703187939707538401925300075351e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 1.8988339954292094724107966344995
y[1] (numeric) = 1.8988339954292094889062794237672
absolute error = 1.64954827892677e-17
relative error = 8.6871642434119612538005012898633e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 1.9001790277384359307011948067402
y[1] (numeric) = 1.9001790277384359472403837221841
absolute error = 1.65391889154439e-17
relative error = 8.7040161342737216439392731873158e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 1.9015249602267651423490023805138
y[1] (numeric) = 1.9015249602267651589319628142178
absolute error = 1.65829604337040e-17
relative error = 8.7208744458060701264152794826176e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 1.9028717942401297078444754364303
y[1] (numeric) = 1.9028717942401297244712728242498
absolute error = 1.66267973878195e-17
relative error = 8.7377391572820324483408851997286e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 1.904219531125363752788350991549
y[1] (numeric) = 1.9042195311253637694590508131762
absolute error = 1.66706998216272e-17
relative error = 8.7546102479975504489832222602449e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 1.905568172230204274726084836296
y[1] (numeric) = 1.9055681722302042914407526153258
absolute error = 1.67146677790298e-17
relative error = 8.7714876972717227124114597583204e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 1.9069177189032924908849613913407
y[1] (numeric) = 1.9069177189032925076436626953358
absolute error = 1.67587013039951e-17
relative error = 8.7883714844463100378996671937468e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 1.9082681724941751868154233216519
y[1] (numeric) = 1.9082681724941752036182237622086
absolute error = 1.68028004405567e-17
relative error = 8.8052615888860290697934333093358e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 1.9096195343533060659379695491762
y[1] (numeric) = 1.9096195343533060827849347819899
absolute error = 1.68469652328137e-17
relative error = 8.8221579899783210258455255257305e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 1.9109718058320470999969712111494
y[1] (numeric) = 1.9109718058320471168881669360803
absolute error = 1.68911957249309e-17
relative error = 8.8390606671333830617215071672415e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 1.9123249882826698804227560179691
y[1] (numeric) = 1.9123249882826698973582479791079
absolute error = 1.69354919611388e-17
relative error = 8.8559695997840949261295054614756e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 1.9136790830583569706033123728253
y[1] (numeric) = 1.913679083058356987583166358559
absolute error = 1.69798539857337e-17
relative error = 8.8728847673859981906188171271102e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 1.9150340915132032590669655249064
y[1] (numeric) = 1.9150340915132032760912473679839
absolute error = 1.70242818430775e-17
relative error = 8.8898061494171189204409745855158e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.821
y[1] (analytic) = 1.9163900150022173135773789389687
y[1] (numeric) = 1.9163900150022173306461545165668
absolute error = 1.70687755775981e-17
relative error = 8.9067337253781041947145713090235e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 1.9177468548813227361422349763842
y[1] (numeric) = 1.9177468548813227532555702101735
absolute error = 1.71133352337893e-17
relative error = 8.9236674747920973331409047977718e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 1.9191046125073595189369498964607
y[1] (numeric) = 1.9191046125073595360949107526714
absolute error = 1.71579608562107e-17
relative error = 8.9406073772046136597462993694516e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 1.9204632892380854011447791018607
y[1] (numeric) = 1.9204632892380854183474315913487
absolute error = 1.72026524894880e-17
relative error = 8.9575534121836250849492165419523e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 1.921822886432177226714669468339
y[1] (numeric) = 1.9218228864321772439620796466517
absolute error = 1.72474101783127e-17
relative error = 8.9745055593193321334180362517145e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 1.9231834054492323030382165167636
y[1] (numeric) = 1.9231834054492323203304504842063
absolute error = 1.72922339674427e-17
relative error = 8.9914637982244049210891047801655e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.827
y[1] (analytic) = 1.924544847649769760547085104491
y[1] (numeric) = 1.9245448476497697778842090061926
absolute error = 1.73371239017016e-17
relative error = 9.0084281085335476336720180203021e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 1.9259072143952319132322532336284
y[1] (numeric) = 1.9259072143952319306143332596078
absolute error = 1.73820800259794e-17
relative error = 9.0253984699037917903850135665531e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=118.2MB, alloc=4.3MB, time=18.82
x[1] = 0.829
y[1] (analytic) = 1.9272705070479856200864394955422
y[1] (numeric) = 1.9272705070479856375135418807745
absolute error = 1.74271023852323e-17
relative error = 9.0423748620143212907020374086026e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 1.9286347269713236474710755941516
y[1] (numeric) = 1.9286347269713236649432666186342
absolute error = 1.74721910244826e-17
relative error = 9.0593572645663500606479419367126e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 1.9299998755294660324091863150949
y[1] (numeric) = 1.9299998755294660499265323039138
absolute error = 1.75173459888189e-17
relative error = 9.0763456572831556665587552096383e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 1.9313659540875614468055402337609
y[1] (numeric) = 1.9313659540875614643681075571572
absolute error = 1.75625673233963e-17
relative error = 9.0933400199101127944818014993270e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 1.9327329640116885625954353824508
y[1] (numeric) = 1.9327329640116885802032904558868
absolute error = 1.76078550734360e-17
relative error = 9.1103403322144161539541021764876e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 1.9341009066688574178234850255693
y[1] (numeric) = 1.9341009066688574354766943097951
absolute error = 1.76532092842258e-17
relative error = 9.1273465739852698972595278612692e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 1.9354697834270107836537696217447
y[1] (numeric) = 1.9354697834270108013523996228646
absolute error = 1.76986300011199e-17
relative error = 9.1443587250337145743040349462613e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.836
y[1] (analytic) = 1.9368395956550255323127219831442
y[1] (numeric) = 1.9368395956550255500568392526834
absolute error = 1.77441172695392e-17
relative error = 9.1613767651927129813051143177167e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 1.9382103447227140059661135749834
y[1] (numeric) = 1.9382103447227140237557847099541
absolute error = 1.77896711349707e-17
relative error = 9.1784006743167713072025830039675e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 1.9395820320008253865315108323297
y[1] (numeric) = 1.9395820320008254043668024752981
absolute error = 1.78352916429684e-17
relative error = 9.1954304322823352570476634162485e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 1.9409546588610470664275713067712
y[1] (numeric) = 1.940954658861047084308550145924
absolute error = 1.78809788391528e-17
relative error = 9.2124660189874632093477571481139e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 1.9423282266760060202615503923608
y[1] (numeric) = 1.9423282266760060381882831615719
absolute error = 1.79267327692111e-17
relative error = 9.2295074143518611585318773888362e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 1.9437027368192701774563903184567
y[1] (numeric) = 1.9437027368192701954289437973539
absolute error = 1.79725534788972e-17
relative error = 9.2465545983168146208632909933487e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 1.9450781906653497958187640366623
y[1] (numeric) = 1.9450781906653498138372050506942
absolute error = 1.80184410140319e-17
relative error = 9.2636075508452236603917550730666e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 1.9464545895896988360494475700248
y[1] (numeric) = 1.9464545895896988541138429905274
absolute error = 1.80643954205026e-17
relative error = 9.2806662519213808966383096684569e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.844
y[1] (analytic) = 1.9478319349687163371973953349781
y[1] (numeric) = 1.9478319349687163553078120792419
absolute error = 1.81104167442638e-17
relative error = 9.2977306815511611742165415215928e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 1.9492102281797477930588938902212
y[1] (numeric) = 1.9492102281797478112153989215581
