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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,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> djd_debug2,
> glob_max_opt_iter,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_relerr,
> glob_reached_optimal_h,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_last_good_h,
> glob_hmin,
> years_in_century,
> glob_normmax,
> MAX_UNCHANGED,
> glob_dump_analytic,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> days_in_year,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10abserr,
> glob_max_hours,
> glob_hmax,
> glob_orig_start_sec,
> glob_abserr,
> glob_initial_pass,
> sec_in_min,
> glob_subiter_method,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_current_iter,
> glob_not_yet_start_msg,
> glob_log10relerr,
> glob_small_float,
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_log10_relerr,
> glob_disp_incr,
> glob_optimal_done,
> hours_in_day,
> djd_debug,
> glob_optimal_clock_start_sec,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_fact_1,
> array_y,
> array_x,
> array_type_pole,
> array_norms,
> array_m1,
> array_pole,
> array_tmp1_g,
> array_1st_rel_error,
> array_y_init,
> array_y_set_initial,
> array_poles,
> array_fact_2,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel,
glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2,
glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec,
glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h,
glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin,
years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic,
glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium,
days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr,
glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr,
glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter,
glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_percent_done, glob_current_iter,
glob_not_yet_start_msg, glob_log10relerr, glob_small_float,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr,
glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug,
glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1,
array_y, array_x, array_type_pole, array_norms, array_m1, array_pole,
array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial,
array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work,
array_real_pole, array_y_higher, array_complex_pole, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> djd_debug2,
> glob_max_opt_iter,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_relerr,
> glob_reached_optimal_h,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_last_good_h,
> glob_hmin,
> years_in_century,
> glob_normmax,
> MAX_UNCHANGED,
> glob_dump_analytic,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> days_in_year,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10abserr,
> glob_max_hours,
> glob_hmax,
> glob_orig_start_sec,
> glob_abserr,
> glob_initial_pass,
> sec_in_min,
> glob_subiter_method,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_current_iter,
> glob_not_yet_start_msg,
> glob_log10relerr,
> glob_small_float,
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_log10_relerr,
> glob_disp_incr,
> glob_optimal_done,
> hours_in_day,
> djd_debug,
> glob_optimal_clock_start_sec,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_fact_1,
> array_y,
> array_x,
> array_type_pole,
> array_norms,
> array_m1,
> array_pole,
> array_tmp1_g,
> array_1st_rel_error,
> array_y_init,
> array_y_set_initial,
> array_poles,
> array_fact_2,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel,
glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2,
glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec,
glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h,
glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin,
years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic,
glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium,
days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr,
glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr,
glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter,
glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_percent_done, glob_current_iter,
glob_not_yet_start_msg, glob_log10relerr, glob_small_float,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr,
glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug,
glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1,
array_y, array_x, array_type_pole, array_norms, array_m1, array_pole,
array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial,
array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work,
array_real_pole, array_y_higher, array_complex_pole, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> djd_debug2,
> glob_max_opt_iter,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_relerr,
> glob_reached_optimal_h,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_last_good_h,
> glob_hmin,
> years_in_century,
> glob_normmax,
> MAX_UNCHANGED,
> glob_dump_analytic,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> days_in_year,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10abserr,
> glob_max_hours,
> glob_hmax,
> glob_orig_start_sec,
> glob_abserr,
> glob_initial_pass,
> sec_in_min,
> glob_subiter_method,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_current_iter,
> glob_not_yet_start_msg,
> glob_log10relerr,
> glob_small_float,
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_log10_relerr,
> glob_disp_incr,
> glob_optimal_done,
> hours_in_day,
> djd_debug,
> glob_optimal_clock_start_sec,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_fact_1,
> array_y,
> array_x,
> array_type_pole,
> array_norms,
> array_m1,
> array_pole,
> array_tmp1_g,
> array_1st_rel_error,
> array_y_init,
> array_y_set_initial,
> array_poles,
> array_fact_2,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel,
glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2,
glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec,
glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h,
glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin,
years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic,
glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium,
days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr,
glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr,
glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter,
glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_percent_done, glob_current_iter,
glob_not_yet_start_msg, glob_log10relerr, glob_small_float,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr,
glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug,
glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1,
array_y, array_x, array_type_pole, array_norms, array_m1, array_pole,
array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial,
array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work,
array_real_pole, array_y_higher, array_complex_pole, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> djd_debug2,
> glob_max_opt_iter,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_relerr,
> glob_reached_optimal_h,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_last_good_h,
> glob_hmin,
> years_in_century,
> glob_normmax,
> MAX_UNCHANGED,
> glob_dump_analytic,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> days_in_year,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10abserr,
> glob_max_hours,
> glob_hmax,
> glob_orig_start_sec,
> glob_abserr,
> glob_initial_pass,
> sec_in_min,
> glob_subiter_method,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_current_iter,
> glob_not_yet_start_msg,
> glob_log10relerr,
> glob_small_float,
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_log10_relerr,
> glob_disp_incr,
> glob_optimal_done,
> hours_in_day,
> djd_debug,
> glob_optimal_clock_start_sec,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_fact_1,
> array_y,
> array_x,
> array_type_pole,
> array_norms,
> array_m1,
> array_pole,
> array_tmp1_g,
> array_1st_rel_error,
> array_y_init,
> array_y_set_initial,
> array_poles,
> array_fact_2,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel,
glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2,
glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec,
glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h,
glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin,
years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic,
glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium,
days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr,
glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr,
glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter,
glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_percent_done, glob_current_iter,
glob_not_yet_start_msg, glob_log10relerr, glob_small_float,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr,
glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug,
glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1,
array_y, array_x, array_type_pole, array_norms, array_m1, array_pole,
array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial,
array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work,
array_real_pole, array_y_higher, array_complex_pole, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> djd_debug2,
> glob_max_opt_iter,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_relerr,
> glob_reached_optimal_h,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_last_good_h,
> glob_hmin,
> years_in_century,
> glob_normmax,
> MAX_UNCHANGED,
> glob_dump_analytic,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> days_in_year,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10abserr,
> glob_max_hours,
> glob_hmax,
> glob_orig_start_sec,
> glob_abserr,
> glob_initial_pass,
> sec_in_min,
> glob_subiter_method,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_current_iter,
> glob_not_yet_start_msg,
> glob_log10relerr,
> glob_small_float,
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_log10_relerr,
> glob_disp_incr,
> glob_optimal_done,
> hours_in_day,
> djd_debug,
> glob_optimal_clock_start_sec,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_fact_1,
> array_y,
> array_x,
> array_type_pole,
> array_norms,
> array_m1,
> array_pole,
> array_tmp1_g,
> array_1st_rel_error,
> array_y_init,
> array_y_set_initial,
> array_poles,
> array_fact_2,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global INFO, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel,
glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2,
glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec,
glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h,
glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin,
years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic,
glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium,
days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr,
glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr,
glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter,
glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_percent_done, glob_current_iter,
glob_not_yet_start_msg, glob_log10relerr, glob_small_float,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr,
glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug,
glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1,
array_y, array_x, array_type_pole, array_norms, array_m1, array_pole,
array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial,
array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work,
array_real_pole, array_y_higher, array_complex_pole, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> djd_debug2,
> glob_max_opt_iter,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_relerr,
> glob_reached_optimal_h,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_last_good_h,
> glob_hmin,
> years_in_century,
> glob_normmax,
> MAX_UNCHANGED,
> glob_dump_analytic,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> days_in_year,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10abserr,
> glob_max_hours,
> glob_hmax,
> glob_orig_start_sec,
> glob_abserr,
> glob_initial_pass,
> sec_in_min,
> glob_subiter_method,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_current_iter,
> glob_not_yet_start_msg,
> glob_log10relerr,
> glob_small_float,
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_log10_relerr,
> glob_disp_incr,
> glob_optimal_done,
> hours_in_day,
> djd_debug,
> glob_optimal_clock_start_sec,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_fact_1,
> array_y,
> array_x,
> array_type_pole,
> array_norms,
> array_m1,
> array_pole,
> array_tmp1_g,
> array_1st_rel_error,
> array_y_init,
> array_y_set_initial,
> array_poles,
> array_fact_2,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_complex_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cos $eq_no = 1
> array_tmp1_g[1] := sin(array_x[1]);
> array_tmp1[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] 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 cos $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 cos $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 cos $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 cos $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 cos $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, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel,
glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2,
glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec,
glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h,
glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin,
years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic,
glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium,
days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr,
glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr,
glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter,
glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_percent_done, glob_current_iter,
glob_not_yet_start_msg, glob_log10relerr, glob_small_float,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr,
glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug,
glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1,
array_y, array_x, array_type_pole, array_norms, array_m1, array_pole,
array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial,
array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work,
array_real_pole, array_y_higher, array_complex_pole, glob_last;
array_tmp1_g[1] := sin(array_x[1]);
array_tmp1[1] := cos(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 + sin(x);
> end;
exact_soln_y := proc(x) 1.0 + sin(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,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,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_optimal_start,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> djd_debug2,
> glob_max_opt_iter,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_relerr,
> glob_reached_optimal_h,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_last_good_h,
> glob_hmin,
> years_in_century,
> glob_normmax,
> MAX_UNCHANGED,
> glob_dump_analytic,
> glob_look_poles,
> glob_h,
> glob_almost_1,
> centuries_in_millinium,
> days_in_year,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10abserr,
> glob_max_hours,
> glob_hmax,
> glob_orig_start_sec,
> glob_abserr,
> glob_initial_pass,
> sec_in_min,
> glob_subiter_method,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_large_float,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_current_iter,
> glob_not_yet_start_msg,
> glob_log10relerr,
> glob_small_float,
> glob_log10_abserr,
> glob_hmin_init,
> glob_dump,
> glob_log10_relerr,
> glob_disp_incr,
> glob_optimal_done,
> hours_in_day,
> djd_debug,
> glob_optimal_clock_start_sec,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_fact_1,
> array_y,
> array_x,
> array_type_pole,
> array_norms,
> array_m1,
> array_pole,
> array_tmp1_g,
> array_1st_rel_error,
> array_y_init,
> array_y_set_initial,
> array_poles,
> array_fact_2,
> array_y_higher_work2,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_complex_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> DEBUGL := 3;
> glob_iolevel := 5;
> glob_optimal_start := 0.0;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> glob_clock_sec := 0.0;
> djd_debug2 := true;
> glob_max_opt_iter := 10;
> glob_curr_iter_when_opt := 0;
> glob_max_sec := 10000.0;
> glob_smallish_float := 0.1e-100;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_reached_optimal_h := false;
> glob_start := 0;
> glob_warned2 := false;
> glob_warned := false;
> glob_last_good_h := 0.1;
> glob_hmin := 0.00000000001;
> years_in_century := 100.0;
> glob_normmax := 0.0;
> MAX_UNCHANGED := 10;
> glob_dump_analytic := false;
> glob_look_poles := false;
> glob_h := 0.1;
> glob_almost_1 := 0.9990;
> centuries_in_millinium := 10.0;
> days_in_year := 365.0;
> glob_log10normmin := 0.1;
> glob_max_minutes := 0.0;
> glob_log10abserr := 0.0;
> glob_max_hours := 0.0;
> glob_hmax := 1.0;
> glob_orig_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_initial_pass := true;
> sec_in_min := 60.0;
> glob_subiter_method := 3;
> glob_iter := 0;
> glob_unchanged_h_cnt := 0;
> glob_large_float := 9.0e100;
> glob_display_flag := true;
> glob_html_log := true;
> glob_optimal_expect_sec := 0.1;
> glob_percent_done := 0.0;
> glob_current_iter := 0;
> glob_not_yet_start_msg := true;
> glob_log10relerr := 0.0;
> glob_small_float := 0.1e-50;
> glob_log10_abserr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_dump := false;
> glob_log10_relerr := 0.1e-10;
> glob_disp_incr := 0.1;
> glob_optimal_done := false;
> hours_in_day := 24.0;
> djd_debug := true;
> glob_optimal_clock_start_sec := 0.0;
> min_in_hour := 60.0;
> #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/cospostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( 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 := 1.6;");
> omniout_str(ALWAYS,"x_end := 10.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 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 + sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_y_set_initial := 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_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_fact_1[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_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=max_terms do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_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 := 1.6;
> x_end := 10.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 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 ) = cos ( 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,"2012-06-17T19:54:25-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cos")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( 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,"cos diffeq.mxt")
> ;
> logitem_str(html_log_file,"cos 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, glob_max_terms, DEBUGMASSIVE, ALWAYS, DEBUGL, glob_iolevel,
glob_optimal_start, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec, djd_debug2,
glob_max_opt_iter, glob_curr_iter_when_opt, glob_max_sec,
glob_smallish_float, glob_max_iter, glob_relerr, glob_reached_optimal_h,
glob_start, glob_warned2, glob_warned, glob_last_good_h, glob_hmin,
years_in_century, glob_normmax, MAX_UNCHANGED, glob_dump_analytic,
glob_look_poles, glob_h, glob_almost_1, centuries_in_millinium,
days_in_year, glob_log10normmin, glob_max_minutes, glob_log10abserr,
glob_max_hours, glob_hmax, glob_orig_start_sec, glob_abserr,
glob_initial_pass, sec_in_min, glob_subiter_method, glob_iter,
glob_unchanged_h_cnt, glob_large_float, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_percent_done, glob_current_iter,
glob_not_yet_start_msg, glob_log10relerr, glob_small_float,
glob_log10_abserr, glob_hmin_init, glob_dump, glob_log10_relerr,
glob_disp_incr, glob_optimal_done, hours_in_day, djd_debug,
glob_optimal_clock_start_sec, min_in_hour, array_const_1, array_const_0D0,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error, array_fact_1,
array_y, array_x, array_type_pole, array_norms, array_m1, array_pole,
array_tmp1_g, array_1st_rel_error, array_y_init, array_y_set_initial,
array_poles, array_fact_2, array_y_higher_work2, array_y_higher_work,
array_real_pole, array_y_higher, array_complex_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
ALWAYS := 1;
DEBUGL := 3;
glob_iolevel := 5;
glob_optimal_start := 0.;
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
glob_clock_sec := 0.;
djd_debug2 := true;
glob_max_opt_iter := 10;
glob_curr_iter_when_opt := 0;
glob_max_sec := 10000.0;
glob_smallish_float := 0.1*10^(-100);
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_reached_optimal_h := false;
glob_start := 0;
glob_warned2 := false;
glob_warned := false;
glob_last_good_h := 0.1;
glob_hmin := 0.1*10^(-10);
years_in_century := 100.0;
glob_normmax := 0.;
MAX_UNCHANGED := 10;
glob_dump_analytic := false;
glob_look_poles := false;
glob_h := 0.1;
glob_almost_1 := 0.9990;
centuries_in_millinium := 10.0;
days_in_year := 365.0;
glob_log10normmin := 0.1;
glob_max_minutes := 0.;
glob_log10abserr := 0.;
glob_max_hours := 0.;
glob_hmax := 1.0;
glob_orig_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_initial_pass := true;
sec_in_min := 60.0;
glob_subiter_method := 3;
glob_iter := 0;
glob_unchanged_h_cnt := 0;
glob_large_float := 0.90*10^101;
glob_display_flag := true;
glob_html_log := true;
glob_optimal_expect_sec := 0.1;
glob_percent_done := 0.;
glob_current_iter := 0;
glob_not_yet_start_msg := true;
glob_log10relerr := 0.;
glob_small_float := 0.1*10^(-50);
glob_log10_abserr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_dump := false;
glob_log10_relerr := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_optimal_done := false;
hours_in_day := 24.0;
djd_debug := true;
glob_optimal_clock_start_sec := 0.;
min_in_hour := 60.0;
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/cospostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( 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 := 1.6;");
omniout_str(ALWAYS, "x_end := 10.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 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 + sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_y_set_initial := 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_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_const_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 := 1.6;
x_end := 10.0;
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 ) = cos ( 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, "2012-06-17T19:54:25-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "cos");
logitem_str(html_log_file, "diff ( y , x , 1 ) = cos ( 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,
"cos diffeq.mxt");
logitem_str(html_log_file,
"cos 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/cospostode.ode#################
diff ( y , x , 1 ) = cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 1.6;
x_end := 10.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 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 + sin(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 1.6
y[1] (analytic) = 1.9995736030415051643421138255462
y[1] (numeric) = 1.9995736030415051643421138255462
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.601
y[1] (analytic) = 1.9995439037373105905689497577459
y[1] (numeric) = 1.9995439037373105905203596539172
absolute error = 4.85901038287e-20
relative error = 2.4300593619315451943525779077936e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.602
y[1] (analytic) = 1.9995132048892955748077300527509
y[1] (numeric) = 1.9995132048892955747105512983293
absolute error = 9.71787544216e-20
relative error = 4.8601206625679858234868036479976e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.603
y[1] (analytic) = 1.9994815065281589625152332224708
y[1] (numeric) = 1.9994815065281589623694673192807
absolute error = 1.457659031901e-19
relative error = 7.2901851162006313613202679888312e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.604
y[1] (analytic) = 1.9994488086855991121865415527359
y[1] (numeric) = 1.9994488086855991119921900511887
absolute error = 1.943515015472e-19
relative error = 9.7202539371319590846331854485445e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.605
y[1] (analytic) = 1.9994151113943138636566852497442
y[1] (numeric) = 1.9994151113943138634137497488371
absolute error = 2.429355009071e-19
relative error = 1.2150328339655604957410507896997e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.606
y[1] (analytic) = 1.9993804146880005054028053298515
y[1] (numeric) = 1.9993804146880005051112874771657
absolute error = 2.915178526858e-19
relative error = 1.4580409538086367824555820386130e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.607
y[1] (analytic) = 1.9993447186013557408468679505378
y[1] (numeric) = 1.9993447186013557405067694422367
absolute error = 3.400985083011e-19
relative error = 1.7010498746760206722874537872622e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.608
y[1] (analytic) = 1.9993080231700756536589638798324
y[1] (numeric) = 1.9993080231700756532702864606601
absolute error = 3.886774191723e-19
relative error = 1.9440597180019232947922611852500e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.609
y[1] (analytic) = 1.9992703284308556720612278008973
y[1] (numeric) = 1.9992703284308556716239732641768
absolute error = 4.372545367205e-19
relative error = 2.1870706052226711307153605676759e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.61
y[1] (analytic) = 1.9992316344213905321324131478443
y[1] (numeric) = 1.9992316344213905316465833354758
absolute error = 4.858298123685e-19
relative error = 2.4300826577762055238237271325293e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.611
y[1] (analytic) = 1.9991919411803742401131591682098
y[1] (numeric) = 1.9991919411803742395787559706687
absolute error = 5.344031975411e-19
relative error = 2.6730959971035829324468618932402e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.612
y[1] (analytic) = 1.9991512487475000337119879068157
y[1] (numeric) = 1.9991512487475000331290132631508
absolute error = 5.829746436649e-19
relative error = 2.9161107446479742887706458619264e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.613
y[1] (analytic) = 1.9991095571634603424120698050174
y[1] (numeric) = 1.9991095571634603417805257028489
absolute error = 6.315441021685e-19
relative error = 3.1591270218556651196501936631896e-17 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.20
NO POLE
x[1] = 1.614
y[1] (analytic) = 1.9990668664699467467787976085685
y[1] (numeric) = 1.9990668664699467460986860840861
absolute error = 6.801115244824e-19
relative error = 3.4021449501755550825057211513167e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.615
y[1] (analytic) = 1.999023176709649936768209276527
y[1] (numeric) = 1.9990231767096499360395324144878
absolute error = 7.286768620392e-19
relative error = 3.6451646510601581619008939038156e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.616
y[1] (analytic) = 1.9989784879262596690363015827741
y[1] (numeric) = 1.9989784879262596682590615165005
absolute error = 7.772400662736e-19
relative error = 3.8881862459656024775720365963546e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.617
y[1] (analytic) = 1.9989328001644647232492771008306
y[1] (numeric) = 1.9989328001644647224234760122083
absolute error = 8.258010886223e-19
relative error = 4.1312098563511298200172240044787e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.618
y[1] (analytic) = 1.9988861134699528573947682617194
y[1] (numeric) = 1.998886113469952856520408381195
absolute error = 8.743598805244e-19
relative error = 4.3742356036810965023359185227469e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.619
y[1] (analytic) = 1.9988384278894107620940831736458
y[1] (numeric) = 1.9988384278894107611711667802247
absolute error = 9.229163934211e-19
relative error = 4.6172636094234724527603812027227e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.62
y[1] (analytic) = 1.9987897434705240139155188912468
y[1] (numeric) = 1.998789743470524012944048312491
absolute error = 9.714705787558e-19
relative error = 4.8602939950503413007755365015686e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.621
y[1] (analytic) = 1.9987400602619770276887888210922
y[1] (numeric) = 1.9987400602619770266687664331178
absolute error = 1.0200223879744e-18
relative error = 5.1033268820394011576067692770123e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.622
y[1] (analytic) = 1.9986893783134530078206119490054
y[1] (numeric) = 1.9986893783134530067520401764804
absolute error = 1.0685717725250e-18
relative error = 5.3463623918724636497110433165149e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.623
y[1] (analytic) = 1.9986376976756338986115125736116
y[1] (numeric) = 1.9986376976756338974943938897533
absolute error = 1.1171186838583e-18
relative error = 5.5894006460374551069102581717758e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.624
y[1] (analytic) = 1.9985850184002003335738802293083
y[1] (numeric) = 1.9985850184002003324082171558809
absolute error = 1.1656630734274e-18
relative error = 5.8324417660274159323682056334826e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.625
y[1] (analytic) = 1.9985313405398315837513404805954
y[1] (numeric) = 1.9985313405398315825371355879076
absolute error = 1.2142048926878e-18
relative error = 6.0754858733405005492361714050315e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.626
y[1] (analytic) = 1.9984766641482055050394882683887
y[1] (numeric) = 1.9984766641482055037767441752909
absolute error = 1.2627440930978e-18
relative error = 6.3185330894819788660612577477140e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.627
y[1] (analytic) = 1.9984209892799984845080364875794
y[1] (numeric) = 1.9984209892799984831967558614612
absolute error = 1.3112806261182e-18
relative error = 6.5615835359627353042965616999604e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.628
y[1] (analytic) = 1.9983643159908853857244334736866
y[1] (numeric) = 1.9983643159908853843646190304742
absolute error = 1.3598144432124e-18
relative error = 6.8046373342997692141472674443570e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.629
y[1] (analytic) = 1.998306644337539493079004074981
y[1] (numeric) = 1.9983066443375394916706585791343
absolute error = 1.4083454958467e-18
relative error = 7.0476946060176962186535949265605e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.63
y[1] (analytic) = 1.9982479743776324551116699849331
y[1] (numeric) = 1.9982479743776324536547962494432
absolute error = 1.4568737354899e-18
relative error = 7.2907554726467467501836511924238e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.631
y[1] (analytic) = 1.9981883061698342268403060082628
y[1] (numeric) = 1.9981883061698342253349068946489
absolute error = 1.5053991136139e-18
relative error = 7.5338200557257687683023718661394e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.632
y[1] (analytic) = 1.9981276397738130110907899322266
y[1] (numeric) = 1.9981276397738130095368683505334
absolute error = 1.5539215816932e-18
relative error = 7.7768884767997258611817527186720e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.633
y[1] (analytic) = 1.9980659752502351988288046730904
y[1] (numeric) = 1.998065975250235197226363581885
absolute error = 1.6024410912054e-18
relative error = 8.0199608574221997350431459316914e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.634
y[1] (analytic) = 1.9980033126607653084934523659789
y[1] (numeric) = 1.9980033126607653068424947723478
absolute error = 1.6509575936311e-18
relative error = 8.2630373191548901680277642017783e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.635
y[1] (analytic) = 1.9979396520680659243327410644828
y[1] (numeric) = 1.9979396520680659226332700240291
absolute error = 1.6994710404537e-18
relative error = 8.5061179835666143618662145784570e-17 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=0.44
NO POLE
x[1] = 1.636
y[1] (analytic) = 1.9978749935357976337410057145331
y[1] (numeric) = 1.9978749935357976319930243313733
absolute error = 1.7479813831598e-18
relative error = 8.7492029722353092941268659050419e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.637
y[1] (analytic) = 1.9978093371286189635983260651146
y[1] (numeric) = 1.9978093371286189618018374918756
absolute error = 1.7964885732390e-18
relative error = 8.9922924067470311709085278518649e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.638
y[1] (analytic) = 1.9977426829121863156120051763966
y[1] (numeric) = 1.9977426829121863137670126142126
absolute error = 1.8449925621840e-18
relative error = 9.2353864086964563830638480648078e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.639
y[1] (analytic) = 1.9976750309531539006601731837968
y[1] (numeric) = 1.9976750309531538987666798823057
absolute error = 1.8934933014911e-18
relative error = 9.4784850996893848920370858896511e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.64
y[1] (analytic) = 1.9976063813191736721375819743679
y[1] (numeric) = 1.9976063813191736701955912317085
absolute error = 1.9419907426594e-18
relative error = 9.7215886013387363459267284203104e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.641
y[1] (analytic) = 1.9975367340788952583036574297089
y[1] (numeric) = 1.9975367340788952563131725925174
absolute error = 1.9904848371915e-18
relative error = 9.9646970352680546266664237682618e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.642
y[1] (analytic) = 1.997466089301965893632876887341
y[1] (numeric) = 1.9974660893019658915939013507478
absolute error = 2.0389755365932e-18
relative error = 1.0207810523110006786880676957981e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.643
y[1] (analytic) = 1.9973944470590303491675404701666
y[1] (numeric) = 1.9973944470590303470800776777926
absolute error = 2.0874627923740e-18
relative error = 1.0450929186508886895386037250447e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.644
y[1] (analytic) = 1.9973218074217308618730059312328
