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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_hours,
> glob_dump_analytic,
> glob_hmax,
> sec_in_min,
> glob_no_eqs,
> glob_hmin_init,
> glob_initial_pass,
> glob_almost_1,
> glob_html_log,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_disp_incr,
> centuries_in_millinium,
> hours_in_day,
> glob_current_iter,
> glob_abserr,
> glob_percent_done,
> glob_start,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_clock_sec,
> djd_debug,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> days_in_year,
> min_in_hour,
> glob_normmax,
> glob_iter,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> years_in_century,
> glob_log10_abserr,
> glob_optimal_done,
> glob_display_flag,
> glob_dump,
> glob_log10normmin,
> glob_log10relerr,
> glob_optimal_start,
> glob_relerr,
> glob_h,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_type_pole,
> array_pole,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_set_initial,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE,
glob_max_minutes, glob_warned, glob_max_hours, glob_dump_analytic,
glob_hmax, sec_in_min, glob_no_eqs, glob_hmin_init, glob_initial_pass,
glob_almost_1, glob_html_log, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_disp_incr,
centuries_in_millinium, hours_in_day, glob_current_iter, glob_abserr,
glob_percent_done, glob_start, glob_smallish_float,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_subiter_method,
glob_log10abserr, glob_curr_iter_when_opt, glob_max_iter, glob_log10_relerr,
glob_not_yet_finished, glob_clock_sec, djd_debug, glob_look_poles,
glob_last_good_h, glob_hmin, days_in_year, min_in_hour, glob_normmax,
glob_iter, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2,
years_in_century, glob_log10_abserr, glob_optimal_done, glob_display_flag,
glob_dump, glob_log10normmin, glob_log10relerr, glob_optimal_start,
glob_relerr, glob_h, glob_max_opt_iter, glob_optimal_expect_sec,
array_const_0D0, array_const_1, array_m1, array_y, array_x, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error,
array_1st_rel_error, array_norms, array_type_pole, array_pole,
array_y_higher_work, array_complex_pole, array_y_higher_work2,
array_real_pole, array_poles, array_y_higher, array_y_set_initial,
glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_hours,
> glob_dump_analytic,
> glob_hmax,
> sec_in_min,
> glob_no_eqs,
> glob_hmin_init,
> glob_initial_pass,
> glob_almost_1,
> glob_html_log,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_disp_incr,
> centuries_in_millinium,
> hours_in_day,
> glob_current_iter,
> glob_abserr,
> glob_percent_done,
> glob_start,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_clock_sec,
> djd_debug,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> days_in_year,
> min_in_hour,
> glob_normmax,
> glob_iter,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> years_in_century,
> glob_log10_abserr,
> glob_optimal_done,
> glob_display_flag,
> glob_dump,
> glob_log10normmin,
> glob_log10relerr,
> glob_optimal_start,
> glob_relerr,
> glob_h,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_type_pole,
> array_pole,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_set_initial,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE,
glob_max_minutes, glob_warned, glob_max_hours, glob_dump_analytic,
glob_hmax, sec_in_min, glob_no_eqs, glob_hmin_init, glob_initial_pass,
glob_almost_1, glob_html_log, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_disp_incr,
centuries_in_millinium, hours_in_day, glob_current_iter, glob_abserr,
glob_percent_done, glob_start, glob_smallish_float,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_subiter_method,
glob_log10abserr, glob_curr_iter_when_opt, glob_max_iter, glob_log10_relerr,
glob_not_yet_finished, glob_clock_sec, djd_debug, glob_look_poles,
glob_last_good_h, glob_hmin, days_in_year, min_in_hour, glob_normmax,
glob_iter, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2,
years_in_century, glob_log10_abserr, glob_optimal_done, glob_display_flag,
glob_dump, glob_log10normmin, glob_log10relerr, glob_optimal_start,
glob_relerr, glob_h, glob_max_opt_iter, glob_optimal_expect_sec,
array_const_0D0, array_const_1, array_m1, array_y, array_x, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error,
array_1st_rel_error, array_norms, array_type_pole, array_pole,
array_y_higher_work, array_complex_pole, array_y_higher_work2,
array_real_pole, array_poles, array_y_higher, array_y_set_initial,
glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_hours,
> glob_dump_analytic,
> glob_hmax,
> sec_in_min,
> glob_no_eqs,
> glob_hmin_init,
> glob_initial_pass,
> glob_almost_1,
> glob_html_log,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_disp_incr,
> centuries_in_millinium,
> hours_in_day,
> glob_current_iter,
> glob_abserr,
> glob_percent_done,
> glob_start,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_clock_sec,
> djd_debug,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> days_in_year,
> min_in_hour,
> glob_normmax,
> glob_iter,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> years_in_century,
> glob_log10_abserr,
> glob_optimal_done,
> glob_display_flag,
> glob_dump,
> glob_log10normmin,
> glob_log10relerr,
> glob_optimal_start,
> glob_relerr,
> glob_h,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_type_pole,
> array_pole,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_set_initial,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE,
glob_max_minutes, glob_warned, glob_max_hours, glob_dump_analytic,
glob_hmax, sec_in_min, glob_no_eqs, glob_hmin_init, glob_initial_pass,
glob_almost_1, glob_html_log, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_disp_incr,
centuries_in_millinium, hours_in_day, glob_current_iter, glob_abserr,
glob_percent_done, glob_start, glob_smallish_float,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_subiter_method,
glob_log10abserr, glob_curr_iter_when_opt, glob_max_iter, glob_log10_relerr,
glob_not_yet_finished, glob_clock_sec, djd_debug, glob_look_poles,
glob_last_good_h, glob_hmin, days_in_year, min_in_hour, glob_normmax,
glob_iter, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2,
years_in_century, glob_log10_abserr, glob_optimal_done, glob_display_flag,
glob_dump, glob_log10normmin, glob_log10relerr, glob_optimal_start,
glob_relerr, glob_h, glob_max_opt_iter, glob_optimal_expect_sec,
array_const_0D0, array_const_1, array_m1, array_y, array_x, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error,
array_1st_rel_error, array_norms, array_type_pole, array_pole,
array_y_higher_work, array_complex_pole, array_y_higher_work2,
array_real_pole, array_poles, array_y_higher, array_y_set_initial,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_hours,
> glob_dump_analytic,
> glob_hmax,
> sec_in_min,
> glob_no_eqs,
> glob_hmin_init,
> glob_initial_pass,
> glob_almost_1,
> glob_html_log,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_disp_incr,
> centuries_in_millinium,
> hours_in_day,
> glob_current_iter,
> glob_abserr,
> glob_percent_done,
> glob_start,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_clock_sec,
> djd_debug,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> days_in_year,
> min_in_hour,
> glob_normmax,
> glob_iter,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> years_in_century,
> glob_log10_abserr,
> glob_optimal_done,
> glob_display_flag,
> glob_dump,
> glob_log10normmin,
> glob_log10relerr,
> glob_optimal_start,
> glob_relerr,
> glob_h,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_type_pole,
> array_pole,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_set_initial,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE,
glob_max_minutes, glob_warned, glob_max_hours, glob_dump_analytic,
glob_hmax, sec_in_min, glob_no_eqs, glob_hmin_init, glob_initial_pass,
glob_almost_1, glob_html_log, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_disp_incr,
centuries_in_millinium, hours_in_day, glob_current_iter, glob_abserr,
glob_percent_done, glob_start, glob_smallish_float,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_subiter_method,
glob_log10abserr, glob_curr_iter_when_opt, glob_max_iter, glob_log10_relerr,
glob_not_yet_finished, glob_clock_sec, djd_debug, glob_look_poles,
glob_last_good_h, glob_hmin, days_in_year, min_in_hour, glob_normmax,
glob_iter, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2,
years_in_century, glob_log10_abserr, glob_optimal_done, glob_display_flag,
glob_dump, glob_log10normmin, glob_log10relerr, glob_optimal_start,
glob_relerr, glob_h, glob_max_opt_iter, glob_optimal_expect_sec,
array_const_0D0, array_const_1, array_m1, array_y, array_x, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error,
array_1st_rel_error, array_norms, array_type_pole, array_pole,
array_y_higher_work, array_complex_pole, array_y_higher_work2,
array_real_pole, array_poles, array_y_higher, array_y_set_initial,
glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_hours,
> glob_dump_analytic,
> glob_hmax,
> sec_in_min,
> glob_no_eqs,
> glob_hmin_init,
> glob_initial_pass,
> glob_almost_1,
> glob_html_log,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_disp_incr,
> centuries_in_millinium,
> hours_in_day,
> glob_current_iter,
> glob_abserr,
> glob_percent_done,
> glob_start,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_clock_sec,
> djd_debug,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> days_in_year,
> min_in_hour,
> glob_normmax,
> glob_iter,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> years_in_century,
> glob_log10_abserr,
> glob_optimal_done,
> glob_display_flag,
> glob_dump,
> glob_log10normmin,
> glob_log10relerr,
> glob_optimal_start,
> glob_relerr,
> glob_h,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_type_pole,
> array_pole,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_set_initial,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global INFO, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE,
glob_max_minutes, glob_warned, glob_max_hours, glob_dump_analytic,
glob_hmax, sec_in_min, glob_no_eqs, glob_hmin_init, glob_initial_pass,
glob_almost_1, glob_html_log, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_disp_incr,
centuries_in_millinium, hours_in_day, glob_current_iter, glob_abserr,
glob_percent_done, glob_start, glob_smallish_float,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_subiter_method,
glob_log10abserr, glob_curr_iter_when_opt, glob_max_iter, glob_log10_relerr,
glob_not_yet_finished, glob_clock_sec, djd_debug, glob_look_poles,
glob_last_good_h, glob_hmin, days_in_year, min_in_hour, glob_normmax,
glob_iter, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2,
years_in_century, glob_log10_abserr, glob_optimal_done, glob_display_flag,
glob_dump, glob_log10normmin, glob_log10relerr, glob_optimal_start,
glob_relerr, glob_h, glob_max_opt_iter, glob_optimal_expect_sec,
array_const_0D0, array_const_1, array_m1, array_y, array_x, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error,
array_1st_rel_error, array_norms, array_type_pole, array_pole,
array_y_higher_work, array_complex_pole, array_y_higher_work2,
array_real_pole, array_poles, array_y_higher, array_y_set_initial,
glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_hours,
> glob_dump_analytic,
> glob_hmax,
> sec_in_min,
> glob_no_eqs,
> glob_hmin_init,
> glob_initial_pass,
> glob_almost_1,
> glob_html_log,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_disp_incr,
> centuries_in_millinium,
> hours_in_day,
> glob_current_iter,
> glob_abserr,
> glob_percent_done,
> glob_start,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_clock_sec,
> djd_debug,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> days_in_year,
> min_in_hour,
> glob_normmax,
> glob_iter,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> years_in_century,
> glob_log10_abserr,
> glob_optimal_done,
> glob_display_flag,
> glob_dump,
> glob_log10normmin,
> glob_log10relerr,
> glob_optimal_start,
> glob_relerr,
> glob_h,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_type_pole,
> array_pole,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_set_initial,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_y[1] * (array_y[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 mult $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_y,array_y,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 mult $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_y,array_y,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 mult $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_y,array_y,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 mult $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_y,array_y,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 mult $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_y,array_y,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, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE,
glob_max_minutes, glob_warned, glob_max_hours, glob_dump_analytic,
glob_hmax, sec_in_min, glob_no_eqs, glob_hmin_init, glob_initial_pass,
glob_almost_1, glob_html_log, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_disp_incr,
centuries_in_millinium, hours_in_day, glob_current_iter, glob_abserr,
glob_percent_done, glob_start, glob_smallish_float,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_subiter_method,
glob_log10abserr, glob_curr_iter_when_opt, glob_max_iter, glob_log10_relerr,
glob_not_yet_finished, glob_clock_sec, djd_debug, glob_look_poles,
glob_last_good_h, glob_hmin, days_in_year, min_in_hour, glob_normmax,
glob_iter, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2,
years_in_century, glob_log10_abserr, glob_optimal_done, glob_display_flag,
glob_dump, glob_log10normmin, glob_log10relerr, glob_optimal_start,
glob_relerr, glob_h, glob_max_opt_iter, glob_optimal_expect_sec,
array_const_0D0, array_const_1, array_m1, array_y, array_x, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error,
array_1st_rel_error, array_norms, array_type_pole, array_pole,
array_y_higher_work, array_complex_pole, array_y_higher_work2,
array_real_pole, array_poles, array_y_higher, array_y_set_initial,
glob_last;
array_tmp1[1] := array_y[1]*array_y[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_y, array_y, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_y, array_y, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_y, array_y, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_y, array_y, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_y, array_y, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0/(1.0 - 2.0*x);
> end;
exact_soln_y := proc(x) 2.0/(1.0 - 2.0*x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> INFO,
> ALWAYS,
> glob_max_terms,
> glob_iolevel,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_hours,
> glob_dump_analytic,
> glob_hmax,
> sec_in_min,
> glob_no_eqs,
> glob_hmin_init,
> glob_initial_pass,
> glob_almost_1,
> glob_html_log,
> MAX_UNCHANGED,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_large_float,
> glob_disp_incr,
> centuries_in_millinium,
> hours_in_day,
> glob_current_iter,
> glob_abserr,
> glob_percent_done,
> glob_start,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_subiter_method,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_clock_sec,
> djd_debug,
> glob_look_poles,
> glob_last_good_h,
> glob_hmin,
> days_in_year,
> min_in_hour,
> glob_normmax,
> glob_iter,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_trunc_err,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> djd_debug2,
> glob_warned2,
> years_in_century,
> glob_log10_abserr,
> glob_optimal_done,
> glob_display_flag,
> glob_dump,
> glob_log10normmin,
> glob_log10relerr,
> glob_optimal_start,
> glob_relerr,
> glob_h,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_type_pole,
> array_pole,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_set_initial,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> ALWAYS := 1;
> glob_max_terms := 30;
> glob_iolevel := 5;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_max_minutes := 0.0;
> glob_warned := false;
> glob_max_hours := 0.0;
> glob_dump_analytic := false;
> glob_hmax := 1.0;
> sec_in_min := 60.0;
> glob_no_eqs := 0;
> glob_hmin_init := 0.001;
> glob_initial_pass := true;
> glob_almost_1 := 0.9990;
> glob_html_log := true;
> MAX_UNCHANGED := 10;
> glob_unchanged_h_cnt := 0;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_disp_incr := 0.1;
> centuries_in_millinium := 10.0;
> hours_in_day := 24.0;
> glob_current_iter := 0;
> glob_abserr := 0.1e-10;
> glob_percent_done := 0.0;
> glob_start := 0;
> glob_smallish_float := 0.1e-100;
> glob_optimal_clock_start_sec := 0.0;
> glob_reached_optimal_h := false;
> glob_subiter_method := 3;
> glob_log10abserr := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_max_iter := 1000;
> glob_log10_relerr := 0.1e-10;
> glob_not_yet_finished := true;
> glob_clock_sec := 0.0;
> djd_debug := true;
> glob_look_poles := false;
> glob_last_good_h := 0.1;
> glob_hmin := 0.00000000001;
> days_in_year := 365.0;
> min_in_hour := 60.0;
> glob_normmax := 0.0;
> glob_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_max_sec := 10000.0;
> glob_max_trunc_err := 0.1e-10;
> glob_not_yet_start_msg := true;
> glob_clock_start_sec := 0.0;
> djd_debug2 := true;
> glob_warned2 := false;
> years_in_century := 100.0;
> glob_log10_abserr := 0.1e-10;
> glob_optimal_done := false;
> glob_display_flag := true;
> glob_dump := false;
> glob_log10normmin := 0.1;
> glob_log10relerr := 0.0;
> glob_optimal_start := 0.0;
> glob_relerr := 0.1e-10;
> glob_h := 0.1;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/nonlinear2postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 0.2 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.01;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"2.0/(1.0 - 2.0*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_m1:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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 <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_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_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_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 0.2 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.01;
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = y * y;");
> 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,"2012-06-13T18:17:33-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"nonlinear2")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"nonlinear2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"nonlinear2 maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp;
global INFO, ALWAYS, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE,
glob_max_minutes, glob_warned, glob_max_hours, glob_dump_analytic,
glob_hmax, sec_in_min, glob_no_eqs, glob_hmin_init, glob_initial_pass,
glob_almost_1, glob_html_log, MAX_UNCHANGED, glob_unchanged_h_cnt,
glob_small_float, glob_max_rel_trunc_err, glob_large_float, glob_disp_incr,
centuries_in_millinium, hours_in_day, glob_current_iter, glob_abserr,
glob_percent_done, glob_start, glob_smallish_float,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_subiter_method,
glob_log10abserr, glob_curr_iter_when_opt, glob_max_iter, glob_log10_relerr,
glob_not_yet_finished, glob_clock_sec, djd_debug, glob_look_poles,
glob_last_good_h, glob_hmin, days_in_year, min_in_hour, glob_normmax,
glob_iter, glob_orig_start_sec, glob_max_sec, glob_max_trunc_err,
glob_not_yet_start_msg, glob_clock_start_sec, djd_debug2, glob_warned2,
years_in_century, glob_log10_abserr, glob_optimal_done, glob_display_flag,
glob_dump, glob_log10normmin, glob_log10relerr, glob_optimal_start,
glob_relerr, glob_h, glob_max_opt_iter, glob_optimal_expect_sec,
array_const_0D0, array_const_1, array_m1, array_y, array_x, array_y_init,
array_tmp0, array_tmp1, array_tmp2, array_last_rel_error,
array_1st_rel_error, array_norms, array_type_pole, array_pole,
array_y_higher_work, array_complex_pole, array_y_higher_work2,
array_real_pole, array_poles, array_y_higher, array_y_set_initial,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
ALWAYS := 1;
glob_max_terms := 30;
glob_iolevel := 5;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_max_minutes := 0.;
glob_warned := false;
glob_max_hours := 0.;
glob_dump_analytic := false;
glob_hmax := 1.0;
sec_in_min := 60.0;
glob_no_eqs := 0;
glob_hmin_init := 0.001;
glob_initial_pass := true;
glob_almost_1 := 0.9990;
glob_html_log := true;
MAX_UNCHANGED := 10;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_disp_incr := 0.1;
centuries_in_millinium := 10.0;
hours_in_day := 24.0;
glob_current_iter := 0;
glob_abserr := 0.1*10^(-10);
glob_percent_done := 0.;
glob_start := 0;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_clock_start_sec := 0.;
glob_reached_optimal_h := false;
glob_subiter_method := 3;
glob_log10abserr := 0.;
glob_curr_iter_when_opt := 0;
glob_max_iter := 1000;
glob_log10_relerr := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_clock_sec := 0.;
djd_debug := true;
glob_look_poles := false;
glob_last_good_h := 0.1;
glob_hmin := 0.1*10^(-10);
days_in_year := 365.0;
min_in_hour := 60.0;
glob_normmax := 0.;
glob_iter := 0;
glob_orig_start_sec := 0.;
glob_max_sec := 10000.0;
glob_max_trunc_err := 0.1*10^(-10);
glob_not_yet_start_msg := true;
glob_clock_start_sec := 0.;
djd_debug2 := true;
glob_warned2 := false;
years_in_century := 100.0;
glob_log10_abserr := 0.1*10^(-10);
glob_optimal_done := false;
glob_display_flag := true;
glob_dump := false;
glob_log10normmin := 0.1;
glob_log10relerr := 0.;
glob_optimal_start := 0.;
glob_relerr := 0.1*10^(-10);
glob_h := 0.1;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/nonlinear2postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 0.2 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.01;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "2.0/(1.0 - 2.0*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_m1 := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