absolute error = 1.81565050313369e-17
relative error = 9.3148008197618513162576282066365e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 1.9505894706010865295231705117997
y[1] (numeric) = 1.9505894706010865477258308396097
absolute error = 1.82026603278100e-17
relative error = 9.3318766466019806066910087191973e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 1.9519696636119750828658339401138
y[1] (numeric) = 1.9519696636119751011147166199524
absolute error = 1.82488826798386e-17
relative error = 9.3489581421416130719105717067365e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 1.9533508085926065789915255924094
y[1] (numeric) = 1.9533508085926065972866977260543
absolute error = 1.82951721336449e-17
relative error = 9.3660452864719218137002307061770e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 1.9547329069241261136271604835166
y[1] (numeric) = 1.9547329069241261319686892190351
absolute error = 1.83415287355185e-17
relative error = 9.3831380597054813642438769993467e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 1.9561159599886321334671380481937
y[1] (numeric) = 1.9561159599886321518550905800096
absolute error = 1.83879525318159e-17
relative error = 9.4002364419759453489913387649384e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 1.9574999691691778182719040104007
y[1] (numeric) = 1.9574999691691778367063475793616
absolute error = 1.84344435689609e-17
relative error = 9.4173404134381852932385396673729e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 1.9588849358497724639212453981807
y[1] (numeric) = 1.9588849358497724824022472916253
absolute error = 1.84810018934446e-17
relative error = 9.4344499542682246502752392506212e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=122.0MB, alloc=4.3MB, time=19.44
x[1] = 0.853
y[1] (analytic) = 1.9602708614153828664237017575585
y[1] (numeric) = 1.9602708614153828849513293093838
absolute error = 1.85276275518253e-17
relative error = 9.4515650446631221028785009396189e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 1.9616577472519347068834765749841
y[1] (numeric) = 1.9616577472519347254577971657127
absolute error = 1.85743205907286e-17
relative error = 9.4686856648409573214182692490319e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 1.9630455947463139374262338753463
y[1] (numeric) = 1.963045594746313956047314932194
absolute error = 1.86210810568477e-17
relative error = 9.4858117950409186723957470074440e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 1.9644344052863681680851659214704
y[1] (numeric) = 1.9644344052863681867530749184133
absolute error = 1.86679089969429e-17
relative error = 9.5029434155229833203209926329920e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 1.9658241802609080546487189012813
y[1] (numeric) = 1.9658241802609080733635233591236
absolute error = 1.87148044578423e-17
relative error = 9.5200805065682091238353259918212e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 1.9672149210597086874713644504755
y[1] (numeric) = 1.9672149210597087062331319369167
absolute error = 1.87617674864412e-17
relative error = 9.5372230484783644692850068151365e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 1.9686066290735109812488058215868
y[1] (numeric) = 1.9686066290735110000576039512895
absolute error = 1.88087981297027e-17
relative error = 9.5543710215761692484825928626666e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 1.96999930569402306575900847477
y[1] (numeric) = 1.9699993056940230846149049094276
absolute error = 1.88558964346576e-17
relative error = 9.5715244062051794924964748497537e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 1.9713929523139216775704458314477
y[1] (numeric) = 1.9713929523139216964735082798518
absolute error = 1.89030624484041e-17
relative error = 9.5886831827295710498137213934257e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 1.9727875703268535527189518991824
y[1] (numeric) = 1.9727875703268535716692481172905
absolute error = 1.89502962181081e-17
relative error = 9.6058473315342283268807161429536e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 1.974183161127436820354573444742
y[1] (numeric) = 1.9741831611274368393521712357455
absolute error = 1.89975977910035e-17
relative error = 9.6230168330248326601853626678046e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 1.9755797261112623973598153623282
y[1] (numeric) = 1.97557972611126241640478257672
absolute error = 1.90449672143918e-17
relative error = 9.6401916676275959940943620052865e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 1.9769772666748953839406738553282
y[1] (numeric) = 1.9769772666748954030330783909707
absolute error = 1.90924045356425e-17
relative error = 9.6573718157894003524292271874362e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 1.97837578421587646019185302274
y[1] (numeric) = 1.9783757842158764793317628249328
absolute error = 1.91399098021928e-17
relative error = 9.6745572579775829005114832069067e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 1.9797752801327232836375614156033
y[1] (numeric) = 1.9797752801327233028250444771515
absolute error = 1.91874830615482e-17
relative error = 9.6917479746801765221620312071740e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 1.9811757558249318877492861043507
y[1] (numeric) = 1.9811757558249319069844104656325
absolute error = 1.92351243612818e-17
relative error = 9.7089439464054932078652016584508e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 1.9825772126929780814419427749675
y[1] (numeric) = 1.9825772126929781007247765240024
absolute error = 1.92828337490349e-17
relative error = 9.7261451536823649275231077809989e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 1.9839796521383188495498013502289
y[1] (numeric) = 1.9839796521383188688804126227459
absolute error = 1.93306112725170e-17
relative error = 9.7433515770600810673545188809700e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 1.9853830755633937542835876120562
y[1] (numeric) = 1.9853830755633937736620445915616
absolute error = 1.93784569795054e-17
relative error = 9.7605631971081246657948048092665e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
y[1] (analytic) = 1.9867874843716263376701622822093
y[1] (numeric) = 1.9867874843716263570965332000554
absolute error = 1.94263709178461e-17
relative error = 9.7777799944165640969632726338038e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 1.988192879967425524976180001114
y[1] (numeric) = 1.9881928799674255444505331365668
absolute error = 1.94743531354528e-17
relative error = 9.7950019495954874591268863219538e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 1.9895992637561870291171316285968
y[1] (numeric) = 1.9895992637561870486395353089048
absolute error = 1.95224036803080e-17
relative error = 9.8122290432754948556435350612625e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.875
y[1] (analytic) = 1.99100663714429475605317427569
y[1] (numeric) = 1.9910066371442947756236968761519
absolute error = 1.95705226004619e-17
relative error = 9.8294612561070836279266006160081e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 1.9924150015391222111731544634505
y[1] (numeric) = 1.9924150015391222307918644074842
absolute error = 1.96187099440337e-17
relative error = 9.8466985687612407686614805497859e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=125.8MB, alloc=4.3MB, time=20.05
x[1] = 0.877
y[1] (analytic) = 1.9938243583490339066682307929366
y[1] (numeric) = 1.9938243583490339263351965521472
absolute error = 1.96669657592106e-17
relative error = 9.8639409619288792693710169248216e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 1.9952347089833867698965035000792
y[1] (numeric) = 1.9952347089833867896117935943278
absolute error = 1.97152900942486e-17
relative error = 9.8811884163211790121561823316032e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 1.9966460548525315527400592601973
y[1] (numeric) = 1.996646054852531572503742257669
absolute error = 1.97636829974717e-17
relative error = 9.8984409126691248798653933306248e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 1.9980583973678142419558405993168
y[1] (numeric) = 1.99805839736781426176798511659
absolute error = 1.98121445172732e-17
relative error = 9.9156984317240978507159635815216e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 1.9994717379415774705217502632838
y[1] (numeric) = 1.9994717379415774903824249653981
absolute error = 1.98606747021143e-17
relative error = 9.9329609542571132376547699084151e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 2.0008860779871619299794018908897
y[1] (numeric) = 2.000886077987161949888675491415
absolute error = 1.99092736005253e-17
relative error = 9.9502284610593615863541573653321e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 2.0023014189189077837749293338801