y[1] (numeric) = 1.9973218074217308597370593751864
absolute error = 2.1359465560464e-18
relative error = 1.0694053147117112384960091060431e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.645
y[1] (analytic) = 1.9972481704627070629954576585605
y[1] (numeric) = 1.9972481704627070608110308794336
absolute error = 2.1844267791269e-18
relative error = 1.0937182526600231355160820095760e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.646
y[1] (analytic) = 1.9971735362555959054222814822617
y[1] (numeric) = 1.9971735362555959031893780691266
absolute error = 2.2329034131351e-18
relative error = 1.1180317446632417544370794732926e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.647
y[1] (analytic) = 1.9970979048750315900451179235668
y[1] (numeric) = 1.9970979048750315877637415139723
absolute error = 2.2813764095945e-18
relative error = 1.1423458028900476657431586414841e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.648
y[1] (analytic) = 1.9970212763966454911256675227001
y[1] (numeric) = 1.9970212763966454887958218026681
absolute error = 2.3298457200320e-18
relative error = 1.1666604395101343912740645321155e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.649
y[1] (analytic) = 1.9969436508970660806643228797941
y[1] (numeric) = 1.9969436508970660782860115838157
absolute error = 2.3783112959784e-18
relative error = 1.1909756666944588679364201593550e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.65
y[1] (analytic) = 1.9968650284539188517717030402022
y[1] (numeric) = 1.9968650284539188493449299512342
absolute error = 2.4267730889680e-18
relative error = 1.2152914966150412642153728666333e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.651
y[1] (analytic) = 1.9967854091458262410431668526709
y[1] (numeric) = 1.9967854091458262385679358021318
absolute error = 2.4752310505391e-18
relative error = 1.2396079414452154750955445039782e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.652
y[1] (analytic) = 1.9967047930524075499363829258502
y[1] (numeric) = 1.9967047930524075474126977936165
absolute error = 2.5236851322337e-18
relative error = 1.2639250133594790177610995731693e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.653
y[1] (analytic) = 1.9966231802542788651520348055667
y[1] (numeric) = 1.9966231802542788625798995199689
absolute error = 2.5721352855978e-18
relative error = 1.2882427245336433998353258474280e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.654
y[1] (analytic) = 1.996540570833052978017740992147
y[1] (numeric) = 1.9965405708330529753971595299658
absolute error = 2.6205814621812e-18
relative error = 1.3125610871447340924927338748199e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.655
y[1] (analytic) = 1.9964569648713393028752704138649
y[1] (numeric) = 1.9964569648713393002062468003272
absolute error = 2.6690236135377e-18
relative error = 1.3368801133710908350877035156857e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.656
y[1] (analytic) = 1.9963723624527437944711349692902
y[1] (numeric) = 1.9963723624527437917536732780651
absolute error = 2.7174616912251e-18
relative error = 1.3611998153923677844152858380524e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.657
y[1] (analytic) = 1.9962867636618688643506417479393
y[1] (numeric) = 1.9962867636618688615847461011339
absolute error = 2.7658956468054e-18
relative error = 1.3855202053896338514788294164142e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.658
y[1] (analytic) = 1.9962001685843132962554885351691
y[1] (numeric) = 1.9962001685843132934411631033244
absolute error = 2.8143254318447e-18
relative error = 1.4098412955453227801766240716554e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.69
NO POLE
x[1] = 1.659
y[1] (analytic) = 1.9961125773066721605249872037106
y[1] (numeric) = 1.9961125773066721576622362057975
absolute error = 2.8627509979131e-18
relative error = 1.4341630980431832148001580152034e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.66
y[1] (analytic) = 1.996023989916536727501000590613
y[1] (numeric) = 1.9960239899165367245898282940278
absolute error = 2.9111722965852e-18
relative error = 1.4584856250685293532774464046202e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.661
y[1] (analytic) = 1.9959344065024943799366794546528
y[1] (numeric) = 1.9959344065024943769770901752132
absolute error = 2.9595892794396e-18
relative error = 1.4828088888079906503970712485268e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.662
y[1] (analytic) = 1.995843827154128524409087105465
y[1] (numeric) = 1.9958438271541285214010852074058
absolute error = 3.0080018980592e-18
relative error = 1.5071329014496622885369564814974e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.663
y[1] (analytic) = 1.9957522519620185017358002917634
y[1] (numeric) = 1.9957522519620184986793901877318
absolute error = 3.0564101040316e-18
relative error = 1.5314576751833057969319881542690e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.664
y[1] (analytic) = 1.9956596810177394963955759320416
y[1] (numeric) = 1.9956596810177394932907620830932
absolute error = 3.1048138489484e-18
relative error = 1.5557832221999985322835640415286e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.665
y[1] (analytic) = 1.9955661144138624449531742670819
y[1] (numeric) = 1.9955661144138624417999611826758
absolute error = 3.1532130844061e-18
relative error = 1.5801095546925848413163901830978e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.666
y[1] (analytic) = 1.9954715522439539434884300094387
y[1] (numeric) = 1.9954715522439539402868222474334
absolute error = 3.2016077620053e-18
relative error = 1.6044366848552754229653142913305e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.667
y[1] (analytic) = 1.9953759946025761540296640608207
y[1] (numeric) = 1.9953759946025761507796662274693
absolute error = 3.2499978333514e-18
relative error = 1.6287646248839983170198607817332e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.668
y[1] (analytic) = 1.9952794415852867099915293639491
y[1] (numeric) = 1.9952794415852867066931461138948
absolute error = 3.2983832500543e-18
relative error = 1.6530933869762488121722280789148e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.669
y[1] (analytic) = 1.9951818932886386206173854510412
y[1] (numeric) = 1.9951818932886386172706214873126
absolute error = 3.3467639637286e-18
relative error = 1.6774229833311899166776298497319e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.67
y[1] (analytic) = 1.9950833498101801744262972465342
y[1] (numeric) = 1.9950833498101801710311573205407
absolute error = 3.3951399259935e-18
relative error = 1.7017534261496024908037895233429e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.671
y[1] (analytic) = 1.9949838112484548416647546770444
y[1] (numeric) = 1.9949838112484548382212435885712
absolute error = 3.4435110884732e-18
relative error = 1.7260847276340859952450621476253e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.672
y[1] (analytic) = 1.9948832777030011757632106368326
y[1] (numeric) = 1.9948832777030011722713332340362
absolute error = 3.4918774027964e-18
relative error = 1.7504168999888081478122860560104e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.673
y[1] (analytic) = 1.9947817492743527137975358522306
y[1] (numeric) = 1.9947817492743527102572970316337
absolute error = 3.5402388205969e-18
relative error = 1.7747499554198059456069950571306e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.674
y[1] (analytic) = 1.9946792260640378759554901835647
y[1] (numeric) = 1.9946792260640378723668948900514
absolute error = 3.5885952935133e-18
relative error = 1.7990839061348355808190577978220e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.675
y[1] (analytic) = 1.9945757081745798640083108980974
y[1] (numeric) = 1.9945757081745798603713641249084
absolute error = 3.6369467731890e-18
relative error = 1.8234187643433727209971273216407e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.676
y[1] (analytic) = 1.99447119570949655878751944239
y[1] (numeric) = 1.9944711957094965551022262311175
absolute error = 3.6852932112725e-18
relative error = 1.8477545422567632072444236656160e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.677
y[1] (analytic) = 1.994365688773300416667049237271
y[1] (numeric) = 1.9943656887733004129334146778535
absolute error = 3.7336345594175e-18
relative error = 1.8720912520882735196361842827374e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.678
y[1] (analytic) = 1.9942591874714983650507980132736
y[1] (numeric) = 1.9942591874714983612688272439909
absolute error = 3.7819707692827e-18
relative error = 1.8964289060529908299030648515190e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.679
y[1] (analytic) = 1.9941516919105916968657091989816
y[1] (numeric) = 1.9941516919105916930354074064498
absolute error = 3.8303017925318e-18
relative error = 1.9207675163678233182041766234038e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.68
y[1] (analytic) = 1.9940432021980759640604878691936
y[1] (numeric) = 1.9940432021980759601818602883598
absolute error = 3.8786275808338e-18
relative error = 1.9451070952516509403626923193668e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.681
y[1] (analytic) = 1.9939337184424408701100577541801
y[1] (numeric) = 1.9939337184424408661831096683173
absolute error = 3.9269480858628e-18
relative error = 1.9694476549252254863161256120610e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.93
NO POLE
x[1] = 1.682
y[1] (analytic) = 1.9938232407531701615258668055684
y[1] (numeric) = 1.9938232407531701575506035462699
absolute error = 3.9752632592985e-18
relative error = 1.9937892076114216927548580167245e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.683
y[1] (analytic) = 1.9937117692407415183721498085394
y[1] (numeric) = 1.9937117692407415143485767557138
absolute error = 4.0235730528256e-18
relative error = 2.0181317655349367075387174006506e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.684
y[1] (analytic) = 1.9935993040166264437882575240663
y[1] (numeric) = 1.993599304016626439716380105932
absolute error = 4.0718774181343e-18
relative error = 2.0424753409225412222331159309791e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.685
y[1] (analytic) = 1.9934858451932901525171628388552
y[1] (numeric) = 1.9934858451932901483969865319349
absolute error = 4.1201763069203e-18
relative error = 2.0668199460030798750976586080533e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.686
y[1] (analytic) = 1.9933713928841914584402553944733
y[1] (numeric) = 1.9933713928841914542717857235886
absolute error = 4.1684696708847e-18
relative error = 2.0911655930074214913177034566937e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.687
y[1] (analytic) = 1.9932559472037826611185371608599
y[1] (numeric) = 1.9932559472037826569017796991258
absolute error = 4.2167574617341e-18
relative error = 2.1155122941685096475296554078247e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.688
y[1] (analytic) = 1.993139508267509431340332413016
y[1] (numeric) = 1.9931395082675094270752927818351
absolute error = 4.2650396311809e-18
relative error = 2.1398600617215136010143196046725e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.689
y[1] (analytic) = 1.9930220761918106956756265631518
y[1] (numeric) = 1.9930220761918106913623104322092
absolute error = 4.3133161309426e-18
relative error = 2.1642089079034775246451640190922e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.69
y[1] (analytic) = 1.9929036510941185200371492939456
y[1] (numeric) = 1.9929036510941185156755623812026
absolute error = 4.3615869127430e-18
relative error = 2.1885588449539230035254342975087e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.691
y[1] (analytic) = 1.9927842330928579922483184318185
y[1] (numeric) = 1.9927842330928579878384665035073
absolute error = 4.4098519283112e-18
relative error = 2.2129098851143477664407156434940e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.692
y[1] (analytic) = 1.9926638223074471036181619922741
y[1] (numeric) = 1.9926638223074470991600508628919
absolute error = 4.4581111293822e-18
relative error = 2.2372620406285271864457529440189e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.693
y[1] (analytic) = 1.9925424188582966295233368223692
y[1] (numeric) = 1.9925424188582966250169723546724
absolute error = 4.5063644676968e-18
relative error = 2.2616153237424645834332809706531e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.694
y[1] (analytic) = 1.9924200228668100089973632582879
y[1] (numeric) = 1.9924200228668100044427513632862
absolute error = 4.5546118950017e-18
relative error = 2.2859697467044418926700700031705e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.695
y[1] (analytic) = 1.9922966344553832233271962087742
y[1] (numeric) = 1.9922966344553832187243428457248
absolute error = 4.6028533630494e-18
relative error = 2.3103253217649699688446224824434e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.696
y[1] (analytic) = 1.992172253747404673657254067842
y[1] (numeric) = 1.9921722537474046690061652442435
absolute error = 4.6510888235985e-18
relative error = 2.3346820611769396609363397933797e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.697
y[1] (analytic) = 1.9920468808672550576010278527229
y[1] (numeric) = 1.9920468808672550529017096243093
absolute error = 4.6993182284136e-18
relative error = 2.3590399771955721487308203529947e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.698
y[1] (analytic) = 1.991920515940307244860393955433
y[1] (numeric) = 1.9919205159403072401128524261679
absolute error = 4.7475415292651e-18
relative error = 2.3833990820783190617062066090170e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.699
y[1] (analytic) = 1.9917931590929261518527548886357
y[1] (numeric) = 1.9917931590929261470569962107058
absolute error = 4.7957586779299e-18
relative error = 2.4077593880852144173258992377833e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.7
y[1] (analytic) = 1.9916648104524686153461333986479
y[1] (numeric) = 1.9916648104524686105021637724571
absolute error = 4.8439696261908e-18
relative error = 2.4321209074785739778365558481927e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.701
y[1] (analytic) = 1.991535470147283265102346310487
y[1] (numeric) = 1.9915354701472832602101719846502
absolute error = 4.8921743258368e-18
relative error = 2.4564836525231464077242136542966e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.702
y[1] (analytic) = 1.9914051383067103955283854617728
y[1] (numeric) = 1.9914051383067103905880127331096
absolute error = 4.9403727286632e-18
relative error = 2.4808476354861640617472278411498e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.703
y[1] (analytic) = 1.9912738150610818363361340740934
y[1] (numeric) = 1.9912738150610818313475692876217
absolute error = 4.9885647864717e-18
relative error = 2.5052128686373937968800708407976e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.704
y[1] (analytic) = 1.9911415005417208222105479021069
y[1] (numeric) = 1.9911415005417208171737974510367
absolute error = 5.0367504510702e-18
relative error = 2.5295793642490371412338985244327e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=1.18
NO POLE
x[1] = 1.705
y[1] (analytic) = 1.9910081948809418614864314921887
y[1] (numeric) = 1.9910081948809418564015018179157
absolute error = 5.0849296742730e-18
relative error = 2.5539471345958313304215414742205e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.706
y[1] (analytic) = 1.9908738982120506038339408738353
y[1] (numeric) = 1.9908738982120505987008384659343
absolute error = 5.1331024079010e-18
relative error = 2.5783161919551503882447723733601e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.707
y[1] (analytic) = 1.9907386106693437069529449983121
y[1] (numeric) = 1.9907386106693437017716763945308
absolute error = 5.1812686037813e-18
relative error = 2.6026865486068048569766549971839e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.708
y[1] (analytic) = 1.9906023323881087022763792301723
y[1] (numeric) = 1.9906023323881086970469510164245
absolute error = 5.2294282137478e-18
relative error = 2.6270582168333438105609091870476e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.709
y[1] (analytic) = 1.9904650635046238596827251882821
y[1] (numeric) = 1.9904650635046238544051439986412
absolute error = 5.2775811896409e-18
relative error = 2.6514312089199048401843783209907e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.71
y[1] (analytic) = 1.9903268041561580512177522238611
y[1] (numeric) = 1.9903268041561580458920247405535
absolute error = 5.3257274833076e-18
relative error = 2.6758055371542649545106157812819e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.711
y[1] (analytic) = 1.9901875544809706138256568137853
y[1] (numeric) = 1.9901875544809706084517897671836
absolute error = 5.3738670466017e-18
relative error = 2.7001812138269417517144963173211e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.712
y[1] (analytic) = 1.9900473146183112110897371380016
y[1] (numeric) = 1.9900473146183112056677373066181
absolute error = 5.4219998313835e-18
relative error = 2.7245582512310433881456937370575e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.713
y[1] (analytic) = 1.9899060847084196939827411003679
y[1] (numeric) = 1.9899060847084196885126153108477
absolute error = 5.4701257895202e-18
relative error = 2.7489366616624702632785834061216e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.714
y[1] (analytic) = 1.9897638648925259606270270425593
y[1] (numeric) = 1.9897638648925259551087821696732
absolute error = 5.5182448728861e-18
relative error = 2.7733164574200162802426169851699e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.715
y[1] (analytic) = 1.9896206553128498150646773908669
y[1] (numeric) = 1.9896206553128498094983203575051
absolute error = 5.5663570333618e-18
relative error = 2.7976976508049675466094231503008e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.716
y[1] (analytic) = 1.989476456112600825037706465766
y[1] (numeric) = 1.9894764561126008194232442429307
absolute error = 5.6144622228353e-18
relative error = 2.8220802541216559313046131465644e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.717
y[1] (analytic) = 1.9893312674359781787785046740318
y[1] (numeric) = 1.9893312674359781731159442808303
absolute error = 5.6625603932015e-18
relative error = 2.8464642796772085759351121839802e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.718
y[1] (analytic) = 1.9891850894281705408106622929473
y[1] (numeric) = 1.9891850894281705351000107965852
absolute error = 5.7106514963621e-18
relative error = 2.8708497397814983894299675799702e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.719
y[1] (analytic) = 1.9890379222353559067603170457685
y[1] (numeric) = 1.9890379222353559010015815615424
absolute error = 5.7587354842261e-18
relative error = 2.8952366467473961784621353464680e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.72
y[1] (analytic) = 1.9888897660047014571781706570855
y[1] (numeric) = 1.9888897660047014513713583483761
absolute error = 5.8068123087094e-18
relative error = 2.9196250128905703806741690633546e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.721
y[1] (analytic) = 1.9887406208843634103723205660523
y[1] (numeric) = 1.9887406208843634045174386443171
absolute error = 5.8548819217352e-18
relative error = 2.9440148505296889780421977168262e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.722
y[1] (analytic) = 1.9885904870234868742520539646404
y[1] (numeric) = 1.9885904870234868683491096894065
absolute error = 5.9029442752339e-18
relative error = 2.9684061719863700713305963089952e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.723
y[1] (analytic) = 1.9884393645722056971827523171103
y[1] (numeric) = 1.988439364572205691231752995967
absolute error = 5.9509993211433e-18
relative error = 2.9927989895852833094670702128445e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.724
y[1] (analytic) = 1.9882872536816423178520555057834
y[1] (numeric) = 1.9882872536816423118530084943752
absolute error = 5.9990470114082e-18
relative error = 3.0171933156539496030807743883569e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.725
y[1] (analytic) = 1.9881341545039076141474357369385
y[1] (numeric) = 1.9881341545039076081003484389576
absolute error = 6.0470872979809e-18
relative error = 3.0415891625229934367378415941216e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.726
y[1] (analytic) = 1.9879800671921007510453323292455
y[1] (numeric) = 1.9879800671921007449502121964243
absolute error = 6.0951201328212e-18
relative error = 3.0659865425261437907998128983480e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.727
y[1] (analytic) = 1.9878249919003090275119994955896
y[1] (numeric) = 1.9878249919003090213688540276934
absolute error = 6.1431454678962e-18
relative error = 3.0903854680001344568404128240982e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.2MB, time=1.43
NO POLE
x[1] = 1.728
y[1] (analytic) = 1.9876689287836077224162202174247
y[1] (numeric) = 1.987668928783607716225056962244
absolute error = 6.1911632551807e-18
relative error = 3.1147859512849061727142895776758e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.729
y[1] (analytic) = 1.9875118779980599394540402989299
y[1] (numeric) = 1.9875118779980599332148668522731
absolute error = 6.2391734466568e-18
relative error = 3.1391880047234063447415099354565e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.73
y[1] (analytic) = 1.9873538397007164510856776762221
y[1] (numeric) = 1.9873538397007164447985016819078
absolute error = 6.2871759943143e-18
relative error = 3.1635916406617912256294251085231e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.731
y[1] (analytic) = 1.9871948140496155414847630447017
y[1] (numeric) = 1.9871948140496155351495921945511
absolute error = 6.3351708501506e-18
relative error = 3.1879968714493765828493696224118e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.732
y[1] (analytic) = 1.987034801203782848500068855279
y[1] (numeric) = 1.9870348012037828421169108891079
absolute error = 6.3831579661711e-18
relative error = 3.2124037094388399801148554022546e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.733
y[1] (analytic) = 1.986873801323231204629884717737
y[1] (numeric) = 1.9868738013232311981987474233486
absolute error = 6.4311372943884e-18
relative error = 3.2368121669858191985412897853997e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.734
y[1] (analytic) = 1.9867118145689604770091982368449
y[1] (numeric) = 1.9867118145689604705300894500215
absolute error = 6.4791087868234e-18
relative error = 3.2612222564494668220347621770476e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.735
y[1] (analytic) = 1.986548841102957406409841294025
y[1] (numeric) = 1.9865488411029573998827688985205
absolute error = 6.5270723955045e-18
relative error = 3.2856339901920486665536801373982e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.736
y[1] (analytic) = 1.9863848810881954452537627744158
y[1] (numeric) = 1.9863848810881954386787347019477
absolute error = 6.5750280724681e-18
relative error = 3.3100473805791964731827651292729e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.737
y[1] (analytic) = 1.9862199346886345946395897260435
y[1] (numeric) = 1.9862199346886345880166139562849
absolute error = 6.6229757697586e-18
relative error = 3.3344624399799089969779238361123e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.738
y[1] (analytic) = 1.986054002069221240382639924528
y[1] (numeric) = 1.9860540020692212337117244850998
absolute error = 6.6709154394282e-18
relative error = 3.3588791807664524002262858601909e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.739
y[1] (analytic) = 1.9858870833958879880685498032969
y[1] (numeric) = 1.9858870833958879813497027697596
absolute error = 6.7188470335373e-18
relative error = 3.3832976153145627333918236610803e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.74
y[1] (analytic) = 1.9857191788355534971206826956656
y[1] (numeric) = 1.9857191788355534903539121915113
absolute error = 6.7667705041543e-18
relative error = 3.4077177560033463663164352210633e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.741
y[1] (analytic) = 1.9855502885561223138814833213618
y[1] (numeric) = 1.9855502885561223070667975180061
absolute error = 6.8146858033557e-18
relative error = 3.4321396152153314666498872600237e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.742
y[1] (analytic) = 1.9853804127264847037079454361259
y[1] (numeric) = 1.9853804127264846968453525528998
absolute error = 6.8625928832261e-18
relative error = 3.4565632053364691420776186515284e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.743
y[1] (analytic) = 1.9852095515165164820813605489057
y[1] (numeric) = 1.985209551516516475170868853047
absolute error = 6.9104916958587e-18
relative error = 3.4809885387563864515157248892276e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.744
y[1] (analytic) = 1.985037705097078844731516596882
y[1] (numeric) = 1.9850377050970788377731344035275
absolute error = 6.9583821933545e-18
relative error = 3.5054156278679846539956641047407e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.745
y[1] (analytic) = 1.9848648736400181967755164541134
y[1] (numeric) = 1.9848648736400181897692521262904
absolute error = 7.0062643278230e-18
relative error = 3.5298444850677929740202066261438e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.746
y[1] (analytic) = 1.9846910573181659808713871349669
y[1] (numeric) = 1.9846910573181659738172490835847
absolute error = 7.0541380513822e-18
relative error = 3.5542751227559698573688776053055e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.747
y[1] (analytic) = 1.9845162563053385043866515387101
y[1] (numeric) = 1.9845162563053384972846482225519
absolute error = 7.1020033161582e-18
relative error = 3.5787075533361026738937135812870e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.748
y[1] (analytic) = 1.9843404707763367655820355666807
y[1] (numeric) = 1.9843404707763367584321754923948
absolute error = 7.1498600742859e-18
relative error = 3.6031417892155616608610125758470e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.749
y[1] (analytic) = 1.9841637009069462788104844283096
y[1] (numeric) = 1.9841637009069462716127761504011
absolute error = 7.1977082779085e-18
relative error = 3.6275778428052492717069739457932e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.75
memory used=26.7MB, alloc=4.2MB, time=1.68
y[1] (analytic) = 1.983985946873936898731662936968
y[1] (numeric) = 1.9839859468739368914861150577902
absolute error = 7.2455478791778e-18
relative error = 3.6520157265197526262346147192831e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.751
y[1] (analytic) = 1.9838072088550626435421155811236
y[1] (numeric) = 1.9838072088550626362487367508695
absolute error = 7.2933788302541e-18
relative error = 3.6764554527772944162442125584815e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.752
y[1] (analytic) = 1.9836274870290615172212631406304
y[1] (numeric) = 1.9836274870290615098800620573238
absolute error = 7.3412010833066e-18
relative error = 3.7008970339999358544441712433654e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.753
y[1] (analytic) = 1.9834467815756553307934136021408
y[1] (numeric) = 1.9834467815756553234043990116279
absolute error = 7.3890145905129e-18
relative error = 3.7253404826133259847535736610913e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.754
y[1] (analytic) = 1.9832650926755495226059661116152
y[1] (numeric) = 1.9832650926755495151691468075555
absolute error = 7.4368193040597e-18
relative error = 3.7497858110470559250243365464492e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.755
y[1] (analytic) = 1.9830824205104329776239876857083
y[1] (numeric) = 1.9830824205104329701393725095662
absolute error = 7.4846151761421e-18
relative error = 3.7742330317343073392607893205934e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.756
y[1] (analytic) = 1.9828987652629778457413433874426
y[1] (numeric) = 1.9828987652629778382089412284782
absolute error = 7.5324021589644e-18
relative error = 3.7986821571122571906319883570811e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.757
y[1] (analytic) = 1.9827141271168393591085616550214
y[1] (numeric) = 1.982714127116839351528381450282
absolute error = 7.5801802047394e-18
relative error = 3.8231331996217261870397379794907e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.758
y[1] (analytic) = 1.9825285062566556484776174559031
y[1] (numeric) = 1.9825285062566556408496681902138
absolute error = 7.6279492656893e-18
relative error = 3.8475861717076340873692655938337e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.759
y[1] (analytic) = 1.982341902868047558563816921336
y[1] (numeric) = 1.9823419028680475508881076272911
absolute error = 7.6757092940449e-18
relative error = 3.8720410858185976985903290220929e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.76
y[1] (analytic) = 1.982154317137618462424968099456
y[1] (numeric) = 1.9821543171376184547015078574098
absolute error = 7.7234602420462e-18
relative error = 3.8964979544072349552955835141270e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.761
y[1] (analytic) = 1.9819657492529540748580234477586
y[1] (numeric) = 1.9819657492529540670868213858164
absolute error = 7.7712020619422e-18
relative error = 3.9209567899300655385064148671822e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.762
y[1] (analytic) = 1.9817761994026222648133806682892
y[1] (numeric) = 1.981776199402622256994445962298
absolute error = 7.8189347059912e-18
relative error = 3.9454176048476637438421722816505e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.763
y[1] (analytic) = 1.9815856677761728668270294712338
y[1] (numeric) = 1.9815856677761728589603713447733
absolute error = 7.8666581264605e-18
relative error = 3.9698804116245086566570009927476e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.764
y[1] (analytic) = 1.9813941545641374914707328347483
y[1] (numeric) = 1.9813941545641374835563605591216
absolute error = 7.9143722756267e-18
relative error = 3.9943452227291370649625319293833e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.765
y[1] (analytic) = 1.9812016599580293348204323108292
y[1] (numeric) = 1.9812016599580293268583552050535
absolute error = 7.9620771057757e-18
relative error = 4.0188120506341450445770258098671e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.766
y[1] (analytic) = 1.9810081841503429869430679088044
y[1] (numeric) = 1.9810081841503429789332953396018
absolute error = 8.0097725692026e-18
relative error = 4.0432809078161390731887266359232e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.767
y[1] (analytic) = 1.9808137273345542394020040696088
y[1] (numeric) = 1.9808137273345542313445454513969
absolute error = 8.0574586182119e-18
relative error = 4.0677518067558385757363405963580e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.768
y[1] (analytic) = 1.9806182897051198917812542254018
y[1] (numeric) = 1.9806182897051198836761190202842
absolute error = 8.1051352051176e-18
relative error = 4.0922247599381280479167877153301e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.769
y[1] (analytic) = 1.9804218714574775572286974202867
y[1] (numeric) = 1.9804218714574775490758951380434
absolute error = 8.1528022822433e-18
relative error = 4.1166997798521092180310205400125e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.77
y[1] (analytic) = 1.9802244727880454670184814488984
y[1] (numeric) = 1.9802244727880454588180216469768
absolute error = 8.2004598019216e-18
relative error = 4.1411768789907997523169473140485e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.771
y[1] (analytic) = 1.9800260938942222741328079504419
y[1] (numeric) = 1.9800260938942222658847002339466
absolute error = 8.2481077164953e-18
relative error = 4.1656560698517408659028420163101e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.772
y[1] (analytic) = 1.9798267349743868558632958763769
y[1] (numeric) = 1.9798267349743868475675498980607
absolute error = 8.2957459783162e-18
relative error = 4.1901373649363930790038075948637e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.773
memory used=30.5MB, alloc=4.2MB, time=1.92
y[1] (analytic) = 1.9796263962278981154321207303721
y[1] (numeric) = 1.9796263962278981070887461906259
absolute error = 8.3433745397462e-18
relative error = 4.2146207767506934514109480126318e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.774
y[1] (analytic) = 1.9794250778550947826331279593709
y[1] (numeric) = 1.9794250778550947742421346062141
absolute error = 8.3909933531568e-18
relative error = 4.2391063178048048466842682869193e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.775
y[1] (analytic) = 1.9792227800572952134931198546392
y[1] (numeric) = 1.9792227800572952050545174837102
absolute error = 8.4386023709290e-18
relative error = 4.2635940006130671512819235706054e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.776
y[1] (analytic) = 1.9790195030367971889535163014928
y[1] (numeric) = 1.9790195030367971804673147560389
absolute error = 8.4862015454539e-18
relative error = 4.2880838376943021813038915941883e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.777
y[1] (analytic) = 1.9788152469968777125725906960248
y[1] (numeric) = 1.9788152469968777040387998668925
absolute error = 8.5337908291323e-18
relative error = 4.3125758415716134318475302040028e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.778
y[1] (analytic) = 1.9786100121417928072484833265824
y[1] (numeric) = 1.9786100121417927986671131522074
absolute error = 8.5813701743750e-18
relative error = 4.3370700247725394942327080983244e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.779
y[1] (analytic) = 1.978403798676777310963195496961
y[1] (numeric) = 1.9784037986767773023342559633584
absolute error = 8.6289395336026e-18
relative error = 4.3615663998289548473341205960918e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.78
y[1] (analytic) = 1.9781966068080446715477686473056
y[1] (numeric) = 1.9781966068080446628712697880598
absolute error = 8.6764988592458e-18
relative error = 4.3860649792772233501813850344438e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.781
y[1] (analytic) = 1.9779884367427867404688537075226
y[1] (numeric) = 1.9779884367427867317448056037775
absolute error = 8.7240481037451e-18