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_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_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_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_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.;
x_end := 0.2;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.01;
glob_look_poles := true;
glob_max_iter := 1000000;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = y * y;");
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, "2012-06-13T18:17:33-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"nonlinear2");
logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file, "nonlinear2 diffeq.mxt");
logitem_str(html_log_file, "nonlinear2 maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/nonlinear2postode.ode#################
diff ( y , x , 1 ) = y * y;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 0.2 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.01;
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0/(1.0 - 2.0*x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 2
y[1] (numeric) = 2
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0001
y[1] (analytic) = 2.0004000800160032006401280256051
y[1] (numeric) = 2.0004000800160032006446218458494
absolute error = 4.4938202443e-21
relative error = 2.2464607401255700000000000000000e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0002
y[1] (analytic) = 2.0008003201280512204881952781112
y[1] (numeric) = 2.0008003201280512204971910161896
absolute error = 8.9957380784e-21
relative error = 4.4960698915843200000000000000001e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0003
y[1] (analytic) = 2.0012007204322593556133680208125
y[1] (numeric) = 2.001200720432259355626873788369
absolute error = 1.35057675565e-20
relative error = 6.7488320479830500000000000000000e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0004
y[1] (analytic) = 2.001601281024819855884707766213
y[1] (numeric) = 2.0016012810248198559027316889724
absolute error = 1.80239227594e-20
relative error = 9.0047518105962399999999999999999e-19 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0005
y[1] (analytic) = 2.002002002002002002002002002002
y[1] (numeric) = 2.0020020020020020020245522197959
absolute error = 2.25502177939e-20
relative error = 1.1263833788053050000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0006
y[1] (analytic) = 2.0024028834601521826191429715659
y[1] (numeric) = 2.0024028834601521826462276383589
absolute error = 2.70846667930e-20
relative error = 1.3526082596424200000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0007
y[1] (analytic) = 2.0028039254956939715601842579611
y[1] (numeric) = 2.0028039254956939715918115418775
absolute error = 3.16272839164e-20
relative error = 1.5791502859458520000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0008
y[1] (analytic) = 2.0032051282051282051282051282051
y[1] (numeric) = 2.003205128205128205164383211555
absolute error = 3.61780833499e-20
relative error = 1.8060099208270080000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0009
y[1] (analytic) = 2.0036064916850330595071128030455
y[1] (numeric) = 2.0036064916850330595478498823514
absolute error = 4.07370793059e-20
relative error = 2.0331876281574690000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.14
NO POLE
x[1] = 0.001
y[1] (analytic) = 2.0040080160320641282565130260521
y[1] (numeric) = 2.0040080160320641283018173120756
absolute error = 4.53042860235e-20
relative error = 2.2606838725726500000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0011
y[1] (analytic) = 2.0044097013429544998997795149329
y[1] (numeric) = 2.0044097013429544999496592327009
absolute error = 4.98797177680e-20
relative error = 2.4884991194455199999999999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0012
y[1] (analytic) = 2.0048115477145148356054530874098
y[1] (numeric) = 2.0048115477145148356599164762415
absolute error = 5.44633888317e-20
relative error = 2.7166338349251960000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0013
y[1] (analytic) = 2.0052135552436334469621014638059
y[1] (numeric) = 2.0052135552436334470211567773393
absolute error = 5.90553135334e-20
relative error = 2.9450884859106580000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0014
y[1] (analytic) = 2.0056157240272763738467709586843
y[1] (numeric) = 2.0056157240272763739104264649029
absolute error = 6.36555062186e-20
relative error = 3.1738635400593960000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0015
y[1] (analytic) = 2.0060180541624874623871614844534
y[1] (numeric) = 2.006018054162487462455425465713
absolute error = 6.82639812596e-20
relative error = 3.4029594657910599999999999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0016
y[1] (analytic) = 2.0064205457463884430176565008026
y[1] (numeric) = 2.0064205457463884430905372538584
absolute error = 7.28807530558e-20
relative error = 3.6323767323010719999999999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0017
y[1] (analytic) = 2.0068231988761790086293397551676
y[1] (numeric) = 2.0068231988761790087068455912009
absolute error = 7.75058360333e-20
relative error = 3.8621158095393389999999999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0018
y[1] (analytic) = 2.0072260136491368928141308711361
y[1] (numeric) = 2.0072260136491368928962701157812
absolute error = 8.21392446451e-20
relative error = 4.0921771682188820000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0019
y[1] (analytic) = 2.0076289901626179482031720538045
y[1] (numeric) = 2.0076289901626179482899530471758
absolute error = 8.67809933713e-20
relative error = 4.3225612798244529999999999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 2.0080321285140562248995983935743
y[1] (numeric) = 2.0080321285140562249910294902935
absolute error = 9.14310967192e-20
relative error = 4.5532686166161600000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0021
y[1] (analytic) = 2.0084354288009640490058244627435
y[1] (numeric) = 2.0084354288009640491019140319665
absolute error = 9.60895692230e-20
relative error = 4.7842996516131700000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0022
y[1] (analytic) = 2.008838891120932101245480112495
y[1] (numeric) = 2.0088388911209321013462365379391
absolute error = 1.007564254441e-19
relative error = 5.0156548586072979999999999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0023
y[1] (analytic) = 2.009242515571629495680128591521
y[1] (numeric) = 2.0092425155716294957855602714924
absolute error = 1.054316799714e-19
relative error = 5.2473347121765780000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0024
y[1] (analytic) = 2.0096463022508038585209003215434
y[1] (numeric) = 2.0096463022508038586310156689643
absolute error = 1.101153474209e-19
relative error = 5.4793396876639840000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.28
NO POLE
x[1] = 0.0025
y[1] (analytic) = 2.010050251256281407035175879397
y[1] (numeric) = 2.0100502512562814071499833218328
absolute error = 1.148074424358e-19
relative error = 5.7116702611810500000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0026
y[1] (analytic) = 2.0104543626859670285484519501407
y[1] (numeric) = 2.0104543626859670286679599298278
absolute error = 1.195079796871e-19
relative error = 5.9443269096363540000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0027
y[1] (analytic) = 2.0108586366378443595415242308466
y[1] (numeric) = 2.0108586366378443596657412047194
absolute error = 1.242169738728e-19
relative error = 6.1773101106943439999999999999999e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0028
y[1] (analytic) = 2.0112630732099758648431214802896
y[1] (numeric) = 2.0112630732099758649720559200085
absolute error = 1.289344397189e-19
relative error = 6.4106203428237080000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0029
y[1] (analytic) = 2.0116676725005029169181251257292
y[1] (numeric) = 2.0116676725005029170517855177077
absolute error = 1.336603919785e-19
relative error = 6.6442580852512350000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 2.012072434607645875251509054326
y[1] (numeric) = 2.0120724346076458753899038997586
absolute error = 1.383948454326e-19
relative error = 6.8782238180002199999999999999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0031
y[1] (analytic) = 2.0124773596297041658281344334876
y[1] (numeric) = 2.0124773596297041659712722483776
absolute error = 1.431378148900e-19
relative error = 7.1125180218841000000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0032
y[1] (analytic) = 2.0128824476650563607085346215781
y[1] (numeric) = 2.012882447665056360856423936765
absolute error = 1.478893151869e-19
relative error = 7.3471411784851920000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0033
y[1] (analytic) = 2.0132876988121602577008254479565
y[1] (numeric) = 2.013287698812160257853474809144
absolute error = 1.526493611875e-19
relative error = 7.5820937701831250000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0034
y[1] (analytic) = 2.0136931131695529601288763592429
y[1] (numeric) = 2.0136931131695529602862943270267
absolute error = 1.574179677838e-19
relative error = 7.8173762801435079999999999999998e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0035
y[1] (analytic) = 2.0140986908358509566968781470292
y[1] (numeric) = 2.0140986908358509568590732969252
absolute error = 1.621951498960e-19
relative error = 8.0529891923364000000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0036
y[1] (analytic) = 2.014504431909750201450443190975
y[1] (numeric) = 2.0145044319097502016174241134468
absolute error = 1.669809224718e-19
relative error = 8.2889329915001520000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0037
y[1] (analytic) = 2.0149103364900261938343743703405
y[1] (numeric) = 2.0149103364900261940061496708277
absolute error = 1.717753004872e-19
relative error = 8.5252081631797360000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0038
y[1] (analytic) = 2.0153164046755340588472390165256
y[1] (numeric) = 2.0153164046755340590238173154719
absolute error = 1.765782989463e-19
relative error = 8.7618151937154060000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0039
y[1] (analytic) = 2.0157226365652086272928844990929
y[1] (numeric) = 2.0157226365652086274742744319742
absolute error = 1.813899328813e-19
relative error = 8.9987545702412930000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=0.43
NO POLE
x[1] = 0.004
y[1] (analytic) = 2.0161290322580645161290322580645
y[1] (numeric) = 2.016129032258064516315242475417
absolute error = 1.862102173525e-19
relative error = 9.2360267806840000000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0041
y[1] (analytic) = 2.0165355918531962089130873159911
y[1] (numeric) = 2.0165355918531962091041264834396
absolute error = 1.910391674485e-19
relative error = 9.4736323137711150000000000000001e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0042
y[1] (analytic) = 2.016942315449778136345300524405
y[1] (numeric) = 2.0169423154497781365411773226913
absolute error = 1.958767982863e-19
relative error = 9.7115716590347540000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0043
y[1] (analytic) = 2.0173492031470647569094210207787
y[1] (numeric) = 2.01734920314706475711014414579
absolute error = 2.007231250113e-19
relative error = 9.9498453068101410000000000000000e-18 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0044
y[1] (analytic) = 2.0177562550443906376109765940274
y[1] (numeric) = 2.0177562550443906378165547568247
absolute error = 2.055781627973e-19
relative error = 1.0188453748234188000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0045
y[1] (analytic) = 2.0181634712411705348133198789102
y[1] (numeric) = 2.0181634712411705350237618057567
absolute error = 2.104419268465e-19
relative error = 1.0427397475244075000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0046
y[1] (analytic) = 2.0185708518368994751715785224061
y[1] (numeric) = 2.0185708518368994753868929547959
absolute error = 2.153144323898e-19
relative error = 1.0666676980590692000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0047
y[1] (analytic) = 2.0189783969311528366646476882697
y[1] (numeric) = 2.0189783969311528368848433829562
absolute error = 2.201956946865e-19
relative error = 1.0906292757822345000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0048
y[1] (analytic) = 2.0193861066235864297253634894992
y[1] (numeric) = 2.0193861066235864299504492185239
absolute error = 2.250857290247e-19
relative error = 1.1146245301303144000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0049
y[1] (analytic) = 2.0197939810139365784689961623914
y[1] (numeric) = 2.0197939810139365786989807131127
absolute error = 2.299845507213e-19
relative error = 1.1386535106211563000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 2.020202020202020202020202020202
y[1] (numeric) = 2.0202020202020202022550941953238
absolute error = 2.348921751218e-19
relative error = 1.1627162668529100000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0051
y[1] (analytic) = 2.0206102242877348959385734491817
y[1] (numeric) = 2.0206102242877348961783820667823
absolute error = 2.398086176006e-19
relative error = 1.1868128485053694000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0052
y[1] (analytic) = 2.0210185933710590137429264349232
y[1] (numeric) = 2.0210185933710590139876603284845
absolute error = 2.447338935613e-19
relative error = 1.2109433053413124000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0053
y[1] (analytic) = 2.0214271275520517485344653325248
y[1] (numeric) = 2.0214271275520517487841333509607
absolute error = 2.496680184359e-19
relative error = 1.2351076872023973000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0054
y[1] (analytic) = 2.0218358269308532147189648200566
y[1] (numeric) = 2.0218358269308532149735758277426
absolute error = 2.546110076860e-19
relative error = 1.2593060440149560000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=15.2MB, alloc=3.9MB, time=0.59
x[1] = 0.0055
y[1] (analytic) = 2.0222446916076845298281092012133
y[1] (numeric) = 2.0222446916076845300876720780152
absolute error = 2.595628768019e-19
relative error = 1.2835384257853955000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0056
y[1] (analytic) = 2.0226537216828478964401294498382
y[1] (numeric) = 2.0226537216828478967046530911413
absolute error = 2.645236413031e-19
relative error = 1.3078048826025264000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0057
y[1] (analytic) = 2.023062917256726684199878616225
y[1] (numeric) = 2.0230629172567266844693719329635
absolute error = 2.694933167385e-19
relative error = 1.3321054646384055000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0058
y[1] (analytic) = 2.0234722784297855119384864427357
y[1] (numeric) = 2.0234722784297855122129583614218
absolute error = 2.744719186861e-19
relative error = 1.3564402221467062000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0059
y[1] (analytic) = 2.023881805302570329892734264319
y[1] (numeric) = 2.0238818053025703301721937270721
absolute error = 2.794594627531e-19
relative error = 1.3808092054630671000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 2.0242914979757085020242914979757
y[1] (numeric) = 2.0242914979757085023087474625521
absolute error = 2.844559645764e-19
relative error = 1.4052124650074160000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0061
y[1] (analytic) = 2.0247013565499088884389552541
y[1] (numeric) = 2.0247013565499088887284166939221
absolute error = 2.894614398221e-19
relative error = 1.4296500512813519000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0062
y[1] (analytic) = 2.0251113811259619279060348319158
y[1] (numeric) = 2.0251113811259619282005107361016
absolute error = 2.944759041858e-19
relative error = 1.4541220148694804000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0063
y[1] (analytic) = 2.0255215718047397204780230909459
y[1] (numeric) = 2.0255215718047397207775224643389
absolute error = 2.994993733930e-19
relative error = 1.4786284064412410000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0064
y[1] (analytic) = 2.0259319286871961102106969205835
y[1] (numeric) = 2.0259319286871961105152287837818
absolute error = 3.045318631983e-19
relative error = 1.5031692767468088000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0065
y[1] (analytic) = 2.026342451874366767983789260385
y[1] (numeric) = 2.0263424518743667682933626497714
absolute error = 3.095733893864e-19
relative error = 1.5277446766218840000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0066
y[1] (analytic) = 2.0267531414673692744223753546818
y[1] (numeric) = 2.0267531414673692747369993224533
absolute error = 3.146239677715e-19
relative error = 1.5523546569845810000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0067
y[1] (analytic) = 2.0271639975674032029191161564971
y[1] (numeric) = 2.0271639975674032032387997706949
absolute error = 3.196836141978e-19
relative error = 1.5769992688377474000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0068
y[1] (analytic) = 2.027575020275750202757502027575
y[1] (numeric) = 2.0275750202757502030822543721143
absolute error = 3.247523445393e-19
relative error = 1.6016785632678276000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0069
y[1] (analytic) = 2.0279862096937740823362401135672
y[1] (numeric) = 2.027986209693774082666070288267
absolute error = 3.298301746998e-19
relative error = 1.6263925914447138000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 2.0283975659229208924949290060852
y[1] (numeric) = 2.0283975659229208928298461266984
absolute error = 3.349171206132e-19
relative error = 1.6511414046230760000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=3.9MB, time=0.75
NO POLE
x[1] = 0.0071
y[1] (analytic) = 2.0288090890647190099411645364171
y[1] (numeric) = 2.0288090890647190102811777346607
absolute error = 3.400131982436e-19
relative error = 1.6759250541427044000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0072
y[1] (analytic) = 2.0292207792207792207792207792208
y[1] (numeric) = 2.0292207792207792211243392028058
absolute error = 3.451184235850e-19
relative error = 1.7007435914268800000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0073
y[1] (analytic) = 2.0296326364927948041404505784453
y[1] (numeric) = 2.029632636492794804490683391107
absolute error = 3.502328126617e-19
relative error = 1.7255970679841959000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0074
y[1] (analytic) = 2.0300446609825416159155501421031
y[1] (numeric) = 2.0300446609825416162709065236313
absolute error = 3.553563815282e-19
relative error = 1.7504855354079132000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0075
y[1] (analytic) = 2.0304568527918781725888324873096
y[1] (numeric) = 2.0304568527918781729493216335789
absolute error = 3.604891462693e-19
relative error = 1.7754090453763025000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0076
y[1] (analytic) = 2.030869212022745735174654752234
y[1] (numeric) = 2.030869212022745735540285875234
absolute error = 3.656311230000e-19
relative error = 1.8003676496520000000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0077
y[1] (analytic) = 2.0312817387771683932561446272598
y[1] (numeric) = 2.031281738777168393626926955126
absolute error = 3.707823278662e-19
relative error = 1.8253614000853026000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0078
y[1] (analytic) = 2.0316944331572531491263713937424
y[1] (numeric) = 2.0316944331572531495023141707862
absolute error = 3.759427770438e-19
relative error = 1.8503903486095836000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0079
y[1] (analytic) = 2.0321072952651900020321072952652
y[1] (numeric) = 2.0321072952651900024132197820047
absolute error = 3.811124867395e-19
relative error = 1.8754545472450795000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 2.032520325203252032520325203252
y[1] (numeric) = 2.0325203252032520329066166764427
absolute error = 3.862914731907e-19
relative error = 1.9005540480982440000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0081
y[1] (analytic) = 2.032933523073795486887578776174
y[1] (numeric) = 2.0329335230737954872790585288391
absolute error = 3.914797526651e-19
relative error = 1.9256889033596269000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0082
y[1] (analytic) = 2.0333468889792598617324115494103
y[1] (numeric) = 2.0333468889792598621290888908719
absolute error = 3.966773414616e-19
relative error = 1.9508591653081488000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0083
y[1] (analytic) = 2.0337604230221679886109416310759
y[1] (numeric) = 2.0337604230221679890128258869854
absolute error = 4.018842559095e-19
relative error = 1.9760648863070115000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0084
y[1] (analytic) = 2.0341741253051261187957689178194
y[1] (numeric) = 2.0341741253051261192028694301888
absolute error = 4.071005123694e-19
relative error = 2.0013061188079704000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0085
y[1] (analytic) = 2.0345879959308240081383519837233
y[1] (numeric) = 2.0345879959308240085506781109559
absolute error = 4.123261272326e-19
relative error = 2.0265829153482290000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=22.8MB, alloc=4.0MB, time=0.91
x[1] = 0.0086
y[1] (analytic) = 2.035002035002035002035002035002
y[1] (numeric) = 2.0350020350020350024525631519233
absolute error = 4.175611169213e-19
relative error = 2.0518953285512682000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0087
y[1] (analytic) = 2.0354162426216161204966415631997
y[1] (numeric) = 2.0354162426216161209194470610885
absolute error = 4.228054978888e-19
relative error = 2.0772434111276744000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0088