y[1] (numeric) = 2.0023014189189078037328705949853
absolute error = 1.99579412611052e-17
relative error = 9.9675009329419482076877667408009e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 2.003717762152156081599267964773
y[1] (numeric) = 2.0037177621521561016059456972946
absolute error = 2.00066777325216e-17
relative error = 9.9847783507357835412125482316056e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 2.0051351091032501747293223128853
y[1] (numeric) = 2.0051351091032501947848053763962
absolute error = 2.00554830635109e-17
relative error = 1.0002060695291623605777605902990e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 2.0065534611895371323714353698541
y[1] (numeric) = 2.0065534611895371524757926727326
absolute error = 2.01043573028785e-17
relative error = 1.0019347947480110285386008491151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 2.0079728198293691590085759082392
y[1] (numeric) = 2.0079728198293691791618764077379
absolute error = 2.01533004994987e-17
relative error = 1.0036640088191662045991431377875e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 2.009393186442105012752661160513
y[1] (numeric) = 2.0093931864421050329549738628276
absolute error = 2.02023127023146e-17
relative error = 1.0053937098336365121388218021863e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 2.010814562448111424703433210878
y[1] (numeric) = 2.0108145624481114449548271712165
absolute error = 2.02513939603385e-17
relative error = 1.0071238958844113822179313819185e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 2.0122369492687645193153084589075
y[1] (numeric) = 2.0122369492687645396158527815591
absolute error = 2.03005443226516e-17
relative error = 1.0088545650664402384755452614895e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 2.0136603483264512357736205219758
y[1] (numeric) = 2.0136603483264512561233843603801
absolute error = 2.03497638384043e-17
relative error = 1.0105857154766415673232901629280e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 2.015084761044570750381677952841
y[1] (numeric) = 2.0150847610445707707807305096571
absolute error = 2.03990525568161e-17
relative error = 1.0123173452138921000452291677746e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 2.0165101888475358999600591595555
y[1] (numeric) = 2.0165101888475359204084696867312
absolute error = 2.04484105271757e-17
relative error = 1.0140494523790259594631599648052e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 2.0179366331607746062595679271181
y[1] (numeric) = 2.0179366331607746267574057259592
absolute error = 2.04978377988411e-17
relative error = 1.0157820350748338108322061351367e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 2.0193640954107313013892739539417
y[1] (numeric) = 2.0193640954107313219366083751813
absolute error = 2.05473344212396e-17
relative error = 1.0175150914060570648719809686613e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 2.0207925770248683542610638312966
y[1] (numeric) = 2.0207925770248683748579642751644
absolute error = 2.05969004438678e-17
relative error = 1.0192486194793821059501479356646e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 2.0222220794316674980521289103984
y[1] (numeric) = 2.0222220794316675186986648266901
absolute error = 2.06465359162917e-17
relative error = 1.0209826174034394903818787289640e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 2.0236526040606312586868175197475
y[1] (numeric) = 2.0236526040606312793830584078943
absolute error = 2.06962408881468e-17
relative error = 1.0227170832888031487244779476145e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 2.0250841523422843843392800146921
y[1] (numeric) = 2.0250841523422844050852954238303
absolute error = 2.07460154091382e-17
relative error = 1.0244520152479895920274364877207e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 2.0265167257081752759583361619784
y[1] (numeric) = 2.0265167257081752967541956910186
absolute error = 2.07958595290402e-17
relative error = 1.0261874113954324491203342949430e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.4MB, time=20.67
NO POLE
x[1] = 0.901
y[1] (analytic) = 2.027950325590877418815995384274
y[1] (numeric) = 2.027950325590877439661768681971
absolute error = 2.08457732976970e-17
relative error = 1.0279232698475113543876399406432e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 2.0293849534239908150810614133052
y[1] (numeric) = 2.0293849534239908359768181783277
absolute error = 2.08957567650225e-17
relative error = 1.0296595887225363652932836819585e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 2.0308206106421434174192539253319
y[1] (numeric) = 2.0308206106421434383650639063319
absolute error = 2.09458099810000e-17
relative error = 1.0313963661407275223253683400773e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 2.0322572986809925636212807592003
y[1] (numeric) = 2.032257298680992584617213754883
absolute error = 2.09959329956827e-17
relative error = 1.0331336002242338612677062609822e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 2.0336950189772264122602953451661
y[1] (numeric) = 2.0336950189772264333064212043599
absolute error = 2.10461258591938e-17
relative error = 1.0348712890971326768547072948139e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 2.0351337729685653793801750020656
y[1] (numeric) = 2.0351337729685654004765636237917
absolute error = 2.10963886217261e-17
relative error = 1.0366094308854042216274573040612e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 2.0365735620937635762160567912313
y[1] (numeric) = 2.0365735620937635973627781247737
absolute error = 2.11467213335424e-17
relative error = 1.0383480237169457942415458933214e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 2.0380143877926102479485686478091
y[1] (numeric) = 2.0380143877926102691456926927844
absolute error = 2.11971240449753e-17
relative error = 1.0400870657215563282234758943962e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 2.0394562515059312134931945438271
y[1] (numeric) = 2.0394562515059312347407913502547
absolute error = 2.12475968064276e-17
relative error = 1.0418265550309504662003935310387e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 2.040899154675590306326213472502
y[1] (numeric) = 2.0408991546755903276243531408741
absolute error = 2.12981396683721e-17
relative error = 1.0435664897787431762042896005215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 2.0423430987444908163486530798417
y[1] (numeric) = 2.0423430987444908376974057611932
absolute error = 2.13487526813515e-17
relative error = 1.0453068681004393300194902386046e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 2.0437880851565769327896998076174
y[1] (numeric) = 2.0437880851565769541891357035963
absolute error = 2.13994358959789e-17
relative error = 1.0470476881334526835288394463659e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 2.0452341153568351881510084512367
y[1] (numeric) = 2.0452341153568352096011978141743
absolute error = 2.14501893629376e-17
relative error = 1.0487889480170905512221143794227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 2.0466811907912959031933550769469
y[1] (numeric) = 2.0466811907912959246943682099279
absolute error = 2.15010131329810e-17
relative error = 1.0505306458925434320946493723638e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 2.0481293129070346329670782851415
y[1] (numeric) = 2.0481293129070346545189855420745
absolute error = 2.15519072569330e-17
relative error = 1.0522727799028990925840168681377e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 2.0495784831521736138877548503328
y[1] (numeric) = 2.0495784831521736354906266360203
absolute error = 2.16028717856875e-17
relative error = 1.0540153481931126788533395157911e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 2.0510287029758832118585568135853
y[1] (numeric) = 2.0510287029758832335124635837946
absolute error = 2.16539067702093e-17
relative error = 1.0557583489100452147252194824441e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 2.0524799738283833714407381498894
y[1] (numeric) = 2.0524799738283833931457504114225
absolute error = 2.17050122615331e-17
relative error = 1.0575017802024093659750148943258e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 2.053932297160945066073700181081
y[1] (numeric) = 2.0539322971609450878298884918456
absolute error = 2.17561883107646e-17
relative error = 1.0592456402208176779287392688379e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.92
y[1] (analytic) = 2.0553856744258917493460859544949
y[1] (numeric) = 2.0553856744258917711535209235747
absolute error = 2.18074349690798e-17
relative error = 1.0609899271177430342940339957609e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 2.0568401070766008073193548585663