relative error = 4.4105657756580485002772163241947e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.782
y[1] (analytic) = 1.9777792886891735656368768966163
y[1] (numeric) = 1.9777792886891735568652896770648
absolute error = 8.7715872195515e-18
relative error = 4.4350688015168292227629883757092e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.783
y[1] (analytic) = 1.9775691628563531832360091597658
y[1] (numeric) = 1.97756916285635317441689300064
absolute error = 8.8191161591258e-18
relative error = 4.4595740694033079535802925279379e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.784
y[1] (analytic) = 1.9773580594544514085761474131563
y[1] (numeric) = 1.9773580594544513997095125382174
absolute error = 8.8666348749389e-18
relative error = 4.4840815918717242320165553576322e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.785
y[1] (analytic) = 1.9771459786945716259671167445668
y[1] (numeric) = 1.9771459786945716170529734250945
absolute error = 8.9141433194723e-18
relative error = 4.5085913814810695547657555881129e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.786
y[1] (analytic) = 1.9769329207887945776153036954926
y[1] (numeric) = 1.9769329207887945686536622502751
absolute error = 8.9616414452175e-18
relative error = 4.5331034507947859850721951505442e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.787
y[1] (analytic) = 1.9767188859501781515429317281535
y[1] (numeric) = 1.9767188859501781425338025234772
absolute error = 9.0091292046763e-18
relative error = 4.5576178123809198755101473773138e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.788
y[1] (analytic) = 1.9765038743927571685301909580939
y[1] (numeric) = 1.9765038743927571594735844077329
absolute error = 9.0566065503610e-18
relative error = 4.5821344788122251038285332472894e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.789
y[1] (analytic) = 1.976287886331543168080435210227
y[1] (numeric) = 1.9762878863315431589763617754327
absolute error = 9.1040734347943e-18
relative error = 4.6066534626661145848560696508633e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.79
y[1] (analytic) = 1.9760709219825241934086604331086
y[1] (numeric) = 1.9760709219825241842571306225993
absolute error = 9.1515298105093e-18
relative error = 4.6311747765246623646665022077830e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.791
y[1] (analytic) = 1.9758529815626645754534794829444
y[1] (numeric) = 1.9758529815626645662545038528947
absolute error = 9.1989756300497e-18
relative error = 4.6556984329747069464632686717536e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.792
y[1] (analytic) = 1.9756340652899047159128092653371
y[1] (numeric) = 1.9756340652899047066663984193676
absolute error = 9.2464108459695e-18
relative error = 4.6802244446077016099526603075993e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.793
y[1] (analytic) = 1.9754141733831608693034871990695
y[1] (numeric) = 1.9754141733831608600096517882359
absolute error = 9.2938354108336e-18
relative error = 4.7047528240200202401253363461212e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.794
y[1] (analytic) = 1.9751933060623249240450349422872
y[1] (numeric) = 1.9751933060623249147037856650698
absolute error = 9.3412492772174e-18
relative error = 4.7292835838127570891288952509911e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.795
y[1] (analytic) = 1.9749714635482641825677882973008
y[1] (numeric) = 1.9749714635482641731791358995936
absolute error = 9.3886523977072e-18
relative error = 4.7538167365919314819159762754090e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.796
memory used=34.3MB, alloc=4.3MB, time=2.17
y[1] (analytic) = 1.9747486460628211404456131858575
y[1] (numeric) = 1.9747486460628211310095684609579
absolute error = 9.4360447248996e-18
relative error = 4.7783522949681862748719593172821e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.797
y[1] (analytic) = 1.9745248538288132645534285621498
y[1] (numeric) = 1.9745248538288132550700023507474
absolute error = 9.4834262114024e-18
relative error = 4.8028902715572457951425623775253e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.798
y[1] (analytic) = 1.9743000870700327702497581060178
y[1] (numeric) = 1.9743000870700327607189612961836
absolute error = 9.5307968098342e-18
relative error = 4.8274306789797156385185226387056e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.799
y[1] (analytic) = 1.9740743460112463975845335137761
y[1] (numeric) = 1.9740743460112463880063770409517
absolute error = 9.5781564728244e-18
relative error = 4.8519735298610849667632273396935e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.8
y[1] (analytic) = 1.9738476308781951865323731788434
y[1] (numeric) = 1.9738476308781951769068680258302
absolute error = 9.6255051530132e-18
relative error = 4.8765188368317288150858576797441e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.801
y[1] (analytic) = 1.9736199418975942512515610288767
y[1] (numeric) = 1.9736199418975942415787182258247
absolute error = 9.6728428030520e-18
relative error = 4.9010666125271130829107798093087e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.802
y[1] (analytic) = 1.9733912792971325533689512604129
y[1] (numeric) = 1.9733912792971325436487818848097
absolute error = 9.7201693756032e-18
relative error = 4.9256168695876956303414510973038e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.803
y[1] (analytic) = 1.9731616433054726742910256860942
y[1] (numeric) = 1.973161643305472664523540862754
absolute error = 9.7674848233402e-18
relative error = 4.9501696206589286754055987421268e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.804
y[1] (analytic) = 1.9729310341522505865413313834007
y[1] (numeric) = 1.9729310341522505767265422844531
absolute error = 9.8147890989476e-18
relative error = 4.9747248783913625737934241498398e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.805
y[1] (analytic) = 1.9726994520680754241245273074336
y[1] (numeric) = 1.9726994520680754142624451523126
absolute error = 9.8620821551210e-18
relative error = 4.9992826554405469125220255061726e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.806
y[1] (analytic) = 1.9724668972845292519172695036838
y[1] (numeric) = 1.9724668972845292420079055591163
absolute error = 9.9093639445675e-18
relative error = 5.0238429644672864284678970893286e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.807
y[1] (analytic) = 1.9722333700341668340861655298801
y[1] (numeric) = 1.9722333700341668241295311098749
absolute error = 9.9566344200052e-18
relative error = 5.0484058181373900777330763050882e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.808
y[1] (analytic) = 1.9719988705505154015330296689451
y[1] (numeric) = 1.9719988705505153915291361347815
absolute error = 1.00038935341636e-17
relative error = 5.0729712291218763258391031440000e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.809
y[1] (analytic) = 1.9717633990680744183676714877829
y[1] (numeric) = 1.9717633990680744083165302479991
absolute error = 1.00511412397838e-17
relative error = 5.0975392100970771611154355966154e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.81
y[1] (analytic) = 1.9715269558223153474084512690904
y[1] (numeric) = 1.9715269558223153373100737794725
absolute error = 1.00983774896179e-17
relative error = 5.1221097737443364155978289800338e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.811
y[1] (analytic) = 1.9712895410496814147108368156187
y[1] (numeric) = 1.971289541049681404565234579189
absolute error = 1.01456022364297e-17
relative error = 5.1466829327503673448612098806709e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.812
y[1] (analytic) = 1.9710511549875873731241970983066
y[1] (numeric) = 1.9710511549875873629313816653122
absolute error = 1.01928154329944e-17
relative error = 5.1712586998071031315871430125385e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.813
y[1] (analytic) = 1.970811797874419264877069191474
y[1] (numeric) = 1.970811797874419254637052159375
absolute error = 1.02400170320990e-17
relative error = 5.1958370876119024740287710422902e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.814
y[1] (analytic) = 1.9705714699495341831911359097873
y[1] (numeric) = 1.9705714699495341729039289232455
absolute error = 1.02872069865418e-17
relative error = 5.2204181088672986136086572918922e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.815
y[1] (analytic) = 1.9703301714532600329241525330003
y[1] (numeric) = 1.9703301714532600225897672838676
absolute error = 1.03343852491327e-17
relative error = 5.2450017762811542117910173968632e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.816
y[1] (analytic) = 1.9700879026268952902420619755244
y[1] (numeric) = 1.9700879026268952798605102028307
absolute error = 1.03815517726937e-17
relative error = 5.2695881025669178679039446091106e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.817
y[1] (analytic) = 1.9698446637127087613205387286904
y[1] (numeric) = 1.9698446637127087508918322186323
absolute error = 1.04287065100581e-17
relative error = 5.2941771004432208858549729686757e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.818
y[1] (analytic) = 1.9696004549539393400762028741411
y[1] (numeric) = 1.9696004549539393296003534600699
absolute error = 1.04758494140712e-17
relative error = 5.3187687826342353277483498294900e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.819
memory used=38.1MB, alloc=4.3MB, time=2.41
y[1] (analytic) = 1.9693552765947957649277464371182
y[1] (numeric) = 1.9693552765947957544047659995281
absolute error = 1.05229804375901e-17
relative error = 5.3433631618695753405791490774626e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.82
y[1] (analytic) = 1.969109128880456374587215318498
y[1] (numeric) = 1.9691091288804563640171157850141
absolute error = 1.05700995334839e-17
relative error = 5.3679602508844015569349597893964e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.821
y[1] (analytic) = 1.9688620120570688628816910142727
y[1] (numeric) = 1.9688620120570688522644843596393
absolute error = 1.06172066546334e-17
relative error = 5.3925600624192716301016789846217e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.822
y[1] (analytic) = 1.9686139263717500326056173007762
y[1] (numeric) = 1.9686139263717500219413155468447
absolute error = 1.06643017539315e-17
relative error = 5.4171626092203462464952639934502e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.823
y[1] (analytic) = 1.9683648720725855484040180333065
y[1] (numeric) = 1.9683648720725855376926332490235
absolute error = 1.07113847842830e-17
relative error = 5.4417679040392904819111831419327e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.824
y[1] (analytic) = 1.9681148494086296886868531749068
y[1] (numeric) = 1.9681148494086296779283974763017
absolute error = 1.07584556986051e-17
relative error = 5.4663759596335307632088558297255e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.825
y[1] (analytic) = 1.9678638586299050965747611409276
y[1] (numeric) = 1.9678638586299050857692466911009
absolute error = 1.08055144498267e-17
relative error = 5.4909867887659022378018981828576e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.826
y[1] (analytic) = 1.9676118999874025298764365136082
y[1] (numeric) = 1.9676118999874025190238755227191
absolute error = 1.08525609908891e-17
relative error = 5.5156004042050074058331763851054e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.827
y[1] (analytic) = 1.9673589737330806100978931492779
y[1] (numeric) = 1.9673589737330805991982978745321
absolute error = 1.08995952747458e-17
relative error = 5.5402168187251175713393216706128e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.828
y[1] (analytic) = 1.9671050801198655704838636688928
y[1] (numeric) = 1.9671050801198655595372464145304
absolute error = 1.09466172543624e-17
relative error = 5.5648360451061250641496928182009e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.829
y[1] (analytic) = 1.9668502194016510030915872904893
y[1] (numeric) = 1.9668502194016509920979604077722
absolute error = 1.09936268827171e-17
relative error = 5.5894580961338004909612617981843e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.83
y[1] (analytic) = 1.9665943918332976048972389297428
y[1] (numeric) = 1.9665943918332975938566148169426
absolute error = 1.10406241128002e-17
relative error = 5.6140829845995417034822912755886e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.831
y[1] (analytic) = 1.966337597670632922935253462184
y[1] (numeric) = 1.9663375976706329118476445645695
absolute error = 1.10876088976145e-17
relative error = 5.6387107233005802848647737233113e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.832
y[1] (analytic) = 1.9660798371704510984708000077252
y[1] (numeric) = 1.9660798371704510873362188175501
absolute error = 1.11345811901751e-17
relative error = 5.6633413250398830320398000723803e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.833
y[1] (analytic) = 1.9658211105905126102056620650027
y[1] (numeric) = 1.9658211105905125990241211214928
absolute error = 1.11815409435099e-17
relative error = 5.6879748026264094562078659606492e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.834
y[1] (analytic) = 1.9655614181895440165177802896318
y[1] (numeric) = 1.9655614181895440052892921789729
absolute error = 1.12284881106589e-17
relative error = 5.7126111688747589846348655361358e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.835
y[1] (analytic) = 1.9653007602272376967347156768128
y[1] (numeric) = 1.9653007602272376854592930321376
absolute error = 1.12754226446752e-17
relative error = 5.7372504366056829007665385116668e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.836
y[1] (analytic) = 1.9650391369642515914412918748
y[1] (numeric) = 1.9650391369642515801189473761759
absolute error = 1.13223444986241e-17
relative error = 5.7618926186456298001980958021406e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.837
y[1] (analytic) = 1.9647765486622089418216763215732
y[1] (numeric) = 1.9647765486622089304524226959893
absolute error = 1.13692536255839e-17
relative error = 5.7865377278271559328711876521268e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.838
y[1] (analytic) = 1.9645129955836980280361608626057
y[1] (numeric) = 1.9645129955836980166200108839603
absolute error = 1.14161499786454e-17
relative error = 5.8111857769886741428350417371684e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.839
y[1] (analytic) = 1.9642484779922719066329034729287
y[1] (numeric) = 1.9642484779922718951698699620165
absolute error = 1.14630335109122e-17
relative error = 5.8358367789746098973446941085230e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.84
y[1] (analytic) = 1.9639829961524481469948936717271
y[1] (numeric) = 1.9639829961524481354849894962264
absolute error = 1.15099041755007e-17
relative error = 5.8604907466354047014339383100565e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.841
y[1] (analytic) = 1.9637165503297085668224051824804
y[1] (numeric) = 1.96371655032970855526564325694
absolute error = 1.15567619255404e-17
relative error = 5.8851476928276722975419256508356e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.842
memory used=41.9MB, alloc=4.3MB, time=2.66
y[1] (analytic) = 1.9634491407904989666512003561727
y[1] (numeric) = 1.9634491407904989550475936419991
absolute error = 1.16036067141736e-17
relative error = 5.9098076304140494186930224985672e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.843
y[1] (analytic) = 1.9631807678022288634067518393463
y[1] (numeric) = 1.9631807678022288517563133447909
absolute error = 1.16504384945554e-17
relative error = 5.9344705722631992440930822917206e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.844
y[1] (analytic) = 1.962911431633271222994747932755
y[1] (numeric) = 1.962911431633271211297490712901
absolute error = 1.16972572198540e-17
relative error = 5.9591365312499677021151613133355e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.845
y[1] (analytic) = 1.9626411325529621919281490500886
y[1] (numeric) = 1.962641132552962180184086206838
absolute error = 1.17440628432506e-17
relative error = 5.9838055202553361056573693870971e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.846
y[1] (analytic) = 1.962369870831600827991063649691
y[1] (numeric) = 1.9623698708316008162002083317512
absolute error = 1.17908553179398e-17
relative error = 6.0084775521666285533891286056400e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.847
y[1] (analytic) = 1.962097646740448829939712975372
y[1] (numeric) = 1.9620976467404488181020783782429
absolute error = 1.18376345971291e-17
relative error = 6.0331526398772608215825726049717e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.848
y[1] (analytic) = 1.961824460551730266240754905327
y[1] (numeric) = 1.9618244605517302543563542712879
absolute error = 1.18844006340391e-17
relative error = 6.0578307962868458689332552396586e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.849
y[1] (analytic) = 1.9615503125386313028472381708177
y[1] (numeric) = 1.9615503125386312909160847889139
absolute error = 1.19311533819038e-17
relative error = 6.0825120343013504200040414731900e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.85
y[1] (analytic) = 1.9612752029752999300124591686361
y[1] (numeric) = 1.9612752029752999180345663746656
absolute error = 1.19778927939705e-17
relative error = 6.1071963668330477421981821528784e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.851
y[1] (analytic) = 1.9609991321368456881419945534734
y[1] (numeric) = 1.9609991321368456761173757299736
absolute error = 1.20246188234998e-17
relative error = 6.1318838068005213889363564841572e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.852
y[1] (analytic) = 1.9607221002993393926841837581374
y[1] (numeric) = 1.9607221002993393806128523343718
absolute error = 1.20713314237656e-17
relative error = 6.1565743671286689571809749381790e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.853
y[1] (analytic) = 1.9604441077398128580593365511139
y[1] (numeric) = 1.9604441077398128459413060030586
absolute error = 1.21180305480553e-17
relative error = 6.1812680607488078769014003296251e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.854
y[1] (analytic) = 1.9601651547362586206279417022404
y[1] (numeric) = 1.9601651547362586084632255525705
absolute error = 1.21647161496699e-17
relative error = 6.2059649005987302856725293578974e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.855
y[1] (analytic) = 1.9598852415676296606981537882613
y[1] (numeric) = 1.9598852415676296484867656063377
absolute error = 1.22113881819236e-17
relative error = 6.2306648996225028448506910710341e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.856
y[1] (analytic) = 1.9596043685138391235728361307546
y[1] (numeric) = 1.95960436851383911131478953261
absolute error = 1.22580465981446e-17
relative error = 6.2553680707708787638758666412222e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.857
y[1] (analytic) = 1.9593225358557600396364388193626
y[1] (numeric) = 1.9593225358557600273317474676883
absolute error = 1.23046913516743e-17
relative error = 6.2800744270008935815306842789948e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.858
y[1] (analytic) = 1.9590397438752250434819917334276
y[1] (numeric) = 1.9590397438752250311306693375595
absolute error = 1.23513223958681e-17
relative error = 6.3047839812762773367803519915699e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.859
y[1] (analytic) = 1.9587559928550260920784934350135
y[1] (numeric) = 1.9587559928550260796805537509186
absolute error = 1.23979396840949e-17
relative error = 6.3294967465672034212003603672229e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.86
y[1] (analytic) = 1.9584712830789141819789777659032
y[1] (numeric) = 1.9584712830789141695344345961658
absolute error = 1.24445431697374e-17
relative error = 6.3542127358504457069590638211742e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.861
y[1] (analytic) = 1.9581856148315990655695409404804
y[1] (numeric) = 1.9581856148315990530784081342883
absolute error = 1.24911328061921e-17
relative error = 6.3789319621093826200370395921465e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.862
y[1] (analytic) = 1.9578989883987489663596128854452
y[1] (numeric) = 1.9578989883987489538219043385757
absolute error = 1.25377085468695e-17
relative error = 6.4036544383341033790810299275210e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.863
y[1] (analytic) = 1.9576114040669902933137575360685
y[1] (numeric) = 1.9576114040669902807294871908748
absolute error = 1.25842703451937e-17
relative error = 6.4283801775212078435437585688668e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.864
y[1] (analytic) = 1.9573228621239073542252877571615
y[1] (numeric) = 1.9573228621239073415944696025586
absolute error = 1.26308181546029e-17
relative error = 6.4531091926740660087425442842958e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.865
y[1] (analytic) = 1.9570333628580420681319815151212
y[1] (numeric) = 1.9570333628580420554546295865718
absolute error = 1.26773519285494e-17
memory used=45.7MB, alloc=4.3MB, time=2.91
relative error = 6.4778414968028222530894880422890e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.866
y[1] (analytic) = 1.9567429065588936767741868853113
y[1] (numeric) = 1.9567429065588936640503152648119
absolute error = 1.27238716204994e-17
relative error = 6.5025771029242973907779171311029e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.867
y[1] (analytic) = 1.9564514935169184550956044366501
y[1] (numeric) = 1.9564514935169184423252272527169
absolute error = 1.27703771839332e-17
relative error = 6.5273160240620951009292611197118e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.868
y[1] (analytic) = 1.956159124023529420787036492599
y[1] (numeric) = 1.9561591240235294079701679202537
absolute error = 1.28168685723453e-17
relative error = 6.5520582732466573429266665696374e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.869
y[1] (analytic) = 1.9558657983710960428733937247771
y[1] (numeric) = 1.9558657983710960300100479855329
absolute error = 1.28633457392442e-17
relative error = 6.5768038635151664488051313121808e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.87
y[1] (analytic) = 1.9555715168529439493442504921726
y[1] (numeric) = 1.9555715168529439364344418540198
absolute error = 1.29098086381528e-17
relative error = 6.6015528079117539551108507426145e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.871
y[1] (analytic) = 1.9552762797633546338282412953696
y[1] (numeric) = 1.9552762797633546208719840727613
absolute error = 1.29562572226083e-17
relative error = 6.6263051194874539169303009436544e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.872
y[1] (analytic) = 1.9549800873975651613115916713705
y[1] (numeric) = 1.9549800873975651483089002252086
absolute error = 1.30026914461619e-17
relative error = 6.6510608113000538893275634175812e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.873
y[1] (analytic) = 1.9546829400517678729010778104589
y[1] (numeric) = 1.9546829400517678598519665480794
absolute error = 1.30491112623795e-17
relative error = 6.6758198964144573769554309080332e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.874
y[1] (analytic) = 1.9543848380231100896317101321172
y[1] (numeric) = 1.9543848380231100765361935072759
absolute error = 1.30955166248413e-17
relative error = 6.7005823879024837893420636999350e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.875
y[1] (analytic) = 1.9540857816096938153194370122924
y[1] (numeric) = 1.9540857816096938021775295251504
absolute error = 1.31419074871420e-17
relative error = 6.7253482988429752748537814325949e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.876
y[1] (analytic) = 1.9537857711105754384591658092802
y[1] (numeric) = 1.9537857711105754252708820063896
absolute error = 1.31882838028906e-17
relative error = 6.7501176423216989341301368160497e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.877
y[1] (analytic) = 1.953484806825765433168399290183
y[1] (numeric) = 1.9534848068257654199337537644721
absolute error = 1.32346455257109e-17
relative error = 6.7748904314316072895119488617970e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.878
y[1] (analytic) = 1.9531828890562280591767865142787
y[1] (numeric) = 1.9531828890562280458957939050376
absolute error = 1.32809926092411e-17
relative error = 6.7996666792726382212205805631169e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.879
y[1] (analytic) = 1.9528800181038810608618881837261
y[1] (numeric) = 1.9528800181038810475345631765919
absolute error = 1.33273250071342e-17
relative error = 6.8244463989519243820138168336913e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.88
y[1] (analytic) = 1.9525761942715953653314574258151
y[1] (numeric) = 1.9525761942715953519578147527574
absolute error = 1.33736426730577e-17
relative error = 6.8492296035836443182486464341963e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.881
y[1] (analytic) = 1.952271417863194779552537924457
y[1] (numeric) = 1.9522714178631947661325923637629
absolute error = 1.34199455606941e-17
relative error = 6.8740163062892832435768182626277e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.882
y[1] (analytic) = 1.9519656891834556865276822717902
y[1] (numeric) = 1.9519656891834556730614486480498
absolute error = 1.34662336237404e-17
relative error = 6.8988065201973817653592673245054e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.883
y[1] (analytic) = 1.9516590085381067405185943636589
y[1] (numeric) = 1.9516590085381067270060875477504
absolute error = 1.35125068159085e-17
relative error = 6.9236002584437455337869854707570e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.884
y[1] (analytic) = 1.9513513762338285613175006152962
y[1] (numeric) = 1.9513513762338285477587355243709
absolute error = 1.35587650909253e-17
relative error = 6.9483975341715013611790483689309e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.885
y[1] (analytic) = 1.9510427925782534275665557258151
y[1] (numeric) = 1.9510427925782534139615473232826
absolute error = 1.36050084025325e-17
relative error = 6.9731983605309996434570577363492e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.886
y[1] (analytic) = 1.9507332578799649691255896720762
y[1] (numeric) = 1.9507332578799649554743529675894
absolute error = 1.36512367044868e-17
relative error = 6.9980027506799217529089119615767e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.887
y[1] (analytic) = 1.9504227724484978584885035641592
y[1] (numeric) = 1.9504227724484978447910536135993
absolute error = 1.36974499505599e-17
relative error = 7.0228107177832850038648370034056e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.888
y[1] (analytic) = 1.9501113365943375012486229460171
y[1] (numeric) = 1.9501113365943374875049748514786
absolute error = 1.37436480945385e-17
memory used=49.5MB, alloc=4.3MB, time=3.15
relative error = 7.0476222750134476359581410987812e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.889
y[1] (analytic) = 1.9497989506289197256133180759338
y[1] (numeric) = 1.9497989506289197118234869857093
absolute error = 1.37898310902245e-17
relative error = 7.0724374355502163895494963542063e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.89
y[1] (analytic) = 1.9494856148646304709682016721383
y[1] (numeric) = 1.9494856148646304571322027807033
absolute error = 1.38359988914350e-17
relative error = 7.0972562125808516062915779126325e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.891
y[1] (analytic) = 1.9491713296148054754912155593528
y[1] (numeric) = 1.9491713296148054616090641073507
absolute error = 1.38821514520021e-17
relative error = 7.1220786192999697401025449331943e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.892
y[1] (analytic) = 1.9488560951937299628169186021618
y[1] (numeric) = 1.9488560951937299488886298763885
absolute error = 1.39282887257733e-17
relative error = 7.1469046689097536594850793589299e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.893
y[1] (analytic) = 1.9485399119166383277512892608872
y[1] (numeric) = 1.948539911916638313776878594276
absolute error = 1.39744106666112e-17
relative error = 7.1717343746198039234168217419611e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.894
y[1] (analytic) = 1.9482227800997138210373570551425
y[1] (numeric) = 1.9482227800997138070168398267484
absolute error = 1.40205172283941e-17
relative error = 7.1965677496474518850089816686015e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.895
y[1] (analytic) = 1.9479047000600882331719781694058
y[1] (numeric) = 1.9479047000600882191053698043906
absolute error = 1.40666083650152e-17
relative error = 7.2214048072173543932178404561030e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.896
y[1] (analytic) = 1.9475856721158415772740713838128
y[1] (numeric) = 1.9475856721158415631613873534293
absolute error = 1.41126840303835e-17
relative error = 7.2462455605619609862016200358016e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.897
y[1] (analytic) = 1.9472656965860017710046314619044
y[1] (numeric) = 1.947265696586001756845887283481
absolute error = 1.41587441784234e-17
relative error = 7.2710900229213139537759328211345e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.898
y[1] (analytic) = 1.9469447737905443175388380752907
y[1] (numeric) = 1.9469447737905443033340493122162
absolute error = 1.42047887630745e-17
relative error = 7.2959382075429509416867389994772e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.899
y[1] (analytic) = 1.9466229040503919855905792930964
y[1] (numeric) = 1.9466229040503919713397615548039
absolute error = 1.42508177382925e-17
relative error = 7.3207901276823725533305318280661e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.9
y[1] (analytic) = 1.946300087687414488489709611635
y[1] (numeric) = 1.9463000876874144741928785535868
absolute error = 1.42968310580482e-17
relative error = 7.3456457966025342175828014804252e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.901
y[1] (analytic) = 1.9459763250244281623123634470302
y[1] (numeric) = 1.9459763250244281479695347707018
absolute error = 1.43428286763284e-17
relative error = 7.3705052275743139382626822928270e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.902
y[1] (analytic) = 1.9456516163851956430646459604419
y[1] (numeric) = 1.9456516163851956286758354133063
absolute error = 1.43888105471356e-17
relative error = 7.3953684338763637633742804561963e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.903
y[1] (analytic) = 1.9453259620944255429200240321793
y[1] (numeric) = 1.9453259620944255284852474076915
absolute error = 1.44347766244878e-17
relative error = 7.4202354287950125250225975324275e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.904
y[1] (analytic) = 1.9449993624777721255107411472845
y[1] (numeric) = 1.9449993624777721110300142848656
absolute error = 1.44807268624189e-17
relative error = 7.4451062256244769780701563473538e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.905
y[1] (analytic) = 1.9446718178618349802735809011434
y[1] (numeric) = 1.9446718178618349657469196861648
absolute error = 1.45266612149786e-17
relative error = 7.4699808376668160518343091986152e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.906
y[1] (analytic) = 1.9443433285741586958503047793337
y[1] (numeric) = 1.944343328574158681277725143101
absolute error = 1.45725796362327e-17
relative error = 7.4948592782320907942183687107320e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.907
y[1] (analytic) = 1.9440138949432325325430908112447
y[1] (numeric) = 1.9440138949432325179246087309819
absolute error = 1.46184820802628e-17
relative error = 7.5197415606382158520157580630044e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.908
y[1] (analytic) = 1.9436835172984900938253006420035
y[1] (numeric) = 1.9436835172984900791609321408371
absolute error = 1.46643685011664e-17
relative error = 7.5446276982110166088752357494944e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.909
y[1] (analytic) = 1.9433521959703089969079035119126
y[1] (numeric) = 1.9433521959703089821976646588556
absolute error = 1.47102388530570e-17
relative error = 7.5695177042842863947671088320214e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.91
y[1] (analytic) = 1.9430199312900105423618865769482
y[1] (numeric) = 1.9430199312900105276057934868838
absolute error = 1.47560930900644e-17
relative error = 7.5944115921999466999943475464671e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.911
y[1] (analytic) = 1.94268672358985938279698194788
y[1] (numeric) = 1.9426867235898593679950507815457
absolute error = 1.48019311663343e-17
relative error = 7.6193093753078472418950356612450e-16 %
h = 0.001
memory used=53.4MB, alloc=4.3MB, time=3.40
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.912
y[1] (analytic) = 1.9423525732030631905970417692598
y[1] (numeric) = 1.9423525732030631757492887332311
absolute error = 1.48477530360287e-17
relative error = 7.6442110669659777113723171845811e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.913
y[1] (analytic) = 1.9420174804637723247123936028736
y[1] (numeric) = 1.9420174804637723098188349495481
absolute error = 1.48935586533255e-17
relative error = 7.6691166805402678088022383608109e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.914
y[1] (analytic) = 1.9416814457070794965095093232775
y[1] (numeric) = 1.9416814457070794815701613508581
absolute error = 1.49393479724194e-17
relative error = 7.6940262294050566093663804339307e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.915
y[1] (analytic) = 1.9413444692690194346783216757165
y[1] (numeric) = 1.9413444692690194196932007281956
absolute error = 1.49851209475209e-17
relative error = 7.7189397269425837266708525827412e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.916
y[1] (analytic) = 1.9410065514865685491975235890855
y[1] (numeric) = 1.9410065514865685341666460562284
absolute error = 1.50308775328571e-17
relative error = 7.7438571865434073146261923731935e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.917
y[1] (analytic) = 1.9406676926976445943581862786025
y[1] (numeric) = 1.9406676926976445792815685959312
absolute error = 1.50766176826713e-17
relative error = 7.7687786216062041753570812557445e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.918