y[1] (analytic) = 2.0358306188925081433224755700326
y[1] (numeric) = 2.0358306188925081437505348566524
absolute error = 4.280592866198e-19
relative error = 2.1026272158764576000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0089
y[1] (analytic) = 2.0362451639177356953777234779067
y[1] (numeric) = 2.0362451639177356958110459775367
absolute error = 4.333224996300e-19
relative error = 2.1280467956829300000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 2.0366598778004073319755600814664
y[1] (numeric) = 2.0366598778004073324141552349326
absolute error = 4.385951534662e-19
relative error = 2.1535022035190420000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0091
y[1] (analytic) = 2.0370747606437156243634141372988
y[1] (numeric) = 2.0370747606437156248072914020057
absolute error = 4.438772647069e-19
relative error = 2.1789934924461721000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0092
y[1] (analytic) = 2.0374898125509372453137734311328
y[1] (numeric) = 2.0374898125509372457629422810944
absolute error = 4.491688499616e-19
relative error = 2.2045207156115328000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0093
y[1] (analytic) = 2.0379050336254330548196454045241
y[1] (numeric) = 2.0379050336254330552741153303955
absolute error = 4.544699258714e-19
relative error = 2.2300839262509598000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0094
y[1] (analytic) = 2.0383204239706481858948226661231
y[1] (numeric) = 2.0383204239706481863546031752321
absolute error = 4.597805091090e-19
relative error = 2.2556831776887540000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0095
y[1] (analytic) = 2.0387359836901121304791029561672
y[1] (numeric) = 2.0387359836901121309442035725458
absolute error = 4.651006163786e-19
relative error = 2.2813185233370330000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0096
y[1] (analytic) = 2.0391517128874388254486133768352
y[1] (numeric) = 2.0391517128874388259190436412514
absolute error = 4.704302644162e-19
relative error = 2.3069900166970448000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0097
y[1] (analytic) = 2.0395676116663267387313889455435
y[1] (numeric) = 2.0395676116663267392071584155327
absolute error = 4.757694699892e-19
relative error = 2.3326977113570476000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0098
y[1] (analytic) = 2.0399836801305589555283557731538
y[1] (numeric) = 2.0399836801305589560094740230508
absolute error = 4.811182498970e-19
relative error = 2.3584416609950940000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0099
y[1] (analytic) = 2.0403999183840032646398694144052
y[1] (numeric) = 2.040399918384003265126346035376
absolute error = 4.864766209708e-19
relative error = 2.3842219193778908000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 2.0408163265306122448979591836735
y[1] (numeric) = 2.0408163265306122453898037837472
absolute error = 4.918446000737e-19
relative error = 2.4100385403611300000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0101
y[1] (analytic) = 2.0412329046744233517044294754031
y[1] (numeric) = 2.0412329046744233522016516795041
absolute error = 4.972222041010e-19
relative error = 2.4358915778907990000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.0MB, time=1.07
NO POLE
x[1] = 0.0102
y[1] (analytic) = 2.0416496529195590036749693752552
y[1] (numeric) = 2.0416496529195590041775788252348
absolute error = 5.026094499796e-19
relative error = 2.4617810860000808000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0103
y[1] (analytic) = 2.0420665713702266693894220951603
y[1] (numeric) = 2.0420665713702266698974284498292
absolute error = 5.080063546689e-19
relative error = 2.4877071188136033000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0104
y[1] (analytic) = 2.0424836601307189542483660130719
y[1] (numeric) = 2.0424836601307189547617789482321
absolute error = 5.134129351602e-19
relative error = 2.5136697305443392000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0105
y[1] (analytic) = 2.0429009193054136874361593462717
y[1] (numeric) = 2.042900919305413687954988554749
absolute error = 5.188292084773e-19
relative error = 2.5396689754963835000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0106
y[1] (analytic) = 2.0433183489987740089906007355946
y[1] (numeric) = 2.0433183489987740095148559272707
absolute error = 5.242551916761e-19
relative error = 2.5657049080628334000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0107
y[1] (analytic) = 2.0437359493153484569793582669119
y[1] (numeric) = 2.0437359493153484575090491687569
absolute error = 5.296909018450e-19
relative error = 2.5917775827275850000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0108
y[1] (analytic) = 2.0441537203597710547833197056419
y[1] (numeric) = 2.0441537203597710553184560617466
absolute error = 5.351363561047e-19
relative error = 2.6178870540641924000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0109
y[1] (analytic) = 2.0445716622367613984870169699448
y[1] (numeric) = 2.0445716622367613990276085415535
absolute error = 5.405915716087e-19
relative error = 2.6440333767381517000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 2.0449897750511247443762781186094
y[1] (numeric) = 2.0449897750511247449223346841521
absolute error = 5.460565655427e-19
relative error = 2.6702166055038030000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0111
y[1] (analytic) = 2.0454080589077520965432603804459
y[1] (numeric) = 2.0454080589077520970947917355712
absolute error = 5.515313551253e-19
relative error = 2.6964367952075917000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0112
y[1] (analytic) = 2.0458265139116202945990180032733
y[1] (numeric) = 2.0458265139116202951560339608812
absolute error = 5.570159576079e-19
relative error = 2.7226940007874152000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0113
y[1] (analytic) = 2.0462451401677921014937589523225
y[1] (numeric) = 2.0462451401677921020562693425969
absolute error = 5.625103902744e-19
relative error = 2.7489882772709928000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0114
y[1] (analytic) = 2.0466639377814162914449447400737
y[1] (numeric) = 2.0466639377814162920129594105154
absolute error = 5.680146704417e-19
relative error = 2.7753196797781462000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0115
y[1] (analytic) = 2.0470829068577277379733879222108
y[1] (numeric) = 2.0470829068577277385469167376705
absolute error = 5.735288154597e-19
relative error = 2.8016882635206345000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0116
y[1] (analytic) = 2.047502047502047502047502047502
y[1] (numeric) = 2.0475020475020475026265548902131
absolute error = 5.790528427111e-19
relative error = 2.8280940838010124000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0117
y[1] (analytic) = 2.0479213598197829203358591030104
y[1] (numeric) = 2.0479213598197829209204458726222
absolute error = 5.845867696118e-19
relative error = 2.8545371960144194000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.0MB, time=1.24
NO POLE
x[1] = 0.0118
y[1] (analytic) = 2.0483408439164276935682097501024
y[1] (numeric) = 2.0483408439164276941583403637132
absolute error = 5.901306136108e-19
relative error = 2.8810176556479256000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0119
y[1] (analytic) = 2.0487604998975619750051219012497
y[1] (numeric) = 2.04876049989756197560080629344
absolute error = 5.956843921903e-19
relative error = 2.9075355182808543000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 2.049180327868852459016393442623
y[1] (numeric) = 2.0491803278688524596176415654886
absolute error = 6.012481228656e-19
relative error = 2.9340908395841279999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0121
y[1] (analytic) = 2.0496003279360524697683951629432
y[1] (numeric) = 2.049600327936052470375216986129
absolute error = 6.068218231858e-19
relative error = 2.9606836753235182000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0122
y[1] (analytic) = 2.050020500205002050020500205002
y[1] (numeric) = 2.0500205002050020506329057157348
absolute error = 6.124055107328e-19
relative error = 2.9873140813545984000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0123
y[1] (analytic) = 2.0504408447816280500307566126717
y[1] (numeric) = 2.050440844781628050648755815794
absolute error = 6.179992031223e-19
relative error = 3.0139821136274571000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0124
y[1] (analytic) = 2.0508613617719442165709598031173
y[1] (numeric) = 2.0508613617719442171945627211209
absolute error = 6.236029180036e-19
relative error = 3.0406878281855536000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0125
y[1] (analytic) = 2.0512820512820512820512820512821
y[1] (numeric) = 2.0512820512820512826804987243414
absolute error = 6.292166730593e-19
relative error = 3.0674312811640874999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0126
y[1] (analytic) = 2.0517029134181370537546163315552
y[1] (numeric) = 2.0517029134181370543894568175614
absolute error = 6.348404860062e-19
relative error = 3.0942125287942188000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0127
y[1] (analytic) = 2.052123948286476503180792119844
y[1] (numeric) = 2.0521239482864765038212664944383
absolute error = 6.404743745943e-19
relative error = 3.1210316273980239000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0128
y[1] (analytic) = 2.0525451559934318555008210180624
y[1] (numeric) = 2.0525451559934318561469393746701
absolute error = 6.461183566077e-19
relative error = 3.1478886333927144000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0129
y[1] (analytic) = 2.0529665366454526791213303223157
y[1] (numeric) = 2.0529665366454526797731027721801
absolute error = 6.517724498644e-19
relative error = 3.1747836032894924000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 2.0533880903490759753593429158111
y[1] (numeric) = 2.0533880903490759760167795880273
absolute error = 6.574366722162e-19
relative error = 3.2017165936928940000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0131
y[1] (analytic) = 2.053809817210926268227562127747
y[1] (numeric) = 2.0538098172109262688906731692962
absolute error = 6.631110415492e-19
relative error = 3.2286876613030548000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0132
y[1] (analytic) = 2.0542317173377156943303204601479
y[1] (numeric) = 2.0542317173377156949991160359314
absolute error = 6.687955757835e-19
relative error = 3.2556968629140780000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.0MB, time=1.40
x[1] = 0.0133
y[1] (analytic) = 2.0546537908362440928703513457982
y[1] (numeric) = 2.0546537908362440935448416386714
absolute error = 6.744902928732e-19
relative error = 3.2827442554138644000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0134
y[1] (analytic) = 2.0550760378133990957665433621044
y[1] (numeric) = 2.0550760378133990964467385729112
absolute error = 6.801952108068e-19
relative error = 3.3098298957858888000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0135
y[1] (analytic) = 2.0554984583761562178828365878726
y[1] (numeric) = 2.0554984583761562185687469354797
absolute error = 6.859103476071e-19
relative error = 3.3369538411085414999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0136
y[1] (analytic) = 2.0559210526315789473684210526316
y[1] (numeric) = 2.055921052631578948060056773963
absolute error = 6.916357213314e-19
relative error = 3.3641161485559296000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0137
y[1] (analytic) = 2.0563438206868188361093974912605
y[1] (numeric) = 2.0563438206868188368067688413318
absolute error = 6.973713500713e-19
relative error = 3.3913168753967319000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0138
y[1] (analytic) = 2.0567667626491155902920608802962
y[1] (numeric) = 2.0567667626491155909951781322491
absolute error = 7.031172519529e-19
relative error = 3.4185560789949998000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0139
y[1] (analytic) = 2.0571898786257971610779674963999
y[1] (numeric) = 2.057189878625797161786840941537
absolute error = 7.088734451371e-19
relative error = 3.4458338168114431000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 2.0576131687242798353909465020576
y[1] (numeric) = 2.0576131687242798361055864498769
absolute error = 7.146399478193e-19
relative error = 3.4731501464017980000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0141
y[1] (analytic) = 2.0580366330520683268162173286684
y[1] (numeric) = 2.0580366330520683275366341068983
absolute error = 7.204167782299e-19
relative error = 3.5005051254190841000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0142
y[1] (analytic) = 2.0584602717167558666117743927542
y[1] (numeric) = 2.0584602717167558673379783473879
absolute error = 7.262039546337e-19
relative error = 3.5278988116105146000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0143
y[1] (analytic) = 2.0588840848260242948322009470867
y[1] (numeric) = 2.0588840848260242955642024424175
absolute error = 7.320014953308e-19
relative error = 3.5553312628216956000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0144
y[1] (analytic) = 2.0593080724876441515650741350906
y[1] (numeric) = 2.0593080724876441523028835537468
absolute error = 7.378094186562e-19
relative error = 3.5828025369945072000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0145
y[1] (analytic) = 2.0597322348094747682801235839341
y[1] (numeric) = 2.0597322348094747690237513269138
absolute error = 7.436277429797e-19
relative error = 3.6103126921664435000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0146
y[1] (analytic) = 2.0601565718994643592913061392666
y[1] (numeric) = 2.0601565718994643600407626259731
absolute error = 7.494564867065e-19
relative error = 3.6378617864733510000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0147
y[1] (analytic) = 2.0605810838656501133319596126108
y[1] (numeric) = 2.0605810838656501140872552808876
absolute error = 7.552956682768e-19
relative error = 3.6654498781473103999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0148
y[1] (analytic) = 2.0610057708161582852431986809563
y[1] (numeric) = 2.0610057708161582860043439871225
absolute error = 7.611453061662e-19
relative error = 3.6930770255184024000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=1.56
NO POLE
x[1] = 0.0149
y[1] (analytic) = 2.0614306328592042877757163471449
y[1] (numeric) = 2.0614306328592042885427217660304
absolute error = 7.670054188855e-19
relative error = 3.7207432870135605000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 2.0618556701030927835051546391753
y[1] (numeric) = 2.0618556701030927842780306641563
absolute error = 7.728760249810e-19
relative error = 3.7484487211578499999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0151
y[1] (analytic) = 2.0622808826562177768612084965972
y[1] (numeric) = 2.0622808826562177776399656396318
absolute error = 7.787571430346e-19
relative error = 3.7761933865747754000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0152
y[1] (analytic) = 2.0627062706270627062706270627063
y[1] (numeric) = 2.0627062706270627070552758543697
absolute error = 7.846487916634e-19
relative error = 3.8039773419841631999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0153
y[1] (analytic) = 2.0631318341242005364142768722921
y[1] (numeric) = 2.0631318341242005372048278618127
absolute error = 7.905509895206e-19
relative error = 3.8318006462063482000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0154
y[1] (analytic) = 2.0635575732562938505984316962443
y[1] (numeric) = 2.063557573256293851394895451539
absolute error = 7.964637552947e-19
relative error = 3.8596633581581162000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0155
y[1] (analytic) = 2.0639834881320949432404540763674
y[1] (numeric) = 2.0639834881320949440428411840776
absolute error = 8.023871077102e-19
relative error = 3.8875655368559190000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0156
y[1] (analytic) = 2.0644095788604459124690338563171
y[1] (numeric) = 2.0644095788604459132773549218446
absolute error = 8.083210655275e-19
relative error = 3.9155072414152100000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0157
y[1] (analytic) = 2.0648358455502787528391492876316
y[1] (numeric) = 2.0648358455502787536534149351744
absolute error = 8.142656475428e-19
relative error = 3.9434885310497804000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0158
y[1] (analytic) = 2.0652622883106154481619165634036
y[1] (numeric) = 2.0652622883106154489821374359918
absolute error = 8.202208725882e-19
relative error = 3.9715094650720643999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0159
y[1] (analytic) = 2.0656889072505680644494939062177
y[1] (numeric) = 2.0656889072505680652756806657501
absolute error = 8.261867595324e-19
relative error = 3.9995701028963484000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 2.0661157024793388429752066115702
y[1] (numeric) = 2.0661157024793388438073699388498
absolute error = 8.321633272796e-19
relative error = 4.0276705040332640000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0161
y[1] (analytic) = 2.0665426741062202934490597230833
y[1] (numeric) = 2.0665426741062202942872103178539
absolute error = 8.381505947706e-19
relative error = 4.0558107280949334000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0162
y[1] (analytic) = 2.0669698222405952873088052914427
y[1] (numeric) = 2.0669698222405952881529538724254
absolute error = 8.441485809827e-19
relative error = 4.0839908347943026000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0163
y[1] (analytic) = 2.0673971469919371511267314451106
y[1] (numeric) = 2.0673971469919371519768887500396
absolute error = 8.501573049290e-19
relative error = 4.1122108839415730000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0164
y[1] (analytic) = 2.0678246484698097601323407775021
y[1] (numeric) = 2.0678246484698097609885175631617
absolute error = 8.561767856596e-19
relative error = 4.1404709354498255999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.1MB, time=1.72
NO POLE
x[1] = 0.0165
y[1] (analytic) = 2.0682523267838676318510858324716
y[1] (numeric) = 2.0682523267838676327132928747326
absolute error = 8.622070422610e-19
relative error = 4.1687710493319349999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0166
y[1] (analytic) = 2.068680182043856019859329747621
y[1] (numeric) = 2.0686801820438560207275778414772
absolute error = 8.682480938562e-19
relative error = 4.1971112857008708000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0167
y[1] (analytic) = 2.0691082143596110076557003931306
y[1] (numeric) = 2.0691082143596110085300003527355
absolute error = 8.742999596049e-19
relative error = 4.2254917047704816999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0168
y[1] (analytic) = 2.0695364238410596026490066225166
y[1] (numeric) = 2.0695364238410596035293692812204
absolute error = 8.803626587038e-19
relative error = 4.2539123668567615999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0169
y[1] (analytic) = 2.069964810598219830262885530946
y[1] (numeric) = 2.0699648105982198311493217413322
absolute error = 8.864362103862e-19
relative error = 4.2823733323757321999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 2.0703933747412008281573498964803
y[1] (numeric) = 2.0703933747412008290498705304028
absolute error = 8.925206339225e-19
relative error = 4.3108746618456750000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0171
y[1] (analytic) = 2.0708221163802029405674052598882
y[1] (numeric) = 2.070822116380202941466021208508
absolute error = 8.986159486198e-19
relative error = 4.3394164158850141999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0172
y[1] (analytic) = 2.0712510356255178127589063794532
y[1] (numeric) = 2.0712510356255178136636285532759
absolute error = 9.047221738227e-19
relative error = 4.3679986552159956000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0173
y[1] (analytic) = 2.0716801325875284856018230785167
y[1] (numeric) = 2.0716801325875284865126624074294
absolute error = 9.108393289127e-19
relative error = 4.3966214406616029000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0174
y[1] (analytic) = 2.0721094073767094902610857853295
y[1] (numeric) = 2.0721094073767094911780532186382
absolute error = 9.169674333087e-19
relative error = 4.4252848331477861999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0175
y[1] (analytic) = 2.0725388601036269430051813471503
y[1] (numeric) = 2.0725388601036269439282878536171
absolute error = 9.231065064668e-19
relative error = 4.4539888937023099999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0176
y[1] (analytic) = 2.0729684908789386401326699834163
y[1] (numeric) = 2.0729684908789386410619265512967
absolute error = 9.292565678804e-19
relative error = 4.4827336834550495999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0177
y[1] (analytic) = 2.0733982998133941530167945262285
y[1] (numeric) = 2.0733982998133941539522121633092
absolute error = 9.354176370807e-19
relative error = 4.5115192636402161000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0178
y[1] (analytic) = 2.0738282870178349232683533803401
y[1] (numeric) = 2.0738282870178349242099431139762
absolute error = 9.415897336361e-19
relative error = 4.5403456955932742000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0179
y[1] (analytic) = 2.0742584526031943580170089193113
y[1] (numeric) = 2.0742584526031943589647817964641
absolute error = 9.477728771528e-19
relative error = 4.5692130407536488000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=4.1MB, time=1.88
x[1] = 0.018
y[1] (analytic) = 2.0746887966804979253112033195021
y[1] (numeric) = 2.0746887966804979262651704067767
absolute error = 9.539670872746e-19
relative error = 4.5981213606635719999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0181
y[1] (analytic) = 2.0751193193608632496368541191118
y[1] (numeric) = 2.0751193193608632505970265027952
absolute error = 9.601723836834e-19