y[1] (numeric) = 2.0568401070766008291781071462916
absolute error = 2.18587522877253e-17
relative error = 1.0627346390475279023148279075157e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 2.0582955965675050119052897990764
y[1] (numeric) = 2.0582955965675050338154301170948
absolute error = 2.19101403180184e-17
relative error = 1.0644797741663838224958074253725e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 2.0597521443540939752988903136701
y[1] (numeric) = 2.0597521443540939972604894250175
absolute error = 2.19615991113474e-17
relative error = 1.0662253306324006108727223543009e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 2.0612097518929156054681060576613
y[1] (numeric) = 2.0612097518929156274812347768321
absolute error = 2.20131287191708e-17
relative error = 1.0679713066055021559714054098910e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=21.29
NO POLE
x[1] = 0.925
y[1] (analytic) = 2.062668420641577562701866150978
y[1] (numeric) = 2.0626684206415775847665953439963
absolute error = 2.20647291930183e-17
relative error = 1.0697177002474896692780947004844e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 2.0641281520587487172178609344011
y[1] (numeric) = 2.0641281520587487393342615188916
absolute error = 2.21164005844905e-17
relative error = 1.0714645097220217722748092895383e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 2.0655889476041606078315337429978
y[1] (numeric) = 2.0655889476041606299996766882565
absolute error = 2.21681429452587e-17
relative error = 1.0732117331945995095127786533796e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 2.0670508087386089016877413658641
y[1] (numeric) = 2.0670508087386089239076976929292
absolute error = 2.22199563270651e-17
relative error = 1.0749593688325707769577124109362e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 2.0685137369239548550565429239574
y[1] (numeric) = 2.0685137369239548773283837056807
absolute error = 2.22718407817233e-17
relative error = 1.0767074148051492352359236639967e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 2.0699777336231267751945779619315
y[1] (numeric) = 2.0699777336231267975183743230493
absolute error = 2.23237963611178e-17
relative error = 1.0784558692833848333883401742895e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 2.0714428003001214832734956154724
y[1] (numeric) = 2.0714428003001215056493187326765
absolute error = 2.23758231172041e-17
relative error = 1.0802047304401634233208137116037e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 2.0729089384200057783768977826866
y[1] (numeric) = 2.0729089384200058008048188846954
absolute error = 2.24279211020088e-17
relative error = 1.0819539964502063763849407312435e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 2.0743761494489179025672602966067
y[1] (numeric) = 2.0743761494489179250473506642368
absolute error = 2.24800903676301e-17
relative error = 1.0837036654900894849633836413235e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 2.0758444348540690070242971658585
y[1] (numeric) = 2.0758444348540690295566281320957
absolute error = 2.25323309662372e-17
relative error = 1.0854537357382087938036950961945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 2.0773137961037446192562340219749
y[1] (numeric) = 2.0773137961037446418408769720456
absolute error = 2.25846429500707e-17
relative error = 1.0872042053747947157327864122854e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 2.0787842346673061113854579847528
y[1] (numeric) = 2.0787842346673061340224843561955
absolute error = 2.26370263714427e-17
relative error = 1.0889550725819116564657837287670e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 2.0802557520151921695100122314256
y[1] (numeric) = 2.0802557520151921921994935141621
absolute error = 2.26894812827365e-17
relative error = 1.0907063355434384129825878278684e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.938
y[1] (analytic) = 2.0817283496189202641424046312673
y[1] (numeric) = 2.0817283496189202868844123676743
absolute error = 2.27420077364070e-17
relative error = 1.0924579924450822813632195923599e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 2.0832020289510881217272008845605
y[1] (numeric) = 2.0832020289510881445218066695412
absolute error = 2.27946057849807e-17
relative error = 1.0942100414743739040172896490295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 2.0846767914853751972388736836433
y[1] (numeric) = 2.084676791485375220086149164699
absolute error = 2.28472754810557e-17
relative error = 1.0959624808206621391340974532962e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 2.0861526386965441478613804940074
y[1] (numeric) = 2.0861526386965441707613973713091
absolute error = 2.29000168773017e-17
relative error = 1.0977153086751089522743272919802e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 2.087629572060442307750943635148
y[1] (numeric) = 2.0876295720604423307037736616079
absolute error = 2.29528300264599e-17
relative error = 1.0994685232306795399027887241793e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 2.0891075930540031638835074240675
y[1] (numeric) = 2.0891075930540031868892224054112
absolute error = 2.30057149813437e-17
relative error = 1.1012221226821707891024121191566e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.944
y[1] (analytic) = 2.0905867031552478329883482290151
y[1] (numeric) = 2.090586703155247856047020023853
absolute error = 2.30586717948379e-17
relative error = 1.1029761052261678667271754329035e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 2.0920669038432865395693143671931
y[1] (numeric) = 2.0920669038432865626810148870926
absolute error = 2.31117005198995e-17
relative error = 1.1047304690610774724295222363410e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 2.0935481965983200950151738677954
y[1] (numeric) = 2.0935481965983201181799750773524
absolute error = 2.31648012095570e-17
relative error = 1.1064852123870893023337265895568e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 2.0950305829016413778005492108464
y[1] (numeric) = 2.0950305829016414010185231277577
absolute error = 2.32179739169113e-17
relative error = 1.1082403334062140477400826511192e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 2.0965140642356368147789192429016
y[1] (numeric) = 2.0965140642356368380501379380366
absolute error = 2.32712186951350e-17
relative error = 1.1099958303222449158466434704173e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=21.91
NO POLE
x[1] = 0.949
y[1] (analytic) = 2.0979986420837878635691695627324
y[1] (numeric) = 2.0979986420837878868937051602052
absolute error = 2.33245355974728e-17
relative error = 1.1117517013407717449443741208109e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 2.0994843179306724960371737636705
y[1] (numeric) = 2.0994843179306725194150984409123
absolute error = 2.33779246772418e-17
relative error = 1.1135079446691902970654586179272e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 2.1009710932619666828738890143169
y[1] (numeric) = 2.1009710932619667063052750021479
absolute error = 2.34313859878310e-17
relative error = 1.1152645585166734338684091419373e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 2.102458969564445879271450555834
y[1] (numeric) = 2.1024589695644459027563701385357
absolute error = 2.34849195827017e-17
relative error = 1.1170215410941852221573328037119e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 2.1039479483259865116987507920395
y[1] (numeric) = 2.103947948325986535237276307427
absolute error = 2.35385255153875e-17
relative error = 1.1187788906144759680558355225745e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 2.1054380310355674657779897480053
y[1] (numeric) = 2.1054380310355674893701935874996
absolute error = 2.35922038394943e-17
relative error = 1.1205366052920772725598634518296e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 2.1069292191832715752636847738351
y[1] (numeric) = 2.1069292191832715989096393825356
absolute error = 2.36459546087005e-17
relative error = 1.1222946833433066008818846390467e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 2.1084215142602871121256284727558
y[1] (numeric) = 2.1084215142602871358254063495127
absolute error = 2.36997778767569e-17
relative error = 1.1240531229862576040580627064378e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 2.1099149177589092777372849366033
y[1] (numeric) = 2.10991491775890930149095863409
absolute error = 2.37536736974867e-17
relative error = 1.1258119224407952214465678623964e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 2.1114094311725416951711154772244
y[1] (numeric) = 2.1114094311725417189787576020102
absolute error = 2.38076421247858e-17
relative error = 1.1275710799285650128571392415636e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 2.112905055995697902602326149244