y[1] (analytic) = 1.9403278932411063308460331145497
y[1] (numeric) = 1.9403278932411063157236917633262
absolute error = 1.51223413512235e-17
relative error = 7.7937040455380335110610298056494e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.919
y[1] (analytic) = 1.939987153456753186882707174779
y[1] (numeric) = 1.9399871534567531717146586819891
absolute error = 1.51680484927899e-17
relative error = 7.8186334717540854997138821655922e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.92
y[1] (analytic) = 1.939645473685324918426371339687
y[1] (numeric) = 1.9396454736853249032126322780236
absolute error = 1.52137390616634e-17
relative error = 7.8435669136779451781350751047671e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.921
y[1] (analytic) = 1.9393028542685012684319807290311
y[1] (numeric) = 1.9393028542685012531725677168775
absolute error = 1.52594130121536e-17
relative error = 7.8685043847415987931270680279177e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.922
y[1] (analytic) = 1.9389592955489016251715682202849
y[1] (numeric) = 1.9389592955489016098664979216985
absolute error = 1.53050702985864e-17
relative error = 7.8934458983852338778326420636651e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.923
y[1] (analytic) = 1.9386147978700846796148847282204
y[1] (numeric) = 1.9386147978700846642641738529159
absolute error = 1.53507108753045e-17
relative error = 7.9183914680575033785063750514598e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.924
y[1] (analytic) = 1.9382693615765480818707368650469
y[1] (numeric) = 1.9382693615765480664744021683796
absolute error = 1.53963346966673e-17
relative error = 7.9433411072154805221573842531385e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.925
y[1] (analytic) = 1.9379229870137280966893655397411
y[1] (numeric) = 1.93792298701372808124742382269
absolute error = 1.54419417170511e-17
relative error = 7.9682948293247684553801404996870e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.926
y[1] (analytic) = 1.9375756745279992580262099941604
y[1] (numeric) = 1.9375756745279992425386781033116
absolute error = 1.54875318908488e-17
relative error = 7.9932526478593519608330011326806e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.927
y[1] (analytic) = 1.9372274244666740226674027121474
y[1] (numeric) = 1.9372274244666740071342975396771
absolute error = 1.55331051724703e-17
relative error = 8.0182145763018103697187956565281e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.928
y[1] (analytic) = 1.936878237178002422917341576101
y[1] (numeric) = 1.9368782371780024073386800597587
absolute error = 1.55786615163423e-17
relative error = 8.0431806281432209412700842460273e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.929
y[1] (analytic) = 1.9365281130111717183486865834136
y[1] (numeric) = 1.9365281130111717027244857065052
absolute error = 1.56242008769084e-17
relative error = 8.0681508168832170687310105253146e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.93
y[1] (analytic) = 1.9361770523163060466151293727488
y[1] (numeric) = 1.9361770523163060309454061641194
absolute error = 1.56697232086294e-17
relative error = 8.0931251560301498590092014170319e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.931
y[1] (analytic) = 1.9358250554444660733272847473596
y[1] (numeric) = 1.9358250554444660576120562813768
absolute error = 1.57152284659828e-17
relative error = 8.1181036591008366423770607315754e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.932
y[1] (analytic) = 1.9354721227476486409920543195285
y[1] (numeric) = 1.9354721227476486252313377160652
absolute error = 1.57607166034633e-17
relative error = 8.1430863396208258920618684212744e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.933
y[1] (analytic) = 1.9351182545787864170158133367354
y[1] (numeric) = 1.9351182545787864012096257611524
absolute error = 1.58061875755830e-17
relative error = 8.1680732111245074184548503143910e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.934
y[1] (analytic) = 1.9347634512917475407717726863362
y[1] (numeric) = 1.9347634512917475249201313494654
absolute error = 1.58516413368708e-17
relative error = 8.1930642871548092123007277021997e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=3.64
NO POLE
x[1] = 1.935
y[1] (analytic) = 1.9344077132413352697318690113633
y[1] (numeric) = 1.9344077132413352538347911694904
absolute error = 1.58970778418729e-17
relative error = 8.2180595812634626184843028218595e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.936
y[1] (analytic) = 1.9340510407832876246635368055256
y[1] (numeric) = 1.9340510407832876087210397603728
absolute error = 1.59424970451528e-17
relative error = 8.2430591070110092917238687156979e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.937
y[1] (analytic) = 1.9336934342742770338917172906085
y[1] (numeric) = 1.9336934342742770179038183893171
absolute error = 1.59878989012914e-17
relative error = 8.2680628779668598894363489725111e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.938
y[1] (analytic) = 1.9333348940719099766264598142336
y[1] (numeric) = 1.9333348940719099605931764493468
absolute error = 1.60332833648868e-17
relative error = 8.2930709077091976724364949677085e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.939
y[1] (analytic) = 1.9329754205347266253564724403485
y[1] (numeric) = 1.932975420534726609277822049794
absolute error = 1.60786503905545e-17
relative error = 8.3180832098250889479887415876654e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.94
y[1] (analytic) = 1.9326150140222004873089793388657
y[1] (numeric) = 1.9326150140222004711849794059381
absolute error = 1.61239999329276e-17
relative error = 8.3430997979105936506084381370994e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.941
y[1] (analytic) = 1.9322536748947380449762435145626
y[1] (numeric) = 1.9322536748947380288069115679062
absolute error = 1.61693319466564e-17
relative error = 8.3681206855705655434905021757915e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.942
y[1] (analytic) = 1.9318914035136783957091143486912
y[1] (numeric) = 1.9318914035136783794944679622823
absolute error = 1.62146463864089e-17
relative error = 8.3931458864189180752370570421538e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.943
y[1] (analytic) = 1.9315282002412928903779603597194
y[1] (numeric) = 1.9315282002412928741180171528486
absolute error = 1.62599432068708e-17
relative error = 8.4181754140786316879185526077695e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.944
y[1] (analytic) = 1.9311640654407847711013485222403
y[1] (numeric) = 1.9311640654407847547961261594951
absolute error = 1.63052223627452e-17
relative error = 8.4432092821816058021941288154370e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.945
y[1] (analytic) = 1.9307989994762888080428324153414
y[1] (numeric) = 1.9307989994762887916923486065884
absolute error = 1.63504838087530e-17
relative error = 8.4682475043688731941032351341904e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.946
y[1] (analytic) = 1.9304330027128709352762124036138
y[1] (numeric) = 1.9304330027128709188804849039812
absolute error = 1.63957274996326e-17
relative error = 8.4932900942904520168946921254563e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.947
y[1] (analytic) = 1.9300660755165278857196319855127
y[1] (numeric) = 1.9300660755165278692786785953721
absolute error = 1.64409533901406e-17
relative error = 8.5183370656057157865206793840408e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.948
y[1] (analytic) = 1.9296982182541868251388753749397
y[1] (numeric) = 1.9296982182541868086527139398889
absolute error = 1.64861614350508e-17
relative error = 8.5433884319828828377692352128053e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.949
y[1] (analytic) = 1.9293294312937049852202323127222
y[1] (numeric) = 1.9293294312937049686888807235668
absolute error = 1.65313515891554e-17
relative error = 8.5684442070996455041344431963637e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.95
y[1] (analytic) = 1.9289597150038692957132970350915
y[1] (numeric) = 1.9289597150038692791367732278273
absolute error = 1.65765238072642e-17
relative error = 8.5935044046427632057857240251719e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.951
y[1] (analytic) = 1.9285890697543960156440692563316
y[1] (numeric) = 1.9285890697543959990223912121268
absolute error = 1.66216780442048e-17
relative error = 8.6185690383081735992909830931023e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.952
y[1] (analytic) = 1.9282174959159303635987259524672
y[1] (numeric) = 1.928217495915930346931911697644
absolute error = 1.66668142548232e-17
relative error = 8.6436381218013113153932441867812e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.953
y[1] (analytic) = 1.9278449938600461470784336621868
y[1] (numeric) = 1.9278449938600461303665012682037
absolute error = 1.67119323939831e-17
relative error = 8.6687116688367527529134143515847e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.954
y[1] (analytic) = 1.9274715639592453909255719501591
y[1] (numeric) = 1.9274715639592453741685395335928
absolute error = 1.67570324165663e-17
relative error = 8.6937896931384311723724856767281e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.955
y[1] (analytic) = 1.9270972065869579648217396064882
y[1] (numeric) = 1.9270972065869579480196253290153
absolute error = 1.68021142774729e-17
relative error = 8.7188722084397482713144357703005e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.956
y[1] (analytic) = 1.9267219221175412098579160842691
y[1] (numeric) = 1.9267219221175411930107381526482
absolute error = 1.68471779316209e-17
relative error = 8.7439592284833744956662062949583e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.957
y[1] (analytic) = 1.9263457109262795641771516050526
y[1] (numeric) = 1.9263457109262795472849282711058
absolute error = 1.68922233339468e-17
relative error = 8.7690507670215682507351937176153e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=3.89
NO POLE
x[1] = 1.958
y[1] (analytic) = 1.9259685733893841876901602894971
y[1] (numeric) = 1.925968573389384170752909850092
absolute error = 1.69372504394051e-17
relative error = 8.7941468378159243604277931848654e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.959
y[1] (analytic) = 1.9255905098839925858641915975835
y[1] (numeric) = 1.9255905098839925688819323946147
absolute error = 1.69822592029688e-17
relative error = 8.8192474546376415678514758637211e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.96
y[1] (analytic) = 1.92521152078816823258555628949
y[1] (numeric) = 1.925211520788168215558306709861
absolute error = 1.70272495796290e-17
relative error = 8.8443526312673228852539901134864e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.961
y[1] (analytic) = 1.92483160648090019209618404457
y[1] (numeric) = 1.9248316064809001750239625201745
absolute error = 1.70722215243955e-17
relative error = 8.8694623814952952497128907297788e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.962
y[1] (analytic) = 1.9244507673421027400045908018431
y[1] (numeric) = 1.924450767342102722887415809547
absolute error = 1.71171749922961e-17
relative error = 8.8945767191212540555513080351845e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.963
y[1] (analytic) = 1.9240690037526149833716348110015
y[1] (numeric) = 1.9240690037526149662095248726239
absolute error = 1.71621099383776e-17
relative error = 8.9196956579547908244683217729896e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.964
y[1] (analytic) = 1.9236863160942004798714413081424
y[1] (numeric) = 1.9236863160942004626644149904375
absolute error = 1.72070263177049e-17
relative error = 8.9448192118149338324262144507508e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.965
y[1] (analytic) = 1.923302704749546856027876655272
y[1] (numeric) = 1.9233027047495468387759525699103
absolute error = 1.72519240853617e-17
relative error = 8.9699473945305201066749006799461e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.966
y[1] (analytic) = 1.9229181701022654245269537070733
y[1] (numeric) = 1.9229181701022654072301505106231
absolute error = 1.72968031964502e-17
relative error = 8.9950802199400478402332777820281e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.967
y[1] (analytic) = 1.9225327125368908006055510925018
y[1] (numeric) = 1.9225327125368907832638874864104
absolute error = 1.73416636060914e-17
relative error = 9.0202177018918407336805437051190e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.968
y[1] (analytic) = 1.9221463324388805175168300224568
y[1] (numeric) = 1.9221463324388805001303247530321
absolute error = 1.73865052694247e-17
relative error = 9.0453598542438483742056229904458e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.969
y[1] (analytic) = 1.9217590301946146410727331580806
y[1] (numeric) = 1.921759030194614623641405016472
absolute error = 1.74313281416086e-17
relative error = 9.0705066908640187817978794188080e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.97
y[1] (analytic) = 1.9213708061913953832639509971532
y[1] (numeric) = 1.921370806191395365787818819333
absolute error = 1.74761321778202e-17
relative error = 9.0956582256300468676256282750260e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.971
y[1] (analytic) = 1.9209816608174467149577421585852
y[1] (numeric) = 1.9209816608174466974368248253298
absolute error = 1.75209173332554e-17
relative error = 9.1208144724294870008147207993639e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.972
y[1] (analytic) = 1.9205915944619139776739948671558
y[1] (numeric) = 1.9205915944619139601083113040267
absolute error = 1.75656835631291e-17
relative error = 9.1459754451598657275064177521600e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.973
y[1] (analytic) = 1.9202006075148634944399178624018
y[1] (numeric) = 1.9202006075148634768294870397268
absolute error = 1.76104308226750e-17
relative error = 9.1711411577285863317770038199178e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.974
y[1] (analytic) = 1.9198087003672821797237498769349
y[1] (numeric) = 1.9198087003672821620685908097889
absolute error = 1.76551590671460e-17
relative error = 9.1963116240531458271331421628844e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.975
y[1] (analytic) = 1.9194158734110771484478777504443
y[1] (numeric) = 1.9194158734110771307480094986306
absolute error = 1.76998682518137e-17
relative error = 9.2214868580608833372603626882783e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.976
y[1] (analytic) = 1.9190221270390753240817541662356
y[1] (numeric) = 1.9190221270390753063371958342666
absolute error = 1.77445583319690e-17
relative error = 9.2466668736893013924245230612917e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.977
y[1] (analytic) = 1.9186274616450230458150069173535
y[1] (numeric) = 1.9186274616450230280257776544317
absolute error = 1.77892292629218e-17
relative error = 9.2718516848859185518922795602469e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.978
y[1] (analytic) = 1.9182318776235856748111325291483
y[1] (numeric) = 1.918231877623585656977251529147
absolute error = 1.78338810000013e-17
relative error = 9.2970413056084346489541689914960e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.979
y[1] (analytic) = 1.9178353753703471995421679845577
y[1] (numeric) = 1.9178353753703471816636544860022
absolute error = 1.78785134985555e-17
relative error = 9.3222357498244791196327899876995e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.98
y[1] (analytic) = 1.917437955281809840204735217402
y[1] (numeric) = 1.9174379552818098222816085034499
absolute error = 1.79231267139521e-17
relative error = 9.3474350315120891760200053241944e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=4.14
NO POLE
x[1] = 1.981
y[1] (analytic) = 1.9170396177553936522178539576119
y[1] (numeric) = 1.9170396177553936342501333560341
absolute error = 1.79677206015778e-17
relative error = 9.3726391646593539701938641433956e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.982
y[1] (analytic) = 1.9166403631894361288029194305462
y[1] (numeric) = 1.9166403631894361107906243137074
absolute error = 1.80122951168388e-17
relative error = 9.3978481632646844268057979155873e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.983
y[1] (analytic) = 1.9162401919831918026462423303861
y[1] (numeric) = 1.9162401919831917845893921152256
absolute error = 1.80568502151605e-17
relative error = 9.4230620413366659446768817658177e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.984
y[1] (analytic) = 1.915839104536831846644549405035
y[1] (numeric) = 1.9158391045368318285431635530471
absolute error = 1.81013858519879e-17
relative error = 9.4482808128942763053643680464320e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.985
y[1] (analytic) = 1.9154371012514436737338439069878
y[1] (numeric) = 1.9154371012514436555879419242025
absolute error = 1.81459019827853e-17
relative error = 9.4735044919667384198828937419768e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.986
y[1] (analytic) = 1.9150341825290305358020260812782
y[1] (numeric) = 1.9150341825290305176116275182416
absolute error = 1.81903985630366e-17
relative error = 9.4987330925936862168159074477216e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.987
y[1] (analytic) = 1.9146303487725111216856747778477
y[1] (numeric) = 1.9146303487725111034507992296025
absolute error = 1.82348755482452e-17
relative error = 9.5239666288251218384371762361612e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.988
y[1] (analytic) = 1.9142256003857191542513921915236
y[1] (numeric) = 1.9142256003857191359720592975894
absolute error = 1.82793328939342e-17
relative error = 9.5492051147215295205416451888703e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.989
y[1] (analytic) = 1.9138199377734029865621146482255
y[1] (numeric) = 1.9138199377734029682383440925794
absolute error = 1.83237705556461e-17
relative error = 9.5744485643537283756718830374049e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.99
y[1] (analytic) = 1.9134133613412251971287932710576
y[1] (numeric) = 1.9134133613412251787606047821142
absolute error = 1.83681884889434e-17
relative error = 9.5996969918031953690299703610344e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.991
y[1] (analytic) = 1.9130058714957621842478492745711
y[1] (numeric) = 1.913005871495762165835262625163
absolute error = 1.84125866494081e-17
relative error = 9.6249504111618137113836302909360e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.992
y[1] (analytic) = 1.9125974686445037594248095497085
y[1] (numeric) = 1.9125974686445037409678445570665
absolute error = 1.84569649926420e-17
relative error = 9.6502088365320392265732014051260e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.993
y[1] (analytic) = 1.9121881531958527398845291157598
y[1] (numeric) = 1.9121881531958527213832056414929
absolute error = 1.85013234742669e-17
relative error = 9.6754722820270146521968289624658e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.994
y[1] (analytic) = 1.9117779255591245401684079290744
y[1] (numeric) = 1.9117779255591245216227458791503
absolute error = 1.85456620499241e-17
relative error = 9.7007407617703179527414198627920e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.995
y[1] (analytic) = 1.9113667861445467628190104512782
y[1] (numeric) = 1.9113667861445467442290297760029
absolute error = 1.85899806752753e-17
relative error = 9.7260142898964427852436442449348e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.996
y[1] (analytic) = 1.9109547353632587881524972923409
y[1] (numeric) = 1.9109547353632587695182179863393
absolute error = 1.86342793060016e-17
relative error = 9.7512928805502853343573461541360e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.997
y[1] (analytic) = 1.9105417736273113631192791560302
y[1] (numeric) = 1.9105417736273113444407212582255
absolute error = 1.86785578978047e-17
relative error = 9.7765765478877820061694819059925e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.998
y[1] (analytic) = 1.9101279013496661892533042270611
y[1] (numeric) = 1.9101279013496661705304878206555
absolute error = 1.87228164064056e-17
relative error = 9.8018653060752391527160351463259e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.999
y[1] (analytic) = 1.9097131189441955097103910506228
y[1] (numeric) = 1.9097131189441954909433362630767
absolute error = 1.87670547875461e-17
relative error = 9.8271591692901281307253210029136e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2
y[1] (analytic) = 1.9092974268256816953960198659117
y[1] (numeric) = 1.909297426825681676584746868924
absolute error = 1.88112729969877e-17
relative error = 9.8524581517205196554164657468563e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.001
y[1] (analytic) = 1.9088808254098168301829962658482
y[1] (numeric) = 1.9088808254098168113275252753359
absolute error = 1.88554709905123e-17
relative error = 9.8777622675654603938960503697145e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.002
y[1] (analytic) = 1.9084633151132022952194019652766
y[1] (numeric) = 1.9084633151132022763197532413547
absolute error = 1.88996487239219e-17
relative error = 9.9030715310348260862247386745968e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.003
y[1] (analytic) = 1.908044896353348352327248369664
y[1] (numeric) = 1.9080448963533483333834422166254
absolute error = 1.89438061530386e-17
relative error = 9.9283859563493317198417597312565e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=4.38
NO POLE
x[1] = 2.004
y[1] (analytic) = 1.9076255695486737264922495456098
y[1] (numeric) = 1.9076255695486737075043063119047
absolute error = 1.89879432337051e-17
relative error = 9.9537055577408038397013842799379e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.005
y[1] (analytic) = 1.9072053351185051874451321033573
y[1] (numeric) = 1.907205335118505168413072181573
absolute error = 1.90320599217843e-17
relative error = 9.9790303494519813399733022636852e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.006
y[1] (analytic) = 1.9067841934830771303349004099636
y[1] (numeric) = 1.906784193483077111258744236804
absolute error = 1.90761561731596e-17
relative error = 1.0004360345736683119936714831730e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.007
y[1] (analytic) = 1.9063621450635311554944764598267
y[1] (numeric) = 1.9063621450635311363742445160921
absolute error = 1.91202319437346e-17
relative error = 1.0029695560859661243305250679026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.008
y[1] (analytic) = 1.9059391902819156472991346368961
y[1] (numeric) = 1.9059391902819156281348474474625
absolute error = 1.91642871894336e-17
relative error = 1.0055036009096873659898534029795e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.009
y[1] (analytic) = 1.9055153295611853521181525100957
y[1] (numeric) = 1.9055153295611853329098306438942
absolute error = 1.92083218662015e-17
relative error = 1.0080381704735442431879097347767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.01
y[1] (analytic) = 1.9050905633252009553600997102737
y[1] (numeric) = 1.9050905633252009361077637802703
absolute error = 1.92523359300034e-17
relative error = 1.0105732662073454449041826957654e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.011
y[1] (analytic) = 1.9046648919987286576121878433562
y[1] (numeric) = 1.9046648919987286383158585065308
absolute error = 1.92963293368254e-17
relative error = 1.0131088895420391926217875068385e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.012
y[1] (analytic) = 1.9042383160074397498741053003172
y[1] (numeric) = 1.9042383160074397305338032576432
absolute error = 1.93403020426740e-17
relative error = 1.0156450419096828292826541174936e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.013
y[1] (analytic) = 1.9038108357779101878867617300969
y[1] (numeric) = 1.9038108357779101685025077265204
absolute error = 1.93842540035765e-17
relative error = 1.0181817247434648953460463462731e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.014
y[1] (analytic) = 1.9033824517376201655563678466871
y[1] (numeric) = 1.9033824517376201461281826711061
absolute error = 1.94281851755810e-17
relative error = 1.0207189394777062210478130151570e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.015
y[1] (analytic) = 1.9029531643149536874742771462688
y[1] (numeric) = 1.9029531643149536680021816315125
absolute error = 1.94720955147563e-17
relative error = 1.0232566875478557668926887869544e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.016
y[1] (analytic) = 1.9025229739391981405330170145245
y[1] (numeric) = 1.9025229739391981210170320373325
absolute error = 1.95159849771920e-17
relative error = 1.0257949703904969725908923345417e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.017
y[1] (analytic) = 1.9020918810405438646389376080588
y[1] (numeric) = 1.90209188104054384507908408906
absolute error = 1.95598535189988e-17
relative error = 1.0283337894433646310470542705521e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.018
y[1] (analytic) = 1.9016598860500837225219077972415
y[1] (numeric) = 1.9016598860500837029182067009335
absolute error = 1.96037010963080e-17
relative error = 1.0308731461453197185404434106443e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.019
y[1] (analytic) = 1.9012269893998126686424883607435
y[1] (numeric) = 1.9012269893998126489949606954713
absolute error = 1.96475276652722e-17
relative error = 1.0334130419363873094552737028502e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.02
y[1] (analytic) = 1.9007931915226273171970135245537
y[1] (numeric) = 1.900793191522627297505680342489
absolute error = 1.96913331820647e-17
relative error = 1.0359534782577261520278930232235e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.021
y[1] (analytic) = 1.9003584928523255092210128403617
y[1] (numeric) = 1.9003584928523254894858952374817
absolute error = 1.97351176028800e-17
relative error = 1.0384944565516560880011110716573e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.022
y[1] (analytic) = 1.8999228938236058787914062998471
y[1] (numeric) = 1.8999228938236058590125254159134
absolute error = 1.97788808839337e-17
relative error = 1.0410359782616539313789610558426e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.023
y[1] (analytic) = 1.8994863948720674183279064826446
y[1] (numeric) = 1.899486394872067398505283501182
absolute error = 1.98226229814626e-17
relative error = 1.0435780448323598724442138210676e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.024
y[1] (analytic) = 1.899048996434209042994062436546
y[1] (numeric) = 1.8990489964342090231277185848215
absolute error = 1.98663438517245e-17
relative error = 1.0461206577095680949769498592349e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.025
y[1] (analytic) = 1.8986106989474291541983808888597
y[1] (numeric) = 1.8986106989474291342883374378612
absolute error = 1.99100434509985e-17
relative error = 1.0486638183402437172780843302654e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.026
y[1] (analytic) = 1.8981715028500252021959612877695
y[1] (numeric) = 1.8981715028500251822422395521844
absolute error = 1.99537217355851e-17
relative error = 1.0512075281725292219223451266159e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=4.63
NO POLE
x[1] = 2.027
y[1] (analytic) = 1.8977314085811932477910820720215
y[1] (numeric) = 1.8977314085811932277937034102155
absolute error = 1.99973786618060e-17
relative error = 1.0537517886557350878736741710399e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.028
y[1] (analytic) = 1.8972904165810275231411764663162
y[1] (numeric) = 1.8972904165810275031001622803119
absolute error = 2.00410141860043e-17
relative error = 1.0562966012403514940218174918743e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.029
y[1] (analytic) = 1.896848527290519991662636998393
y[1] (numeric) = 1.8968485272905199715780087338487
absolute error = 2.00846282645443e-17
relative error = 1.0588419673780389531679679379544e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.03
y[1] (analytic) = 1.8964057411515599070388888319676
y[1] (numeric) = 1.8964057411515598869106679781553
absolute error = 2.01282208538123e-17
relative error = 1.0613878885216716659810264408866e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.031
y[1] (analytic) = 1.895962058606933371331172907409
y[1] (numeric) = 1.8959620586069333511593809971937
absolute error = 2.01717919102153e-17
relative error = 1.0639343661252701757877136413673e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.032
y[1] (analytic) = 1.8955174801003228921924807793401
y[1] (numeric) = 1.8955174801003228719771393891576
absolute error = 2.02153413901825e-17
relative error = 1.0664814016440816474652478557475e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.033
y[1] (analytic) = 1.8950720060763069391850839371867
y[1] (numeric) = 1.8950720060763069189262146870223
absolute error = 2.02588692501644e-17
relative error = 1.0690289965345336167528971647253e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.034
y[1] (analytic) = 1.8946256369803594992021012911108
y[1] (numeric) = 1.8946256369803594788997258444777
absolute error = 2.03023754466331e-17
relative error = 1.0715771522542510132379569628321e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.035
y[1] (analytic) = 1.8941783732588496309935494017223
y[1] (numeric) = 1.89417837325884961064768946564
absolute error = 2.03458599360823e-17
relative error = 1.0741258702620573711101289881933e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.036
y[1] (analytic) = 1.8937302153590410187973209274834
y[1] (numeric) = 1.8937302153590409984079982524557
absolute error = 2.03893226750277e-17
relative error = 1.0766751520179971657186120951732e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.037
y[1] (analytic) = 1.893281163729091525075537658788
y[1] (numeric) = 1.8932811637290915046427740387815
absolute error = 2.04327636200065e-17
relative error = 1.0792249989833106471316074996545e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.038
y[1] (analytic) = 1.892831218818052742356725402327
y[1] (numeric) = 1.8928312188180527218805426747493
absolute error = 2.04761827275777e-17
relative error = 1.0817754126204509044037554346178e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.039
y[1] (analytic) = 1.8923803810758695441842588735278
y[1] (numeric) = 1.8923803810758695236646789192056
absolute error = 2.05195799543222e-17
relative error = 1.0843263943930903872071136820798e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.04
y[1] (analytic) = 1.8919286509533796351715256485842
y[1] (numeric) = 1.8919286509533796146085703917413
absolute error = 2.05629552568429e-17
relative error = 1.0868779457661274385741302573273e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.041
y[1] (analytic) = 1.8914760289023131001642591208761
y[1] (numeric) = 1.8914760289023130795579505291117
absolute error = 2.06063085917644e-17
relative error = 1.0894300682056716913068803182184e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.042
y[1] (analytic) = 1.891022515375291952510491299409
y[1] (numeric) = 1.8910225153752919318608513836756
absolute error = 2.06496399157334e-17
relative error = 1.0919827631790664621984824554859e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.043
y[1] (analytic) = 1.8905681108258296814385771792814
y[1] (numeric) = 1.8905681108258296607456279938629
absolute error = 2.06929491854185e-17
relative error = 1.0945360321548794437469336350821e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.044
y[1] (analytic) = 1.8901128157083307985437433061198
y[1] (numeric) = 1.8901128157083307778075069486092
absolute error = 2.07362363575106e-17
relative error = 1.0970898766029251283773731982594e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.045
y[1] (analytic) = 1.889656630478090383383614047893
y[1] (numeric) = 1.8896566304780903626041126591706
absolute error = 2.07795013887224e-17
relative error = 1.0996442979942396391805472292151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.046
y[1] (analytic) = 1.8891995555912936281831699785436
y[1] (numeric) = 1.8891995555912936073604257427547
absolute error = 2.08227442357889e-17
relative error = 1.1021992978011084584562271588344e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.047
y[1] (analytic) = 1.8887415915050153816495936684384
y[1] (numeric) = 1.8887415915050153607836288129712
absolute error = 2.08659648554672e-17
relative error = 1.1047548774970571365532944364575e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.048
y[1] (analytic) = 1.8882827386772196918974590667558
y[1] (numeric) = 1.888282738677219670988295862219
absolute error = 2.09091632045368e-17
relative error = 1.1073110385568684680915947232685e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.049
y[1] (analytic) = 1.8878229975667593484847215505806
y[1] (numeric) = 1.8878229975667593275323823107813
absolute error = 2.09523392397993e-17
relative error = 1.1098677824565679123945606322126e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=4.88
NO POLE
x[1] = 2.05
y[1] (analytic) = 1.8873623686333754235599666046803
y[1] (numeric) = 1.8873623686333754025644736866017
absolute error = 2.09954929180786e-17
relative error = 1.1124251106734354864219005513940e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.051
y[1] (analytic) = 1.8869008523376968121213759846744
y[1] (numeric) = 1.8869008523376967910827517884532
absolute error = 2.10386241962212e-17
relative error = 1.1149830246860229765766625332653e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.052
y[1] (analytic) = 1.886438449141239771387871104592
y[1] (numeric) = 1.8864384491412397503061380734964
absolute error = 2.10817330310956e-17
relative error = 1.1175415259741234686607907360637e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.053
y[1] (analytic) = 1.8859751595064074592828942776381
y[1] (numeric) = 1.8859751595064074381580748980449
absolute error = 2.11248193795932e-17
relative error = 1.1201006160188203692563611470011e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.054
y[1] (analytic) = 1.8855109838964894720312893263458
y[1] (numeric) = 1.8855109838964894508634061277182
absolute error = 2.11678831986276e-17
relative error = 1.1226602963024516435274056896873e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.055