relative error = 4.6270707169703046000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0182
y[1] (analytic) = 2.07555002075550020755500207555
y[1] (numeric) = 2.0755500207555002085213908616486
absolute error = 9.663887860986e-19
relative error = 4.6560611714230548000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0183
y[1] (analytic) = 2.0759809009757110234585841810255
y[1] (numeric) = 2.0759809009757110244312004953033
absolute error = 9.726163142778e-19
relative error = 4.6850927858761626000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0184
y[1] (analytic) = 2.0764119601328903654485049833887
y[1] (numeric) = 2.0764119601328903664273599714051
absolute error = 9.788549880164e-19
relative error = 4.7141656222869824000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0185
y[1] (analytic) = 2.0768431983385254413291796469367
y[1] (numeric) = 2.0768431983385254423142844740848
absolute error = 9.851048271481e-19
relative error = 4.7432797427181014999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0186
y[1] (analytic) = 2.0772746157041960947237224761113
y[1] (numeric) = 2.0772746157041960957150883276562
absolute error = 9.913658515449e-19
relative error = 4.7724352093371486000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0187
y[1] (analytic) = 2.0777062123415749013089549137752
y[1] (numeric) = 2.0777062123415749023065929948919
absolute error = 9.976380811167e-19
relative error = 4.8016320844146771000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0188
y[1] (analytic) = 2.0781379883624272651704073150457
y[1] (numeric) = 2.0781379883624272661743288508578
absolute error = 1.0039215358121e-18
relative error = 4.8308704303278252000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0189
y[1] (analytic) = 2.0785699438786115152774890875078
y[1] (numeric) = 2.0785699438786115162877053231257
absolute error = 1.0102162356179e-18
relative error = 4.8601503095577169000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 2.0790020790020790020790020790021
y[1] (numeric) = 2.0790020790020790030955242795617
absolute error = 1.0165222005596e-18
relative error = 4.8894717846916760000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0191
y[1] (analytic) = 2.0794343938448741942191723851112
y[1] (numeric) = 2.0794343938448741952420118358124
absolute error = 1.0228394507012e-18
relative error = 4.9188349184220708000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0192
y[1] (analytic) = 2.0798668885191347753743760399334
y[1] (numeric) = 2.0798668885191347764035440460787
absolute error = 1.0291680061453e-18
relative error = 4.9482397735466024000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0193
y[1] (analytic) = 2.0802995631370917412107343457458
y[1] (numeric) = 2.0802995631370917422462422327791
absolute error = 1.0355078870333e-18
relative error = 4.9776864129690731000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0194
y[1] (analytic) = 2.0807324178110694964627548897212
y[1] (numeric) = 2.0807324178110694975046140032669
absolute error = 1.0418591135457e-18
relative error = 5.0071748997006342000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0195
y[1] (analytic) = 2.0811654526534859521331945889698
y[1] (numeric) = 2.0811654526534859531814162948714
absolute error = 1.0482217059016e-18
relative error = 5.0367052968571880000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.1MB, time=2.04
NO POLE
x[1] = 0.0196
y[1] (analytic) = 2.0815986677768526228143213988343
y[1] (numeric) = 2.0815986677768526238689170831934
absolute error = 1.0545956843591e-18
relative error = 5.0662776676611164000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0197
y[1] (analytic) = 2.0820320632937747241307516135748
y[1] (numeric) = 2.0820320632937747251917326827905
absolute error = 1.0609810692157e-18
relative error = 5.0958920754430071000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0198
y[1] (analytic) = 2.0824656393169512703040399833403
y[1] (numeric) = 2.0824656393169512713714178641479
absolute error = 1.0673778808076e-18
relative error = 5.1255485836380951999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0199
y[1] (analytic) = 2.082899395959175171839200166632
y[1] (numeric) = 2.0828993959591751729129863061428
absolute error = 1.0737861395108e-18
relative error = 5.1552472557913507999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 2.0833333333333333333333333333333
y[1] (numeric) = 2.0833333333333333344135391990736
absolute error = 1.0802058657403e-18
relative error = 5.1849881555534400000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0201
y[1] (analytic) = 2.0837674515524067514065430297979
y[1] (numeric) = 2.0837674515524067524931801097483
absolute error = 1.0866370799504e-18
relative error = 5.2147713466819695999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0202
y[1] (analytic) = 2.0842017507294706127553147144644
y[1] (numeric) = 2.0842017507294706138483945170997
absolute error = 1.0930798026353e-18
relative error = 5.2445968930441693999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0203
y[1] (analytic) = 2.0846362309776943923285386700021
y[1] (numeric) = 2.0846362309776943934280727243306
absolute error = 1.0995340543285e-18
relative error = 5.2744648586138145000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0204
y[1] (analytic) = 2.0850708924103419516263552960801
y[1] (numeric) = 2.0850708924103419527323551516832
absolute error = 1.1059998556031e-18
relative error = 5.3043753074724675999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0205
y[1] (analytic) = 2.0855057351407716371220020855057
y[1] (numeric) = 2.085505735140771638234479312578
absolute error = 1.1124772270723e-18
relative error = 5.3343283038116785000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0206
y[1] (analytic) = 2.0859407592824363788068418856904
y[1] (numeric) = 2.0859407592824363799258080750792
absolute error = 1.1189661893888e-18
relative error = 5.3643239119299072000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0207
y[1] (analytic) = 2.086375964948883788858752347173
y[1] (numeric) = 2.0863759649488837899842191104183
absolute error = 1.1254667632453e-18
relative error = 5.3943621962347228999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0208
y[1] (analytic) = 2.0868113522537562604340567612688
y[1] (numeric) = 2.0868113522537562615660357306435
absolute error = 1.1319789693747e-18
relative error = 5.4244432212435624000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0209
y[1] (analytic) = 2.0872469213107910665831767898142
y[1] (numeric) = 2.087246921310791067721679618364
absolute error = 1.1385028285498e-18
relative error = 5.4545670515820918000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 2.0876826722338204592901878914405
y[1] (numeric) = 2.087682672233820460435226253024
absolute error = 1.1450383615835e-18
relative error = 5.4847337519849650000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0211
y[1] (analytic) = 2.0881186051367717686364585508457
y[1] (numeric) = 2.0881186051367717697880441401749
absolute error = 1.1515855893292e-18
relative error = 5.5149433872975388000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.1MB, time=2.20
NO POLE
x[1] = 0.0212
y[1] (analytic) = 2.0885547201336675020885547201337
y[1] (numeric) = 2.0885547201336675032466992528142
absolute error = 1.1581445326805e-18
relative error = 5.5451960224742339999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0213
y[1] (analytic) = 2.0889910173386254439105911844579
y[1] (numeric) = 2.0889910173386254450753063970294
absolute error = 1.1647152125715e-18
relative error = 5.5754917225797705000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0214
y[1] (analytic) = 2.0894274968658587547012118679482
y[1] (numeric) = 2.0894274968658587558725095179249
absolute error = 1.1712976499767e-18
relative error = 5.6058305527884862000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0215
y[1] (analytic) = 2.089864158829676071055381400209
y[1] (numeric) = 2.0898641588296760722332732661204
absolute error = 1.1778918659114e-18
relative error = 5.6362125783860490000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0216
y[1] (analytic) = 2.0903010033444816053511705685619
y[1] (numeric) = 2.0903010033444816065356684499933
absolute error = 1.1844978814314e-18
relative error = 5.6666378647678175999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0217
y[1] (analytic) = 2.0907380305247752456617185866611
y[1] (numeric) = 2.0907380305247752468528343042945
absolute error = 1.1911157176334e-18
relative error = 5.6971064774405522000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0218
y[1] (analytic) = 2.0911752404851526557925554161439
y[1] (numeric) = 2.0911752404851526569903008117988
absolute error = 1.1977453956549e-18
relative error = 5.7276184820217317999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0219
y[1] (analytic) = 2.0916126333403053754444676845848
y[1] (numeric) = 2.0916126333403053766488546212592
absolute error = 1.2043869366744e-18
relative error = 5.7581739442403064000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 2.0920502092050209205020920502092
y[1] (numeric) = 2.0920502092050209217131324121205
absolute error = 1.2110403619113e-18
relative error = 5.7887729299360140000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0221
y[1] (analytic) = 2.092487968194182883448420171584
y[1] (numeric) = 2.0924879681941828846661258642103
absolute error = 1.2177056926263e-18
relative error = 5.8194155050610877000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0222
y[1] (analytic) = 2.0929259104227710339053997488489
y[1] (numeric) = 2.0929259104227710351297826989701
absolute error = 1.2243829501212e-18
relative error = 5.8501017356790936000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0223
y[1] (analytic) = 2.093364036005861419300816411974
y[1] (numeric) = 2.0933640360058614205318885677132
absolute error = 1.2310721557392e-18
relative error = 5.8808316879661584000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0224
y[1] (analytic) = 2.0938023450586264656616415410385
y[1] (numeric) = 2.0938023450586264668994148719032
absolute error = 1.2377733308647e-18
relative error = 5.9116054282098072000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0225
y[1] (analytic) = 2.0942408376963350785340314136126
y[1] (numeric) = 2.0942408376963350797785179105363
absolute error = 1.2444864969237e-18
relative error = 5.9424230228106674999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0226
y[1] (analytic) = 2.0946795140343527440301633850021
y[1] (numeric) = 2.0946795140343527452813750603861
absolute error = 1.2512116753840e-18
relative error = 5.9732845382832160000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0227
y[1] (analytic) = 2.0951183741881416300020951183742
y[1] (numeric) = 2.0951183741881416312600440061288
absolute error = 1.2579488877546e-18
relative error = 6.0041900412527058000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.1MB, time=2.37
NO POLE
x[1] = 0.0228
y[1] (analytic) = 2.0955574182732606873428331936295
y[1] (numeric) = 2.095557418273260688607531349216
absolute error = 1.2646981555865e-18
relative error = 6.0351395984587780000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0229
y[1] (analytic) = 2.0959966464053657514147977363236
y[1] (numeric) = 2.095996646405365752686257236796
absolute error = 1.2714595004724e-18
relative error = 6.0661332767538204000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 2.0964360587002096436058700209644
y[1] (numeric) = 2.0964360587002096448841029650114
absolute error = 1.2782329440470e-18
relative error = 6.0971711431041899999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0231
y[1] (analytic) = 2.0968756552736422730132103166282
y[1] (numeric) = 2.0968756552736422742982288246154
absolute error = 1.2850185079872e-18
relative error = 6.1282532645909568000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0232
y[1] (analytic) = 2.097315436241610738255033557047
y[1] (numeric) = 2.0973154362416107395468497710585
absolute error = 1.2918162140115e-18
relative error = 6.1593797084068319999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0233
y[1] (analytic) = 2.0977554017201594294105307321166
y[1] (numeric) = 2.0977554017201594307091568159977
absolute error = 1.2986260838811e-18
relative error = 6.1905505418612037000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0234
y[1] (analytic) = 2.0981955518254301300881242131767
y[1] (numeric) = 2.0981955518254301313935723525758
absolute error = 1.3054481393991e-18
relative error = 6.2217658323761105999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0235
y[1] (analytic) = 2.0986358866736621196222455403987
y[1] (numeric) = 2.09863588667366212093452794281
absolute error = 1.3122824024113e-18
relative error = 6.2530256474898445000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0236
y[1] (analytic) = 2.0990764063811922753988245172124
y[1] (numeric) = 2.099076406381192276717953412018
absolute error = 1.3191288948056e-18
relative error = 6.2843300548538784000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0237
y[1] (analytic) = 2.099517111064455175309678773882
y[1] (numeric) = 2.0995171110644551766356664123947
absolute error = 1.3259876385127e-18
relative error = 6.3156791222359901000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0238
y[1] (analytic) = 2.0999580008399832003359932801344
y[1] (numeric) = 2.0999580008399832016688519356402
absolute error = 1.3328586555058e-18
relative error = 6.3470729175186196000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0239
y[1] (analytic) = 2.100399075824406637261079605125
y[1] (numeric) = 2.1003990758244066386008215729259
absolute error = 1.3397419678009e-18
relative error = 6.3785115087000848999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 2.1008403361344537815126050420168
y[1] (numeric) = 2.1008403361344537828592426394737
absolute error = 1.3466375974569e-18
relative error = 6.4099949638948440000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0241
y[1] (analytic) = 2.1012817818869510401344820340408
y[1] (numeric) = 2.1012817818869510414880276006161
absolute error = 1.3535455665753e-18
relative error = 6.4415233513318526999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0242
y[1] (analytic) = 2.1017234131988230348886086591005
y[1] (numeric) = 2.1017234131988230362490745564015
absolute error = 1.3604658973010e-18
relative error = 6.4730967393581579999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=61.0MB, alloc=4.1MB, time=2.52
x[1] = 0.0243
y[1] (analytic) = 2.1021652301870927054866512507883
y[1] (numeric) = 2.1021652301870927068540498626101
absolute error = 1.3673986118218e-18
relative error = 6.5047151964363026000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0244
y[1] (analytic) = 2.1026072329688814129520605550883
y[1] (numeric) = 2.1026072329688814143264042874569
absolute error = 1.3743437323686e-18
relative error = 6.5363787911450616000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0245
y[1] (analytic) = 2.1030494216614090431125131440589
y[1] (numeric) = 2.1030494216614090444938144252746
absolute error = 1.3813012812157e-18
relative error = 6.5680875921806535000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0246
y[1] (analytic) = 2.1034917963819941102229701304165
y[1] (numeric) = 2.1034917963819941116112414110972
absolute error = 1.3882712806807e-18
relative error = 6.5998416683560478000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0247
y[1] (analytic) = 2.1039343572480538607195455501788
y[1] (numeric) = 2.1039343572480538621147993033036
absolute error = 1.3952537531248e-18
relative error = 6.6316410886021744000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0248
y[1] (analytic) = 2.1043771043771043771043771043771
y[1] (numeric) = 2.1043771043771043785066258253296
absolute error = 1.4022487209525e-18
relative error = 6.6634859219662800000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0249
y[1] (analytic) = 2.1048200378867606819616922753105
y[1] (numeric) = 2.1048200378867606833709484819226
absolute error = 1.4092562066121e-18
relative error = 6.6953762376140870999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 2.1052631578947368421052631578947
y[1] (numeric) = 2.1052631578947368435215393904905
absolute error = 1.4162762325958e-18
relative error = 6.7273121048300500000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0251
y[1] (analytic) = 2.1057064645188460728574436723521
y[1] (numeric) = 2.1057064645188460742807524937913
absolute error = 1.4233088214392e-18
relative error = 6.7592935930147607999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0252
y[1] (analytic) = 2.1061499578770008424599831508003
y[1] (numeric) = 2.1061499578770008438903371465227
absolute error = 1.4303539957224e-18
relative error = 6.7913207716899552000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0253
y[1] (analytic) = 2.1065936380872129766168106172319
y[1] (numeric) = 2.1065936380872129780542223953009
absolute error = 1.4374117780690e-18
relative error = 6.8233937104935430000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0254
y[1] (analytic) = 2.1070375052675937631689844079225
y[1] (numeric) = 2.1070375052675937646134665990694
absolute error = 1.4444821911469e-18
relative error = 6.8555124791831873999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0255
y[1] (analytic) = 2.1074815595363540569020021074816
y[1] (numeric) = 2.10748155953635405835356736515
absolute error = 1.4515652576684e-18
relative error = 6.8876771476365579999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0256
y[1] (analytic) = 2.1079258010118043844856661045531
y[1] (numeric) = 2.1079258010118043859443271049431
absolute error = 1.4586610003900e-18
relative error = 6.9198877858501600000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0257
y[1] (analytic) = 2.1083702298123550495467004005903
y[1] (numeric) = 2.1083702298123550510124698427027
absolute error = 1.4657694421124e-18
relative error = 6.9521444639391132000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0258
y[1] (analytic) = 2.108814846056516237874314635175
y[1] (numeric) = 2.1088148460565162393472052408559
absolute error = 1.4728906056809e-18
relative error = 6.9844472521388278000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.1MB, time=2.68
NO POLE
x[1] = 0.0259
y[1] (analytic) = 2.1092596498628981227589116220207
y[1] (numeric) = 2.1092596498628981242389361360061
absolute error = 1.4800245139854e-18
relative error = 7.0167962208047813999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 2.109704641350210970464135021097
y[1] (numeric) = 2.1097046413502109719513062110578
absolute error = 1.4871711899608e-18
relative error = 7.0491914404141920000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0261
y[1] (analytic) = 2.1101498206372652458324541042414
y[1] (numeric) = 2.1101498206372652473267847608275
absolute error = 1.4943306565861e-18
relative error = 7.0816329815615279000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0262
y[1] (analytic) = 2.110595187842971718024482904179
y[1] (numeric) = 2.1105951878429717195259858410648
absolute error = 1.5015029368858e-18
relative error = 7.1141209149649203999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0263
y[1] (analytic) = 2.1110407430863415663922313700654
y[1] (numeric) = 2.1110407430863415679009194239946
absolute error = 1.5086880539292e-18
relative error = 7.1466553114626204000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0264
y[1] (analytic) = 2.1114864864864864864864864864865
y[1] (numeric) = 2.1114864864864864880023725173169
absolute error = 1.5158860308304e-18
relative error = 7.1792362420127744000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0265
y[1] (analytic) = 2.1119324181626187961985216473073
y[1] (numeric) = 2.1119324181626187977216185380563
absolute error = 1.5230968907490e-18
relative error = 7.2118637776965150000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0266
y[1] (analytic) = 2.1123785382340515420363329108576
y[1] (numeric) = 2.1123785382340515435666535677473
absolute error = 1.5303206568897e-18
relative error = 7.2445379897158398000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0267
y[1] (analytic) = 2.1128248468201986055356010986689
y[1] (numeric) = 2.1128248468201986070731584511715
absolute error = 1.5375573525026e-18
relative error = 7.2772589493948058000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0268
y[1] (analytic) = 2.1132713440405748098055790363483
y[1] (numeric) = 2.1132713440405748113503860372315
absolute error = 1.5448070008832e-18
relative error = 7.3100267281793023999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0269
y[1] (analytic) = 2.1137180300147960262101035721835
y[1] (numeric) = 2.1137180300147960277621731975562
absolute error = 1.5520696253727e-18
relative error = 7.3428413976382436999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 2.114164904862579281183932346723
y[1] (numeric) = 2.1141649048625792827432775960808
absolute error = 1.5593452493578e-18
relative error = 7.3757030294623940000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0271
y[1] (analytic) = 2.1146119687037428631846056248678
y[1] (numeric) = 2.1146119687037428647512395211387
absolute error = 1.5666338962709e-18
relative error = 7.4086116954650861000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0272
y[1] (analytic) = 2.1150592216582064297800338409475
y[1] (numeric) = 2.1150592216582064313539694305379
absolute error = 1.5739355895904e-18
relative error = 7.4415674675834112000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0273
y[1] (analytic) = 2.1155066638459911148720118468373
y[1] (numeric) = 2.1155066638459911164532621996779
absolute error = 1.5812503528406e-18
relative error = 7.4745704178775162000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0274
y[1] (analytic) = 2.1159542953872196360558611933982
y[1] (numeric) = 2.1159542953872196376444394029901
absolute error = 1.5885782095919e-18