y[1] (numeric) = 2.1129050559956979264640093618665
absolute error = 2.38616832126225e-17
relative error = 1.1293305936729740544518598409863e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 2.1144017937240028478225304680702
y[1] (numeric) = 2.1144017937240028717383274831081
absolute error = 2.39157970150379e-17
relative error = 1.1310904618992050223067864045069e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 2.1158996458541943838648218369242
y[1] (numeric) = 2.1158996458541944078348054230702
absolute error = 2.39699835861460e-17
relative error = 1.1328506828342160381456012444853e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 2.1173986138841247657417513080925
y[1] (numeric) = 2.1173986138841247897659942882257
absolute error = 2.40242429801332e-17
relative error = 1.1346112547067121792926543152530e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 2.1188986993127621482977074165033
y[1] (numeric) = 2.1188986993127621723762826677622
absolute error = 2.40785752512589e-17
relative error = 1.1363721757471690236039809313369e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 2.1203999036401920851771959381319
y[1] (numeric) = 2.1203999036401921093101763919874
absolute error = 2.41329804538555e-17
relative error = 1.1381334441878277982337234463011e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 2.1219022283676190289105185416403
y[1] (numeric) = 2.1219022283676190530979771839684
absolute error = 2.41874586423281e-17
relative error = 1.1398950582626764109423311011569e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 2.1234056749973678321183504190541
y[1] (numeric) = 2.1234056749973678563603602902091
absolute error = 2.42420098711550e-17
relative error = 1.1416570162074682375189193148274e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 2.1249102450328852498367181001795
y[1] (numeric) = 2.1249102450328852741333522950668
absolute error = 2.42966341948873e-17
relative error = 1.1434193162596984749897850057077e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 2.1264159399787414429638797758636
y[1] (numeric) = 2.126415939978741467315211444013
absolute error = 2.43513316681494e-17
relative error = 1.1451819566586229201904699293412e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 2.1279227613406314828306115771036
y[1] (numeric) = 2.1279227613406315072367139227423
absolute error = 2.44061023456387e-17
relative error = 1.1469449356452390735276795351186e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 2.1294307106253768568954043804161
y[1] (numeric) = 2.1294307106253768813563506625421
absolute error = 2.44609462821260e-17
relative error = 1.1487082514623001958165104610671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 2.13093978934092697556607683479
y[1] (numeric) = 2.1309397893409270000819403672452
absolute error = 2.45158635324552e-17
relative error = 1.1504719023542964563118394322200e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 2.1324499989963606801493114319596
y[1] (numeric) = 2.1324499989963607047201655835031
absolute error = 2.45708541515435e-17
relative error = 1.1522358865674596081981384347210e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=22.52
NO POLE
x[1] = 0.973
y[1] (analytic) = 2.1339613411018877519296215696618
y[1] (numeric) = 2.1339613411018877765555397640434
absolute error = 2.46259181943816e-17
relative error = 1.1540002023497676444815472314748e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 2.1354738171688504223792586869687
y[1] (numeric) = 2.1354738171688504470603144030022
absolute error = 2.46810557160335e-17
relative error = 1.1557648479509307031004378064029e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 2.136987428709724884500569681729
y[1] (numeric) = 2.1369874287097249092368364533658
absolute error = 2.47362667716368e-17
relative error = 1.1575298216224004295092543843284e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 2.1385021772381228053023159526022
y[1] (numeric) = 2.1385021772381228300938673690046
absolute error = 2.47915514164024e-17
relative error = 1.1592951216173512426904519239035e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 2.1400180642687928394114665421295
y[1] (numeric) = 2.1400180642687928642583762477446
absolute error = 2.48469097056151e-17
relative error = 1.1610607461907037366494887011293e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 2.1415350913176221438219789927617
y[1] (numeric) = 2.1415350913176221687243206873948
absolute error = 2.49023416946331e-17
relative error = 1.1628266935990966176914405905776e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 2.1430532599016378937820826647506
y[1] (numeric) = 2.1430532599016379187399301036392
absolute error = 2.49578474388886e-17
relative error = 1.1645929621009100896721571426965e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 2.1445725715390087998215804033143
y[1] (numeric) = 2.1445725715390088248350073972013
absolute error = 2.50134269938870e-17
relative error = 1.1663595499562238590328669860177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 2.1460930277490466259206855825028
y[1] (numeric) = 2.1460930277490466509897659977109
absolute error = 2.50690804152081e-17
relative error = 1.1681264554268685110050516097508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 2.1476146300522077088219126947296
y[1] (numeric) = 2.1476146300522077339467204532349
absolute error = 2.51248077585053e-17
relative error = 1.1698936767763835411990379867913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 2.1491373799700944784865407979852
y[1] (numeric) = 2.1491373799700945036671498774911
absolute error = 2.51806090795059e-17
relative error = 1.1716612122700267488670393763719e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 2.1506612790254569796971702773228
y[1] (numeric) = 2.1506612790254570049336547113341
absolute error = 2.52364844340113e-17
relative error = 1.1734290601747789407422818313898e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 2.1521863287421943948078945233001
y[1] (numeric) = 2.1521863287421944201003284011968
absolute error = 2.52924338778967e-17
relative error = 1.1751972187593253828359984214174e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 2.1537125306453565676436092776751
y[1] (numeric) = 2.1537125306453565929920667447868
absolute error = 2.53484574671117e-17
relative error = 1.1769656862940791194909137255262e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 2.1552398862611455285499835457935
y[1] (numeric) = 2.1552398862611455539545388034734
absolute error = 2.54045552576799e-17
relative error = 1.1787344610511577949465971437527e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 2.1567683971169170205956171257642
y[1] (numeric) = 2.1567683971169170460563444314632
absolute error = 2.54607273056990e-17
relative error = 1.1805035413043837563000587735572e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 2.1582980647411820269279109567087
y[1] (numeric) = 2.1582980647411820524448846240498
absolute error = 2.55169736673411e-17
relative error = 1.1822729253292934227561089924325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 2.1598288906636082992841776420814
y[1] (numeric) = 2.159828890663608324857472040934
absolute error = 2.55732943988526e-17
relative error = 1.1840426114031280951921953984225e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 2.1613608764150218876595206592994
y[1] (numeric) = 2.1613608764150219132892102158536
absolute error = 2.56296895565542e-17
relative error = 1.1858125978048294315699456222076e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.992
y[1] (analytic) = 2.1628940235274086711330119236875
y[1] (numeric) = 2.1628940235274086968191711205285
absolute error = 2.56861591968410e-17
relative error = 1.1875828828150395651235328973694e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 2.1644283335339158898536985330442
y[1] (numeric) = 2.164428333533915915596401909227
absolute error = 2.57427033761828e-17
relative error = 1.1893534647161104624735655046089e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 2.1659638079688536781879706789635
y[1] (numeric) = 2.165963807968853703987292830087
absolute error = 2.57993221511235e-17
relative error = 1.1911243417920716900859672492967e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 2.1675004483676965990298238724065
y[1] (numeric) = 2.1675004483676966248858394506887
absolute error = 2.58560155782822e-17
relative error = 1.1928955123286767491910600175332e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 2.1690382562670851792755497939157
y[1] (numeric) = 2.1690382562670852051883335082678
absolute error = 2.59127837143521e-17
relative error = 1.1946669746133477863890729422111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=23.12
NO POLE
x[1] = 0.997