y[1] (analytic) = 1.8850459227756613808697439651976
y[1] (numeric) = 1.8850459227756613596588195200628
absolute error = 2.12109244451348e-17
relative error = 1.1252205683086217462466128671881e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.056
y[1] (analytic) = 1.8845799766089842678712572452345
y[1] (numeric) = 1.8845799766089842466173141691608
absolute error = 2.12539430760737e-17
relative error = 1.1277814335222294908792282001270e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.057
y[1] (analytic) = 1.8841131458624042608840962361454
y[1] (numeric) = 1.8841131458624042395871571877197
absolute error = 2.12969390484257e-17
relative error = 1.1303428934294481940182981794305e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.058
y[1] (analytic) = 1.8836454310027520675857070068426
y[1] (numeric) = 1.8836454310027520462457946876479
absolute error = 2.13399123191947e-17
relative error = 1.1329049495177270275823715947066e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.059
y[1] (analytic) = 1.883176832497742508652045850574
y[1] (numeric) = 1.8831768324977424872691830051664
absolute error = 2.13828628454076e-17
relative error = 1.1354676032758189256718552987195e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.06
y[1] (analytic) = 1.8827073508159740500427975851999
y[1] (numeric) = 1.8827073508159740286170070010861
absolute error = 2.14257905841138e-17
relative error = 1.1380308561937554199264738796314e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.061
y[1] (analytic) = 1.8822369864269283344029486433794
y[1] (numeric) = 1.8822369864269283129342531509939
absolute error = 2.14686954923855e-17
relative error = 1.1405947097628639416886508208066e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.062
y[1] (analytic) = 1.881765739800969711581183551053
y[1] (numeric) = 1.8817657398009696900696060237351
absolute error = 2.15115775273179e-17
relative error = 1.1431591654757798377247839470139e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.063
y[1] (analytic) = 1.8812936114093447682655742757855
y[1] (numeric) = 1.8812936114093447467111376297566
absolute error = 2.15544366460289e-17
relative error = 1.1457242248264318283979807454300e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.064
y[1] (analytic) = 1.880820601724181856737032809242
y[1] (numeric) = 1.8808206017241818351397600035825
absolute error = 2.15972728056595e-17
relative error = 1.1482898893100646635713213827737e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.065
y[1] (analytic) = 1.8803467112184906227409982303038
y[1] (numeric) = 1.8803467112184906011009122669303
absolute error = 2.16400859633735e-17
relative error = 1.1508561604232245873425071225910e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.066
y[1] (analytic) = 1.8798719403661615324778303770984
y[1] (numeric) = 1.8798719403661615107949543007408
absolute error = 2.16828760763576e-17
relative error = 1.1534230396637660606825580301679e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.067
y[1] (analytic) = 1.8793962896419653987123831375107
y[1] (numeric) = 1.8793962896419653769867400356889
absolute error = 2.17256431018218e-17
relative error = 1.1559905285308744586139483769303e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.068
y[1] (analytic) = 1.8789197595215529060032312485622
y[1] (numeric) = 1.8789197595215528842348442515631
absolute error = 2.17683869969991e-17
relative error = 1.1585586285250515482591405758392e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.069
y[1] (analytic) = 1.8784423504814541350520253753917
y[1] (numeric) = 1.8784423504814541132409176562462
absolute error = 2.18111077191455e-17
relative error = 1.1611273411481169173396646305821e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.07
y[1] (analytic) = 1.8779640629990780861734511204438
y[1] (numeric) = 1.8779640629990780643196458949034
absolute error = 2.18538052255404e-17
relative error = 1.1636966679032307063098730064085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.071
y[1] (analytic) = 1.877484897552712201886268492865
y[1] (numeric) = 1.8774848975527121799897890193787
absolute error = 2.18964794734863e-17
relative error = 1.1662666102948790931538890383997e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.072
y[1] (analytic) = 1.8770048546215218886259092470293
y[1] (numeric) = 1.8770048546215218666867788267204
absolute error = 2.19391304203089e-17
relative error = 1.1688371698288810683660550664693e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=5.13
NO POLE
x[1] = 2.073
y[1] (analytic) = 1.8765239346855500375791103775557
y[1] (numeric) = 1.8765239346855500155973523541984
absolute error = 2.19817580233573e-17
relative error = 1.1714083480124005511349983106697e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.074
y[1] (analytic) = 1.8760421382257165446410629361442
y[1] (numeric) = 1.8760421382257165226167006961404
absolute error = 2.20243622400038e-17
relative error = 1.1739801463539372045212451053196e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.075
y[1] (analytic) = 1.8755594657238178294955562130413
y[1] (numeric) = 1.875559465723817807428613185397
absolute error = 2.20669430276443e-17
relative error = 1.1765525663633492287739616945864e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.076
y[1] (analytic) = 1.8750759176625263538185982029511
y[1] (numeric) = 1.8750759176625263317090978592531
absolute error = 2.21095003436980e-17
relative error = 1.1791256095518388598713404150095e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.077
y[1] (analytic) = 1.8745914945253901386059941517309
y[1] (numeric) = 1.8745914945253901164539600061234
absolute error = 2.21520341456075e-17
relative error = 1.1816992774319591854711679528759e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.078
y[1] (analytic) = 1.8741061967968322806253658562534
y[1] (numeric) = 1.8741061967968322584308214654143
absolute error = 2.21945443908391e-17
relative error = 1.1842735715176316449909748124174e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.079
y[1] (analytic) = 1.8736200249621504679930952653746
y[1] (numeric) = 1.8736200249621504457560642284921
absolute error = 2.22370310368825e-17
relative error = 1.1868484933241315351736905015198e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.08
y[1] (analytic) = 1.8731329795075164948766768050246
y[1] (numeric) = 1.8731329795075164725971827637735
absolute error = 2.22794940412511e-17
relative error = 1.1894240443681055268421805767368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.081
y[1] (analytic) = 1.8726450609199757753229637250282
y[1] (numeric) = 1.8726450609199757530010303635463
absolute error = 2.23219333614819e-17
relative error = 1.1920002261675678506563030441283e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.082
y[1] (analytic) = 1.8721562696874468562127946393678
y[1] (numeric) = 1.8721562696874468338484456842323
absolute error = 2.23643489551355e-17
relative error = 1.1945770402419018202062915100402e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.083
y[1] (analytic) = 1.8716666062987209293424873052228
y[1] (numeric) = 1.8716666062987209069357465254263
absolute error = 2.24067407797965e-17
relative error = 1.1971544881118827306494609329972e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.084
y[1] (analytic) = 1.8711760712434613426326875592491
y[1] (numeric) = 1.8711760712434613201835787661763
absolute error = 2.24491087930728e-17
relative error = 1.1997325712996420086173828588765e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.085
y[1] (analytic) = 1.8706846650122031104650622022118
y[1] (numeric) = 1.8706846650122030879736092496152
absolute error = 2.24914529525966e-17
relative error = 1.2023112913287221833822666313177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.086
y[1] (analytic) = 1.8701923880963524231473254952341
y[1] (numeric) = 1.8701923880963524006135522792104
absolute error = 2.25337732160237e-17
relative error = 1.2048906497240410467714582806433e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.087
y[1] (analytic) = 1.8696992409881861555070898025979
y[1] (numeric) = 1.8696992409881861329310202615641
absolute error = 2.25760695410338e-17
relative error = 1.2074706480119092429290696820724e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.088
y[1] (analytic) = 1.869205224180851374615031787203
y[1] (numeric) = 1.8692052241808513519966899018725
absolute error = 2.26183418853305e-17
relative error = 1.2100512877200318381204903526732e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.089
y[1] (analytic) = 1.868710338168364846637866435478
y[1] (numeric) = 1.8687103381683648239772762288363
absolute error = 2.26605902066417e-17
relative error = 1.2126325703775313000169773586393e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.09
y[1] (analytic) = 1.8682145834456125428216220587275
y[1] (numeric) = 1.8682145834456125201188075960086
absolute error = 2.27028144627189e-17
relative error = 1.2152144975149116356558707506280e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.091
y[1] (analytic) = 1.8677179605083491446057102876003
y[1] (numeric) = 1.8677179605083491218606956762624
absolute error = 2.27450146113379e-17
relative error = 1.2177970706640974319401877706578e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.092
y[1] (analytic) = 1.8672204698531975478682859455666
y[1] (numeric) = 1.867220469853197525081095335268
absolute error = 2.27871906102986e-17
relative error = 1.2203802913584247602558857989536e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.093
y[1] (analytic) = 1.8667221119776483663033925560026
y[1] (numeric) = 1.8667221119776483434740501385777
absolute error = 2.28293424174249e-17
relative error = 1.2229641611326374254432764304463e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.094
y[1] (analytic) = 1.8662228873800594339303901056974
y[1] (numeric) = 1.8662228873800594110589201151324
absolute error = 2.28714699905650e-17
relative error = 1.2255486815229046442651782337980e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.095
y[1] (analytic) = 1.8657227965596553067361625553108
y[1] (numeric) = 1.8657227965596552838225892677193
absolute error = 2.29135732875915e-17
relative error = 1.2281338540668280343985054978584e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=83.9MB, alloc=4.3MB, time=5.37
x[1] = 2.096
y[1] (analytic) = 1.8652218400165267634506034545341
y[1] (numeric) = 1.8652218400165267404949511881332
absolute error = 2.29556522664009e-17
relative error = 1.2307196803034164488282118381973e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.097
y[1] (analytic) = 1.8647200182516303054558788864271
y[1] (numeric) = 1.8647200182516302824581720015128
absolute error = 2.29977068849143e-17
relative error = 1.2333061617731251243490490294635e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.098
y[1] (analytic) = 1.8642173317667876558299678316255
y[1] (numeric) = 1.8642173317667876327902307305484
absolute error = 2.30397371010771e-17
relative error = 1.2358933000178412533079043480245e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.099
y[1] (analytic) = 1.8637137810646852575249809088376
y[1] (numeric) = 1.8637137810646852344432380359785
absolute error = 2.30817428728591e-17
relative error = 1.2384810965808909964420359206138e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.1
y[1] (analytic) = 1.863209366648873770680759313269
y[1] (numeric) = 1.8632093666488737475570351550145
absolute error = 2.31237241582545e-17
relative error = 1.2410695530070411418612612969826e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.101
y[1] (analytic) = 1.8627040890237675690742566393353
y[1] (numeric) = 1.8627040890237675459085757240532
absolute error = 2.31656809152821e-17
relative error = 1.2436586708425115056672602849903e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.102
y[1] (analytic) = 1.8621979486946442357052071382378
y[1] (numeric) = 1.8621979486946442124975940362528
absolute error = 2.32076131019850e-17
relative error = 1.2462484516349605046472938422996e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.103
y[1] (analytic) = 1.8616909461676440575185848246937
y[1] (numeric) = 1.8616909461676440342690641482626
absolute error = 2.32495206764311e-17
relative error = 1.2488388969335136789836609148731e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.104
y[1] (analytic) = 1.8611830819497695192643587103173
y[1] (numeric) = 1.8611830819497694959729551136046
absolute error = 2.32914035967127e-17
relative error = 1.2514300082887439070990605373963e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.105
y[1] (analytic) = 1.8606743565488847964950503038573
y[1] (numeric) = 1.8606743565488847731617884829102
absolute error = 2.33332618209471e-17
relative error = 1.2540217872527053339490639841463e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.106
y[1] (analytic) = 1.8601647704737152477016003806879
y[1] (numeric) = 1.8601647704737152243265050734118
absolute error = 2.33750953072761e-17
relative error = 1.2566142353789082223195331921881e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.107
y[1] (analytic) = 1.8596543242338469055880528856467
y[1] (numeric) = 1.8596543242338468821711488717807
absolute error = 2.34169040138660e-17
relative error = 1.2592073542223206514166076358773e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.108
y[1] (analytic) = 1.8591430183397259674855646944923
y[1] (numeric) = 1.8591430183397259440268767955841
absolute error = 2.34586878989082e-17
relative error = 1.2618011453394024929851727293105e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.109
y[1] (analytic) = 1.8586308533026582849062508199289
y[1] (numeric) = 1.85863085330265826140580389931
absolute error = 2.35004469206189e-17
relative error = 1.2643956102880910226379493265167e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.11
y[1] (analytic) = 1.8581178296348088522373755083107
y[1] (numeric) = 1.8581178296348088286951944710718
absolute error = 2.35421810372389e-17
relative error = 1.2669907506277918911237144029608e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.111
y[1] (analytic) = 1.8576039478492012945764005327927
y[1] (numeric) = 1.8576039478492012709925103257585
absolute error = 2.35838902070342e-17
relative error = 1.2695865679194131486984965435312e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.112
y[1] (analytic) = 1.8570892084597173547074028478361
y[1] (numeric) = 1.8570892084597173310818284595405
absolute error = 2.36255743882956e-17
relative error = 1.2721830637253454801405667696313e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.113
y[1] (analytic) = 1.8565736119810963792193746286086
y[1] (numeric) = 1.8565736119810963555521410892696
absolute error = 2.36672335393390e-17
relative error = 1.2747802396094801126733952299841e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.114
y[1] (analytic) = 1.8560571589289348037669195769361
y[1] (numeric) = 1.856057158928934780058051958431
absolute error = 2.37088676185051e-17
relative error = 1.2773780971371944290089040238878e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.115
y[1] (analytic) = 1.8555398498196856374738602330676
y[1] (numeric) = 1.8555398498196856137233836489076
absolute error = 2.37504765841600e-17
relative error = 1.2799766378753860616396095632971e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.116
y[1] (analytic) = 1.8550216851706579464802718896016
y[1] (numeric) = 1.8550216851706579226882114949069
absolute error = 2.37920603946947e-17
relative error = 1.2825758633924477475573462862353e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.117
y[1] (analytic) = 1.8545026655000163366334595604984
y[1] (numeric) = 1.8545026655000163127998405519731
absolute error = 2.38336190085253e-17
relative error = 1.2851757752582798887082152317249e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.118
y[1] (analytic) = 1.8539827913267804353233953141574
y[1] (numeric) = 1.8539827913267804114482429300642
absolute error = 2.38751523840932e-17
relative error = 1.2877763750443031353702778958426e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.119
memory used=87.7MB, alloc=4.3MB, time=5.61
y[1] (analytic) = 1.8534620631708243724631341350795
y[1] (numeric) = 1.8534620631708243485464736552143
absolute error = 2.39166604798652e-17
relative error = 1.2903776643234655972839834925653e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.12
y[1] (analytic) = 1.8529404815528762606147273336542
y[1] (numeric) = 1.8529404815528762366565840793212
absolute error = 2.39581432543330e-17
relative error = 1.2929796446702176879062804510488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.121
y[1] (analytic) = 1.8524180469945176742611533781168
y[1] (numeric) = 1.8524180469945176502615527121029
absolute error = 2.39996006660139e-17
relative error = 1.2955823176605517082218887510757e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.122
y[1] (analytic) = 1.8518947600181831282247868766995
y[1] (numeric) = 1.851894760018183104183754203249
absolute error = 2.40410326734505e-17
relative error = 1.2981856848719875006463055612204e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.123
y[1] (analytic) = 1.8513706211471595552329272914649
y[1] (numeric) = 1.8513706211471595311504880562541
absolute error = 2.40824392352108e-17
relative error = 1.3007897478835796861496706168372e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.124
y[1] (analytic) = 1.8508456309055857826309098182495
y[1] (numeric) = 1.8508456309055857585070895083612
absolute error = 2.41238203098883e-17
relative error = 1.3033945082759249155458290010164e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.125
y[1] (analytic) = 1.8503197898184520082433217195624
y[1] (numeric) = 1.8503197898184519840781458634607
absolute error = 2.41651758561017e-17
relative error = 1.3059999676311475171314692961904e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.126
y[1] (analytic) = 1.8497930984115992753838482491804
y[1] (numeric) = 1.8497930984115992511773424166847
absolute error = 2.42065058324957e-17
relative error = 1.3086061275329445878084773230798e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.127
y[1] (analytic) = 1.8492655572117189470142731585474
y[1] (numeric) = 1.8492655572117189227664629608071
absolute error = 2.42478101977403e-17
relative error = 1.3112129895665500498680043745224e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.128
y[1] (analytic) = 1.8487371667463521790531596259367
y[1] (numeric) = 1.8487371667463521547640707154057
absolute error = 2.42890889105310e-17
relative error = 1.3138205553187473300642351457911e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.129
y[1] (analytic) = 1.8482079275438893928347382996491
y[1] (numeric) = 1.8482079275438893685043963700599
absolute error = 2.43303419295892e-17
relative error = 1.3164288263778928835376544282032e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.13
y[1] (analytic) = 1.8476778401335697467185299963159
y[1] (numeric) = 1.8476778401335697223469607826541
absolute error = 2.43715692136618e-17
relative error = 1.3190378043338964624714855711149e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.131
y[1] (analytic) = 1.84714690504548060685023144464
y[1] (numeric) = 1.8471469050454805824374607231183
absolute error = 2.44127707215217e-17
relative error = 1.3216474907782500764752760796322e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.132
y[1] (analytic) = 1.8466151228105570170743933136445
y[1] (numeric) = 1.8466151228105569926204469016773
absolute error = 2.44539464119672e-17
relative error = 1.3242578873039974363589305283794e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.133
y[1] (analytic) = 1.846082493960581167999420612708
y[1] (numeric) = 1.8460824939605811435043243688853
absolute error = 2.44950962438227e-17
relative error = 1.3268689955057737663702798874819e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.134
y[1] (analytic) = 1.8455490190281818652154263983403
y[1] (numeric) = 1.8455490190281818406792062224019
absolute error = 2.45362201759384e-17
relative error = 1.3294808169797915027958303957006e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.135
y[1] (analytic) = 1.8450146985468339966654705698019
y[1] (numeric) = 1.8450146985468339720881524026115
absolute error = 2.45773181671904e-17
relative error = 1.3320933533238476497331467788315e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.136
y[1] (analytic) = 1.844479533050857999170716382283
y[1] (numeric) = 1.8444795330508579745523262058024
absolute error = 2.46183901764806e-17
relative error = 1.3347066061373203063521976672364e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.137
y[1] (analytic) = 1.8439435230754193241100381524421
y[1] (numeric) = 1.8439435230754192994506019897052
absolute error = 2.46594361627369e-17
relative error = 1.3373205770211814594511397489958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.138
y[1] (analytic) = 1.8434066691565279022546144766512
y[1] (numeric) = 1.8434066691565278775541583917377
absolute error = 2.47004560849135e-17
relative error = 1.3399352675780152249243260921596e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.139
y[1] (analytic) = 1.8428689718310376077580421273097
y[1] (numeric) = 1.8428689718310375830165922253192
absolute error = 2.47414499019905e-17
relative error = 1.3425506794119981387909096911091e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.14
y[1] (analytic) = 1.8423304316366457213025066370689
y[1] (numeric) = 1.8423304316366456965200890640949
absolute error = 2.47824175729740e-17
relative error = 1.3451668141289065551708880229655e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.141
y[1] (analytic) = 1.8417910491118923924015464247522
y[1] (numeric) = 1.8417910491118923675781873678558
absolute error = 2.48233590568964e-17
relative error = 1.3477836733361349180661999886912e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.142
y[1] (analytic) = 1.8412508247961601008599481601604
y[1] (numeric) = 1.8412508247961600759956738473443
absolute error = 2.48642743128161e-17
relative error = 1.3504012586426814805963892784073e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.3MB, time=5.86
NO POLE
x[1] = 2.143
y[1] (analytic) = 1.840709759229673117391311907824
y[1] (numeric) = 1.840709759229673092486148608006
absolute error = 2.49051632998180e-17
relative error = 1.3530195716591774624722784341085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.144
y[1] (analytic) = 1.8401678529534969633938254320903
y[1] (numeric) = 1.8401678529534969384477994550774
absolute error = 2.49460259770129e-17
relative error = 1.3556386139978564836343144589556e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.145
y[1] (analytic) = 1.8396251065095378698847878877284
y[1] (numeric) = 1.83962510650953784489792558419
absolute error = 2.49868623035384e-17
relative error = 1.3582583872726054841067000039552e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.146
y[1] (analytic) = 1.8390815204405422355944239614801
y[1] (numeric) = 1.8390815204405422105667517229222
absolute error = 2.50276722385579e-17
relative error = 1.3608788930989124234476240195022e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.147
y[1] (analytic) = 1.8385370952900960842195303707013
y[1] (numeric) = 1.8385370952900960591510746294396
absolute error = 2.50684557412617e-17
relative error = 1.3635001330939281105756764517580e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.148
y[1] (analytic) = 1.8379918316026245208374974653982
y[1] (numeric) = 1.837991831602624495728284694532
absolute error = 2.51092127708662e-17
relative error = 1.3661221088764247716250230597869e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.149
y[1] (analytic) = 1.8374457299233911874812495195948
y[1] (numeric) = 1.8374457299233911623313062329804
absolute error = 2.51499432866144e-17
relative error = 1.3687448220668252963638430314703e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.15
y[1] (analytic) = 1.8368987907984977178756481370438
y[1] (numeric) = 1.836898790798497692685000889268
absolute error = 2.51906472477758e-17
relative error = 1.3713682742871998748578875284809e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.151
y[1] (analytic) = 1.8363510147748831913359040348326
y[1] (numeric) = 1.8363510147748831661045794211862
absolute error = 2.52313246136464e-17
relative error = 1.3739924671612680756112699641066e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.152
y[1] (analytic) = 1.8358024024003235858285433064282
y[1] (numeric) = 1.8358024024003235605565679628794
absolute error = 2.52719753435488e-17
relative error = 1.3766174023144063765047423704213e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.153
y[1] (analytic) = 1.8352529542234312301954751031475
y[1] (numeric) = 1.8352529542234312048828757063151
absolute error = 2.53125993968324e-17
relative error = 1.3792430813736611599482460845736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.154
y[1] (analytic) = 1.8347026707936542555417085099405
y[1] (numeric) = 1.8347026707936542301885117770675
absolute error = 2.53531967328730e-17
relative error = 1.3818695059677290304403347771299e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.155
y[1] (analytic) = 1.8341515526612760457872672277244
y[1] (numeric) = 1.834151552661276020393499916651
absolute error = 2.53937673110734e-17
relative error = 1.3844966777269916196909155578409e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.156
y[1] (analytic) = 1.8335996003774146873838515103066
y[1] (numeric) = 1.8335996003774146619495404194437
absolute error = 2.54343110908629e-17
relative error = 1.3871245982834904650810274155925e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.157
y[1] (analytic) = 1.8330468144940224181967976391905
y[1] (numeric) = 1.8330468144940223927219696074926
absolute error = 2.54748280316979e-17
relative error = 1.3897532692709618540150683599747e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.158
y[1] (analytic) = 1.8324931955638850755528860542571
y[1] (numeric) = 1.8324931955638850500375679611958
absolute error = 2.55153180930613e-17
relative error = 1.3923826923248062486474312562703e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.159
y[1] (analytic) = 1.8319387441406215434545500924698
y[1] (numeric) = 1.8319387441406215178987688580067
absolute error = 2.55557812344631e-17
relative error = 1.3950128690821231614340002291503e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.16
y[1] (analytic) = 1.8313834607786831989610381203463
y[1] (numeric) = 1.8313834607786831733648207049062
absolute error = 2.55962174154401e-17
relative error = 1.3976438011816969526894007583817e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.161
y[1] (analytic) = 1.8308273460333533577370826789904
y[1] (numeric) = 1.8308273460333533321004560834341
absolute error = 2.56366265955563e-17
relative error = 1.4002754902640208382832158543894e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.162
y[1] (analytic) = 1.8302704004607467187696310929671
y[1] (numeric) = 1.8302704004607466930926223585648
absolute error = 2.56770087344023e-17
relative error = 1.4029079379712663062484482628682e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.163
y[1] (analytic) = 1.8297126246178088082531928262459
y[1] (numeric) = 1.8297126246178087825358290346498
absolute error = 2.57173637915961e-17
relative error = 1.4055411459473289941467079849994e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.164
y[1] (analytic) = 1.8291540190623154226443596998165
y[1] (numeric) = 1.8291540190623153968866679730338
absolute error = 2.57576917267827e-17
relative error = 1.4081751158378090481068979630203e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.165
y[1] (analytic) = 1.8285945843528720708860559164118
y[1] (numeric) = 1.8285945843528720450880634167779
absolute error = 2.57979924996339e-17
relative error = 1.4108098492900023851621516200157e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.3MB, time=6.11
NO POLE
x[1] = 2.166
y[1] (analytic) = 1.8280343210489134158020756680418
y[1] (numeric) = 1.8280343210489133899638095981925
absolute error = 2.58382660698493e-17
relative error = 1.4134453479529575856262424426532e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.167
y[1] (analytic) = 1.8274732297107027146624669317521
y[1] (numeric) = 1.8274732297107026887839545345971
absolute error = 2.58785123971550e-17
relative error = 1.4160816134774070351746863268702e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.168
y[1] (analytic) = 1.8269113108993312589203208881803
y[1] (numeric) = 1.8269113108993312330015894468754
absolute error = 2.59187314413049e-17
relative error = 1.4187186475158402586471723137474e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.169
y[1] (analytic) = 1.82634856517671781312052722607
y[1] (numeric) = 1.8263485651767177871616040639901
absolute error = 2.59589231620799e-17
relative error = 1.4213564517224624074905735258651e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.17
y[1] (analytic) = 1.8257849931056080529810564239434
y[1] (numeric) = 1.8257849931056080269819689046552
absolute error = 2.59990875192882e-17
relative error = 1.4239950277532129204351926541938e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.171
y[1] (analytic) = 1.8252205952495740026473309276027
y[1] (numeric) = 1.8252205952495739766081064548372
absolute error = 2.60392244727655e-17
relative error = 1.4266343772657787417479240239397e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.172
y[1] (analytic) = 1.824655372173013471120247969041
y[1] (numeric) = 1.8246553721730134450409139866661
absolute error = 2.60793339823749e-17
relative error = 1.4292745019195911244324706488208e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.173
y[1] (analytic) = 1.8240893244411494878584175986943
y[1] (numeric) = 1.8240893244411494617390015906875
absolute error = 2.61194160080068e-17
relative error = 1.4319154033758224293758195829332e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.174
y[1] (analytic) = 1.8235224526200297375551803287493
y[1] (numeric) = 1.82352245262002971139570981917
absolute error = 2.61594705095793e-17
relative error = 1.4345570832974103398290276170946e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.175
y[1] (analytic) = 1.8229547572765259940909696104411
y[1] (numeric) = 1.8229547572765259678914721634034
absolute error = 2.61994974470377e-17
relative error = 1.4371995433490327525272318903657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.176
y[1] (analytic) = 1.8223862389783335536615851929335
y[1] (numeric) = 1.8223862389783335274220884125782
absolute error = 2.62394967803553e-17
relative error = 1.4398427851971539587779052879252e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.177
y[1] (analytic) = 1.8218168982939706670829442354582
y[1] (numeric) = 1.8218168982939706408034757659256
absolute error = 2.62794684695326e-17
relative error = 1.4424868105099830894509749439041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.178
y[1] (analytic) = 1.8212467357927779712728778679176
y[1] (numeric) = 1.8212467357927779449534653933195
absolute error = 2.63194124745981e-17
relative error = 1.4451316209575203358236969003474e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.179
y[1] (analytic) = 1.8206757520449179199105417181047
y[1] (numeric) = 1.8206757520449178935512129624971
absolute error = 2.63593287556076e-17
relative error = 1.4477772182115208720943453444187e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.18
y[1] (analytic) = 1.8201039476213742132740097460839
y[1] (numeric) = 1.820103947621374186874792473439
absolute error = 2.63992172726449e-17
relative error = 1.4504236039455356305451102344516e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.181
y[1] (analytic) = 1.8195313230939512272566215480908
y[1] (numeric) = 1.8195313230939512008175435622692
absolute error = 2.64390779858216e-17
relative error = 1.4530707798349026921059356567308e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.182
y[1] (analytic) = 1.8189578790352734415626541135548
y[1] (numeric) = 1.818957879035273415083743258278
absolute error = 2.64789108552768e-17
relative error = 1.4557187475567331649170077000243e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.183
y[1] (analytic) = 1.8183836160187848670828898395281
y[1] (numeric) = 1.8183836160187848405641739983504
absolute error = 2.65187158411777e-17
relative error = 1.4583675087899465324864517887702e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.184
y[1] (analytic) = 1.8178085346187484724506534269022
y[1] (numeric) = 1.8178085346187484458921605231828
absolute error = 2.65584929037194e-17
relative error = 1.4610170652152620616279491518144e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.185
y[1] (analytic) = 1.8172326354102456097788911023289
y[1] (numeric) = 1.8172326354102455831806490992041
absolute error = 2.65982420031248e-17
relative error = 1.4636674185151956988587419550262e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.186
y[1] (analytic) = 1.8166559189691754395788664287185
y[1] (numeric) = 1.8166559189691754129409033290739
absolute error = 2.66379630996446e-17
relative error = 1.4663185703740624673400937446021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.187
y[1] (analytic) = 1.8160783858722543548610477855718
y[1] (numeric) = 1.8160783858722543281833916320138
absolute error = 2.66776561535580e-17
relative error = 1.4689705224780174147637579119332e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.188
y[1] (analytic) = 1.8155000366970154044187634182087
y[1] (numeric) = 1.815500036697015377701442293037
absolute error = 2.67173211251717e-17
relative error = 1.4716232765150030031549002272264e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.3MB, time=6.36
NO POLE
x[1] = 2.189
y[1] (analytic) = 1.8149208720218077152952007721934
y[1] (numeric) = 1.8149208720218076885382427973724
absolute error = 2.67569579748210e-17
relative error = 1.4742768341748121074746259116835e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.19
y[1] (analytic) = 1.814340892425795914434327645905
y[1] (numeric) = 1.8143408924257958876377609830361
absolute error = 2.67965666628689e-17
relative error = 1.4769311971490409038046075655113e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.191
y[1] (analytic) = 1.8137600984889595495163135102877
y[1] (numeric) = 1.813760098488959522680166360581
absolute error = 2.68361471497067e-17