relative error = 7.5076206185313194000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.1MB, time=2.84
NO POLE
x[1] = 0.0275
y[1] (analytic) = 2.1164021164021164021164021164021
y[1] (numeric) = 2.1164021164021164037123212998628
absolute error = 1.5959191834607e-18
relative error = 7.5407181418518075000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0276
y[1] (analytic) = 2.1168501270110076206604572396274
y[1] (numeric) = 2.1168501270110076222637305377372
absolute error = 1.6032732981098e-18
relative error = 7.5738630602706952000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0277
y[1] (analytic) = 2.1172983273343214058860893499894
y[1] (numeric) = 2.1172983273343214074967299272375
absolute error = 1.6106405772481e-18
relative error = 7.6070554463427763000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0278
y[1] (analytic) = 2.1177467174925878864887759423973
y[1] (numeric) = 2.1177467174925878881067969870285
absolute error = 1.6180210446312e-18
relative error = 7.6402953727485264000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0279
y[1] (analytic) = 2.1181952976064393137047235755137
y[1] (numeric) = 2.1181952976064393153301382995748
absolute error = 1.6254147240611e-18
relative error = 7.6735829122924530999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 2.1186440677966101694915254237288
y[1] (numeric) = 2.1186440677966101711243470631154
absolute error = 1.6328216393866e-18
relative error = 7.7069181379047520000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0281
y[1] (analytic) = 2.1190930281839372748463657554567
y[1] (numeric) = 2.1190930281839372764866075699596
absolute error = 1.6402418145029e-18
relative error = 7.7403011226391850999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0282
y[1] (analytic) = 2.1195421788893598982619754133107
y[1] (numeric) = 2.1195421788893598999096506866632
absolute error = 1.6476752733525e-18
relative error = 7.7737319396770950000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0283
y[1] (analytic) = 2.1199915200339198643205427178291
y[1] (numeric) = 2.1199915200339198659756647577535
absolute error = 1.6551220399244e-18
relative error = 7.8072106623233948000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0284
y[1] (analytic) = 2.1204410517387616624257845631891
y[1] (numeric) = 2.120441051738761664088366701444
absolute error = 1.6625821382549e-18
relative error = 7.8407373640101084000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0285
y[1] (analytic) = 2.1208907741251325556733828207847
y[1] (numeric) = 2.1208907741251325573434384132121
absolute error = 1.6700555924274e-18
relative error = 7.8743121182951910000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0286
y[1] (analytic) = 2.1213406873143826898599915146372
y[1] (numeric) = 2.1213406873143826915375339412098
absolute error = 1.6775424265726e-18
relative error = 7.9079349988632364000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0287
y[1] (analytic) = 2.1217907914279652026310205813707
y[1] (numeric) = 2.121790791427965204316063246239
absolute error = 1.6850426648683e-18
relative error = 7.9416060795242978999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0288
y[1] (analytic) = 2.12224108658743633276740237691
y[1] (numeric) = 2.1222410865874363344599587084501
absolute error = 1.6925563315401e-18
relative error = 7.9753254342169512000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0289
y[1] (analytic) = 2.1226915729144555296115474421567
y[1] (numeric) = 2.1226915729144555313116308930175
absolute error = 1.7000834508608e-18
relative error = 8.0090931370052287999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 2.1231422505307855626326963906582
y[1] (numeric) = 2.1231422505307855643403204378094
absolute error = 1.7076240471512e-18
relative error = 8.0429092620821519999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.1MB, time=3.01
NO POLE
x[1] = 0.0291
y[1] (analytic) = 2.1235931195582926311318751327246
y[1] (numeric) = 2.1235931195582926328470532775042
absolute error = 1.7151781447796e-18
relative error = 8.0767738837671363999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0292
y[1] (analytic) = 2.1240441801189464740866610025489
y[1] (numeric) = 2.1240441801189464758094067707111
absolute error = 1.7227457681622e-18
relative error = 8.1106870765076375999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0293
y[1] (analytic) = 2.1244954323348204801359677076694
y[1] (numeric) = 2.1244954323348204818662946494327
absolute error = 1.7303269417633e-18
relative error = 8.1446489148798531000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0294
y[1] (analytic) = 2.1249468763280917977050573735657
y[1] (numeric) = 2.1249468763280917994429790636607
absolute error = 1.7379216900950e-18
relative error = 8.1786594735870699999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0295
y[1] (analytic) = 2.1253985122210414452709883103082
y[1] (numeric) = 2.1253985122210414470165183480261
absolute error = 1.7455300377179e-18
relative error = 8.2127188274627194999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0296
y[1] (analytic) = 2.1258503401360544217687074829932
y[1] (numeric) = 2.1258503401360544235218594922338
absolute error = 1.7531520092406e-18
relative error = 8.2468270514677824000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0297
y[1] (analytic) = 2.1263023601956198171379970231767
y[1] (numeric) = 2.1263023601956198188987846524969
absolute error = 1.7607876293202e-18
relative error = 8.2809842206929006000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0298
y[1] (analytic) = 2.1267545725223309230114844746916
y[1] (numeric) = 2.1267545725223309247799213973539
absolute error = 1.7684369226623e-18
relative error = 8.3151904103581346000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0299
y[1] (analytic) = 2.12720697723888534354392682408
y[1] (numeric) = 2.127206977238885345320026738101
absolute error = 1.7760999140210e-18
relative error = 8.3494456958127209999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 2.1276595744680851063829787234043
y[1] (numeric) = 2.1276595744680851081667553516034
absolute error = 1.7837766281991e-18
relative error = 8.3837501525357699999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0301
y[1] (analytic) = 2.1281123643328367737816556714194
y[1] (numeric) = 2.1281123643328367755731227614678
absolute error = 1.7914670900484e-18
relative error = 8.4181038561374316000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0302
y[1] (analytic) = 2.1285653469561515538527032779906
y[1] (numeric) = 2.1285653469561515556518746024598
absolute error = 1.7991713244692e-18
relative error = 8.4525068823563016000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0303
y[1] (analytic) = 2.1290185224611454119650840962316
y[1] (numeric) = 2.1290185224611454137719734526428
absolute error = 1.8068893564112e-18
relative error = 8.4869593070634064000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0304
y[1] (analytic) = 2.129471890971039182282793867121
y[1] (numeric) = 2.1294718909710391840974150779939
absolute error = 1.8146212108729e-18
relative error = 8.5214612062591383999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0305
y[1] (analytic) = 2.1299254526091586794462193823216
y[1] (numeric) = 2.129925452609158681268586295224
absolute error = 1.8223669129024e-18
relative error = 8.5560126560767680000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0306
y[1] (analytic) = 2.1303792074989348103962505325948
y[1] (numeric) = 2.1303792074989348122263770201914
absolute error = 1.8301264875966e-18
memory used=76.2MB, alloc=4.1MB, time=3.18
relative error = 8.5906137327784404000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0307
y[1] (analytic) = 2.1308331557639036863413594715534
y[1] (numeric) = 2.1308331557639036881792594316556
absolute error = 1.8378999601022e-18
relative error = 8.6252645127596245999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0308
y[1] (analytic) = 2.1312872975277067348678601875533
y[1] (numeric) = 2.1312872975277067367135475431688
absolute error = 1.8456873556155e-18
relative error = 8.6599650725479259999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0309
y[1] (analytic) = 2.1317416329140908121935621402686
y[1] (numeric) = 2.1317416329140908140470508396508
absolute error = 1.8534886993822e-18
relative error = 8.6947154888019002000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 2.1321961620469083155650319829424
y[1] (numeric) = 2.1321961620469083174263359996402
absolute error = 1.8613040166978e-18
relative error = 8.7295158383126820000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0311
y[1] (analytic) = 2.1326508850501172957986777564513
y[1] (numeric) = 2.1326508850501172976678110893589
absolute error = 1.8691333329076e-18
relative error = 8.7643661980037363999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0312
y[1] (analytic) = 2.1331058020477815699658703071672
y[1] (numeric) = 2.1331058020477815718428469805745
absolute error = 1.8769766734073e-18
relative error = 8.7992666449334224000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0313
y[1] (analytic) = 2.1335609131640708342223170471517
y[1] (numeric) = 2.1335609131640708361071511107937
absolute error = 1.8848340636420e-18
relative error = 8.8342172562900540000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0314
y[1] (analytic) = 2.1340162185232607767819035424669
y[1] (numeric) = 2.1340162185232607786746090715744
absolute error = 1.8927055291075e-18
relative error = 8.8692181093977450000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0315
y[1] (analytic) = 2.1344717182497331910352187833511
y[1] (numeric) = 2.1344717182497331929358098787008
absolute error = 1.9005910953497e-18
relative error = 8.9042692817133445000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0316
y[1] (analytic) = 2.1349274124679760888129803586678
y[1] (numeric) = 2.1349274124679760907214711466327
absolute error = 1.9084907879649e-18
relative error = 8.9393708508275916000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0317
y[1] (analytic) = 2.1353833013025838137945761264147
y[1] (numeric) = 2.1353833013025838157109807590146
absolute error = 1.9164046325999e-18
relative error = 8.9745228944653317000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0318
y[1] (analytic) = 2.1358393848782571550619393421615
y[1] (numeric) = 2.1358393848782571569862719971137
absolute error = 1.9243326549522e-18
relative error = 9.0097254904862003999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0319
y[1] (analytic) = 2.1362956633198034607989745780816
y[1] (numeric) = 2.1362956633198034627312494588516
absolute error = 1.9322748807700e-18
relative error = 9.0449787168843700000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 2.1367521367521367521367521367521
y[1] (numeric) = 2.1367521367521367540769834726044
absolute error = 1.9402313358523e-18
relative error = 9.0802826517887640000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0321
y[1] (analytic) = 2.1372088053002778371446890361188
y[1] (numeric) = 2.1372088053002778390928910821678
absolute error = 1.9482020460490e-18
relative error = 9.1156373734632710000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=80.1MB, alloc=4.1MB, time=3.34
x[1] = 0.0322
y[1] (analytic) = 2.1376656690893544249679350149637
y[1] (numeric) = 2.1376656690893544269241220522248
absolute error = 1.9561870372611e-18
relative error = 9.1510429603074257999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0323
y[1] (analytic) = 2.1381227282446012401111823818687
y[1] (numeric) = 2.1381227282446012420753687173096
absolute error = 1.9641863354409e-18
relative error = 9.1864994908570893000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0324
y[1] (analytic) = 2.138579982891360136869118905047
y[1] (numeric) = 2.1385799828913601388413188716388
absolute error = 1.9721999665918e-18
relative error = 9.2220070437832568000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0325
y[1] (analytic) = 2.139037433155080213903743315508
y[1] (numeric) = 2.1390374331550802158839712722766
absolute error = 1.9802279567686e-18
relative error = 9.2575656978932050000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0326
y[1] (analytic) = 2.1394950791613179289687633718442
y[1] (numeric) = 2.139495079161317930957033703922
absolute error = 1.9882703320778e-18
relative error = 9.2931755321316372000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0327
y[1] (analytic) = 2.1399529210357372137812968114701
y[1] (numeric) = 2.1399529210357372157776239301473
absolute error = 1.9963271186772e-18
relative error = 9.3288366255785556000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0328
y[1] (analytic) = 2.140410958904109589041095890411
y[1] (numeric) = 2.1404109589041095910454942331875
absolute error = 2.0043983427765e-18
relative error = 9.3645490574518079999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0329
y[1] (analytic) = 2.1408691928923142795975165917362
y[1] (numeric) = 2.1408691928923142816100006223737
absolute error = 2.0124840306375e-18
relative error = 9.4003129071077625000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 2.1413276231263383297644539614561
y[1] (numeric) = 2.1413276231263383317850381700295
absolute error = 2.0205842085734e-18
relative error = 9.4361282540377780000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0331
y[1] (analytic) = 2.1417862497322767187834654101521
y[1] (numeric) = 2.141786249732276720812164313102
absolute error = 2.0286989029499e-18
relative error = 9.4719951778730830999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0332
y[1] (analytic) = 2.1422450728363324764353041988003
y[1] (numeric) = 2.1422450728363324784721323389851
absolute error = 2.0368281401848e-18
relative error = 9.5079137583826464000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0333
y[1] (analytic) = 2.1427040925648167988000857081637
y[1] (numeric) = 2.1427040925648168008450576549116
absolute error = 2.0449719467479e-18
relative error = 9.5438840754724493000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0334
y[1] (analytic) = 2.1431633090441491641663094727818
y[1] (numeric) = 2.1431633090441491662194398219436
absolute error = 2.0531303491618e-18
relative error = 9.5799062091889588000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0335
y[1] (analytic) = 2.1436227224008574490889603429796
y[1] (numeric) = 2.143622722400857451150263716981
absolute error = 2.0613033740014e-18
relative error = 9.6159802397165310000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0336
y[1] (analytic) = 2.1440823327615780445969125214408
y[1] (numeric) = 2.144082332761578046666403569335
absolute error = 2.0694910478942e-18
relative error = 9.6521062473785488000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0337
y[1] (analytic) = 2.1445421402530559725498606047609
y[1] (numeric) = 2.1445421402530559746275540022815
absolute error = 2.0776933975206e-18
relative error = 9.6882843126385577999999999999999e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.1MB, time=3.51
NO POLE
x[1] = 0.0338
y[1] (analytic) = 2.1450021450021450021450021450021
y[1] (numeric) = 2.1450021450021450042309125946159
absolute error = 2.0859104496138e-18
relative error = 9.7245145160995356000000000000002e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0339
y[1] (analytic) = 2.1454623471358077665736966316241
y[1] (numeric) = 2.1454623471358077686678388625839
absolute error = 2.0941422309598e-18
relative error = 9.7607969385036278000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 2.1459227467811158798283261802575
y[1] (numeric) = 2.1459227467811158819307149486555
absolute error = 2.1023887683980e-18
relative error = 9.7971316607346800000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0341
y[1] (analytic) = 2.1463833440652500536595836016313
y[1] (numeric) = 2.146383344065250055770233690452
absolute error = 2.1106500888207e-18
relative error = 9.8335187638156412999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0342
y[1] (analytic) = 2.14684413911550021468441391155
y[1] (numeric) = 2.1468441391155002168033401307239
absolute error = 2.1189262191739e-18
relative error = 9.8699583289120262000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0343
y[1] (analytic) = 2.1473051320592656216448357311574
y[1] (numeric) = 2.147305132059265623772052917614
absolute error = 2.1272171864566e-18
relative error = 9.9064504373283862000000000000000e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0344
y[1] (analytic) = 2.1477663230240549828178694158076
y[1] (numeric) = 2.1477663230240549849533924335292
absolute error = 2.1355230177216e-18
relative error = 9.9429951705117695999999999999998e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0345
y[1] (analytic) = 2.1482277121374865735767991407089
y[1] (numeric) = 2.1482277121374865757206428807844
absolute error = 2.1438437400755e-18
relative error = 9.9795926100514525000000000000001e-17 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0346
y[1] (analytic) = 2.1486892995272883541039965620971
y[1] (numeric) = 2.1486892995272883562561759427754
absolute error = 2.1521793806783e-18
relative error = 1.0016242837676808200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0347
y[1] (analytic) = 2.1491510853212980872555340640447
y[1] (numeric) = 2.1491510853212980894160640307889
absolute error = 2.1605299667442e-18
relative error = 1.0052945935260762600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0348
y[1] (analytic) = 2.1496130696474634565778159931212
y[1] (numeric) = 2.1496130696474634587467115186626
absolute error = 2.1688955255414e-18
relative error = 1.0089701984818592800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0349
y[1] (analytic) = 2.1500752526338421844764566759837
y[1] (numeric) = 2.1500752526338421866537327603758
absolute error = 2.1772760843921e-18
relative error = 1.0126511068507657100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 2.1505376344086021505376344086022
y[1] (numeric) = 2.1505376344086021527233060792751
absolute error = 2.1856716706729e-18
relative error = 1.0163373268628985000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0351
y[1] (analytic) = 2.1510002151000215100021510002151
y[1] (numeric) = 2.1510002151000215121962333120299
absolute error = 2.1940823118148e-18
relative error = 1.0200288667627005200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0352
y[1] (analytic) = 2.1514629948364888123924268502582
y[1] (numeric) = 2.1514629948364888145949348855612
absolute error = 2.2025080353030e-18
relative error = 1.0237257348088344000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0353
y[1] (analytic) = 2.1519259737465031202926619324295
y[1] (numeric) = 2.1519259737465031225036108011073
absolute error = 2.2109488686778e-18
relative error = 1.0274279392745736600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.1MB, time=3.68
NO POLE
x[1] = 0.0354
y[1] (analytic) = 2.152389151958674128282393456737
y[1] (numeric) = 2.1523891519586741305017982962707
absolute error = 2.2194048395337e-18
relative error = 1.0311354884473570200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0355
y[1] (analytic) = 2.1528525296017222820236813778256
y[1] (numeric) = 2.1528525296017222842515573533461
absolute error = 2.2278759755205e-18
relative error = 1.0348483906292722500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0356
y[1] (analytic) = 2.1533161068044788975021533161068
y[1] (numeric) = 2.1533161068044788997385156204494
absolute error = 2.2363623043426e-18
relative error = 1.0385666541367034400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0357
y[1] (analytic) = 2.1537798836958862804221408572044
y[1] (numeric) = 2.1537798836958862826670047109642
absolute error = 2.2448638537598e-18
relative error = 1.0422902873006751400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0358
y[1] (analytic) = 2.1542438604049978457561395950022
y[1] (numeric) = 2.1542438604049978480095202465891
absolute error = 2.2533806515869e-18
relative error = 1.0460192984666389800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0359
y[1] (analytic) = 2.1547080370609782374488256841198
y[1] (numeric) = 2.1547080370609782397107384098141
absolute error = 2.2619127256943e-18
relative error = 1.0497536959947246300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 2.1551724137931034482758620689655
y[1] (numeric) = 2.155172413793103450546322172973
absolute error = 2.2704601040075e-18
relative error = 1.0534934882594800000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0361
y[1] (analytic) = 2.1556369907307609398577279586118
y[1] (numeric) = 2.1556369907307609421367507731195
absolute error = 2.2790228145077e-18
relative error = 1.0572386836501220300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0362
y[1] (analytic) = 2.1561017680034497628288055196205
y[1] (numeric) = 2.1561017680034497651164064048525
absolute error = 2.2876008852320e-18
relative error = 1.0609892905706016000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0363
y[1] (analytic) = 2.1565667457407806771619581626051
y[1] (numeric) = 2.1565667457407806794581525068781
absolute error = 2.2961943442730e-18
relative error = 1.0647453174393901000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0364
y[1] (analytic) = 2.157031924072476272648835202761
y[1] (numeric) = 2.1570319240724762749536384225404
absolute error = 2.3048032197794e-18
relative error = 1.0685067726897298400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0365
y[1] (analytic) = 2.1574973031283710895361380798274
y[1] (numeric) = 2.1574973031283710918495656197835
absolute error = 2.3134275399561e-18
relative error = 1.0722736647696523500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0366
y[1] (analytic) = 2.1579628830384117393180837289599
y[1] (numeric) = 2.1579628830384117416401510620238
absolute error = 2.3220673330639e-18
relative error = 1.0760460021418112600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0367
y[1] (analytic) = 2.1584286639326570256853011007986
y[1] (numeric) = 2.1584286639326570280160237282188