y[1] (analytic) = 2.1705772332048274464643912432871
y[1] (numeric) = 2.1705772332048274724340178593887
absolute error = 2.59696266161016e-17
relative error = 1.1964387269352218948252238596669e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 2.1721173807199004665866978294874
y[1] (numeric) = 2.1721173807199004926132421698607
absolute error = 2.60265443403733e-17
relative error = 1.1982107675851005387868498942999e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 2.1736587003524518830611202090955
y[1] (numeric) = 2.1736587003524519091446571531807
absolute error = 2.60835369440852e-17
relative error = 1.1999830948555004051816727490925e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 2.1752011936438014568823818505956
y[1] (numeric) = 2.1752011936438014830229863348253
absolute error = 2.61406044842297e-17
relative error = 1.2017557070406028988374791581260e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.001
y[1] (analytic) = 2.1767448621364426079411684724173
y[1] (numeric) = 2.1767448621364426341389154902918
absolute error = 2.61977470178745e-17
relative error = 1.2035286024362911388150563643520e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.002
y[1] (analytic) = 2.1782897073740439575176764747447
y[1] (numeric) = 2.1782897073740439837726410769067
absolute error = 2.62549646021620e-17
relative error = 1.2053017793401179361366394512319e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.003
y[1] (analytic) = 2.1798357309014508719503628587685
y[1] (numeric) = 2.1798357309014508982626201530783
absolute error = 2.63122572943098e-17
relative error = 1.2070752360513243701863000354204e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.004
y[1] (analytic) = 2.1813829342646870074814403022609
y[1] (numeric) = 2.1813829342646870338510654538717
absolute error = 2.63696251516108e-17
relative error = 1.2088489708708399491875636798897e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.005
y[1] (analytic) = 2.1829313190109558562806622370981
y[1] (numeric) = 2.1829313190109558827077304685308
absolute error = 2.64270682314327e-17
relative error = 1.2106229821012552839726021243872e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.006
y[1] (analytic) = 2.1844808866886422936489439526415
y[1] (numeric) = 2.18448088668864232013353054386
absolute error = 2.64845865912185e-17
relative error = 1.2123972680468406554501251627464e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.007
y[1] (analytic) = 2.1860316388473141264033669287306
y[1] (numeric) = 2.1860316388473141529455472172174
absolute error = 2.65421802884868e-17
relative error = 1.2141718270135553541748097033311e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.008
y[1] (analytic) = 2.1875835770377236424451147834195
y[1] (numeric) = 2.1875835770377236690449641642506
absolute error = 2.65998493808311e-17
relative error = 1.2159466573090112675806316599304e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.009
y[1] (analytic) = 2.1891367028118091615118904035219
y[1] (numeric) = 2.1891367028118091881694843294424
absolute error = 2.66575939259205e-17
relative error = 1.2177217572425005742278125916697e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.01
y[1] (analytic) = 2.1906910177226965871163650105115
y[1] (numeric) = 2.1906910177226966138317789920112
absolute error = 2.67154139814997e-17
relative error = 1.2194971251249913669016291013311e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.011
y[1] (analytic) = 2.1922465233247009596722111003567
y[1] (numeric) = 2.1922465233247009864455207057454
absolute error = 2.67733096053887e-17
relative error = 1.2212727592691096096421045003656e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.012
y[1] (analytic) = 2.1938032211733280108092723834503
y[1] (numeric) = 2.1938032211733280376405532389333
absolute error = 2.68312808554830e-17
relative error = 1.2230486579891439629661258359366e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.013
y[1] (analytic) = 2.1953611128252757188794250399352
y[1] (numeric) = 2.1953611128252757457687528296892
absolute error = 2.68893277897540e-17
relative error = 1.2248248196010596986936030630156e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.014
y[1] (analytic) = 2.1969201998384358656546857964166
y[1] (numeric) = 2.1969201998384358926021362626652
absolute error = 2.69474504662486e-17
relative error = 1.2266012424224761408807084804348e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.015
y[1] (analytic) = 2.1984804837718955942191235222982
y[1] (numeric) = 2.1984804837718956212247724653877
absolute error = 2.70056489430895e-17
relative error = 1.2283779247726760428247756308895e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.016
y[1] (analytic) = 2.2000419661859389680561322377839
y[1] (numeric) = 2.200041966185938995120055516259
absolute error = 2.70639232784751e-17
relative error = 1.2301548649725967426649372687453e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.017
y[1] (analytic) = 2.201604648642048531332624620948
y[1] (numeric) = 2.2016046486420485584548981516279
absolute error = 2.71222735306799e-17
relative error = 1.2319320613448440672586961431842e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.018
y[1] (analytic) = 2.2031685327029068703817062981981
y[1] (numeric) = 2.203168532702906897562406056252
absolute error = 2.71806997580539e-17
relative error = 1.2337095122136607876213775885450e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.019
y[1] (analytic) = 2.204733619932398176385392400933
y[1] (numeric) = 2.2047336199323982036245944199566
absolute error = 2.72392020190236e-17
relative error = 1.2354872159049677796666021939227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.02
y[1] (analytic) = 2.2062999118956098092589290712457
y[1] (numeric) = 2.2062999118956098365567094433369
absolute error = 2.72977803720912e-17
relative error = 1.2372651707463234251225825155861e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=23.75
NO POLE
x[1] = 1.021
y[1] (analytic) = 2.20786741015883386273828380112
y[1] (numeric) = 2.207867410158833890094718676955
absolute error = 2.73564348758350e-17
relative error = 1.2390433750669375361801450522424e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.022
y[1] (analytic) = 2.2094361162895687306723696927437
y[1] (numeric) = 2.2094361162895687580875352816532
absolute error = 2.74151655889095e-17
relative error = 1.2408218271976716427078626484992e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.023
y[1] (analytic) = 2.2110060318565206745215699322922
y[1] (numeric) = 2.2110060318565207019955425023376
absolute error = 2.74739725700454e-17
relative error = 1.2426005254710347552926652654541e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.024
y[1] (analytic) = 2.2125771584296053920641299758375
y[1] (numeric) = 2.2125771584296054195969858538873
absolute error = 2.75328558780498e-17
relative error = 1.2443794682211881854193321115663e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.025
y[1] (analytic) = 2.2141494975799495873119861539068
y[1] (numeric) = 2.2141494975799496149038017257128
absolute error = 2.75918155718060e-17
relative error = 1.2461586537839322793535599469963e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.026
y[1] (analytic) = 2.2157230508798925416376006106481
y[1] (numeric) = 2.2157230508798925692884523209216
absolute error = 2.76508517102735e-17
relative error = 1.2479380804967022347605257102689e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.027
y[1] (analytic) = 2.2172978199029876861133737045701
y[1] (numeric) = 2.2172978199029877138233380570587
absolute error = 2.77099643524886e-17
relative error = 1.2497177466985909950123033280011e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.028
y[1] (analytic) = 2.2188738062240041750652062103997
y[1] (numeric) = 2.2188738062240042028343597679637
absolute error = 2.77691535575640e-17
relative error = 1.2514976507303269779336470920958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.029
y[1] (analytic) = 2.2204510114189284608417848757502
y[1] (numeric) = 2.2204510114189284886702042604389
absolute error = 2.78284193846887e-17
relative error = 1.2532777909342654099368985993187e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.03
y[1] (analytic) = 2.2220294370649658698011661020161
y[1] (numeric) = 2.2220294370649658976889279951449
absolute error = 2.78877618931288e-17
relative error = 1.2550581656544202004724407166368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.031
y[1] (analytic) = 2.223609084740542179516233736212
y[1] (numeric) = 2.2236090847405422074634148784387
absolute error = 2.79471811422267e-17
relative error = 1.2568387732364237254424659997789e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.032
y[1] (analytic) = 2.2251899560253051972006081793416
y[1] (numeric) = 2.2251899560253052252072853707432