relative error = 1.4795863671311243701520037371118e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.192
y[1] (analytic) = 1.8131784907920925089780301603084
y[1] (numeric) = 1.8131784907920924821023307645544
absolute error = 2.68756993957540e-17
relative error = 1.4822423458163387661789740293163e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.193
y[1] (analytic) = 1.8125960699168024412192116775739
y[1] (numeric) = 1.8125960699168024143039883161154
absolute error = 2.69152233614585e-17
relative error = 1.4848991349017930856815405425997e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.194
y[1] (analytic) = 1.8120128364455101729948544978995
y[1] (numeric) = 1.8120128364455101460401354906033
absolute error = 2.69547190072962e-17
relative error = 1.4875567360864425693099603706683e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.195
y[1] (analytic) = 1.8114287909614491269944391913796
y[1] (numeric) = 1.8114287909614491000002528976081
absolute error = 2.69941862937715e-17
relative error = 1.4902151510710967246848316573226e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.196
y[1] (analytic) = 1.8108439340486647386085563756909
y[1] (numeric) = 1.8108439340486647115749311942738
absolute error = 2.70336251814171e-17
relative error = 1.4928743815584163192972594484907e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.197
y[1] (analytic) = 1.810258266292013871883519995953
y[1] (numeric) = 1.8102582662920138448104843651588
absolute error = 2.70730356307942e-17
relative error = 1.4955344292529269416294120061283e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.198
y[1] (analytic) = 1.809671788277164234664552016485
y[1] (numeric) = 1.8096717882771642075521344139927
absolute error = 2.71124176024923e-17
relative error = 1.4981952958610104869716026942670e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.199
y[1] (analytic) = 1.8090845005905937929281233812238
y[1] (numeric) = 1.8090845005905937657763523240945
absolute error = 2.71517710571293e-17
relative error = 1.5008569830909132114689375912601e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.2
y[1] (analytic) = 1.8084964038195901843040369104161
y[1] (numeric) = 1.8084964038195901571129409550641
absolute error = 2.71910959553520e-17
relative error = 1.5035194926527759214525788100942e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.201
y[1] (analytic) = 1.8079074985522501307878386114497
y[1] (numeric) = 1.8079074985522501035574463536143
absolute error = 2.72303922578354e-17
relative error = 1.5061828262585978484659688811900e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.202
y[1] (analytic) = 1.8073177853774788506441446913663
y[1] (numeric) = 1.8073177853774788233744847660832
absolute error = 2.72696599252831e-17
relative error = 1.5088469856222613191788108735754e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.203
y[1] (analytic) = 1.8067272648849894695014723676786
y[1] (numeric) = 1.8067272648849894421925734492512
absolute error = 2.73088989184274e-17
relative error = 1.5115119724595398707327569825238e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.204
y[1] (analytic) = 1.806135937665302430639163382612
y[1] (numeric) = 1.8061359376653024032910541845824
absolute error = 2.73481091980296e-17
relative error = 1.5141777884881174571850747867841e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.205
y[1] (analytic) = 1.8055438043097449044669899337976
y[1] (numeric) = 1.8055438043097448770796992089185
absolute error = 2.73872907248791e-17
relative error = 1.5168444354275412335868263205898e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.206
y[1] (analytic) = 1.8049508654104501971980335417633
y[1] (numeric) = 1.8049508654104501697715900819688
absolute error = 2.74264434597945e-17
relative error = 1.5195119149992850552437513959346e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.207
y[1] (analytic) = 1.8043571215603571587154281812924
y[1] (numeric) = 1.8043571215603571312498608176692
absolute error = 2.74655673636232e-17
relative error = 1.5221802289267299718024154764799e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.208
y[1] (analytic) = 1.8037625733532095896335598098588
y[1] (numeric) = 1.8037625733532095621288974126176
absolute error = 2.75046623972412e-17
relative error = 1.5248493789351557726402193673376e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.209
y[1] (analytic) = 1.8031672213835556475543152318894
y[1] (numeric) = 1.8031672213835556200105867103361
absolute error = 2.75437285215533e-17
relative error = 1.5275193667517547004775400059674e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.21
y[1] (analytic) = 1.802571066246747252518974042556
y[1] (numeric) = 1.8025710662467472249362083450623
absolute error = 2.75827656974937e-17
relative error = 1.5301901941056673844186462628787e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.211
y[1] (analytic) = 1.8019741085389394916563381991531
y[1] (numeric) = 1.8019741085389394640345643131281
absolute error = 2.76217738860250e-17
relative error = 1.5328618627279300546542712645501e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.3MB, time=6.60
NO POLE
x[1] = 2.212
y[1] (analytic) = 1.8013763488570900230276945718856
y[1] (numeric) = 1.8013763488570899953669415237466
absolute error = 2.76607530481390e-17
relative error = 1.5355343743515215776149614427177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.213
y[1] (analytic) = 1.8007777877989584786692066290518
y[1] (numeric) = 1.8007777877989584509695034841951
absolute error = 2.76997031448567e-17
relative error = 1.5382077307113661612450988236563e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.214
y[1] (analytic) = 1.8001784259631058668323322141805
y[1] (numeric) = 1.8001784259631058390937080769525
absolute error = 2.77386241372280e-17
relative error = 1.5408819335443194025100696009771e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.215
y[1] (analytic) = 1.7995782639488939734228651746556
y[1] (numeric) = 1.7995782639488939456453491883238
absolute error = 2.77775159863318e-17
relative error = 1.5435569845891765362407914402825e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.216
y[1] (analytic) = 1.7989773023564847626391994027364
y[1] (numeric) = 1.7989773023564847348228207494602
absolute error = 2.78163786532762e-17
relative error = 1.5462328855866862609235443154844e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.217
y[1] (analytic) = 1.798375541786839776810414650659
y[1] (numeric) = 1.7983755417868397489552025514602
absolute error = 2.78552120991988e-17
relative error = 1.5489096382795701545390418156368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.218
y[1] (analytic) = 1.7977729828417195354347842816829
y[1] (numeric) = 1.797772982841719507540767996417
absolute error = 2.78940162852659e-17
relative error = 1.5515872444124809444080239524627e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.219
y[1] (analytic) = 1.7971696261236829334193059185266
y[1] (numeric) = 1.7971696261236829054865147458532
absolute error = 2.79327911726734e-17
relative error = 1.5542657057320552880310206625325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.22
y[1] (analytic) = 1.7965654722360866385208567496092
y[1] (numeric) = 1.7965654722360866105493200269628
absolute error = 2.79715367226464e-17
relative error = 1.5569450239868943016874140636603e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.221
y[1] (analytic) = 1.7959605217830844879895760518937
y[1] (numeric) = 1.7959605217830844599793231554544
absolute error = 2.80102528964393e-17
relative error = 1.5596252009275718918077446381575e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.222
y[1] (analytic) = 1.7953547753696268844150782868996
y[1] (numeric) = 1.7953547753696268563661386315635
absolute error = 2.80489396553361e-17
relative error = 1.5623062383066542447759221059967e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.223
y[1] (analytic) = 1.7947482336014601907761009236199
y[1] (numeric) = 1.79474823360146016268850396297
absolute error = 2.80875969606499e-17
relative error = 1.5649881378786747834782001585173e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.224
y[1] (analytic) = 1.7941408970851261246941919386457
y[1] (numeric) = 1.7941408970851260965679671649223
absolute error = 2.81262247737234e-17
relative error = 1.5676709014001648117873282582053e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.225
y[1] (analytic) = 1.7935327664279611518920427397597
y[1] (numeric) = 1.7935327664279611237272196838308
absolute error = 2.81648230559289e-17
relative error = 1.5703545306296563450644225130007e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.226
y[1] (analytic) = 1.7929238422380958788570730546151
y[1] (numeric) = 1.7929238422380958506536812859471
absolute error = 2.82033917686680e-17
relative error = 1.5730390273276682157657109667094e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.227
y[1] (analytic) = 1.7923141251244544447108751208649
y[1] (numeric) = 1.7923141251244544164689442474928
absolute error = 2.82419308733721e-17
relative error = 1.5757243932567367874868766128554e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.228
y[1] (analytic) = 1.7917036156967539122851253082462
y[1] (numeric) = 1.7917036156967538840046849767441
absolute error = 2.82804403315021e-17
relative error = 1.5784106301814020831948134521231e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.229
y[1] (analytic) = 1.7910923145655036584045720966571
y[1] (numeric) = 1.7910923145655036300856519921088
absolute error = 2.83189201045483e-17
relative error = 1.5810977398682050532261563693295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.23
y[1] (analytic) = 1.7904802223420047633777101271885
y[1] (numeric) = 1.7904802223420047350203399731573
absolute error = 2.83573701540312e-17
relative error = 1.5837857240857351052007671193261e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.231
y[1] (analytic) = 1.7898673396383493996957508353839
y[1] (numeric) = 1.7898673396383493712999603938832
absolute error = 2.83957904415007e-17
relative error = 1.5864745846045883411055948444562e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.232
y[1] (analytic) = 1.7892536670674202199405009677075
y[1] (numeric) = 1.789253667067420191506320039171
absolute error = 2.84341809285365e-17
relative error = 1.5891643231973927774034481913989e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.233
y[1] (analytic) = 1.7886392052428897439017610732902
y[1] (numeric) = 1.7886392052428897154292194965421
absolute error = 2.84725415767481e-17
relative error = 1.5918549416388112553401155682878e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.234
y[1] (analytic) = 1.7880239547792197449048568535039
y[1] (numeric) = 1.7880239547792197163939845057291
absolute error = 2.85108723477748e-17
relative error = 1.5945464417055443589740960065527e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.3MB, time=6.86
x[1] = 2.235
y[1] (analytic) = 1.787407916291660635348917041782
y[1] (numeric) = 1.7874079162916606067997438384961
absolute error = 2.85491732032859e-17
relative error = 1.5972388251763445303243859648471e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.236
y[1] (analytic) = 1.7867910903962508514565122753565
y[1] (numeric) = 1.7867910903962508228690681703759
absolute error = 2.85874441049806e-17
relative error = 1.5999320938320134255574691658599e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.237
y[1] (analytic) = 1.786173477709816237235270209222
y[1] (numeric) = 1.7861734777098162086095851946341
absolute error = 2.86256850145879e-17
relative error = 1.6026262494553992674235051244414e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.238
y[1] (analytic) = 1.7855550788499694276520829106602
y[1] (numeric) = 1.7855550788499693989881870167933
absolute error = 2.86638958938669e-17
relative error = 1.6053212938314165958673438465537e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.239
y[1] (analytic) = 1.7849358944351092310205233600656
y[1] (numeric) = 1.7849358944351092023184466554587
absolute error = 2.87020767046069e-17
relative error = 1.6080172287470548564878128622033e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.24
y[1] (analytic) = 1.7843159250844200106020886706045
y[1] (numeric) = 1.7843159250844199818618612619777
absolute error = 2.87402274086268e-17
relative error = 1.6107140559913477778977269263461e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.241
y[1] (analytic) = 1.7836951714178710654218884254138
y[1] (numeric) = 1.7836951714178710366435404576377
absolute error = 2.87783479677761e-17
relative error = 1.6134117773554323883025542092876e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.242
y[1] (analytic) = 1.7830736340562160102993973165972
y[1] (numeric) = 1.7830736340562159814829589726631
absolute error = 2.88164383439341e-17
relative error = 1.6161103946325072077255424848078e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.243
y[1] (analytic) = 1.7824513136209921550948920552174
y[1] (numeric) = 1.7824513136209921262403935562067
absolute error = 2.88544984990107e-17
relative error = 1.6188099096178801185227241039021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.244
y[1] (analytic) = 1.7818282107345198831721933057926
y[1] (numeric) = 1.7818282107345198542796649108472
absolute error = 2.88925283949454e-17
relative error = 1.6215103241089153180333889866162e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.245
y[1] (analytic) = 1.7812043260199020290783341825072
y[1] (numeric) = 1.7812043260199020001478061887986
absolute error = 2.89305279937086e-17
relative error = 1.6242116399051092876771059822128e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.246
y[1] (analytic) = 1.780579660101023255440777627412
y[1] (numeric) = 1.7805796601010232264722803701115
absolute error = 2.89684972573005e-17
relative error = 1.6269138588080321358166558764386e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.247
y[1] (analytic) = 1.779954213602549429082805773349
y[1] (numeric) = 1.779954213602549400076369625597
absolute error = 2.90064361477520e-17
relative error = 1.6296169826213811812797693305159e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.248
y[1] (analytic) = 1.7793279871499269963577051761557
y[1] (numeric) = 1.7793279871499269673133605490316
absolute error = 2.90443446271241e-17
relative error = 1.6323210131509503500023977557586e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.249
y[1] (analytic) = 1.7787009813693823577023725819146
y[1] (numeric) = 1.7787009813693823286201499244063
absolute error = 2.90822226575083e-17
relative error = 1.6350259522046557295231387296951e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.25
y[1] (analytic) = 1.7780731968879212414109666755878
y[1] (numeric) = 1.7780731968879212122908964745611
absolute error = 2.91200702010267e-17
relative error = 1.6377318015925443069508647430394e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.251
y[1] (analytic) = 1.7774446343333280766292320373338
y[1] (numeric) = 1.7774446343333280474713448175022
absolute error = 2.91578872198316e-17
relative error = 1.6404385631267745968646195144125e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.252
y[1] (analytic) = 1.7768152943341653655701223121308
y[1] (numeric) = 1.7768152943341653363744486360246
absolute error = 2.91956736761062e-17
relative error = 1.6431462386216591382434497687475e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.253
y[1] (analytic) = 1.7761851775197730549513503770291
y[1] (numeric) = 1.7761851775197730257179208449652
absolute error = 2.92334295320639e-17
relative error = 1.6458548298936282627584126774699e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.254
y[1] (analytic) = 1.7755542845202679066554940684325
y[1] (numeric) = 1.7755542845202678773843393184837
absolute error = 2.92711547499488e-17
relative error = 1.6485643387612613721055794915525e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.255
y[1] (analytic) = 1.7749226159665428676132868092489
y[1] (numeric) = 1.7749226159665428383044375172131
absolute error = 2.93088492920358e-17
relative error = 1.6512747670452957474106991962353e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.256
y[1] (analytic) = 1.774290172490266438910723252567
y[1] (numeric) = 1.7742901724902664095642101319368
absolute error = 2.93465131206302e-17
relative error = 1.6539861165686071988354183084681e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.257
y[1] (analytic) = 1.7736569547238820441206108347022
y[1] (numeric) = 1.7736569547238820147364646366338
absolute error = 2.93841461980684e-17
relative error = 1.6566983891562526941533072741020e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.3MB, time=7.11
x[1] = 2.258
y[1] (analytic) = 1.7730229633006073968591989060056
y[1] (numeric) = 1.7730229633006073674374504192883
absolute error = 2.94217484867173e-17
relative error = 1.6594115866354397591767272744729e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.259
y[1] (analytic) = 1.7723881988544338675685178827555
y[1] (numeric) = 1.7723881988544338381091979337812
absolute error = 2.94593199489743e-17
relative error = 1.6621257108355296667946591663153e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.26
y[1] (analytic) = 1.7717526620201258495250616377403
y[1] (numeric) = 1.771752662020125820028201090472
absolute error = 2.94968605472683e-17
relative error = 1.6648407635880970756565101422445e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.261
y[1] (analytic) = 1.7711163534332201240754471207947
y[1] (numeric) = 1.7711163534332200945410768767361
absolute error = 2.95343702440586e-17
relative error = 1.6675567467268712296058484286807e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.262
y[1] (analytic) = 1.7704792737300252250996859735799
y[1] (numeric) = 1.7704792737300251955278369717445
absolute error = 2.95718490018354e-17
relative error = 1.6702736620877674029998660005365e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.263
y[1] (analytic) = 1.7698414235476208027027036752813
y[1] (numeric) = 1.7698414235476207730934068921612
absolute error = 2.96092967831201e-17
relative error = 1.6729915115089071149809350866905e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.264
y[1] (analytic) = 1.769202803523856986134742527652
y[1] (numeric) = 1.7692028035238569564880289771872
absolute error = 2.96467135504648e-17
relative error = 1.6757102968305931709895502962561e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.265
y[1] (analytic) = 1.7685634142973537459412855589463
y[1] (numeric) = 1.7685634142973537162571862924935
absolute error = 2.96840992664528e-17
relative error = 1.6784300198953411948641689181889e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.266
y[1] (analytic) = 1.7679232565075002553431391967656
y[1] (numeric) = 1.7679232565075002256216853030673
absolute error = 2.97214538936983e-17
relative error = 1.6811506825478659800698188624073e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.267
y[1] (analytic) = 1.7672823307944542508473133296815
y[1] (numeric) = 1.7672823307944542210885359348346
absolute error = 2.97587773948469e-17
relative error = 1.6838722866351130800921597967558e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.268
y[1] (analytic) = 1.7666406377991413920893381467019
y[1] (numeric) = 1.766640637799141362293268414127
absolute error = 2.97960697325749e-17
relative error = 1.6865948340062225436409346691066e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.269
y[1] (analytic) = 1.765998178163254620907657912211
y[1] (numeric) = 1.765998178163254591074327042621
absolute error = 2.98333308695900e-17
relative error = 1.6893183265125718476323541328647e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.27
y[1] (analytic) = 1.7653549525292535196507426019347
y[1] (numeric) = 1.7653549525292534897801818333037
absolute error = 2.98705607686310e-17
relative error = 1.6920427660077622795774239967586e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.271
y[1] (analytic) = 1.7647109615403636687175590927679
y[1] (numeric) = 1.7647109615403636388097997002998
absolute error = 2.99077593924681e-17
relative error = 1.6947681543476392916737956306742e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.272
y[1] (analytic) = 1.7640662058405760033320443659369
y[1] (numeric) = 1.7640662058405759733871176620342
absolute error = 2.99449267039027e-17
relative error = 1.6974944933902845574142389995828e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.273
y[1] (analytic) = 1.7634206860746461695522239489724
y[1] (numeric) = 1.763420686074646139570161283205
absolute error = 2.99820626657674e-17
relative error = 1.7002217849960193539210882812228e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.274
y[1] (analytic) = 1.7627744028880938795146195873191
y[1] (numeric) = 1.7627744028880938494954523463927
absolute error = 3.00191672409264e-17
relative error = 1.7029500310274306447100922453397e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.275
y[1] (analytic) = 1.7621273569272022659145909011215
y[1] (numeric) = 1.7621273569272022358583505088466
absolute error = 3.00562403922749e-17
relative error = 1.7056792333493404717990367951807e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.276
y[1] (analytic) = 1.7614795488390172357232565467904
y[1] (numeric) = 1.7614795488390172056299744640505
absolute error = 3.00932820827399e-17
relative error = 1.7084093938288547605129900361085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.277
y[1] (analytic) = 1.7608309792713468231416411663746
y[1] (numeric) = 1.7608309792713467930113488910948
absolute error = 3.01302922752798e-17
relative error = 1.7111405143353440838606182245907e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.278
y[1] (analytic) = 1.760181648872760541792695170537
y[1] (numeric) = 1.7601816488727605116254242376528
absolute error = 3.01672709328842e-17
relative error = 1.7138725967404357484274622600058e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.279
y[1] (analytic) = 1.7595315582925887361518351630624
y[1] (numeric) = 1.7595315582925887059476171444879
absolute error = 3.02042180185745e-17
relative error = 1.7166056429180513308346691851842e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.28
y[1] (analytic) = 1.7588807081809219322166535763009
y[1] (numeric) = 1.7588807081809219019755200808972
absolute error = 3.02411334954037e-17
relative error = 1.7193396547443988154351450849256e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.281
y[1] (analytic) = 1.758229099188610187416446847784
y[1] (numeric) = 1.7582290991886101571384295213277
absolute error = 3.02780173264563e-17
memory used=114.4MB, alloc=4.3MB, time=7.35
relative error = 1.7220746340979704036383216933838e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.282
y[1] (analytic) = 1.7575767319672624397622122284313
y[1] (numeric) = 1.7575767319672624094473427535828
absolute error = 3.03148694748485e-17
relative error = 1.7248105828595573887895203408196e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.283
y[1] (analytic) = 1.7569236071692458562377640722962
y[1] (numeric) = 1.7569236071692458258860741685681
absolute error = 3.03516899037281e-17
relative error = 1.7275475029122479903465747936825e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.284
y[1] (analytic) = 1.7562697254476851804326212166805
y[1] (numeric) = 1.7562697254476851500441426404058
absolute error = 3.03884785762747e-17
relative error = 1.7302853961414422663514790931362e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.285
y[1] (analytic) = 1.7556150874564620794173178196754
y[1] (numeric) = 1.7556150874564620489920823639758
absolute error = 3.04252354556996e-17
relative error = 1.7330242644348499726554245053318e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.286
y[1] (analytic) = 1.7549596938502144898617907797647
y[1] (numeric) = 1.7549596938502144593998302745188
absolute error = 3.04619605052459e-17
relative error = 1.7357641096824998150917007766846e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.287
y[1] (analytic) = 1.7543035452843359633974976190476
y[1] (numeric) = 1.7543035452843359328988439308589
absolute error = 3.04986536881887e-17
relative error = 1.7385049337767544240944253076407e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.288
y[1] (analytic) = 1.753646642414975011223919467908
y[1] (numeric) = 1.7536466424149749806886045000734
absolute error = 3.05353149678346e-17
relative error = 1.7412467386122854475837747924403e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.289
y[1] (analytic) = 1.7529889858990344479601045445751
y[1] (numeric) = 1.7529889858990344173881602370526
absolute error = 3.05719443075225e-17
relative error = 1.7439895260861227483223223395789e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.29
y[1] (analytic) = 1.7523305763941707347419082779736
y[1] (numeric) = 1.7523305763941707041333666073507
absolute error = 3.06085416706229e-17
relative error = 1.7467332980976181131765546339510e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.291
y[1] (analytic) = 1.7516714145587933215655869765725
y[1] (numeric) = 1.7516714145587932909204799560338
absolute error = 3.06451070205387e-17
relative error = 1.7494780565484945144941201558664e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.292
y[1] (analytic) = 1.7510115010520639888784026995802
y[1] (numeric) = 1.7510115010520639581967623788759
absolute error = 3.06816403207043e-17
relative error = 1.7522238033427983974105764969649e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.293
y[1] (analytic) = 1.7503508365338961884168977398298
y[1] (numeric) = 1.7503508365338961576987562052432
absolute error = 3.07181415345866e-17
relative error = 1.7549705403869604103205390420756e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.294
y[1] (analytic) = 1.749689421664954383293497880022
y[1] (numeric) = 1.7496894216649543525388872543377
absolute error = 3.07546106256843e-17
relative error = 1.7577182695897591141926596121900e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.295
y[1] (analytic) = 1.7490272571066533873321043356696
y[1] (numeric) = 1.7490272571066533565410567781414
absolute error = 3.07910475575282e-17
relative error = 1.7604669928623417856345435459830e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.296
y[1] (analytic) = 1.748364343521157703653335049096
y[1] (numeric) = 1.7483643435211576728258827554145
absolute error = 3.08274522936815e-17
relative error = 1.7632167121182452685545713821909e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.297
y[1] (analytic) = 1.7477006815713808625100767491899
y[1] (numeric) = 1.7477006815713808316462519514505
absolute error = 3.08638247977394e-17
relative error = 1.7659674292733768220675511611002e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.298
y[1] (analytic) = 1.7470362719209847583740099413117
y[1] (numeric) = 1.7470362719209847274738449079822
absolute error = 3.09001650333295e-17
relative error = 1.7687191462460407179852449879696e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.299
y[1] (analytic) = 1.7463711152343789862737697407685
y[1] (numeric) = 1.746371115234378955337296776657
absolute error = 3.09364729641115e-17
relative error = 1.7714718649569248172539154911560e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.3
y[1] (analytic) = 1.7457052121767201773854062116435
y[1] (numeric) = 1.7457052121767201464126576578661
absolute error = 3.09727485537774e-17
relative error = 1.7742255873291157587982684808747e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.301
y[1] (analytic) = 1.7450385634139113338758086204636
y[1] (numeric) = 1.7450385634139113028668168544119
absolute error = 3.10089917660517e-17
relative error = 1.7769803152881141844588804656295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.302
y[1] (analytic) = 1.7443711696126011629997587612248
y[1] (numeric) = 1.7443711696126011319545561965336
absolute error = 3.10452025646912e-17
relative error = 1.7797360507618270693114780795141e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.303
y[1] (analytic) = 1.7437030314401834104512792546678
y[1] (numeric) = 1.7437030314401833793698983411826
absolute error = 3.10813809134852e-17
relative error = 1.7824927956805829754232305941348e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.304
y[1] (analytic) = 1.7430341495647961929699434703985
y[1] (numeric) = 1.7430341495647961618524166941434
absolute error = 3.11175267762551e-17
relative error = 1.7852505519771129192867215799553e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.3MB, time=7.60
NO POLE
x[1] = 2.305
y[1] (analytic) = 1.74236452465532133020281446549
y[1] (numeric) = 1.7423645246553212990491743486347
absolute error = 3.11536401168553e-17
relative error = 1.7880093215866058077309852395980e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.306
y[1] (analytic) = 1.7416941573813836758226810775684
y[1] (numeric) = 1.7416941573813836446329601783961
absolute error = 3.11897208991723e-17
relative error = 1.7907691064466606553780122198609e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.307
y[1] (analytic) = 1.7410230484133504479032600540938
y[1] (numeric) = 1.7410230484133504166774909669686
absolute error = 3.12257690871252e-17
relative error = 1.7935299084973191055623177064604e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.308
y[1] (analytic) = 1.7403511984223305585520338425766
y[1] (numeric) = 1.7403511984223305272902491979105
absolute error = 3.12617846446661e-17
relative error = 1.7962917296810922817438054297114e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.309
y[1] (analytic) = 1.7396786080801739428013944088355
y[1] (numeric) = 1.7396786080801739115036268730561
absolute error = 3.12977675357794e-17
relative error = 1.7990545719429244724336237115423e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.31
y[1] (analytic) = 1.7390052780594708867587641920983
y[1] (numeric) = 1.7390052780594708554250464676162
absolute error = 3.13337177244821e-17
relative error = 1.8018184372302142373139067968397e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.311
y[1] (analytic) = 1.7383312090335513550163660467684
y[1] (numeric) = 1.7383312090335513236467308719444
absolute error = 3.13696351748240e-17
relative error = 1.8045833274928298109630688405380e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.312
y[1] (analytic) = 1.7376564016764843173213147610302
y[1] (numeric) = 1.7376564016764842859157949101425
absolute error = 3.14055198508877e-17
relative error = 1.8073492446831130339497712972435e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.313
y[1] (analytic) = 1.7369808566630770745067034821467
y[1] (numeric) = 1.7369808566630770430653317653582
absolute error = 3.14413717167885e-17
relative error = 1.8101161907558775372688245087598e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.314
y[1] (analytic) = 1.7363045746688745836843591173063
y[1] (numeric) = 1.7363045746688745522071683806317
absolute error = 3.14771907366746e-17
relative error = 1.8128841676684242018720944007267e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.315
y[1] (analytic) = 1.7356275563701587826999415172067
y[1] (numeric) = 1.7356275563701587511869646424798
absolute error = 3.15129768747269e-17
relative error = 1.8156531773805336091676690854657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.316
y[1] (analytic) = 1.7349498024439479138510619872218
y[1] (numeric) = 1.7349498024439478823023318920625
absolute error = 3.15487300951593e-17
relative error = 1.8184232218544872943588332679510e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.317
y[1] (analytic) = 1.7342713135679958468690974079753
y[1] (numeric) = 1.7342713135679958152846470457566
absolute error = 3.15844503622187e-17
relative error = 1.8211943030550717525032710306623e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.318
y[1] (analytic) = 1.7335920904207914011653769834506
y[1] (numeric) = 1.7335920904207913695452393432659
absolute error = 3.16201376401847e-17
relative error = 1.8239664229495651501319735850852e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.319
y[1] (analytic) = 1.7329121336815576673424193703953
y[1] (numeric) = 1.7329121336815576356866274770253
absolute error = 3.16557918933700e-17
relative error = 1.8267395835077644012446794959575e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.32
y[1] (analytic) = 1.7322314440302513279708986777247
y[1] (numeric) = 1.7322314440302512962794855916042
absolute error = 3.16914130861205e-17
relative error = 1.8295137867019949895397448873645e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.321
y[1] (analytic) = 1.7315500221475619776330185589022
y[1] (numeric) = 1.7315500221475619459060173760874
absolute error = 3.17270011828148e-17
relative error = 1.8322890345070861640246857280865e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.322
y[1] (analytic) = 1.7308678687149114422329743538675
y[1] (numeric) = 1.7308678687149114104704182060025
absolute error = 3.17625561478650e-17
relative error = 1.8350653289004211840415726393300e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.323
y[1] (analytic) = 1.7301849844144530975751839699906
y[1] (numeric) = 1.7301849844144530657771060242746
absolute error = 3.17980779457160e-17
relative error = 1.8378426718619009883806636567357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.324
y[1] (analytic) = 1.7295013699290711872109689237674
y[1] (numeric) = 1.7295013699290711553774023829213
absolute error = 3.18335665408461e-17
relative error = 1.8406210653739829457096400948187e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.325
y[1] (analytic) = 1.7288170259423801395543676965162
y[1] (numeric) = 1.7288170259423801076853457987495
absolute error = 3.18690218977667e-17
relative error = 1.8434005114216676393453818903410e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.326
y[1] (analytic) = 1.7281319531387238842677642882063
y[1] (numeric) = 1.7281319531387238523633203071839
absolute error = 3.19044439810224e-17
relative error = 1.8461810119925087681976373132865e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.327
y[1] (analytic) = 1.7274461522031751679180155837332
y[1] (numeric) = 1.7274461522031751359781828285421
absolute error = 3.19398327551911e-17
relative error = 1.8489625690766230723895419110694e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.3MB, time=7.85
NO POLE
x[1] = 2.328
y[1] (analytic) = 1.7267596238215348689037618754551
y[1] (numeric) = 1.726759623821534836928573690571