absolute error = 2.3307226274202e-18
relative error = 1.0798237932837786600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0368
y[1] (analytic) = 2.1588946459412780656303972366149
y[1] (numeric) = 2.1588946459412780679697906880133
absolute error = 2.3393934513984e-18
relative error = 1.0836070466877388800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0369
y[1] (analytic) = 2.159360829194558410710429712805
y[1] (numeric) = 2.1593608291945584130585095462341
absolute error = 2.3480798334291e-18
relative error = 1.0873957708610162100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.1MB, time=3.85
NO POLE
x[1] = 0.037
y[1] (analytic) = 2.1598272138228941684665226781857
y[1] (numeric) = 2.1598272138228941708233044801846
absolute error = 2.3567818019989e-18
relative error = 1.0911899743254907000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0371
y[1] (analytic) = 2.16029379995679412400086411752
y[1] (numeric) = 2.1602937999567941263663635031715
absolute error = 2.3654993856515e-18
relative error = 1.0949896656180793500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0372
y[1] (analytic) = 2.1607605877268798617113223854797
y[1] (numeric) = 2.1607605877268798640855549984674
absolute error = 2.3742326129877e-18
relative error = 1.0987948532907075600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0373
y[1] (analytic) = 2.1612275772638858871839204668252
y[1] (numeric) = 2.1612275772638858895669019794903
absolute error = 2.3829815126651e-18
relative error = 1.1026055459101417700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0374
y[1] (analytic) = 2.1616947686986597492434068309555
y[1] (numeric) = 2.1616947686986597516351529443541
absolute error = 2.3917461133986e-18
relative error = 1.1064217520581923600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0375
y[1] (analytic) = 2.1621621621621621621621621621622
y[1] (numeric) = 2.1621621621621621645626886061225
absolute error = 2.4005264439603e-18
relative error = 1.1102434803316387500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0376
y[1] (analytic) = 2.1626297577854671280276816608997
y[1] (numeric) = 2.1626297577854671304370041940795
absolute error = 2.4093225331798e-18
relative error = 1.1140707393423395200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0377
y[1] (analytic) = 2.1630975556997620592688730261735
y[1] (numeric) = 2.1630975556997620616870074361177
absolute error = 2.4181344099442e-18
relative error = 1.1179035377172036600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0378
y[1] (analytic) = 2.1635655560363479013414106447425
y[1] (numeric) = 2.1635655560363479037683727479409
absolute error = 2.4269621031984e-18
relative error = 1.1217418840983004800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0379
y[1] (analytic) = 2.1640337589266392555723869292361
y[1] (numeric) = 2.1640337589266392580081925711809
absolute error = 2.4358056419448e-18
relative error = 1.1255857871426920800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 2.1645021645021645021645021645022
y[1] (numeric) = 2.1645021645021645046091672197463
absolute error = 2.4446650552441e-18
relative error = 1.1294352555227742000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0381
y[1] (analytic) = 2.1649707728945659233600346395324
y[1] (numeric) = 2.1649707728945659258135750117473
absolute error = 2.4535403722149e-18
relative error = 1.1332902979260623100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0382
y[1] (analytic) = 2.165439584235599826764833261152
y[1] (numeric) = 2.165439584235599829227264883186
absolute error = 2.4624316220340e-18
relative error = 1.1371509230553012000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0383
y[1] (analytic) = 2.1659085986571366688325752653238
y[1] (numeric) = 2.1659085986571366713039140992601
absolute error = 2.4713388339363e-18
relative error = 1.1410171396283897100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0384
y[1] (analytic) = 2.1663778162911611785095320623917
y[1] (numeric) = 2.1663778162911611809897940996072
absolute error = 2.4802620372155e-18
relative error = 1.1448889563786748000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=95.3MB, alloc=4.1MB, time=4.01
x[1] = 0.0385
y[1] (analytic) = 2.1668472372697724810400866738895
y[1] (numeric) = 2.1668472372697724835292879351132
absolute error = 2.4892012612237e-18
relative error = 1.1487663820547375500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0386
y[1] (analytic) = 2.1673168617251842219332466406589
y[1] (numeric) = 2.1673168617251842244314031760306
absolute error = 2.4981565353717e-18
relative error = 1.1526494254205023800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0387
y[1] (analytic) = 2.1677866897897246910903967049642
y[1] (numeric) = 2.1677866897897246935975245940934
absolute error = 2.5071278891292e-18
relative error = 1.1565380952552999600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0388
y[1] (analytic) = 2.1682567215958369470945359930616
y[1] (numeric) = 2.1682567215958369496106513450861
absolute error = 2.5161153520245e-18
relative error = 1.1604324003536994000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0389
y[1] (analytic) = 2.1687269572760789416612448492735
y[1] (numeric) = 2.168726957276078944186363802919
absolute error = 2.5251189536455e-18
relative error = 1.1643323495259400500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 2.1691973969631236442516268980477
y[1] (numeric) = 2.1691973969631236467857656216868
absolute error = 2.5341387236391e-18
relative error = 1.1682379515976251000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0391
y[1] (analytic) = 2.1696680407897591668474723367325
y[1] (numeric) = 2.1696680407897591693906470284438
absolute error = 2.5431746917113e-18
relative error = 1.1721492154097381700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0392
y[1] (analytic) = 2.1701388888888888888888888888889
y[1] (numeric) = 2.1701388888888888914411157765169
absolute error = 2.5522268876280e-18
relative error = 1.1760661498189824000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0393
y[1] (analytic) = 2.1706099413935315823746472758845
y[1] (numeric) = 2.170609941393531584935942617099
absolute error = 2.5612953412145e-18
relative error = 1.1799887636975201500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0394
y[1] (analytic) = 2.1710811984368215371254884932696
y[1] (numeric) = 2.1710811984368215396958685756254
absolute error = 2.5703800823558e-18
relative error = 1.1839170659330814800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0395
y[1] (analytic) = 2.1715526601520086862106406080347
y[1] (numeric) = 2.1715526601520086887901217490315
absolute error = 2.5794811409968e-18
relative error = 1.1878510654290264000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0396
y[1] (analytic) = 2.1720243266724587315377932232841
y[1] (numeric) = 2.1720243266724587341263917704264
absolute error = 2.5885985471423e-18
relative error = 1.1917907711043149200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0397
y[1] (analytic) = 2.1724961981316532696067781881382
y[1] (numeric) = 2.1724961981316532722045105189957
absolute error = 2.5977323308575e-18
relative error = 1.1957361918937072500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0398
y[1] (analytic) = 2.1729682746631899174272055627988
y[1] (numeric) = 2.1729682746631899200340880850665
absolute error = 2.6068825222677e-18
relative error = 1.1996873367475955400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0399
y[1] (analytic) = 2.1734405564007824386003042816779
y[1] (numeric) = 2.1734405564007824412163534332365
absolute error = 2.6160491515586e-18
relative error = 1.2036442146321118600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 2.1739130434782608695652173913043
y[1] (numeric) = 2.1739130434782608721904496402807
absolute error = 2.6252322489764e-18
relative error = 1.2076068345291440000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.1MB, time=4.18
NO POLE
x[1] = 0.0401
y[1] (analytic) = 2.1743857360295716460100021743857
y[1] (numeric) = 2.1743857360295716486444340192136
absolute error = 2.6344318448279e-18
relative error = 1.2115752054363512100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0402
y[1] (analytic) = 2.174858634188777729447585906916
y[1] (numeric) = 2.1748586341887777320912338763969
absolute error = 2.6436479694809e-18
relative error = 1.2155493363673178200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0403
y[1] (analytic) = 2.1753317380900587339569284315858
y[1] (numeric) = 2.1753317380900587366098090849497
absolute error = 2.6528806533639e-18
relative error = 1.2195292363513848300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0404
y[1] (analytic) = 2.1758050478677110530896431679721
y[1] (numeric) = 2.1758050478677110557517730949389
absolute error = 2.6621299269668e-18
relative error = 1.2235149144339412800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0405
y[1] (analytic) = 2.1762785636561479869423286180631
y[1] (numeric) = 2.1762785636561479896137244389034
absolute error = 2.6713958208403e-18
relative error = 1.2275063796761178500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0406
y[1] (analytic) = 2.176752285589899869394862864606
y[1] (numeric) = 2.1767522855898998720755412302027
absolute error = 2.6806783655967e-18
relative error = 1.2315036411551239800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0407
y[1] (analytic) = 2.1772262138036141955149139995646
y[1] (numeric) = 2.1772262138036141982048915914742
absolute error = 2.6899775919096e-18
relative error = 1.2355067079640792800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0408
y[1] (analytic) = 2.1777003484320557491289198606272
y[1] (numeric) = 2.1777003484320557518282133911416
absolute error = 2.6992935305144e-18
relative error = 1.2395155892122124800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0409
y[1] (analytic) = 2.1781746896101067305597908952298
y[1] (numeric) = 2.1781746896101067332684171074379
absolute error = 2.7086262122081e-18
relative error = 1.2435302940247387100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 2.1786492374727668845315904139434
y[1] (numeric) = 2.1786492374727668872495660817929
absolute error = 2.7179756678495e-18
relative error = 1.2475508315429205000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0411
y[1] (analytic) = 2.1791239921551536282414469383308
y[1] (numeric) = 2.1791239921551536309687888666905
absolute error = 2.7273419283597e-18
relative error = 1.2515772109242663300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0412
y[1] (analytic) = 2.1795989537925021795989537925022
y[1] (numeric) = 2.1795989537925021823356788172239
absolute error = 2.7367250247217e-18
relative error = 1.2556094413423159600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0413
y[1] (analytic) = 2.1800741225201656856333115325921
y[1] (numeric) = 2.1800741225201656883794365205729
absolute error = 2.7461249879808e-18
relative error = 1.2596475319867929600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0414
y[1] (analytic) = 2.1805494984736153510684692542521
y[1] (numeric) = 2.1805494984736153538240111034969
absolute error = 2.7555418492448e-18
relative error = 1.2636914920636652800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0415
y[1] (analytic) = 2.1810250817884405670665212649945
y[1] (numeric) = 2.1810250817884405698314969046787
absolute error = 2.7649756396842e-18
relative error = 1.2677413307952057000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0416
y[1] (analytic) = 2.1815008726003490401396160558464
y[1] (numeric) = 2.1815008726003490429140424463782
absolute error = 2.7744263905318e-18
relative error = 1.2717970574197771200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.1MB, time=4.34
NO POLE
x[1] = 0.0417
y[1] (analytic) = 2.1819768710451669212306349552695
y[1] (numeric) = 2.1819768710451669240145290883531
absolute error = 2.7838941330836e-18
relative error = 1.2758586811922138800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0418
y[1] (analytic) = 2.1824530772588389349628982976866
y[1] (numeric) = 2.1824530772588389377562771963852
absolute error = 2.7933788986986e-18
relative error = 1.2799262113836985200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0419
y[1] (analytic) = 2.1829294913774285090591573892163
y[1] (numeric) = 2.182929491377428511862038108015
absolute error = 2.8028807187987e-18
relative error = 1.2839996572816844700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 2.1834061135371179039301310043668
y[1] (numeric) = 2.1834061135371179067425306292359
absolute error = 2.8123996248691e-18
relative error = 1.2880790281900478000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0421
y[1] (analytic) = 2.1838829438742083424328455994759
y[1] (numeric) = 2.1838829438742083452547812479343
absolute error = 2.8219356484584e-18
relative error = 1.2921643334291013600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0422
y[1] (analytic) = 2.1843599825251201397990388816077
y[1] (numeric) = 2.1843599825251201426305277027866
absolute error = 2.8314888211789e-18
relative error = 1.2962555823357004200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0423
y[1] (analytic) = 2.1848372296263928337338868254315
y[1] (numeric) = 2.1848372296263928365749460001379
absolute error = 2.8410591747064e-18
relative error = 1.3003527842631192800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0424
y[1] (analytic) = 2.1853146853146853146853146853147
y[1] (numeric) = 2.1853146853146853175359614260952
absolute error = 2.8506467407805e-18
relative error = 1.3044559485811568000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0425
y[1] (analytic) = 2.1857923497267759562841530054645
y[1] (numeric) = 2.1857923497267759591444045566694
absolute error = 2.8602515512049e-18
relative error = 1.3085650846762417500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0426
y[1] (analytic) = 2.1862702229995627459554000874508
y[1] (numeric) = 2.1862702229995627488252737252981
absolute error = 2.8698736378473e-18
relative error = 1.3126802019513550200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0427
y[1] (analytic) = 2.1867483052700634157008528318391
y[1] (numeric) = 2.1867483052700634185803658644787
absolute error = 2.8795130326396e-18
relative error = 1.3168013098260890800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0428
y[1] (analytic) = 2.1872265966754155730533683289589
y[1] (numeric) = 2.1872265966754155759425380965373
absolute error = 2.8891697675784e-18
relative error = 1.3209284177368444800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0429
y[1] (analytic) = 2.1877050973528768322030190330343
y[1] (numeric) = 2.1877050973528768351018629077587
absolute error = 2.8988438747244e-18
relative error = 1.3250615351365232400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 2.1881838074398249452954048140044
y[1] (numeric) = 2.1881838074398249482039402002075
absolute error = 2.9085353862031e-18
relative error = 1.3292006714948167000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0431
y[1] (analytic) = 2.1886627270737579339023856423725
y[1] (numeric) = 2.1886627270737579368206299765776
absolute error = 2.9182443342051e-18
relative error = 1.3333458362983101900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.1MB, time=4.50
x[1] = 0.0432
y[1] (analytic) = 2.1891418563922942206654991243433
y[1] (numeric) = 2.1891418563922942235934698753288
absolute error = 2.9279707509855e-18
relative error = 1.3374970390501764000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0433
y[1] (analytic) = 2.1896211955331727611123275673309
y[1] (numeric) = 2.1896211955331727640500422361958
absolute error = 2.9377146688649e-18
relative error = 1.3416542892705998300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0434
y[1] (analytic) = 2.1901007446342531756460797196671
y[1] (numeric) = 2.1901007446342531785935558398961
absolute error = 2.9474761202290e-18
relative error = 1.3458175964965614000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0435
y[1] (analytic) = 2.1905805038335158817086527929901
y[1] (numeric) = 2.1905805038335158846659079305188
absolute error = 2.9572551375287e-18
relative error = 1.3499869702818515500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0436
y[1] (analytic) = 2.1910604732690622261174408413672
y[1] (numeric) = 2.1910604732690622290844925946479
absolute error = 2.9670517532807e-18
relative error = 1.3541624201973114800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0437
y[1] (analytic) = 2.1915406530791146175761560376945
y[1] (numeric) = 2.1915406530791146205530220377618
absolute error = 2.9768660000673e-18
relative error = 1.3583439558307089900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0438
y[1] (analytic) = 2.1920210434020166593599298553266
y[1] (numeric) = 2.1920210434020166623466277658632
absolute error = 2.9866979105366e-18
relative error = 1.3625315867867969200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0439
y[1] (analytic) = 2.1925016443762332821749616312212
y[1] (numeric) = 2.1925016443762332851715091486239
absolute error = 2.9965475174027e-18
relative error = 1.3667253226873714700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 2.1929824561403508771929824561404
y[1] (numeric) = 2.1929824561403508801993973095861
absolute error = 3.0064148534457e-18
relative error = 1.3709251731712392000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0441
y[1] (analytic) = 2.1934634788330774292608028076333
y[1] (numeric) = 2.1934634788330774322771027591455
absolute error = 3.0162999515122e-18
relative error = 1.3751311478944119800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0442
y[1] (analytic) = 2.1939447125932426502852128126371
y[1] (numeric) = 2.1939447125932426533114156571523
absolute error = 3.0262028445152e-18
relative error = 1.3793432565300281600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0443
y[1] (analytic) = 2.1944261575597981127935044985736
y[1] (numeric) = 2.1944261575597981158296280640075
absolute error = 3.0361235654339e-18
relative error = 1.3835615087682282300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0444
y[1] (analytic) = 2.1949078138718173836698858647937
y[1] (numeric) = 2.1949078138718173867159480121082
absolute error = 3.0460621473145e-18
relative error = 1.3877859143164862000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0445
y[1] (analytic) = 2.1953896816684961580680570801317
y[1] (numeric) = 2.1953896816684961611240757034019
absolute error = 3.0560186232702e-18
relative error = 1.3920164828995761000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0446
y[1] (analytic) = 2.1958717610891523935002195871761
y[1] (numeric) = 2.1958717610891523965662126136569
absolute error = 3.0659930264808e-18
relative error = 1.3962532242593563200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0447
y[1] (analytic) = 2.1963540522732264441027893696464
y[1] (numeric) = 2.1963540522732264471787747598399
absolute error = 3.0759853901935e-18
relative error = 1.4004961481551005500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.1MB, time=4.68
NO POLE
x[1] = 0.0448
y[1] (analytic) = 2.196836555360281195079086115993
y[1] (numeric) = 2.1968365553602811981650818637159
absolute error = 3.0859957477229e-18
relative error = 1.4047452643634640800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0449
y[1] (analytic) = 2.1973192704900021973192704900022
y[1] (numeric) = 2.1973192704900022004152946224531
absolute error = 3.0960241324509e-18
relative error = 1.4090005826784045900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 2.1978021978021978021978021978022
y[1] (numeric) = 2.1978021978021978053038727756292
absolute error = 3.1060705778270e-18
relative error = 1.4132621129112850000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0451
y[1] (analytic) = 2.1982853374367992965486920202242
y[1] (numeric) = 2.1982853374367992996648271375927
absolute error = 3.1161351173685e-18
relative error = 1.4175298648909306500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0452
y[1] (analytic) = 2.1987686895338610378188214599824
y[1] (numeric) = 2.198768689533861040945039244643
absolute error = 3.1262177846606e-18
relative error = 1.4218038484636408800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0453
y[1] (analytic) = 2.1992522542335605893996041345942
y[1] (numeric) = 2.1992522542335605925359227479507
absolute error = 3.1363186133565e-18
relative error = 1.4260840734932005500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0454
y[1] (analytic) = 2.1997360316761988561372635283766
y[1] (numeric) = 2.1997360316761988592837011655543
absolute error = 3.1464376371777e-18
relative error = 1.4303705498609824200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0455
y[1] (analytic) = 2.20022002200220022002200220022
y[1] (numeric) = 2.2002200220022002231785770901341
absolute error = 3.1565748899141e-18
relative error = 1.4346632874659584500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0456
y[1] (analytic) = 2.200704225352112676056338028169
y[1] (numeric) = 2.2007042253521126792230684335929
absolute error = 3.1667304054239e-18
relative error = 1.4389622962246201600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0457
y[1] (analytic) = 2.2011886418666079683028835571208
y[1] (numeric) = 2.2011886418666079714797877747549
absolute error = 3.1769042176341e-18
relative error = 1.4432675860711716300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0458
y[1] (analytic) = 2.2016732716864817261118450022017
y[1] (numeric) = 2.2016732716864817292989413627422
absolute error = 3.1870963605405e-18
relative error = 1.4475791669574951000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0459
y[1] (analytic) = 2.2021581149526536005285179475886
y[1] (numeric) = 2.2021581149526536037258248157966
absolute error = 3.1973068682080e-18
relative error = 1.4518970488532528000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 2.2026431718061674008810572687225
y[1] (numeric) = 2.2026431718061674040885930434928