absolute error = 2.80066771914016e-17
relative error = 1.2586196120275452036585994774922e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.033
y[1] (analytic) = 2.2267720525001263393565852373399
y[1] (numeric) = 2.2267720525001263674228353374895
absolute error = 2.80662501001496e-17
relative error = 1.2604006803766910316874482209608e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.034
y[1] (analytic) = 2.2283553757471022126466843626585
y[1] (numeric) = 2.2283553757471022407725842907021
absolute error = 2.81258999280436e-17
relative error = 1.2621819766343961418154305751373e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.035
y[1] (analytic) = 2.2299399273495561959903871581727
y[1] (numeric) = 2.2299399273495562241760138929061
absolute error = 2.81856267347334e-17
relative error = 1.2639634991528243654634736594612e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.036
y[1] (analytic) = 2.2315257088920400238876482402829
y[1] (numeric) = 2.2315257088920400521330788202288
absolute error = 2.82454305799459e-17
relative error = 1.2657452462857732760959801596454e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.037
y[1] (analytic) = 2.2331127219603353709707617848513
y[1] (numeric) = 2.2331127219603353992760733083363
absolute error = 2.83053115234850e-17
relative error = 1.2675272163886655770986733796326e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.038
y[1] (analytic) = 2.2347009681414554377861683079736
y[1] (numeric) = 2.234700968141455466151437933205
absolute error = 2.83652696252314e-17
relative error = 1.2693094078185360512319458290641e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.039
y[1] (analytic) = 2.2362904490236465378077874635233
y[1] (numeric) = 2.2362904490236465662330924086668
absolute error = 2.84253049451435e-17
relative error = 1.2710918189340677541150676487864e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.04
y[1] (analytic) = 2.2378811661963896856834638709362
y[1] (numeric) = 2.2378811661963897141688814141926
absolute error = 2.84854175432564e-17
relative error = 1.2728744480955431514740241274576e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.041
y[1] (analytic) = 2.2394731212504021867161142198098
y[1] (numeric) = 2.2394731212504022152617216994926
absolute error = 2.85456074796828e-17
relative error = 1.2746572936648803057246739808673e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.042
y[1] (analytic) = 2.2410663157776392275811651326004
y[1] (numeric) = 2.241066315777639256187039947213
absolute error = 2.86058748146126e-17
relative error = 1.2764403540056109000315984663062e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.043
y[1] (analytic) = 2.242660751371295468281872502986
y[1] (numeric) = 2.2426607513712954969480921112992
absolute error = 2.86662196083132e-17
relative error = 1.2782236274828895686438072248421e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.044
y[1] (analytic) = 2.2442564296258066353441142653486
y[1] (numeric) = 2.2442564296258066640707561864779
absolute error = 2.87266419211293e-17
relative error = 1.2800071124634809081046833197535e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=24.36
NO POLE
x[1] = 1.045
y[1] (analytic) = 2.2458533521368511162522497903002
y[1] (numeric) = 2.2458533521368511450393916037835
absolute error = 2.87871418134833e-17
relative error = 1.2817908073157732594541034853315e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.046
y[1] (analytic) = 2.2474515205013515551276403422456
y[1] (numeric) = 2.2474515205013515839753596881208
absolute error = 2.88477193458752e-17
relative error = 1.2835747104097701839697752927456e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.047
y[1] (analytic) = 2.2490509363174764496514262776354
y[1] (numeric) = 2.2490509363174764785598008565177
absolute error = 2.89083745788823e-17
relative error = 1.2853588201170730822705944094956e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.048
y[1] (analytic) = 2.2506516011846417492331579068184
y[1] (numeric) = 2.2506516011846417782022654799784
absolute error = 2.89691075731600e-17
relative error = 1.2871431348109127620037459028511e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.049
y[1] (analytic) = 2.2522535167035124544268781882594
y[1] (numeric) = 2.2522535167035124834567965777005
absolute error = 2.90299183894411e-17
relative error = 1.2889276528661142706607654885109e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.05
y[1] (analytic) = 2.253856684476004217596256671336
y[1] (numeric) = 2.2538566844760042466870637598727
absolute error = 2.90908070885367e-17
relative error = 1.2907123726591328674341661861248e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.051
y[1] (analytic) = 2.2554611061052849448303753529842
y[1] (numeric) = 2.2554611061052849739821490843196
absolute error = 2.91517737313354e-17
relative error = 1.2924972925680144687268072468910e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.052
y[1] (analytic) = 2.2570667831957763991117683641103
y[1] (numeric) = 2.257066783195776428324586742914
absolute error = 2.92128183788037e-17
relative error = 1.2942824109724094283240017741194e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.053
y[1] (analytic) = 2.2586737173531558047383186539425
y[1] (numeric) = 2.258673717353155834012259745929
absolute error = 2.92739410919865e-17
relative error = 1.2960677262535906859093939217095e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.054
y[1] (analytic) = 2.2602819101843574530006160943544
y[1] (numeric) = 2.2602819101843574823357580263608
absolute error = 2.93351419320064e-17
relative error = 1.2978532367944187470384946252693e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.055
y[1] (analytic) = 2.2618913632975743091163826816498
y[1] (numeric) = 2.2618913632975743385128036417141
absolute error = 2.93964209600643e-17
relative error = 1.2996389409793642861340721358803e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.056
y[1] (analytic) = 2.2635020783022596204235717703699
y[1] (numeric) = 2.263502078302259649881350007809
absolute error = 2.94577782374391e-17
relative error = 1.3014248371944908913398331303835e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.057
y[1] (analytic) = 2.2651140568091285258337495323548
y[1] (numeric) = 2.2651140568091285553529633578429
absolute error = 2.95192138254881e-17
relative error = 1.3032109238274687861250203324412e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.058
y[1] (analytic) = 2.2667273004301596665473680945757
y[1] (numeric) = 2.2667273004301596961280958802228
absolute error = 2.95807277856471e-17
relative error = 1.3049971992675752570314967099994e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.059
y[1] (analytic) = 2.2683418107785967980325410711455
y[1] (numeric) = 2.2683418107785968276748612505753
absolute error = 2.96423201794298e-17
relative error = 1.3067836619056642195908786429544e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.06
y[1] (analytic) = 2.2699575894689504032689334684157
y[1] (numeric) = 2.2699575894689504329729245368444
absolute error = 2.97039910684287e-17
relative error = 1.3085703101342019942720668331097e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.061
y[1] (analytic) = 2.2715746381169993072583792071867
y[1] (numeric) = 2.2715746381169993370241197215015
absolute error = 2.97657405143148e-17
relative error = 1.3103571423472501025891020469609e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.062
y[1] (analytic) = 2.2731929583397922928038407727815
y[1] (numeric) = 2.2731929583397923226314093516189
absolute error = 2.98275685788374e-17
relative error = 1.3121441569404525352326210014682e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.063
y[1] (analytic) = 2.2748125517556497175583267720777
y[1] (numeric) = 2.2748125517556497474478020959024
absolute error = 2.98894753238247e-17
relative error = 1.3139313523110582418863744403881e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.064
y[1] (analytic) = 2.2764334199841651323453844465509
y[1] (numeric) = 2.2764334199841651622968452577342
absolute error = 2.99514608111833e-17
relative error = 1.3157187268578952034145123563559e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.065
y[1] (analytic) = 2.278055564646206900752785461955
y[1] (numeric) = 2.2780555646462069307663105648539
absolute error = 3.00135251028989e-17
relative error = 1.3175062789813972907717436721005e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.066
y[1] (analytic) = 2.2796789873639198200010245684626
y[1] (numeric) = 2.2796789873639198500766928294982
absolute error = 3.00756682610356e-17
relative error = 1.3192940070835695966406330350583e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.067
y[1] (analytic) = 2.2813036897607267430882519998971