absolute error = 3.19751881848841e-17
relative error = 1.8517451846667002836628581843474e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.329
y[1] (analytic) = 1.7260723686803313116546056146241
y[1] (numeric) = 1.7260723686803312796440953798782
absolute error = 3.20105102347459e-17
relative error = 1.8545288607579957201766590780771e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.33
y[1] (analytic) = 1.7253843874668195801028441924754
y[1] (numeric) = 1.7253843874668195480570453230208
absolute error = 3.20457988694546e-17
relative error = 1.8573135993483576395854435743775e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.331
y[1] (analytic) = 1.724695680868980830428443279185
y[1] (numeric) = 1.7246956808689807983473892254635
absolute error = 3.20810540537215e-17
relative error = 1.8600994024382082736995054472549e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.332
y[1] (analytic) = 1.7240062495755216030779379756651
y[1] (numeric) = 1.7240062495755215709616622233738
absolute error = 3.21162757522913e-17
relative error = 1.8628862720305596214628852408134e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.333
y[1] (analytic) = 1.723316094275873134057949759239
y[1] (numeric) = 1.7233160942758731019064858292967
absolute error = 3.21514639299423e-17
relative error = 1.8656742101310292808766997044846e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.334
y[1] (analytic) = 1.7226252156601906655040079296206
y[1] (numeric) = 1.7226252156601906333173893781341
absolute error = 3.21866185514865e-17
relative error = 1.8684632187478505149740861204945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.335
y[1] (analytic) = 1.7219336144193527555253649863199
y[1] (numeric) = 1.7219336144193527233036254045506
absolute error = 3.22217395817693e-17
relative error = 1.8712532998918591134515228264796e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.336
y[1] (analytic) = 1.7212412912449605873264960926017
y[1] (numeric) = 1.7212412912449605550696691069323
absolute error = 3.22568269856694e-17
relative error = 1.8740444555764918432264235883794e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.337
y[1] (analytic) = 1.720548246829337277605973504441
y[1] (numeric) = 1.7205482468293372453140927763413
absolute error = 3.22918807280997e-17
relative error = 1.8768366878178430172391327962151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.338
y[1] (analytic) = 1.719854481865527184233407565541
y[1] (numeric) = 1.7198544818655271519065067915348
absolute error = 3.23269007740062e-17
relative error = 1.8796299986346049121821875250312e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.339
y[1] (analytic) = 1.7191599970472952132051465914183
y[1] (numeric) = 1.7191599970472951808432595030493
absolute error = 3.23618870883690e-17
relative error = 1.8824243900481301957202914458698e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.34
y[1] (analytic) = 1.718464793069126124879428686794
y[1] (numeric) = 1.7184647930691260924825890505922
absolute error = 3.23968396362018e-17
relative error = 1.8852198640824072188310813668119e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.341
y[1] (analytic) = 1.7177688706262238394916792610841
y[1] (numeric) = 1.717768870626223807059920878532
absolute error = 3.24317583825521e-17
relative error = 1.8880164227640759997666827065501e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.342
y[1] (analytic) = 1.717072230414510741950648726632
y[1] (numeric) = 1.717072230414510709484005434131
absolute error = 3.24666432925010e-17
relative error = 1.8908140681224209523974718443553e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.343
y[1] (analytic) = 1.7163748731306269859160855834886
y[1] (numeric) = 1.7163748731306269534145912523249
absolute error = 3.25014943311637e-17
relative error = 1.8936128021894043814505814650843e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.344
y[1] (analytic) = 1.7156767994719297971586408130075
y[1] (numeric) = 1.7156767994719297646223293493184
absolute error = 3.25363114636891e-17
relative error = 1.8964126269996476029812950490966e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.345
y[1] (analytic) = 1.7149780101364927762027002202945
y[1] (numeric) = 1.7149780101364927436316055650344
absolute error = 3.25710946552601e-17
relative error = 1.8992135445904528365918104718799e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.346
y[1] (analytic) = 1.71427850582310520025284208262
y[1] (numeric) = 1.7142785058231051676469982115264
absolute error = 3.26058438710936e-17
relative error = 1.9020155570018076520594336785329e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.347
y[1] (analytic) = 1.7135782872312713244046181772782
y[1] (numeric) = 1.713578287231271291764059100838
absolute error = 3.26405590764402e-17
relative error = 1.9048186662763719206134088107812e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.348
y[1] (analytic) = 1.712877355061209682140356978055
y[1] (numeric) = 1.7128773550612096494651167414702
absolute error = 3.26752402365848e-17
relative error = 1.9076228744595172782879477343518e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.349
y[1] (analytic) = 1.7121757100138523851106885244419
y[1] (numeric) = 1.7121757100138523524008012075956
absolute error = 3.27098873168463e-17
relative error = 1.9104281835993141224240759368940e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.35
y[1] (analytic) = 1.7114733527908444222024911820132
y[1] (numeric) = 1.7114733527908443894579908994356
absolute error = 3.27445002825776e-17
relative error = 1.9132345957465361059206336155971e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.3MB, time=8.09
NO POLE
x[1] = 2.351
y[1] (analytic) = 1.7107702840945429578939612259616
y[1] (numeric) = 1.7107702840945429251148821267959
absolute error = 3.27790790991657e-17
relative error = 1.9160421129546704887655566086162e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.352
y[1] (analytic) = 1.7100665046280166298975068926636
y[1] (numeric) = 1.7100665046280165970838831606318
absolute error = 3.28136237320318e-17
relative error = 1.9188507372799285159830912057499e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.353
y[1] (analytic) = 1.7093620150950448460911692563224
y[1] (numeric) = 1.7093620150950448132430351096912
absolute error = 3.28481341466312e-17
relative error = 1.9216604707812441218398741572165e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.354
y[1] (analytic) = 1.7086568162001170807392729992091
y[1] (numeric) = 1.7086568162001170478566626907555
absolute error = 3.28826103084536e-17
relative error = 1.9244713155202960419242022875810e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.355
y[1] (analytic) = 1.7079509086484321700030108547919
y[1] (numeric) = 1.7079509086484321370859586717691
absolute error = 3.29170521830228e-17
relative error = 1.9272832735614948510651299675415e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.356
y[1] (analytic) = 1.7072442931458976067416662131113
y[1] (numeric) = 1.7072442931458975737902064772144
absolute error = 3.29514597358969e-17
relative error = 1.9300963469719992569311536194904e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.357
y[1] (analytic) = 1.7065369703991288346051790871192
y[1] (numeric) = 1.7065369703991288016193461544508
absolute error = 3.29858329326684e-17
relative error = 1.9329105378217265751020584906817e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.358
y[1] (analytic) = 1.705828941115448541418761347357
y[1] (numeric) = 1.705828941115448508398589608393
absolute error = 3.30201717389640e-17
relative error = 1.9357258481833456442926173103125e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.359
y[1] (analytic) = 1.7051202060028859518602678402994
y[1] (numeric) = 1.7051202060028859188057917198544
absolute error = 3.30544761204450e-17
relative error = 1.9385422801323049128774703604949e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.36
y[1] (analytic) = 1.7044107657701761194310307129327
y[1] (numeric) = 1.7044107657701760863422846701257
absolute error = 3.30887460428070e-17
relative error = 1.9413598357468195263864408627538e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.361
y[1] (analytic) = 1.7037006211267592177208649726753
y[1] (numeric) = 1.7037006211267591845978835008951
absolute error = 3.31229814717802e-17
relative error = 1.9441785171078936010211691464802e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.362
y[1] (analytic) = 1.702989772782779830967954017575
y[1] (numeric) = 1.7029897727827797978107716444461
absolute error = 3.31571823731289e-17
relative error = 1.9469983262992955774748763591466e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.363
y[1] (analytic) = 1.7022782214490862439143245768393
y[1] (numeric) = 1.7022782214490862107229758641869
absolute error = 3.31913487126524e-17
relative error = 1.9498192654076157564764533879209e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.364
y[1] (analytic) = 1.7015659678372297309576212061635
y[1] (numeric) = 1.7015659678372296977321407499792
absolute error = 3.32254804561843e-17
relative error = 1.9526413365222299484124340913123e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.365
y[1] (analytic) = 1.7008530126594638445998911860238
y[1] (numeric) = 1.7008530126594638113403136164309
absolute error = 3.32595775695929e-17
relative error = 1.9554645417353277058655415529353e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.366
y[1] (analytic) = 1.7001393566287437031940913740907
y[1] (numeric) = 1.7001393566287436699004513553096
absolute error = 3.32936400187811e-17
relative error = 1.9582888831419112185351548827774e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.367
y[1] (analytic) = 1.6994250004587252779890292651966
y[1] (numeric) = 1.6994250004587252446613614955103
absolute error = 3.33276677696863e-17
relative error = 1.9611143628397942061215042728735e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.368
y[1] (analytic) = 1.6987099448637646794734512138577
y[1] (numeric) = 1.6987099448637646461117904255767
absolute error = 3.33616607882810e-17
relative error = 1.9639409829296420168451095153075e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.369
y[1] (analytic) = 1.6979941905589174430199914752009
y[1] (numeric) = 1.6979941905589174096243724346288
absolute error = 3.33956190405721e-17
relative error = 1.9667687455149352670901400749820e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.37
y[1] (analytic) = 1.6972777382599378138296964202892
y[1] (numeric) = 1.697277738259937780400153927688
absolute error = 3.34295424926012e-17
relative error = 1.9695976527019923076564517203065e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.371
y[1] (analytic) = 1.6965605886832780311778389812606
y[1] (numeric) = 1.6965605886832779977144078708156
absolute error = 3.34634311104450e-17
relative error = 1.9724277065999976418135049667587e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.372
y[1] (analytic) = 1.6958427425460876119617390804061
y[1] (numeric) = 1.6958427425460875784644542201912
absolute error = 3.34972848602149e-17
relative error = 1.9752589093209832419725360019295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.373
y[1] (analytic) = 1.6951242005662126335513064953075
y[1] (numeric) = 1.6951242005662126000202027872505
absolute error = 3.35311037080570e-17
relative error = 1.9780912629798334166802400282223e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.3MB, time=8.33
x[1] = 2.374
y[1] (analytic) = 1.6944049634621950159430233094326
y[1] (numeric) = 1.6944049634621949823781356892801
absolute error = 3.35648876201525e-17
relative error = 1.9809247696943132976937621776215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.375
y[1] (analytic) = 1.6936850319532718032180837941439
y[1] (numeric) = 1.6936850319532717696194472314263
absolute error = 3.35986365627176e-17
relative error = 1.9837594315850678788351536253004e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.376
y[1] (analytic) = 1.6929644067593744443054102639229
y[1] (numeric) = 1.6929644067593744106730597619196
absolute error = 3.36323505020033e-17
relative error = 1.9865952507756151462658099733841e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.377
y[1] (analytic) = 1.6922430886011280730502641417332
y[1] (numeric) = 1.6922430886011280393842347374375
absolute error = 3.36660294042957e-17
relative error = 1.9894322293923687383861687345487e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.378
y[1] (analytic) = 1.6915210781998507875891721658513
y[1] (numeric) = 1.6915210781998507538894989299355
absolute error = 3.36996732359158e-17
relative error = 1.9922703695646311050886812405926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.379
y[1] (analytic) = 1.69079837627755292903188836318
y[1] (numeric) = 1.6907983762775528952986063999602
absolute error = 3.37332819632198e-17
relative error = 1.9951096734246162218937117816716e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.38
y[1] (analytic) = 1.6900749835569363594511131070202
y[1] (numeric) = 1.6900749835569363256842575544211
absolute error = 3.37668555525991e-17
relative error = 1.9979501431074546122270503934084e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.381
y[1] (analytic) = 1.6893509007613937391806912695238
y[1] (numeric) = 1.6893509007613937053802972990438
absolute error = 3.38003939704800e-17
relative error = 2.0007917807511806248967368167435e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.382
y[1] (analytic) = 1.6886261286150078034230121705686
y[1] (numeric) = 1.6886261286150077695891149872446
absolute error = 3.38338971833240e-17
relative error = 2.0036345884967552112081494978619e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.383
y[1] (analytic) = 1.6879006678425506381663347155952
y[1] (numeric) = 1.687900667842550604298969557967
absolute error = 3.38673651576282e-17
relative error = 2.0064785684880946857598949482916e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.384
y[1] (analytic) = 1.6871745191694829554127618050192
y[1] (numeric) = 1.6871745191694829215119639450949
absolute error = 3.39007978599243e-17
relative error = 2.0093237228720165830495674146530e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.385
y[1] (analytic) = 1.6864476833219533677175887871863
y[1] (numeric) = 1.6864476833219533337833935304066
absolute error = 3.39341952567797e-17
relative error = 2.0121700537983098967910007329299e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.386
y[1] (analytic) = 1.685720161026797662040751415459
y[1] (numeric) = 1.6857201610267976280731941006619
absolute error = 3.39675573147971e-17
relative error = 2.0150175634197165186121897813111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.387
y[1] (analytic) = 1.6849919530115380729110994579277
y[1] (numeric) = 1.6849919530115380389102154573133
absolute error = 3.40008840006144e-17
relative error = 2.0178662538919304334729649455768e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.388
y[1] (analytic) = 1.684263060004382554904222795412
y[1] (numeric) = 1.6842630600043825208700475145071
absolute error = 3.40341752809049e-17
relative error = 2.0207161273736147253778377528882e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.389
y[1] (analytic) = 1.6835334827342240544345575298648
y[1] (numeric) = 1.6835334827342240203671264074875
absolute error = 3.40674311223773e-17
relative error = 2.0235671860264067479086603212697e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.39
y[1] (analytic) = 1.682803221930639780862500311013
y[1] (numeric) = 1.6828032219306397467618488192373
absolute error = 3.41006514917757e-17
relative error = 2.0264194320149233086440113397971e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.391
y[1] (analytic) = 1.6820722783238904769172597740602
y[1] (numeric) = 1.6820722783238904427834234181802
absolute error = 3.41338363558800e-17
relative error = 2.0292728675067896476847890812357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.392
y[1] (analytic) = 1.6813406526449196884361746655369
y[1] (numeric) = 1.6813406526449196542691889840319
absolute error = 3.41669856815050e-17
relative error = 2.0321274946725911729594986966783e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.393
y[1] (analytic) = 1.6806083456253530334212289179227
y[1] (numeric) = 1.6806083456253529992211294824212
absolute error = 3.42000994355015e-17
relative error = 2.0349833156859440743608854194836e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.394
y[1] (analytic) = 1.6798753579974974704134946164617
y[1] (numeric) = 1.6798753579974974361803170317058
absolute error = 3.42331775847559e-17
relative error = 2.0378403327234768305501951863759e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.395
y[1] (analytic) = 1.6791416904943405661862344836678
y[1] (numeric) = 1.679141690494340531920014387478
absolute error = 3.42662200961898e-17
relative error = 2.0406985479648116677894218752080e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.396
y[1] (analytic) = 1.6784073438495497627573961883579
y[1] (numeric) = 1.678407343849549728458169251597
absolute error = 3.42992269367609e-17
relative error = 2.0435579635926234248183333240913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.3MB, time=8.58
x[1] = 2.397
y[1] (analytic) = 1.6776723187974716437222314666549
y[1] (numeric) = 1.6776723187974716093900333931927
absolute error = 3.43321980734622e-17
relative error = 2.0464185817925972417661001775280e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.398
y[1] (analytic) = 1.6769366160731311999067737222834
y[1] (numeric) = 1.6769366160731311655416402489606
absolute error = 3.43651334733228e-17
relative error = 2.0492804047534815502263080014867e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.399
y[1] (analytic) = 1.6762002364122310943429084526159
y[1] (numeric) = 1.6762002364122310599448753492088
absolute error = 3.43980331034071e-17
relative error = 2.0521434346670457491682329505082e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.4
y[1] (analytic) = 1.6754631805511509265657715253413
y[1] (numeric) = 1.6754631805511508921348745945258
absolute error = 3.44308969308155e-17
relative error = 2.0550076737281272970289755587726e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.401
y[1] (analytic) = 1.6747254492269464962342110082933
y[1] (numeric) = 1.6747254492269464617704860856091
absolute error = 3.44637249226842e-17
relative error = 2.0578731241346251882168043903163e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.402
y[1] (analytic) = 1.6739870431773490660750489319168
y[1] (numeric) = 1.6739870431773490315785318857316
absolute error = 3.44965170461852e-17
relative error = 2.0607397880875053601947065238097e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.403
y[1] (analytic) = 1.6732479631407646241518800400492
y[1] (numeric) = 1.6732479631407645896226067715228
absolute error = 3.45292732685264e-17
relative error = 2.0636076677908120915169395069827e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.404
y[1] (analytic) = 1.6725082098562731454591452601561
y[1] (numeric) = 1.6725082098562731108971517032045
absolute error = 3.45619935569516e-17
relative error = 2.0664767654516734512652279701261e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.405
y[1] (analytic) = 1.6717677840636278528422182988858
y[1] (numeric) = 1.6717677840636278182475404201454
absolute error = 3.45946778787404e-17
relative error = 2.0693470832803007814783726966927e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.406
y[1] (analytic) = 1.6710266865032544772442444427958
y[1] (numeric) = 1.6710266865032544426169182415872
absolute error = 3.46273262012086e-17
relative error = 2.0722186234900181001057592585121e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.407
y[1] (analytic) = 1.6702849179162505172804713173498
y[1] (numeric) = 1.6702849179162504826205328256419
absolute error = 3.46599384917079e-17
relative error = 2.0750913882972496734031117529210e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.408
y[1] (analytic) = 1.6695424790443844981408120297924
y[1] (numeric) = 1.6695424790443844634482973121664
absolute error = 3.46925147176260e-17
relative error = 2.0779653799215315140587093869160e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.409
y[1] (analytic) = 1.668799370630095229821381793278
y[1] (numeric) = 1.6687993706300951950963269468915
absolute error = 3.47250548463865e-17
relative error = 2.0808406005855109254699744854886e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.41
y[1] (analytic) = 1.6680555934164910646857498006547
y[1] (numeric) = 1.6680555934164910299281909552052
absolute error = 3.47575588454495e-17
relative error = 2.0837170525149880099315012544749e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.411
y[1] (analytic) = 1.6673111481473491543566487865884
y[1] (numeric) = 1.6673111481473491195666221042775
absolute error = 3.47900266823109e-17
relative error = 2.0865947379388793182108999773604e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.412
y[1] (analytic) = 1.6665660355671147059388853862578
y[1] (numeric) = 1.6665660355671146711164270617549
absolute error = 3.48224583245029e-17
relative error = 2.0894736590892534061865428587057e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.413
y[1] (analytic) = 1.665820256420900237574195067646
y[1] (numeric) = 1.6658202564209002027193413280522
absolute error = 3.48548537395938e-17
relative error = 2.0923538182013244656029614137027e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.414
y[1] (analytic) = 1.665073811454484833328786082513
y[1] (numeric) = 1.6650738114544847984415731873248
absolute error = 3.48872128951882e-17
relative error = 2.0952352175134699607522610602921e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.415
y[1] (analytic) = 1.6643267014143133974143175484422
y[1] (numeric) = 1.6643267014143133624947817895153
absolute error = 3.49195357589269e-17
relative error = 2.0981178592672302873492977993583e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.416
y[1] (analytic) = 1.6635789270474959077430574409217
y[1] (numeric) = 1.6635789270474958727912351424344
absolute error = 3.49518222984873e-17
relative error = 2.1010017457073384862117104838177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.417
y[1] (analytic) = 1.6628304891018066688179669402382
y[1] (numeric) = 1.6628304891018066338338944586557
absolute error = 3.49840724815825e-17
relative error = 2.1038868790816718572153064335939e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.418
y[1] (analytic) = 1.6620813883256835639584582430401
y[1] (numeric) = 1.6620813883256835289421719670774
absolute error = 3.50162862759627e-17
relative error = 2.1067732616413418232057492771111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.419
y[1] (analytic) = 1.6613316254682273068625736127459
y[1] (numeric) = 1.6613316254682272718141099633322
absolute error = 3.50484636494137e-17
relative error = 2.1096608956406094782195652595211e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.42
y[1] (analytic) = 1.6605812012792006925063341065602
y[1] (numeric) = 1.6605812012792006574257295368018
absolute error = 3.50806045697584e-17
relative error = 2.1125497833369815665751407421305e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.3MB, time=8.83
NO POLE
x[1] = 2.421
y[1] (analytic) = 1.6598301165090278473810070796829
y[1] (numeric) = 1.659830116509027812268298074827
absolute error = 3.51127090048559e-17
relative error = 2.1154399269911621290885494239186e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.422
y[1] (analytic) = 1.6590783719087934790690422293838
y[1] (numeric) = 1.6590783719087934439242653067821
absolute error = 3.51447769226017e-17
relative error = 2.1183313288670703198613079369456e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.423
y[1] (analytic) = 1.6583259682302421251594266029431
y[1] (numeric) = 1.6583259682302420899826183120153
absolute error = 3.51768082909278e-17
relative error = 2.1212239912318522411991907234590e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.424
y[1] (analytic) = 1.6575729062257774015032096540404
y[1] (numeric) = 1.6575729062257773662944065762375
absolute error = 3.52088030778029e-17
relative error = 2.1241179163558988435581687326712e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.425
y[1] (analytic) = 1.6568191866484612498099500920047
y[1] (numeric) = 1.6568191866484612145691888407724
absolute error = 3.52407612512323e-17
relative error = 2.1270131065128457672197281870015e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.426
y[1] (analytic) = 1.6560648102520131845858369274149
y[1] (numeric) = 1.6560648102520131493131541481572
absolute error = 3.52726827792577e-17
relative error = 2.1299095639795671450211407476305e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.427
y[1] (analytic) = 1.6553097777908095394142377758687
y[1] (numeric) = 1.6553097777908095041096701459111
absolute error = 3.53045676299576e-17
relative error = 2.1328072910362056349506658178339e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.428
y[1] (analytic) = 1.6545540900198827125794281393073
y[1] (numeric) = 1.6545540900198826772430123678601
absolute error = 3.53364157714472e-17
relative error = 2.1357062899661723151538223718110e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.429
y[1] (analytic) = 1.6537977476949204120342560411039
y[1] (numeric) = 1.6537977476949203766660288692256
absolute error = 3.53682271718783e-17
relative error = 2.1386065630561465784980649427675e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.43
y[1] (analytic) = 1.6530407515722648997124970471899
y[1] (numeric) = 1.6530407515722648643124952477504
absolute error = 3.54000017994395e-17
relative error = 2.1415081125960941750017978427866e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.431
y[1] (analytic) = 1.6522831024089122351866553607985
y[1] (numeric) = 1.6522831024089121997549157384423
absolute error = 3.54317396223562e-17
relative error = 2.1444109408792731991556358197795e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.432
y[1] (analytic) = 1.6515248009625115186719673329637
y[1] (numeric) = 1.651524800962511483208526724073
absolute error = 3.54634406088907e-17
relative error = 2.1473150502022461485063162752835e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.433
y[1] (analytic) = 1.6507658479913641333773643847066
y[1] (numeric) = 1.6507658479913640978822596573648
absolute error = 3.54951047273418e-17
relative error = 2.1502204428648617262609163395026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.434
y[1] (analytic) = 1.6500062442544229872041529898842
y[1] (numeric) = 1.6500062442544229516774210438386
absolute error = 3.55267319460456e-17
relative error = 2.1531271211703093203576820086343e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.435
y[1] (analytic) = 1.6492459905112917537931700199558
y[1] (numeric) = 1.6492459905112917182348477865812
absolute error = 3.55583222333746e-17
relative error = 2.1560350874250705553698663389067e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.436
y[1] (analytic) = 1.6484850875222241129211724034511
y[1] (numeric) = 1.6484850875222240773312968457122
absolute error = 3.55898755577389e-17
relative error = 2.1589443439389980997385111224673e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.437
y[1] (analytic) = 1.6477235360481229902472207036835
y[1] (numeric) = 1.6477235360481229546258288160986
absolute error = 3.56213918875849e-17
relative error = 2.1618548930252429665282391615112e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.438
y[1] (analytic) = 1.6469613368505397964098168682653
y[1] (numeric) = 1.646961336850539760756945676869
absolute error = 3.56528711913963e-17
relative error = 2.1647667370003212633019596132731e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.439
y[1] (analytic) = 1.6461984906916736654755570532208
y[1] (numeric) = 1.6461984906916736297912436155269
absolute error = 3.56843134376939e-17
relative error = 2.1676798781841082317350375284355e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.44
y[1] (analytic) = 1.6454349983343706927400610729825
y[1] (numeric) = 1.6454349983343706570243424779472
absolute error = 3.57157185950353e-17
relative error = 2.1705943188998261929103710947943e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.441
y[1] (analytic) = 1.6446708605421231718819406752776
y[1] (numeric) = 1.6446708605421231361348540432621
absolute error = 3.57470866320155e-17
relative error = 2.1735100614740871807969869374817e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.442
y[1] (analytic) = 1.6439060780790688314705694868712
y[1] (numeric) = 1.6439060780790687956921519696048
absolute error = 3.57784175172664e-17
relative error = 2.1764271082368687803895571015089e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.443
y[1] (analytic) = 1.6431406517099900708284181223353
y[1] (numeric) = 1.6431406517099900350187069028781
absolute error = 3.58097112194572e-17
relative error = 2.1793454615215446711108889224944e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.3MB, time=9.08
NO POLE
x[1] = 2.444
y[1] (analytic) = 1.642374582200313195248718593442
y[1] (numeric) = 1.642374582200313159407750886148
absolute error = 3.58409677072940e-17
relative error = 2.1822651236648665451635993237834e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.445
y[1] (analytic) = 1.6416078703161076505692228014556
y[1] (numeric) = 1.641607870316107614697035851935
absolute error = 3.58721869495206e-17
relative error = 2.1851860970070190738172943915225e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.446
y[1] (analytic) = 1.6408405168240852571028205384981
y[1] (numeric) = 1.6408405168240852211994516235806
absolute error = 3.59033689149175e-17
relative error = 2.1881083838915653274202075131455e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.447
y[1] (analytic) = 1.6400725224915994429257830673099
y[1] (numeric) = 1.6400725224915994069912694950071
absolute error = 3.59345135723028e-17
relative error = 2.1910319866655078902191768854794e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.448
y[1] (analytic) = 1.6393038880866444765243989910949
y[1] (numeric) = 1.6393038880866444405587781005629
absolute error = 3.59656208905320e-17
relative error = 2.1939569076792830446925892703332e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.449
y[1] (analytic) = 1.638534614377854698800769766752
y[1] (numeric) = 1.6385346143778546628040789282544
absolute error = 3.59966908384976e-17
relative error = 2.1968831492867427329953075389743e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.45
y[1] (analytic) = 1.6377647021345037544385328556338
y[1] (numeric) = 1.637764702134503718410809470504
absolute error = 3.60277233851298e-17
relative error = 2.1998107138452036316592388388470e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.451
y[1] (analytic) = 1.6369941521265038226292811460435
y[1] (numeric) = 1.6369941521265037865705626466476
absolute error = 3.60587184993959e-17
relative error = 2.2027396037154169502940850171118e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.452
y[1] (analytic) = 1.6362229651244048471604479209885
y[1] (numeric) = 1.6362229651244048110707717706877
absolute error = 3.60896761503008e-17
relative error = 2.2056698212616053723457777647501e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.453
y[1] (analytic) = 1.6354511418993937658654272832402
y[1] (numeric) = 1.6354511418993937297448309763532
absolute error = 3.61205963068870e-17
relative error = 2.2086013688514695270698638461252e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.454
y[1] (analytic) = 1.6346786832232937394367005875158
y[1] (numeric) = 1.6346786832232937032852216492815
absolute error = 3.61514789382343e-17
relative error = 2.2115342488561761269878685104108e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.455
y[1] (analytic) = 1.6339055898685633796027400665917
y[1] (numeric) = 1.6339055898685633434204160531316
absolute error = 3.61823240134601e-17
relative error = 2.2144684636503827928261869588192e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.456
y[1] (analytic) = 1.6331318626082959766694614743798
y[1] (numeric) = 1.6331318626082959404563299726606
absolute error = 3.62131315017192e-17
relative error = 2.2174040156122323321938662503187e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.457
y[1] (analytic) = 1.6323575022162187264269982044508
y[1] (numeric) = 1.6323575022162186901830968322467
absolute error = 3.62439013722041e-17
relative error = 2.2203409071233776317879276564427e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.458
y[1] (analytic) = 1.631582509466691956422569977165
y[1] (numeric) = 1.6315825094666919201479363830199
absolute error = 3.62746335941451e-17
relative error = 2.2232791405689943616663066671422e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.459
y[1] (analytic) = 1.6308068851347083516002198224772
y[1] (numeric) = 1.6308068851347083152948916856674
absolute error = 3.63053281368098e-17
relative error = 2.2262187183377569234086025457838e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.46
y[1] (analytic) = 1.6300306299958921793081937186159
y[1] (numeric) = 1.6300306299958921429722087491121
absolute error = 3.63359849695038e-17
relative error = 2.2291596428218879470419051271808e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.461
y[1] (analytic) = 1.6292537448264985136747378791905
y[1] (numeric) = 1.6292537448264984773081338176202
absolute error = 3.63666040615703e-17
relative error = 2.2321019164171404130348277092522e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.462
y[1] (analytic) = 1.6284762304034124593530893128656
y[1] (numeric) = 1.6284762304034124229559039304755
absolute error = 3.63971853823901e-17
relative error = 2.2350455415228042851617970648964e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.463
y[1] (analytic) = 1.6276980875041483746364359105474
y[1] (numeric) = 1.6276980875041483382087070091656
absolute error = 3.64277289013818e-17
relative error = 2.2379905205417254487546362651211e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.464
y[1] (analytic) = 1.6269193169068490939436229450571
y[1] (numeric) = 1.626919316906849057485388357055
absolute error = 3.64582345880021e-17
relative error = 2.2409368558803308489700486274384e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.465
y[1] (analytic) = 1.6261399193902851496763834975192
y[1] (numeric) = 1.626139919390285113187681085774