absolute error = 3.2075357747703e-18
relative error = 1.4562212417457162000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0461
y[1] (analytic) = 2.2031284423881912315487992949989
y[1] (numeric) = 2.2031284423881912347665824094298
absolute error = 3.2177831144309e-18
relative error = 1.4605517556401855100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0462
y[1] (analytic) = 2.203613926840017628911414720141
y[1] (numeric) = 2.2036139268400176321394636416032
absolute error = 3.2280489214622e-18
relative error = 1.4648886005595463600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0463
y[1] (analytic) = 2.2040996253030636984791712585409
y[1] (numeric) = 2.2040996253030637017175044887472
absolute error = 3.2383332302063e-18
relative error = 1.4692317865445983100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.1MB, time=4.84
NO POLE
x[1] = 0.0464
y[1] (analytic) = 2.2045855379188712522045855379189
y[1] (numeric) = 2.2045855379188712554532216129942
absolute error = 3.2486360750753e-18
relative error = 1.4735813236541560800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0465
y[1] (analytic) = 2.2050716648291069459757442116869
y[1] (numeric) = 2.205071664829106949234701702238
absolute error = 3.2589574905511e-18
relative error = 1.4779372219649238500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0466
y[1] (analytic) = 2.2055580061755624172915747684164
y[1] (numeric) = 2.2055580061755624205608722796019
absolute error = 3.2692975111855e-18
relative error = 1.4822994915715057000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0467
y[1] (analytic) = 2.2060445621001544231193470108096
y[1] (numeric) = 2.2060445621001544263990031824103
absolute error = 3.2796561716007e-18
relative error = 1.4866681425865973100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0468
y[1] (analytic) = 2.2065313327449249779346866725508
y[1] (numeric) = 2.2065313327449249812247201790398
absolute error = 3.2900335064890e-18
relative error = 1.4910431851408148000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0469
y[1] (analytic) = 2.20701831825204149194438313838
y[1] (numeric) = 2.2070183182520414952448126889937
absolute error = 3.3004295506137e-18
relative error = 1.4954246293830674700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 2.2075055187637969094922737306843
y[1] (numeric) = 2.2075055187637969128031180694925
absolute error = 3.3108443388082e-18
relative error = 1.4998124854801146000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0471
y[1] (analytic) = 2.2079929344226098476484875248399
y[1] (numeric) = 2.207992934422609850969765430817
absolute error = 3.3212779059771e-18
relative error = 1.5042067636170285900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0472
y[1] (analytic) = 2.208480565371024734982332155477
y[1] (numeric) = 2.208480565371024738314062442573
absolute error = 3.3317302870960e-18
relative error = 1.5086074739970688000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0473
y[1] (analytic) = 2.2089684117517119505191075767617
y[1] (numeric) = 2.2089684117517119538613090939731
absolute error = 3.3422015172114e-18
relative error = 1.5130146268416007800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0474
y[1] (analytic) = 2.2094564737074679628811312417145
y[1] (numeric) = 2.2094564737074679662338228731561
absolute error = 3.3526916314416e-18
relative error = 1.5174282323904681600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0475
y[1] (analytic) = 2.2099447513812154696132596685083
y[1] (numeric) = 2.2099447513812154729764603334841
absolute error = 3.3632006649758e-18
relative error = 1.5218483009015495000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0476
y[1] (analytic) = 2.2104332449160035366931918656057
y[1] (numeric) = 2.210433244916003540066920518681
absolute error = 3.3737286530753e-18
relative error = 1.5262748426512657200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0477
y[1] (analytic) = 2.2109219544550077382268405925271
y[1] (numeric) = 2.2109219544550077416111162236
absolute error = 3.3842756310729e-18
relative error = 1.5307078679342726700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0478
y[1] (analytic) = 2.2114108801415302963290579389651
y[1] (numeric) = 2.2114108801415302997238995733386
absolute error = 3.3948416343735e-18
relative error = 1.5351473870636967000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=118.2MB, alloc=4.1MB, time=5.00
x[1] = 0.0479
y[1] (analytic) = 2.2119000221190002211900022119
y[1] (numeric) = 2.2119000221190002245954289103542
absolute error = 3.4054266984542e-18
relative error = 1.5395934103711438200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 2.2123893805309734513274336283186
y[1] (numeric) = 2.2123893805309734547434644871826
absolute error = 3.4160308588640e-18
relative error = 1.5440459482065280000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0481
y[1] (analytic) = 2.2128789555211329940252268200929
y[1] (numeric) = 2.2128789555211329974518809713177
absolute error = 3.4266541512248e-18
relative error = 1.5485050109384871200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0482
y[1] (analytic) = 2.213368747233289065958388667552
y[1] (numeric) = 2.2133687472332890693956852787828
absolute error = 3.4372966112308e-18
relative error = 1.5529706089540754400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0483
y[1] (analytic) = 2.2138587558113792340048704892628
y[1] (numeric) = 2.2138587558113792374528287639119
absolute error = 3.4479582746491e-18
relative error = 1.5574427526589984700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0484
y[1] (analytic) = 2.2143489813994685562444641275465
y[1] (numeric) = 2.2143489813994685597031033048663
absolute error = 3.4586391773198e-18
relative error = 1.5619214524776216800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0485
y[1] (analytic) = 2.2148394241417497231450719822813
y[1] (numeric) = 2.2148394241417497266144113374372
absolute error = 3.4693393551559e-18
relative error = 1.5664067188528888500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0486
y[1] (analytic) = 2.2153300841825431989366415595924
y[1] (numeric) = 2.2153300841825432024167004037361
absolute error = 3.4800588441437e-18
relative error = 1.5708985622464661800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0487
y[1] (analytic) = 2.2158209616662973631730556171061
y[1] (numeric) = 2.2158209616662973666638532974492
absolute error = 3.4907976803431e-18
relative error = 1.5753969931388410300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0488
y[1] (analytic) = 2.2163120567375886524822695035461
y[1] (numeric) = 2.2163120567375886559838254034334
absolute error = 3.5015558998873e-18
relative error = 1.5799020220291497600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0489
y[1] (analytic) = 2.2168033695411217025049878075815
y[1] (numeric) = 2.216803369541121706017321346565
absolute error = 3.5123335389835e-18
relative error = 1.5844136594354568500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 2.2172949002217294900221729490022
y[1] (numeric) = 2.217294900221729493545303582915
absolute error = 3.5231306339128e-18
relative error = 1.5889319158946728000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0491
y[1] (analytic) = 2.2177866489243734752716788644932
y[1] (numeric) = 2.2177866489243734788056260855234
absolute error = 3.5339472210302e-18
relative error = 1.5934568019625171800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0492
y[1] (analytic) = 2.2182786157941437444543034605146
y[1] (numeric) = 2.2182786157941437479990867972796
absolute error = 3.5447833367650e-18
relative error = 1.5979883282136620000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0493
y[1] (analytic) = 2.218770800976259152429554027069
y[1] (numeric) = 2.21877080097625915598519304469
absolute error = 3.5556390176210e-18
relative error = 1.6025265052417847000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0494
y[1] (analytic) = 2.219263204616067465601420328451
y[1] (numeric) = 2.2192632046160674691679346286276
absolute error = 3.5665143001766e-18
relative error = 1.6070713436595759600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.1MB, time=5.17
NO POLE
x[1] = 0.0495
y[1] (analytic) = 2.2197558268590455049944506104329
y[1] (numeric) = 2.2197558268590455085718598315178
absolute error = 3.5774092210849e-18
relative error = 1.6116228540987474500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0496
y[1] (analytic) = 2.2202486678507992895204262877442
y[1] (numeric) = 2.2202486678507992931087501048182
absolute error = 3.5883238170740e-18
relative error = 1.6161810472101296000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0497
y[1] (analytic) = 2.2207417277370641794359316011548
y[1] (numeric) = 2.2207417277370641830351897261015
absolute error = 3.5992581249467e-18
relative error = 1.6207459336634990100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0498
y[1] (analytic) = 2.2212350066637050199911150599733
y[1] (numeric) = 2.2212350066637050236013272415549
absolute error = 3.6102121815816e-18
relative error = 1.6253175241480363200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0499
y[1] (analytic) = 2.2217285047767162852699400133304
y[1] (numeric) = 2.2217285047767162888911260372627
absolute error = 3.6211860239323e-18
relative error = 1.6298958293719282300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 2.2222222222222222222222222222222
y[1] (numeric) = 2.2222222222222222258544019112506
absolute error = 3.6321796890284e-18
relative error = 1.6344808600627800000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0501
y[1] (analytic) = 2.2227161591464769948877528339631
y[1] (numeric) = 2.2227161591464769985309460479379
absolute error = 3.6431932139748e-18
relative error = 1.6390726269672625200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0502
y[1] (analytic) = 2.2232103156958648288128056914184
y[1] (numeric) = 2.223210315695864832467032327371
absolute error = 3.6542266359526e-18
relative error = 1.6436711408514794800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0503
y[1] (analytic) = 2.223704692016900155659328441183
y[1] (numeric) = 2.223704692016900159324608433402
absolute error = 3.6652799922190e-18
relative error = 1.6482764125008843000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0504
y[1] (analytic) = 2.2241992882562277580071174377224
y[1] (numeric) = 2.2241992882562277616834707578299
absolute error = 3.6763533201075e-18
relative error = 1.6528884527203320000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0505
y[1] (analytic) = 2.224694104560622914349276974416
y[1] (numeric) = 2.2246941045606229180367236314439
absolute error = 3.6874466570279e-18
relative error = 1.6575072723340410500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0506
y[1] (analytic) = 2.2251891410769915442812639074321
y[1] (numeric) = 2.2251891410769915479798239478989
absolute error = 3.6985600404668e-18
relative error = 1.6621328821857799200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0507
y[1] (analytic) = 2.2256843979523703538838192744269
y[1] (numeric) = 2.2256843979523703575935127824142
absolute error = 3.7096935079873e-18
relative error = 1.6667652931386938900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0508
y[1] (analytic) = 2.226179875333926981300089047195
y[1] (numeric) = 2.2261798753339269850209361444249
absolute error = 3.7208470972299e-18
relative error = 1.6714045160756710800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0509
y[1] (analytic) = 2.2266755733689601425072366956134
y[1] (numeric) = 2.2266755733689601462392575415253
absolute error = 3.7320208459119e-18
relative error = 1.6760505618990342900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 2.22717149220489977728285077951
y[1] (numeric) = 2.2271714922048997810260655713379
absolute error = 3.7432147918279e-18
relative error = 1.6807034415307271000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.1MB, time=5.33
NO POLE
x[1] = 0.0511
y[1] (analytic) = 2.2276676319893071953664513254622
y[1] (numeric) = 2.2276676319893071991208802983124
absolute error = 3.7544289728502e-18
relative error = 1.6853631659124547800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0512
y[1] (analytic) = 2.2281639928698752228163992869875
y[1] (numeric) = 2.2281639928698752265820627139161
absolute error = 3.7656634269286e-18
relative error = 1.6900297460055556800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0513
y[1] (analytic) = 2.2286605749944283485625139291286
y[1] (numeric) = 2.2286605749944283523394321212194
absolute error = 3.7769181920908e-18
relative error = 1.6947031927911419600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0514
y[1] (analytic) = 2.2291573785109228711547035220687
y[1] (numeric) = 2.2291573785109228749428968285113
absolute error = 3.7881933064426e-18
relative error = 1.6993835172701503600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0515
y[1] (analytic) = 2.2296544035674470457079152731327
y[1] (numeric) = 2.2296544035674470495074040813005
absolute error = 3.7994888081678e-18
relative error = 1.7040707304632583000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0516
y[1] (analytic) = 2.2301516503122212310437109723461
y[1] (numeric) = 2.2301516503122212348545157078748
absolute error = 3.8108047355287e-18
relative error = 1.7087648434110690800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0517
y[1] (analytic) = 2.2306491188935980370287753736337
y[1] (numeric) = 2.2306491188935980408509165004997
absolute error = 3.8221411268660e-18
relative error = 1.7134658671740278000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0518
y[1] (analytic) = 2.2311468094600624721106648817492
y[1] (numeric) = 2.2311468094600624759441629023484
absolute error = 3.8334980205992e-18
relative error = 1.7181738128325614400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0519
y[1] (analytic) = 2.2316447221602320910511046641375
y[1] (numeric) = 2.2316447221602320948959801193642
absolute error = 3.8448754552267e-18
relative error = 1.7228886914870842700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 2.2321428571428571428571428571429
y[1] (numeric) = 2.2321428571428571467134163264689
absolute error = 3.8562734693260e-18
relative error = 1.7276105142580480000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0521
y[1] (analytic) = 2.2326412145568207189104710872963
y[1] (numeric) = 2.2326412145568207227781631888502
absolute error = 3.8676921015539e-18
relative error = 1.7323392922859918100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0522
y[1] (analytic) = 2.2331397945511389012952210808397
y[1] (numeric) = 2.2331397945511389051743524714862
absolute error = 3.8791313906465e-18
relative error = 1.7370750367315027000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0523
y[1] (analytic) = 2.2336385972749609113245476881841
y[1] (numeric) = 2.2336385972749609152151390636036
absolute error = 3.8905913754195e-18
relative error = 1.7418177587753101500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0524
y[1] (analytic) = 2.234137622877569258266309204647
y[1] (numeric) = 2.2341376228775692621683812994156
absolute error = 3.9020720947686e-18
relative error = 1.7465674696184253600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0525
y[1] (analytic) = 2.234636871508379888268156424581
y[1] (numeric) = 2.2346368715083798921817300122501
absolute error = 3.9135735876691e-18
relative error = 1.7513241804819222500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0526
y[1] (analytic) = 2.2351363433169423334823424228878
y[1] (numeric) = 2.2351363433169423374074383160646
absolute error = 3.9250958931768e-18
relative error = 1.7560879026073003200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.1MB, time=5.49
NO POLE
x[1] = 0.0527
y[1] (analytic) = 2.2356360384529398613905656159177
y[1] (numeric) = 2.2356360384529398653272046663454
absolute error = 3.9366390504277e-18
relative error = 1.7608586472563102100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0528
y[1] (analytic) = 2.2361359570661896243291592128801
y[1] (numeric) = 2.2361359570661896282773623115184
absolute error = 3.9482030986383e-18
relative error = 1.7656364257110477600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0529
y[1] (analytic) = 2.2366360993066428092149407291434
y[1] (numeric) = 2.2366360993066428131747288062491
absolute error = 3.9597880771057e-18
relative error = 1.7704212492739584700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 2.2371364653243847874720357941834
y[1] (numeric) = 2.2371364653243847914434298193917
absolute error = 3.9713940252083e-18
relative error = 1.7752131292681101000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0531
y[1] (analytic) = 2.2376370552696352651599910494518
y[1] (numeric) = 2.2376370552696352691430120318567
absolute error = 3.9830209824049e-18
relative error = 1.7800120770367498100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0532
y[1] (analytic) = 2.2381378692927484333034914950761
y[1] (numeric) = 2.2381378692927484372981604833123
absolute error = 3.9946689882362e-18
relative error = 1.7848181039439341600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0533
y[1] (analytic) = 2.2386389075442131184239982090889
y[1] (numeric) = 2.2386389075442131224303362914127
absolute error = 4.0063380823238e-18
relative error = 1.7896312213740414600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0534
y[1] (analytic) = 2.2391401701746529332736229287953
y[1] (numeric) = 2.2391401701746529372916512331666
absolute error = 4.0180283043713e-18
relative error = 1.7944514407322225800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0535
y[1] (analytic) = 2.2396416573348264277715565509518
y[1] (numeric) = 2.2396416573348264318012962451156
absolute error = 4.0297396941638e-18
relative error = 1.7992787734441367000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0536
y[1] (analytic) = 2.2401433691756272401433691756272
y[1] (numeric) = 2.2401433691756272441848414671958
absolute error = 4.0414722915686e-18
relative error = 1.8041132309562230400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0537
y[1] (analytic) = 2.2406453058480842482634998879677
y[1] (numeric) = 2.2406453058480842523167260245027
absolute error = 4.0532261365350e-18
relative error = 1.8089548247355705000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0538
y[1] (analytic) = 2.2411474675033617212012550425818
y[1] (numeric) = 2.2411474675033617252662563116766
absolute error = 4.0650012690948e-18
relative error = 1.8138035662700997600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0539
y[1] (analytic) = 2.2416498542927594709706343869088
y[1] (numeric) = 2.2416498542927594750474321162711
absolute error = 4.0767977293623e-18
relative error = 1.8186594670685220300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 2.2421524663677130044843049327354
y[1] (numeric) = 2.24215246636771300857292049027
absolute error = 4.0886155575346e-18
relative error = 1.8235225386604316000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0541
y[1] (analytic) = 2.2426553038797936757120430589818
y[1] (numeric) = 2.2426553038797936798124978528733
absolute error = 4.1004547938915e-18
relative error = 1.8283927925962198500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.1MB, time=5.66
NO POLE
x[1] = 0.0542
y[1] (analytic) = 2.2431583669807088380439659039928
y[1] (numeric) = 2.2431583669807088421562813827888
absolute error = 4.1123154787960e-18
relative error = 1.8332702404472568000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0543
y[1] (analytic) = 2.2436616558223019968588736818488
y[1] (numeric) = 2.2436616558223020009830713345433
absolute error = 4.1241976526945e-18
relative error = 1.8381548938059386500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0544
y[1] (analytic) = 2.2441651705565529622980251346499
y[1] (numeric) = 2.2441651705565529664341264907668
absolute error = 4.1361013561169e-18
relative error = 1.8430467642856906400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0545
y[1] (analytic) = 2.2446689113355780022446689113356
y[1] (numeric) = 2.2446689113355780063926955410121
absolute error = 4.1480266296765e-18
relative error = 1.8479458635208807500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0546
y[1] (analytic) = 2.2451728783116299955096542433767
y[1] (numeric) = 2.2451728783116299996696277574476
absolute error = 4.1599735140709e-18
relative error = 1.8528522031671788600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0547
y[1] (analytic) = 2.2456770716370985852234448686279
y[1] (numeric) = 2.2456770716370985893953869187091
absolute error = 4.1719420500812e-18
relative error = 1.8577657949011583600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0548
y[1] (analytic) = 2.2461814914645103324348607367475
y[1] (numeric) = 2.2461814914645103366187930153207
absolute error = 4.1839322785732e-18
relative error = 1.8626866504207886400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0549
y[1] (analytic) = 2.246686137946528869916872612896
y[1] (numeric) = 2.2466861379465288741128168533929
absolute error = 4.1959442404969e-18
relative error = 1.8676147814451701900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 2.2471910112359550561797752808989
y[1] (numeric) = 2.247191011235955060387753257786
absolute error = 4.2079779768871e-18
relative error = 1.8725501997147595000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0551
y[1] (analytic) = 2.2476961114857271296920656327265
y[1] (numeric) = 2.2476961114857271339120991615898
absolute error = 4.2200335288633e-18
relative error = 1.8774929169912821700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0552
y[1] (analytic) = 2.2482014388489208633093525179856
y[1] (numeric) = 2.2482014388489208675414634556156
absolute error = 4.2321109376300e-18
relative error = 1.8824429450578240000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0553
y[1] (analytic) = 2.2487069934787497189116258151563
y[1] (numeric) = 2.2487069934787497231558360596332
absolute error = 4.2442102444769e-18