y[1] (numeric) = 2.2813036897607267732261423476337
absolute error = 3.01378903477366e-17
relative error = 1.3210819095680152830285959688466e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.068
y[1] (analytic) = 2.282929673461330202213261757125
y[1] (numeric) = 2.2829296734613302324134531823491
absolute error = 3.02001914252241e-17
relative error = 1.3228699848399272711156975867719e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=24.97
NO POLE
x[1] = 1.069
y[1] (analytic) = 2.2845569400917140334781591987326
y[1] (numeric) = 2.2845569400917140637407307545316
absolute error = 3.02625715557990e-17
relative error = 1.3246582313060712116139577739401e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.07
y[1] (analytic) = 2.2861854912791450028723326417884
y[1] (numeric) = 2.28618549127914503319736344363
absolute error = 3.03250308018416e-17
relative error = 1.3264466473748122683753669340818e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.071
y[1] (analytic) = 2.2878153286521744335393549567999
y[1] (numeric) = 2.2878153286521744639269241826111
absolute error = 3.03875692258112e-17
relative error = 1.3282352314560937063177627537974e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.072
y[1] (analytic) = 2.2894464538406398343284424239016
y[1] (numeric) = 2.2894464538406398647786293141476
absolute error = 3.04501868902460e-17
relative error = 1.3300239819614286738468171130150e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.073
y[1] (analytic) = 2.2910788684756665296320994018676
y[1] (numeric) = 2.2910788684756665601449832596315
absolute error = 3.05128838577639e-17
relative error = 1.3318128973039313027351302004101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.074
y[1] (analytic) = 2.2927125741896692905115786477314
y[1] (numeric) = 2.2927125741896693210872388387931
absolute error = 3.05756601910617e-17
relative error = 1.3336019758982778882803537262169e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.075
y[1] (analytic) = 2.2943475726163539671117884126072
y[1] (numeric) = 2.294347572616353997750304365523
absolute error = 3.06385159529158e-17
relative error = 1.3353912161607336128028888135065e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.076
y[1] (analytic) = 2.2959838653907191223672787287568
y[1] (numeric) = 2.2959838653907191530687299349388
absolute error = 3.07014512061820e-17
relative error = 1.3371806165091399555941618669108e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.077
y[1] (analytic) = 2.2976214541490576670009405940245
y[1] (numeric) = 2.2976214541490576977654066078201
absolute error = 3.07644660137956e-17
relative error = 1.3389701753629152130456053587488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.078
y[1] (analytic) = 2.2992603405289584958170530524755
y[1] (numeric) = 2.2992603405289585266446134912467
absolute error = 3.08275604387712e-17
relative error = 1.3407598911430419683267101145305e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.079
y[1] (analytic) = 2.30090052616930812529031446442
y[1] (numeric) = 2.3009005261693081561810490086235
absolute error = 3.08907345442035e-17
relative error = 1.3425497622720980753258142894002e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.08
y[1] (analytic) = 2.3025420127102923324524955549934
y[1] (numeric) = 2.3025420127102923634064839482598
absolute error = 3.09539883932664e-17
relative error = 1.3443397871742136781299851036975e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.081
y[1] (analytic) = 2.3041848017933977950783531280788
y[1] (numeric) = 2.3041848017933978260956751772927
absolute error = 3.10173220492139e-17
relative error = 1.3461299642751065323320081262684e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.082
y[1] (analytic) = 2.3058288950614137331724446316255
y[1] (numeric) = 2.3058288950614137642531802070051
absolute error = 3.10807355753796e-17
relative error = 1.3479202920020564591152207115325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.083
y[1] (analytic) = 2.3074742941584335517584850613123
y[1] (numeric) = 2.3074742941584335829027140964893
absolute error = 3.11442290351770e-17
relative error = 1.3497107687839145778387982364831e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.084
y[1] (analytic) = 2.309121000729856484972888992051
y[1] (numeric) = 2.3091210007298565161806914841506
absolute error = 3.12078024920996e-17
relative error = 1.3515013930511038372747718690215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.085
y[1] (analytic) = 2.3107690164223892414641418310083
y[1] (numeric) = 2.3107690164223892727355978407292
absolute error = 3.12714560097209e-17
relative error = 1.3532921632356152163724272829072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.086
y[1] (analytic) = 2.3124183428840476510996456916548
y[1] (numeric) = 2.3124183428840476824348353433492
absolute error = 3.13351896516944e-17
relative error = 1.3550830777710039406233292452608e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.087
y[1] (analytic) = 2.3140689817641583129816865958245
y[1] (numeric) = 2.3140689817641583443806900775781
absolute error = 3.13990034817536e-17
relative error = 1.3568741350923857139759644088648e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.088
y[1] (analytic) = 2.3157209347133602447741710198879
y[1] (numeric) = 2.3157209347133602762370685836005
absolute error = 3.14628975637126e-17
relative error = 1.3586653336364588761069234095444e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.089
y[1] (analytic) = 2.3173742033836065333417811119156
y[1] (numeric) = 2.3173742033836065648686530733809
absolute error = 3.15268719614653e-17
relative error = 1.3604566718414660510282715391533e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.09
y[1] (analytic) = 2.3190287894281659867031992191214
y[1] (numeric) = 2.3190287894281660182941259581075
absolute error = 3.15909267389861e-17
relative error = 1.3622481481472206413018098012628e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.091
y[1] (analytic) = 2.3206846945016247873000536789503
y[1] (numeric) = 2.3206846945016248189551156392801
absolute error = 3.16550619603298e-17
relative error = 1.3640397609950987357276970690985e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.092
y[1] (analytic) = 2.3223419202598881465832391428931
y[1] (numeric) = 2.3223419202598881783025168325249
absolute error = 3.17192776896318e-17
relative error = 1.3658315088280439689198266814930e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=25.59
NO POLE
x[1] = 1.093
y[1] (analytic) = 2.3240004683601819609182660194869
y[1] (numeric) = 2.3240004683601819927018400105946
absolute error = 3.17835739911077e-17
relative error = 1.3676233900905465418174349018769e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.094
y[1] (analytic) = 2.3256603404610544688112949419879
y[1] (numeric) = 2.3256603404610545006592458710417
absolute error = 3.18479509290538e-17
relative error = 1.3694154032286610299603786580286e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.095
y[1] (analytic) = 2.32732153822237790945751348689
y[1] (numeric) = 2.327321538222377941369922054737
absolute error = 3.19124085678470e-17
relative error = 1.3712075466899983341857906843701e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.096
y[1] (analytic) = 2.3289840633053501826135136918034
y[1] (numeric) = 2.3289840633053502145904606637484
absolute error = 3.19769469719450e-17
relative error = 1.3729998189237305461816368151984e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.097
y[1] (analytic) = 2.3306479173724965097953302452097
y[1] (numeric) = 2.3306479173724965418368964510959
absolute error = 3.20415662058862e-17
relative error = 1.3747922183805829205216042061507e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.098
y[1] (analytic) = 2.3323131020876710968038005462696
y[1] (numeric) = 2.3323131020876711289100668805595
absolute error = 3.21062663342899e-17
relative error = 1.3765847435128387430774939618296e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.099
y[1] (analytic) = 2.3339796191160587975789091601822
y[1] (numeric) = 2.3339796191160588297499565820384
absolute error = 3.21710474218562e-17
relative error = 1.3783773927743313242636585830279e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.1
y[1] (analytic) = 2.3356474701241767793847805235787
y[1] (numeric) = 2.3356474701241768116206900569447
absolute error = 3.22359095333660e-17
relative error = 1.3801701646204403072671199676000e-15 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = cosh ( x ) ;
Iterations = 1000
Total Elapsed Time = 25 Seconds
Elapsed Time(since restart) = 25 Seconds
Expected Time Remaining = 23 Seconds
Optimized Time Remaining = 23 Seconds
Time to Timeout = 14 Minutes 34 Seconds
Percent Done = 52.68 %
> quit
memory used=161.5MB, alloc=4.4MB, time=25.79