absolute error = 3.64887024117452e-17
relative error = 2.2438845499485983546332133728877e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.466
y[1] (analytic) = 1.6253598957338539934488709531707
y[1] (numeric) = 1.6253598957338539569297386110275
absolute error = 3.65191323421432e-17
relative error = 2.2468336051600880592898753857184e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=9.32
NO POLE
x[1] = 2.467
y[1] (analytic) = 1.6245792467175792166902723369937
y[1] (numeric) = 1.6245792467175791801407479882273
absolute error = 3.65495243487664e-17
relative error = 2.2497840239319675159660446854096e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.468
y[1] (analytic) = 1.6237979731221097706212818864913
y[1] (numeric) = 1.6237979731221097340414034852687
absolute error = 3.65798784012226e-17
relative error = 2.2527358086849754597711458598830e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.469
y[1] (analytic) = 1.6230160757287191856052148850713
y[1] (numeric) = 1.6230160757287191489950204159135
absolute error = 3.66101944691578e-17
relative error = 2.2556889618434716838813519953293e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.47
y[1] (analytic) = 1.6222335553193047898745424048558
y[1] (numeric) = 1.6222335553193047532340698825998
absolute error = 3.66404725222560e-17
relative error = 2.2586434858354315796123533672890e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.471
y[1] (analytic) = 1.6214504126763869276336282323186
y[1] (numeric) = 1.6214504126763868909629157020796
absolute error = 3.66707125302390e-17
relative error = 2.2615993830924406596851233745556e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.472
y[1] (analytic) = 1.6206666485831081765384498739484
y[1] (numeric) = 1.6206666485831081398375354110815
absolute error = 3.67009144628669e-17
relative error = 2.2645566560497322566132248885268e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.473
y[1] (analytic) = 1.61988226382323256455408616215
y[1] (numeric) = 1.6198822638232325278230078722122
absolute error = 3.67310782899378e-17
relative error = 2.2675153071461759431169271352160e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.474
y[1] (analytic) = 1.6190972591811447861907546038325
y[1] (numeric) = 1.6190972591811447494295506225448
absolute error = 3.67612039812877e-17
relative error = 2.2704753388242782703625681311476e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.475
y[1] (analytic) = 1.6183116354418494181191822355812
y[1] (numeric) = 1.61831163544184938132789072879
absolute error = 3.67912915067912e-17
relative error = 2.2734367535302329413962990229020e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.476
y[1] (analytic) = 1.6175253933909701341660943699759
y[1] (numeric) = 1.6175253933909700973447535336152
absolute error = 3.68213408363607e-17
relative error = 2.2763995537138783953970654087929e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.477
y[1] (analytic) = 1.616738533814748919690606237503
y[1] (numeric) = 1.6167385338147488828392542975563
absolute error = 3.68513519399467e-17
relative error = 2.2793637418287233052316380871880e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.478
y[1] (analytic) = 1.6159510575000452853423031476038
y[1] (numeric) = 1.6159510575000452484609783600657
absolute error = 3.68813247875381e-17
relative error = 2.2823293203319721481945193481970e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.479
y[1] (analytic) = 1.6151629652343354802017954107127
y[1] (numeric) = 1.6151629652343354432905360615505
absolute error = 3.69112593491622e-17
relative error = 2.2852962916845322763357955131597e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.48
y[1] (analytic) = 1.6143742578057117043045348806656
y[1] (numeric) = 1.6143742578057116673633792857812
absolute error = 3.69411555948844e-17
relative error = 2.2882646583510024232380828919539e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.481
y[1] (analytic) = 1.6135849360028813205486805935955
y[1] (numeric) = 1.6135849360028812835776670987871
absolute error = 3.69710134948084e-17
relative error = 2.2912344227996921627035708319290e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.482
y[1] (analytic) = 1.6127950006151660659878015953853
y[1] (numeric) = 1.6127950006151660289869685763089
absolute error = 3.70008330190764e-17
relative error = 2.2942055875026414232241338540188e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.483
y[1] (analytic) = 1.6120044524325012625092056649077
y[1] (numeric) = 1.6120044524325012254785915270389
absolute error = 3.70306141378688e-17
relative error = 2.2971781549356090412222890257485e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.484
y[1] (analytic) = 1.6112132922454350268986832546588
y[1] (numeric) = 1.6112132922454349898383264332543
absolute error = 3.70603568214045e-17
relative error = 2.3001521275780985182542832900856e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.485
y[1] (analytic) = 1.6104215208451274802924565839752
y[1] (numeric) = 1.6104215208451274432023955440343
absolute error = 3.70900610399409e-17
relative error = 2.3031275079133652240594330771532e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.486
y[1] (analytic) = 1.6096291390233499570171244328196
y[1] (numeric) = 1.6096291390233499198973976690459
absolute error = 3.71197267637737e-17
relative error = 2.3061042984284111942600032061810e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.487
y[1] (analytic) = 1.6088361475724842128183937961245
y[1] (numeric) = 1.6088361475724841756690398328873
absolute error = 3.71493539632372e-17
relative error = 2.3090825016140109896043847381286e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.488
y[1] (analytic) = 1.6080425472855216324793901698958
y[1] (numeric) = 1.6080425472855215953004475611917
absolute error = 3.71789426087041e-17
relative error = 2.3120621199647065365329026675241e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.489
y[1] (analytic) = 1.6072483389560624368293388507008
y[1] (numeric) = 1.6072483389560623996208461801148
absolute error = 3.72084926705860e-17
relative error = 2.3150431559788455036683831823585e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=9.57
NO POLE
x[1] = 2.49
y[1] (analytic) = 1.6064535233783148891434102397918
y[1] (numeric) = 1.6064535233783148519054061204592
absolute error = 3.72380041193326e-17
relative error = 2.3180256121585388670498478587025e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.491
y[1] (analytic) = 1.6056581013470945009345227519563
y[1] (numeric) = 1.6056581013470944636670458265237
absolute error = 3.72674769254326e-17
relative error = 2.3210094910097242233847696936892e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.492
y[1] (analytic) = 1.6048620736578232371378975372216
y[1] (numeric) = 1.6048620736578231998409864778085
absolute error = 3.72969110594131e-17
relative error = 2.3239947950421358239885063955388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.493
y[1] (analytic) = 1.6040654411065287206891598307957
y[1] (numeric) = 1.6040654411065286833628533389557
absolute error = 3.73263064918400e-17
relative error = 2.3269815267693368595464644848306e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.494
y[1] (analytic) = 1.6032682044898434364967823530747
y[1] (numeric) = 1.6032682044898433991411191597568
absolute error = 3.73556631933179e-17
relative error = 2.3299696887087206531725006676028e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.495
y[1] (analytic) = 1.6024703646050039348096667872084
y[1] (numeric) = 1.6024703646050038974246856527184
absolute error = 3.73849811344900e-17
relative error = 2.3329592833815118554064222662579e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.496
y[1] (analytic) = 1.601671922249850033980659966576
y[1] (numeric) = 1.6016719222498499965663996805374
absolute error = 3.74142602860386e-17
relative error = 2.3359503133128051019437564628671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.497
y[1] (analytic) = 1.6008728782228240226268020085877
y[1] (numeric) = 1.6008728782228239851833013899035
absolute error = 3.74435006186842e-17
relative error = 2.3389427810315163330767842446906e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.498
y[1] (analytic) = 1.6000732333229698611871042345008
y[1] (numeric) = 1.600073233322969823714402131314
absolute error = 3.74727021031868e-17
relative error = 2.3419366890704714592409679677121e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.499
y[1] (analytic) = 1.5992729883499323828786553174019
y[1] (numeric) = 1.5992729883499323453767906070572
absolute error = 3.75018647103447e-17
relative error = 2.3449320399663389697457159819390e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.5
y[1] (analytic) = 1.5984721441039564940518547021862
y[1] (numeric) = 1.5984721441039564565208662911907
absolute error = 3.75309884109955e-17
relative error = 2.3479288362596999687841856862503e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.501
y[1] (analytic) = 1.5976707013858863739455729422307
y[1] (numeric) = 1.5976707013858863363854997662154
absolute error = 3.75600731760153e-17
relative error = 2.3509270804950057561938917647177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.502
y[1] (analytic) = 1.5968686609971646738430391975371
y[1] (numeric) = 1.5968686609971646362539202212176
absolute error = 3.75891189763195e-17
relative error = 2.3539267752206354747651682163457e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.503
y[1] (analytic) = 1.5960660237398317156292567383872
y[1] (numeric) = 1.5960660237398316780111309555251
absolute error = 3.76181257828621e-17
relative error = 2.3569279229888599483836334012724e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.504
y[1] (analytic) = 1.5952627904165246897507478970316
y[1] (numeric) = 1.5952627904165246521036543303952
absolute error = 3.76470935666364e-17
relative error = 2.3599305263558931689720490594997e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.505
y[1] (analytic) = 1.5944589618304768525784305075974
y[1] (numeric) = 1.5944589618304768149024082089226
absolute error = 3.76760222986748e-17
relative error = 2.3629345878818874916198857720574e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.506
y[1] (analytic) = 1.5936545387855167231744284712725
y[1] (numeric) = 1.5936545387855166854695165212242
absolute error = 3.77049119500483e-17
relative error = 2.3659401101309099886383413719394e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.507
y[1] (analytic) = 1.59284952208606727946361967989
y[1] (numeric) = 1.5928495220860672417298571880227
absolute error = 3.77337624918673e-17
relative error = 2.3689470956710003446781043934382e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.508
y[1] (analytic) = 1.5920439125371451538107251262958
y[1] (numeric) = 1.5920439125371451160481512310145
absolute error = 3.77625738952813e-17
relative error = 2.3719555470741598318643912846400e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.509
y[1] (analytic) = 1.591237710944359828003743624345
y[1] (numeric) = 1.591237710944359790212397492866
absolute error = 3.77913461314790e-17
relative error = 2.3749654669163653871350437729882e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.51
y[1] (analytic) = 1.590430918113912827644537155024
y[1] (numeric) = 1.590430918113912789824457983336
absolute error = 3.78200791716880e-17
relative error = 2.3779768577775585799177018554280e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.511
y[1] (analytic) = 1.5896235348525969159473724480472
y[1] (numeric) = 1.5896235348525968780985994608718
absolute error = 3.78487729871754e-17
relative error = 2.3809897222416911612698501792458e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.512
y[1] (analytic) = 1.5888155619677952869462250003178
y[1] (numeric) = 1.5888155619677952490687974510705
absolute error = 3.78774275492473e-17
relative error = 2.3840040628967015157953381367292e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=152.5MB, alloc=4.4MB, time=9.82
x[1] = 2.513
y[1] (analytic) = 1.5880070002674807581116523238833
y[1] (numeric) = 1.5880070002674807202056094946341
absolute error = 3.79060428292492e-17
relative error = 2.3870198823345477143649669370199e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.514
y[1] (analytic) = 1.5871978505602149623780438064436
y[1] (numeric) = 1.5871978505602149244434250078778
absolute error = 3.79346187985658e-17
relative error = 2.3900371831512028631835804802074e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.515
y[1] (analytic) = 1.5863881136551475395820551570956
y[1] (numeric) = 1.5863881136551475016188997284745
absolute error = 3.79631554286211e-17
relative error = 2.3930559679466693473122274501687e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.516
y[1] (analytic) = 1.5855777903620153273130359988119
y[1] (numeric) = 1.5855777903620152893213833079334
absolute error = 3.79916526908785e-17
relative error = 2.3960762393249931155719419096977e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.517
y[1] (analytic) = 1.5847668814911415511762597571587
y[1] (numeric) = 1.5847668814911415131561492003179
absolute error = 3.80201105568408e-17
relative error = 2.3990979998942716969285687210760e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.518
y[1] (analytic) = 1.5839553878534350144697655819554
y[1] (numeric) = 1.5839553878534349764212365839054
absolute error = 3.80485289980500e-17
relative error = 2.4021212522666496125964944668875e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.519
y[1] (analytic) = 1.583143310260389287275622624967
y[1] (numeric) = 1.5831433102603892491987146388793
absolute error = 3.80769079860877e-17
relative error = 2.4051459990583516709623593604508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.52
y[1] (analytic) = 1.5823306495240818949664275822971
y[1] (numeric) = 1.5823306495240818568611800897221
absolute error = 3.81052474925750e-17
relative error = 2.4081722428896847636936734185256e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.521
y[1] (analytic) = 1.5815174064571735061278469949155
y[1] (numeric) = 1.5815174064571734679942995057432
absolute error = 3.81335474891723e-17
relative error = 2.4111999863850333419908862948774e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.522
y[1] (analytic) = 1.5807035818729071198980163847122
y[1] (numeric) = 1.5807035818729070817362084371325
absolute error = 3.81618079475797e-17
relative error = 2.4142292321728928342133999374097e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.523
y[1] (analytic) = 1.5798891765851072527246088866095
y[1] (numeric) = 1.5798891765851072145345800470728
absolute error = 3.81900288395367e-17
relative error = 2.4172599828858588574142620934279e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.524
y[1] (analytic) = 1.5790741914081791245403866195961
y[1] (numeric) = 1.5790741914081790863221764827737
absolute error = 3.82182101368224e-17
relative error = 2.4202922411606480571444894131178e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.525
y[1] (analytic) = 1.5782586271571078443580486210646
y[1] (numeric) = 1.5782586271571078061116968098091
absolute error = 3.82463518112555e-17
relative error = 2.4233260096381063370857565773324e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.526
y[1] (analytic) = 1.5774424846474575952851897495358
y[1] (numeric) = 1.5774424846474575570107359148415
absolute error = 3.82744538346943e-17
relative error = 2.4263612909632171116673733801656e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.527
y[1] (analytic) = 1.5766257646953708189601855407438
y[1] (numeric) = 1.5766257646953707806576693617069
absolute error = 3.83025161790369e-17
relative error = 2.4293980877851222670471030082263e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.528
y[1] (analytic) = 1.5758084681175673994098185811278
y[1] (numeric) = 1.5758084681175673610792797649069
absolute error = 3.83305388162209e-17
relative error = 2.4324364027571114549297321977770e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.529
y[1] (analytic) = 1.574990595731343846329462541038
y[1] (numeric) = 1.5749905957313438079709408228145
absolute error = 3.83585217182235e-17
relative error = 2.4354762385366367473861673942731e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.53
y[1] (analytic) = 1.5741721483545724777866405874022
y[1] (numeric) = 1.5741721483545724394001757303402
absolute error = 3.83864648570620e-17
relative error = 2.4385175977853527448047066116961e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.531
y[1] (analytic) = 1.5733531268057006023487754722264
y[1] (numeric) = 1.5733531268057005639344072674332
absolute error = 3.84143682047932e-17
relative error = 2.4415604831690868919655989629797e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.532
y[1] (analytic) = 1.5725335319037497006359491691127
y[1] (numeric) = 1.5725335319037496621937174355989
absolute error = 3.84422317335138e-17
relative error = 2.4446048973578732902959299555778e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.533
y[1] (analytic) = 1.5717133644683146062994905049646
y[1] (numeric) = 1.5717133644683145678294350896044
absolute error = 3.84700554153602e-17
relative error = 2.4476508430259484381973397297107e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.534
y[1] (analytic) = 1.5708926253195626864272098082259
y[1] (numeric) = 1.5708926253195626479293705857171
absolute error = 3.84978392225088e-17
relative error = 2.4506983228517787842608453466377e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.535
y[1] (analytic) = 1.5700713152782330213761001683481
y[1] (numeric) = 1.5700713152782329828505170411724
absolute error = 3.85255831271757e-17
relative error = 2.4537473395180501492267091291167e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=156.4MB, alloc=4.4MB, time=10.06
x[1] = 2.536
y[1] (analytic) = 1.5692494351656355840333254737188
y[1] (numeric) = 1.5692494351656355454800383721018
absolute error = 3.85532871016170e-17
relative error = 2.4567978957116953466941654765766e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.537
y[1] (analytic) = 1.5684269858036504185063159669933
y[1] (numeric) = 1.5684269858036503799253648488644
absolute error = 3.85809511181289e-17
relative error = 2.4598499941239091361078319820796e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.538
y[1] (analytic) = 1.5676039680147268182427926276654
y[1] (numeric) = 1.5676039680147267796342174786182
absolute error = 3.86085751490472e-17
relative error = 2.4629036374501249449387456386149e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.539
y[1] (analytic) = 1.5667803826218825035815422617857
y[1] (numeric) = 1.5667803826218824649453830950377
absolute error = 3.86361591667480e-17
relative error = 2.4659588283900681046897214163502e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.54
y[1] (analytic) = 1.565956230448702798734765747982
y[1] (numeric) = 1.5659562304487027600710626043349
absolute error = 3.86637031436471e-17
relative error = 2.4690155696477262354768072233999e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.541
y[1] (analytic) = 1.5651315123193398082028224573671
y[1] (numeric) = 1.5651315123193397695116154051664
absolute error = 3.86912070522007e-17
relative error = 2.4720738639314025941284195896663e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.542
y[1] (analytic) = 1.5643062290585115926221944325187
y[1] (numeric) = 1.5643062290585115539035235676139
absolute error = 3.87186708649048e-17
relative error = 2.4751337139536864840059923925487e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.543
y[1] (analytic) = 1.5634803814915013440474944775003
y[1] (numeric) = 1.5634803814915013053013999232046
absolute error = 3.87460945542957e-17
relative error = 2.4781951224314939238837660899306e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.544
y[1] (analytic) = 1.5626539704441565606683428768454
y[1] (numeric) = 1.5626539704441565218948647838959
absolute error = 3.87734780929495e-17
relative error = 2.4812580920860444489118522522958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.545
y[1] (analytic) = 1.56182699674288822096193802656
y[1] (numeric) = 1.5618269967428881821611165730771
absolute error = 3.88008214534829e-17
relative error = 2.4843226256429210705874106983495e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.546
y[1] (analytic) = 1.5609994612146699572821468245029
y[1] (numeric) = 1.5609994612146699184540222159505
absolute error = 3.88281246085524e-17
relative error = 2.4873887258320279256531690408312e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.547
y[1] (analytic) = 1.5601713646870372288859412309866
y[1] (numeric) = 1.5601713646870371900305537001317
absolute error = 3.88553875308549e-17
relative error = 2.4904563953876375207278881498828e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.548
y[1] (analytic) = 1.5593427079880864943980079730907
y[1] (numeric) = 1.5593427079880864555153977799632
absolute error = 3.88826101931275e-17
relative error = 2.4935256370483868204587690251504e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.549
y[1] (analytic) = 1.5585134919464743837143589280114
y[1] (numeric) = 1.5585134919464743448045663598639
absolute error = 3.89097925681475e-17
relative error = 2.4965964535572861526393507923031e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.55
y[1] (analytic) = 1.5576837173914168693457702817662
y[1] (numeric) = 1.5576837173914168304088356530337
absolute error = 3.89369346287325e-17
relative error = 2.4996688476617345581760964676961e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.551
y[1] (analytic) = 1.5568533851526884372018791197471
y[1] (numeric) = 1.5568533851526883982378427720065
absolute error = 3.89640363477406e-17
relative error = 2.5027428221135416099398870351315e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.552
y[1] (analytic) = 1.5560224960606212568167666649541
y[1] (numeric) = 1.5560224960606212178256689668842
absolute error = 3.89910976980699e-17
relative error = 2.5058183796689043115671749488294e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.553
y[1] (analytic) = 1.5551910509461043510168579382599
y[1] (numeric) = 1.5551910509461043119987392856008
absolute error = 3.90181186526591e-17
relative error = 2.5088955230884546495810256189016e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.554
y[1] (analytic) = 1.5543590506405827650319681727342
y[1] (numeric) = 1.5543590506405827259868689882469
absolute error = 3.90450991844873e-17
relative error = 2.5119742551372558264160767625150e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.555
y[1] (analytic) = 1.5535264959760567350503268709131
y[1] (numeric) = 1.5535264959760566959782876043392
absolute error = 3.90720392665739e-17
relative error = 2.5150545785848049148032969770041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.556
y[1] (analytic) = 1.5526933877850808562184109499206
y[1] (numeric) = 1.5526933877850808171194720779418
absolute error = 3.90989388719788e-17
relative error = 2.5181364962050548383539333073828e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.557
y[1] (analytic) = 1.5518597269007632500864189745387
y[1] (numeric) = 1.5518597269007632109606210007362
absolute error = 3.91257979738025e-17
relative error = 2.5212200107764299754178340369067e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.558
y[1] (analytic) = 1.5510255141567647315002190326836
y[1] (numeric) = 1.5510255141567646923476024874977
absolute error = 3.91526165451859e-17
relative error = 2.5243051250818224675844508899630e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.559
y[1] (analytic) = 1.5501907503872979749406033612695
y[1] (numeric) = 1.5501907503872979357612088019592
absolute error = 3.91793945593103e-17
relative error = 2.5273918419086014142113782561005e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=10.32
NO POLE
x[1] = 2.56
y[1] (analytic) = 1.5493554364271266803106833831373
y[1] (numeric) = 1.5493554364271266411045513937395
absolute error = 3.92061319893978e-17
relative error = 2.5304801640486479100834726224491e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.561
y[1] (analytic) = 1.5485195731115647381722593675822
y[1] (numeric) = 1.5485195731115646989394305588713
absolute error = 3.92328288087109e-17
relative error = 2.5335700942983385304542995181408e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.562
y[1] (analytic) = 1.5476831612764753944319994780423
y[1] (numeric) = 1.5476831612764753551725144874895
absolute error = 3.92594849905528e-17
relative error = 2.5366616354585739876742574984904e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.563
y[1] (analytic) = 1.5468462017582704144782635206983
y[1] (numeric) = 1.5468462017582703751921630124309
absolute error = 3.92861005082674e-17
relative error = 2.5397547903347884826073181602332e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.564
y[1] (analytic) = 1.546008695393909246769407257092
y[1] (numeric) = 1.5460086953939092074567319218529
absolute error = 3.93126753352391e-17
relative error = 2.5428495617369461460165217161255e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.565
y[1] (analytic) = 1.5451706430208981858744036923889
y[1] (numeric) = 1.5451706430208981465351942474958
absolute error = 3.93392094448931e-17
relative error = 2.5459459524795698233174989201767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.566
y[1] (analytic) = 1.544332045477289534966618298594
y[1] (numeric) = 1.5443320454772894956009154878987
absolute error = 3.93657028106953e-17
relative error = 2.5490439653817440478957896068355e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.567
y[1] (analytic) = 1.543492903601680767771575678876
y[1] (numeric) = 1.5434929036016807283794202727237
absolute error = 3.93921554061523e-17
relative error = 2.5521436032671244989345577135554e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.568
y[1] (analytic) = 1.5426532182332136899695557251634
y[1] (numeric) = 1.5426532182332136505509885203517
absolute error = 3.94185672048117e-17
relative error = 2.5552448689639669330616463742198e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.569
y[1] (analytic) = 1.5418129902115736000538578663454
y[1] (numeric) = 1.541812990211573560608919686084
absolute error = 3.94449381802614e-17
relative error = 2.5583477653050913477546064605526e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.57
y[1] (analytic) = 1.5409722203769884496455725487458
y[1] (numeric) = 1.5409722203769884101743042426153
absolute error = 3.94712683061305e-17
relative error = 2.5614522951279498539036742929542e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.571
y[1] (analytic) = 1.5401309095702280032656996340259
y[1] (numeric) = 1.5401309095702279637681420779368
absolute error = 3.94975575560891e-17
relative error = 2.5645584612746233439622608414234e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.572
y[1] (analytic) = 1.539289058632602997565453942329
y[1] (numeric) = 1.5392890586326029580416480384813
absolute error = 3.95238059038477e-17
relative error = 2.5676662665917921590308181685044e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.573
y[1] (analytic) = 1.5384466684059643000155987102919
y[1] (numeric) = 1.5384466684059642604655853871338
absolute error = 3.95500133231581e-17
relative error = 2.5707757139308041562848508549467e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.574
y[1] (analytic) = 1.5376037397327020670556482745177
y[1] (numeric) = 1.5376037397327020274794684867049
absolute error = 3.95761797878128e-17
relative error = 2.5738868061476454414165283961533e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.575
y[1] (analytic) = 1.5367602734557449017037818312394
y[1] (numeric) = 1.536760273455744862101476559594
absolute error = 3.96023052716454e-17
relative error = 2.5769995461029760724238924768251e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.576
y[1] (analytic) = 1.535916270418559010628310662188
y[1] (numeric) = 1.5359162704185589709999209136577
absolute error = 3.96283897485303e-17
relative error = 2.5801139366621203012338603107251e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.577
y[1] (analytic) = 1.5350717314651473606815417551302
y[1] (numeric) = 1.5350717314651473210271085627469
absolute error = 3.96544331923833e-17
relative error = 2.5832299806951154078976632579088e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.578
y[1] (analytic) = 1.5342266574400488348968812851386
y[1] (numeric) = 1.534226657440048795216445707978
absolute error = 3.96804355771606e-17
relative error = 2.5863476810766564045588517319941e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.579
y[1] (analytic) = 1.5333810491883373879500219594245
y[1] (numeric) = 1.5333810491883373482436250825644
absolute error = 3.97063968768601e-17
relative error = 2.5894670406861905473924307208926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.58
y[1] (analytic) = 1.5325349075556212010850587644716
y[1] (numeric) = 1.5325349075556211613527416989513
absolute error = 3.97323170655203e-17
relative error = 2.5925880624078555535610791853393e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.581
y[1] (analytic) = 1.5316882333880418365063781892878
y[1] (numeric) = 1.5316882333880417967481820720666
absolute error = 3.97581961172212e-17
relative error = 2.5957107491305481837360536607563e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.582
y[1] (analytic) = 1.5308410275322733912371665328125
y[1] (numeric) = 1.5308410275322733514531325267288
absolute error = 3.97840340060837e-17
relative error = 2.5988351037478950621708901816876e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=10.57
NO POLE
x[1] = 2.583
y[1] (analytic) = 1.529993290835521650445383436903
y[1] (numeric) = 1.5299932908355216106355527306333
absolute error = 3.98098307062697e-17
relative error = 2.6019611291582691470306706121151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.584
y[1] (analytic) = 1.529145024145523240238047318855
y[1] (numeric) = 1.5291450241455232004024611268722
absolute error = 3.98355861919828e-17
relative error = 2.6050888282648454883262672772441e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.585
y[1] (analytic) = 1.5282962283105447799246799091
y[1] (numeric) = 1.5282962283105447400633794716326
absolute error = 3.98613004374674e-17
relative error = 2.6082182039755524750603965787347e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.586
y[1] (analytic) = 1.5274469041793820337507576305664
y[1] (numeric) = 1.5274469041793819938637842135573
absolute error = 3.98869734170091e-17
relative error = 2.6113492592031080244021445476336e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.587
y[1] (analytic) = 1.5265970526013590621020180861816
y[1] (numeric) = 1.5265970526013590221894129812463
absolute error = 3.99126051049353e-17
relative error = 2.6144819968650689877544783332139e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.588
y[1] (analytic) = 1.525746674426327372180470450136
y[1] (numeric) = 1.5257466744263273322422749745221
absolute error = 3.99381954756139e-17
relative error = 2.6176164198837561879125598967805e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.589
y[1] (analytic) = 1.5248957705046650681529590868315
y[1] (numeric) = 1.5248957705046650281892145833767
absolute error = 3.99637445034548e-17
relative error = 2.6207525311863628195629358805363e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.59
y[1] (analytic) = 1.5240443416872760007731302488759
y[1] (numeric) = 1.5240443416872759607838780859671
absolute error = 3.99892521629088e-17
relative error = 2.6238903337048926091475361086198e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.591
y[1] (analytic) = 1.5231923888255889164776522320893
y[1] (numeric) = 1.5231923888255888764629338036209
absolute error = 4.00147184284684e-17
relative error = 2.6270298303762225003879312529006e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.592
y[1] (analytic) = 1.5223399127715566059575398912282
y[1] (numeric) = 1.522339912771556565917396616561
absolute error = 4.00401432746672e-17
relative error = 2.6301710241420735814782178511562e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.593
y[1] (analytic) = 1.5214869143776550522054349450348
y[1] (numeric) = 1.5214869143776550121399082689544
absolute error = 4.00655266760804e-17
relative error = 2.6333139179490542071422978403991e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.594
y[1] (analytic) = 1.5206333944968825780396940232579
y[1] (numeric) = 1.5206333944968825379488254159332
absolute error = 4.00908686073247e-17
relative error = 2.6364585147486638033788841426160e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.595
y[1] (analytic) = 1.5197793539827589931061369314874
y[1] (numeric) = 1.5197793539827589529899678884292
absolute error = 4.01161690430582e-17
relative error = 2.6396048174972966798544527792486e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.596
y[1] (analytic) = 1.518924793689324740358308131983
y[1] (numeric) = 1.5189247936893247002168801740027
absolute error = 4.01414279579803e-17
relative error = 2.6427528291562458498961946831797e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.597
y[1] (analytic) = 1.5180697144711400420171049601642
y[1] (numeric) = 1.5180697144711400018504596333322
absolute error = 4.01666453268320e-17
relative error = 2.6459025526917332072877725205072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.598
y[1] (analytic) = 1.5172141171832840450106266170629
y[1] (numeric) = 1.5172141171832840048188054926667
absolute error = 4.01918211243962e-17
relative error = 2.6490539910749397997225731409624e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.599
y[1] (analytic) = 1.5163580026813539658950984978166
y[1] (numeric) = 1.5163580026813539256781431723196
absolute error = 4.02169553254970e-17
relative error = 2.6522071472819702519195094157007e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.6
y[1] (analytic) = 1.5155013718214642352577269352094
y[1] (numeric) = 1.5155013718214641950156790302092
absolute error = 4.02420479050002e-17
relative error = 2.6553620242938962444402861513471e-15 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = cos ( x ) ;
Iterations = 1000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Expected Time Remaining = 1 Minutes 19 Seconds
Optimized Time Remaining = 1 Minutes 19 Seconds
Time to Timeout = 14 Minutes 49 Seconds
Percent Done = 11.92 %
> quit
memory used=167.0MB, alloc=4.4MB, time=10.75