relative error = 1.8874002957188774300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0554
y[1] (analytic) = 2.2492127755285650022492127755286
y[1] (numeric) = 2.2492127755285650065055442663077
absolute error = 4.2563314907791e-18
relative error = 1.8923649808003878600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0555
y[1] (analytic) = 2.2497187851518560179977502812148
y[1] (numeric) = 2.2497187851518560222662249992123
absolute error = 4.2684747179975e-18
relative error = 1.8973370121498887500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0556
y[1] (analytic) = 2.250225022502250225022502250225
y[1] (numeric) = 2.2502250225022502293031422179034
absolute error = 4.2806399676784e-18
relative error = 1.9023164016362809600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0557
y[1] (analytic) = 2.2507314877335133918523520144047
y[1] (numeric) = 2.2507314877335133961451792958591
absolute error = 4.2928272814544e-18
relative error = 1.9073031611501899200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.1MB, time=5.83
NO POLE
x[1] = 0.0558
y[1] (analytic) = 2.2512381809995497523638000900495
y[1] (numeric) = 2.2512381809995497566688367910938
absolute error = 4.3050367010443e-18
relative error = 1.9122973026038780600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0559
y[1] (analytic) = 2.2517451024544021616752983562261
y[1] (numeric) = 2.251745102454402165992566624479
absolute error = 4.3172682682529e-18
relative error = 1.9172988379311128900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 2.2522522522522522522522522522523
y[1] (numeric) = 2.2522522522522522565817742772243
absolute error = 4.3295220249720e-18
relative error = 1.9223077790875680000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0561
y[1] (analytic) = 2.2527596305474205902230232034242
y[1] (numeric) = 2.2527596305474205945648212166042
absolute error = 4.3417980131800e-18
relative error = 1.9273241380506020000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0562
y[1] (analytic) = 2.2532672374943668319062640829202
y[1] (numeric) = 2.2532672374943668362603603578624
absolute error = 4.3540962749422e-18
relative error = 1.9323479268193483600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0563
y[1] (analytic) = 2.2537750732476898805499211178724
y[1] (numeric) = 2.2537750732476898849163379702834
absolute error = 4.3664168524110e-18
relative error = 1.9373791574147607000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0564
y[1] (analytic) = 2.2542831379621280432822362488729
y[1] (numeric) = 2.2542831379621280476609960366992
absolute error = 4.3787597878263e-18
relative error = 1.9424178418797466800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0565
y[1] (analytic) = 2.2547914317925591882750845546787
y[1] (numeric) = 2.2547914317925591926662096781945
absolute error = 4.3911251235158e-18
relative error = 1.9474639922792573000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0566
y[1] (analytic) = 2.2552999548940009021199819576004
y[1] (numeric) = 2.2552999548940009065234948594949
absolute error = 4.4035129018945e-18
relative error = 1.9525176207000213000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0567
y[1] (analytic) = 2.2558087074216106474170990300023
y[1] (numeric) = 2.2558087074216106518330221954679
absolute error = 4.4159231654656e-18
relative error = 1.9575787392509004800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0568
y[1] (analytic) = 2.2563176895306859205776173285199
y[1] (numeric) = 2.2563176895306859250059732853403
absolute error = 4.4283559568204e-18
relative error = 1.9626473600628012800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0569
y[1] (analytic) = 2.2568269013766644098397652900023
y[1] (numeric) = 2.256826901376664414280576608641
absolute error = 4.4408113186387e-18
relative error = 1.9677234952888079700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 2.2573363431151241534988713318284
y[1] (numeric) = 2.2573363431151241579521606255171
absolute error = 4.4532892936887e-18
relative error = 1.9728071571040941000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0571
y[1] (analytic) = 2.2578460149017836983517724091217
y[1] (numeric) = 2.257846014901783702817562333949
absolute error = 4.4657899248273e-18
relative error = 1.9778983577060111700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0572
y[1] (analytic) = 2.2583559168925022583559168925023
y[1] (numeric) = 2.2583559168925022628342301475029
absolute error = 4.4783132550006e-18
relative error = 1.9829971093142656800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0573
y[1] (analytic) = 2.2588660492432798735035012423763
y[1] (numeric) = 2.2588660492432798779943605696202
absolute error = 4.4908593272439e-18
relative error = 1.9881034241708745300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.1MB, time=5.98
NO POLE
x[1] = 0.0574
y[1] (analytic) = 2.2593764121102575689109805693629
y[1] (numeric) = 2.2593764121102575734144087540444
absolute error = 4.5034281846815e-18
relative error = 1.9932173145400319000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0575
y[1] (analytic) = 2.2598870056497175141242937853107
y[1] (numeric) = 2.2598870056497175186403136558385
absolute error = 4.5160198705278e-18
relative error = 1.9983387927085515000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0576
y[1] (analytic) = 2.2603978300180831826401446654611
y[1] (numeric) = 2.2603978300180831871687790935476
absolute error = 4.5286344280865e-18
relative error = 2.0034678709854676000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0577
y[1] (analytic) = 2.2609088853719195116436807596654
y[1] (numeric) = 2.2609088853719195161849526604169
absolute error = 4.5412719007515e-18
relative error = 2.0086045617023884500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0578
y[1] (analytic) = 2.2614201718679330619629127091814
y[1] (numeric) = 2.2614201718679330665168450411884
absolute error = 4.5539323320070e-18
relative error = 2.0137488772134954000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0579
y[1] (analytic) = 2.2619316896629721782402171454422
y[1] (numeric) = 2.2619316896629721828068329108698
absolute error = 4.5666157654276e-18
relative error = 2.0189008298955419600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 2.2624434389140271493212669683258
y[1] (numeric) = 2.262443438914027153900589213004
absolute error = 4.5793222446782e-18
relative error = 2.0240604321477644000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0581
y[1] (analytic) = 2.2629554197782303688617334238516
y[1] (numeric) = 2.2629554197782303734537852373664
absolute error = 4.5920518135148e-18
relative error = 2.0292276963921901200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0582
y[1] (analytic) = 2.2634676324128564961521050248981
y[1] (numeric) = 2.2634676324128565007569095406826
absolute error = 4.6048045157845e-18
relative error = 2.0344026350735921000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0583
y[1] (analytic) = 2.2639800769753226171609689834729
y[1] (numeric) = 2.2639800769753226217785493788982
absolute error = 4.6175803954253e-18
relative error = 2.0395852606593550100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0584
y[1] (analytic) = 2.2644927536231884057971014492754
y[1] (numeric) = 2.2644927536231884104274809457422
absolute error = 4.6303794964668e-18
relative error = 2.0447755856397388800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0585
y[1] (analytic) = 2.2650056625141562853907134767837
y[1] (numeric) = 2.2650056625141562900339153398142
absolute error = 4.6432018630305e-18
relative error = 2.0499736225279657500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0586
y[1] (analytic) = 2.2655188038060715903942002718623
y[1] (numeric) = 2.2655188038060715950502478111917
absolute error = 4.6560475393294e-18
relative error = 2.0551793838599971600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0587
y[1] (analytic) = 2.266032177656922728302741898935
y[1] (numeric) = 2.2660321776569227329716584686038
absolute error = 4.6689165696688e-18
relative error = 2.0603928821948414400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0588
y[1] (analytic) = 2.2665457842248413417951042611061
y[1] (numeric) = 2.2665457842248413464769132595522
absolute error = 4.6818089984461e-18
relative error = 2.0656141301144193200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=144.9MB, alloc=4.1MB, time=6.14
x[1] = 0.0589
y[1] (analytic) = 2.2670596236681024710949897982317
y[1] (numeric) = 2.2670596236681024757897146683831
absolute error = 4.6947248701514e-18
relative error = 2.0708431402237825400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 2.2675736961451247165532879818594
y[1] (numeric) = 2.2675736961451247212609522112267
absolute error = 4.7076642293673e-18
relative error = 2.0760799251509793000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0591
y[1] (analytic) = 2.2680880018144704014515763211613
y[1] (numeric) = 2.2680880018144704061722034419307
absolute error = 4.7206271207694e-18
relative error = 2.0813244975472284600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0592
y[1] (analytic) = 2.26860254083484573502722323049
y[1] (numeric) = 2.2686025408348457397608368196166
absolute error = 4.7336135891266e-18
relative error = 2.0865768700870052800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0593
y[1] (analytic) = 2.2691173133651009757204447469934
y[1] (numeric) = 2.2691173133651009804670684262942
absolute error = 4.7466236793008e-18
relative error = 2.0918370554678625600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0594
y[1] (analytic) = 2.2696323195642305946436677258284
y[1] (numeric) = 2.2696323195642305994033251620762
absolute error = 4.7596574362478e-18
relative error = 2.0971050664107806800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0595
y[1] (analytic) = 2.2701475595913734392735527809308
y[1] (numeric) = 2.2701475595913734440462676859477
absolute error = 4.7727149050169e-18
relative error = 2.1023809156599444500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0596
y[1] (analytic) = 2.2706630336058128973660308810173
y[1] (numeric) = 2.270663033605812902151827011769
absolute error = 4.7857961307517e-18
relative error = 2.1076646159830486800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0597
y[1] (analytic) = 2.2711787417669770610947081535317
y[1] (numeric) = 2.2711787417669770658936093122214
absolute error = 4.7989011586897e-18
relative error = 2.1129561801710749100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0598
y[1] (analytic) = 2.2716946842344388914129940935938
y[1] (numeric) = 2.2716946842344388962250241277568
absolute error = 4.8120300341630e-18
relative error = 2.1182556210385526000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0599
y[1] (analytic) = 2.2722108611679163826403090206771
y[1] (numeric) = 2.2722108611679163874654918232753
absolute error = 4.8251828025982e-18
relative error = 2.1235629514234678200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 2.2727272727272727272727272727273
y[1] (numeric) = 2.2727272727272727321110867822441
absolute error = 4.8383595095168e-18
relative error = 2.1288781841873920000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0601
y[1] (analytic) = 2.2732439190725164810184132757445
y[1] (numeric) = 2.27324391907251648586997347628
absolute error = 4.8515602005355e-18
relative error = 2.1342013322155664500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0602
y[1] (analytic) = 2.2737608003638017280582082764893
y[1] (numeric) = 2.2737608003638017329229931978555
absolute error = 4.8647849213662e-18
relative error = 2.1395324084168547600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0603
y[1] (analytic) = 2.2742779167614282465317261769388
y[1] (numeric) = 2.2742779167614282514097598947551
absolute error = 4.8780337178163e-18
relative error = 2.1448714257238271100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0604
y[1] (analytic) = 2.2747952684258416742493175614195
y[1] (numeric) = 2.2747952684258416791406241972084
absolute error = 4.8913066357889e-18
relative error = 2.1502183970928004400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.1MB, time=6.30
NO POLE
x[1] = 0.0605
y[1] (analytic) = 2.2753128555176336746302616609784
y[1] (numeric) = 2.2753128555176336795348653822616
absolute error = 4.9046037212832e-18
relative error = 2.1555733355039664000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0606
y[1] (analytic) = 2.2758306781975421028675466545289
y[1] (numeric) = 2.2758306781975421077854716749233
absolute error = 4.9179250203944e-18
relative error = 2.1609362539612993600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0607
y[1] (analytic) = 2.2763487366264511723195993626224
y[1] (numeric) = 2.2763487366264511772508699419365
absolute error = 4.9312705793141e-18
relative error = 2.1663071654926841300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0608
y[1] (analytic) = 2.2768670309653916211293260473588
y[1] (numeric) = 2.2768670309653916260739664916895
absolute error = 4.9446404443307e-18
relative error = 2.1716860831500434400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0609
y[1] (analytic) = 2.2773855613755408790708266909588
y[1] (numeric) = 2.2773855613755408840288613527879
absolute error = 4.9580346618291e-18
relative error = 2.1770730200091578100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 2.277904328018223234624145785877
y[1] (numeric) = 2.2779043280182232395955990641687
absolute error = 4.9714532782917e-18
relative error = 2.1824679891700563000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0611
y[1] (analytic) = 2.2784233310549100022784233310549
y[1] (numeric) = 2.2784233310549100072633196713528
absolute error = 4.9848963402979e-18
relative error = 2.1878710037567483100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0612
y[1] (analytic) = 2.2789425706472196900638103919781
y[1] (numeric) = 2.2789425706472196950621742865027
absolute error = 4.9983638945246e-18
relative error = 2.1932820769173944800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0613
y[1] (analytic) = 2.2794620469569181673125142466378
y[1] (numeric) = 2.2794620469569181723243702343843
absolute error = 5.0118559877465e-18
relative error = 2.1987012218243895500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0614
y[1] (analytic) = 2.2799817601459188326493388052896
y[1] (numeric) = 2.2799817601459188376747114721258
absolute error = 5.0253726668362e-18
relative error = 2.2041284516743573200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0615
y[1] (analytic) = 2.280501710376282782212086659065
y[1] (numeric) = 2.2805017103762827872510006378297
absolute error = 5.0389139787647e-18
relative error = 2.2095637796883209500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0616
y[1] (analytic) = 2.2810218978102189781021897810219
y[1] (numeric) = 2.281021897810218983154669751623
absolute error = 5.0524799706011e-18
relative error = 2.2150072191115222400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0617
y[1] (analytic) = 2.2815423226100844170659365731234
y[1] (numeric) = 2.2815423226100844221320072626367
absolute error = 5.0660706895133e-18
relative error = 2.2204587832136793900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0618
y[1] (analytic) = 2.282062984938384299406663623916
y[1] (numeric) = 2.282062984938384304486349806684
absolute error = 5.0796861827680e-18
relative error = 2.2259184852889376000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0619
y[1] (analytic) = 2.2825838849577721981282812143346
y[1] (numeric) = 2.2825838849577722032216077120657
absolute error = 5.0933264977311e-18
relative error = 2.2313863386559949100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 2.283105022831050228310502283105
y[1] (numeric) = 2.2831050228310502334174939649727
absolute error = 5.1069916818677e-18
relative error = 2.2368623566580526000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.1MB, time=6.47
NO POLE
x[1] = 0.0621
y[1] (analytic) = 2.283626398721169216716145238639
y[1] (numeric) = 2.2836263987211692218368270213814
absolute error = 5.1206817827424e-18
relative error = 2.2423465526628969600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0622
y[1] (analytic) = 2.2841480127912288716308816811329
y[1] (numeric) = 2.2841480127912288767652785291529
absolute error = 5.1343968480200e-18
relative error = 2.2478389400631560000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0623
y[1] (analytic) = 2.2846698652044779529358007767878
y[1] (numeric) = 2.2846698652044779580839377022524
absolute error = 5.1481369254646e-18
relative error = 2.2533395322758554200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0624
y[1] (analytic) = 2.2851919561243144424131627056673
y[1] (numeric) = 2.2851919561243144475750647686085
absolute error = 5.1619020629412e-18
relative error = 2.2588483427430691200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0625
y[1] (analytic) = 2.2857142857142857142857142857143
y[1] (numeric) = 2.2857142857142857194614065941292
absolute error = 5.1756923084149e-18
relative error = 2.2643653849315187500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0626
y[1] (analytic) = 2.2862368541380887059899405578418
y[1] (numeric) = 2.2862368541380887111794482677934
absolute error = 5.1895077099516e-18
relative error = 2.2698906723328298400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0627
y[1] (analytic) = 2.2867596615595700891836268008232
y[1] (numeric) = 2.2867596615595700943869751165414
absolute error = 5.2033483157182e-18
relative error = 2.2754242184635688600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0628
y[1] (analytic) = 2.2872827081427264409881061299177
y[1] (numeric) = 2.2872827081427264462053203039003
absolute error = 5.2172141739826e-18
relative error = 2.2809660368651927200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0629
y[1] (analytic) = 2.2878059940517044154655685197895
y[1] (numeric) = 2.2878059940517044206966738529039
absolute error = 5.2311053331144e-18
relative error = 2.2865161411043042400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 2.2883295194508009153318077803204
y[1] (numeric) = 2.2883295194508009205768296219048
absolute error = 5.2450218415844e-18
relative error = 2.2920745447723828000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0631
y[1] (analytic) = 2.2888532845044632639047837033646
y[1] (numeric) = 2.2888532845044632691637474513304
absolute error = 5.2589637479658e-18
relative error = 2.2976412614862580200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0632
y[1] (analytic) = 2.2893772893772893772893772893773
y[1] (numeric) = 2.2893772893772893825623083903107
absolute error = 5.2729311009334e-18
relative error = 2.3032163048877091200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0633
y[1] (analytic) = 2.2899015342340279367987176551408
y[1] (numeric) = 2.2899015342340279420856416044056
absolute error = 5.2869239492648e-18
relative error = 2.3087996886439381600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0634
y[1] (analytic) = 2.2904260192395785616124599175447
y[1] (numeric) = 2.2904260192395785669134022593844
absolute error = 5.3009423418397e-18
relative error = 2.3143914264472130200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0635
y[1] (analytic) = 2.2909507445589919816723940435281
y[1] (numeric) = 2.2909507445589919869873803711692
absolute error = 5.3149863276411e-18
relative error = 2.3199915320153401500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0636
y[1] (analytic) = 2.2914757103574702108157653528873
y[1] (numeric) = 2.2914757103574702161448213086421
absolute error = 5.3290559557548e-18
relative error = 2.3256000190913947200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.2MB, time=6.62
NO POLE
x[1] = 0.0637
y[1] (analytic) = 2.2920009168003667201466880586752
y[1] (numeric) = 2.2920009168003667254898393340451
absolute error = 5.3431512753699e-18
relative error = 2.3312169014438873700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0638
y[1] (analytic) = 2.2925263640531866116460339293902
y[1] (numeric) = 2.2925263640531866170033062651692
absolute error = 5.3572723357790e-18
relative error = 2.3368421928667998000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0639
y[1] (analytic) = 2.2930520522815867920201788580601
y[1] (numeric) = 2.2930520522815867973915980444387
absolute error = 5.3714191863786e-18
relative error = 2.3424759071797074600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 2.2935779816513761467889908256881
y[1] (numeric) = 2.2935779816513761521745827023573
absolute error = 5.3855918766692e-18
relative error = 2.3481180582277712000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0641
y[1] (analytic) = 2.2941041523285157146134434503326
y[1] (numeric) = 2.2941041523285157200132339065882
absolute error = 5.3997904562556e-18
relative error = 2.3537686598818160400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0642
y[1] (analytic) = 2.294630564479118861863240018357
y[1] (numeric) = 2.2946305644791188672772549932038
absolute error = 5.4140149748468e-18
relative error = 2.3594277260382354400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0643
y[1] (analytic) = 2.2951572182694514574248336011017
y[1] (numeric) = 2.2951572182694514628530990833586
absolute error = 5.4282654822569e-18
relative error = 2.3650952706193313300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0644
y[1] (analytic) = 2.2956841138659320477502295684114
y[1] (numeric) = 2.2956841138659320531927715968163
absolute error = 5.4425420284049e-18
relative error = 2.3707713075731744400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0645
y[1] (analytic) = 2.2962112514351320321469575200918
y[1] (numeric) = 2.2962112514351320376038021834067
absolute error = 5.4568446633149e-18
relative error = 2.3764558508736389500000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0646
y[1] (analytic) = 2.2967386311437758383096003674782
y[1] (numeric) = 2.2967386311437758437807738045946
absolute error = 5.4711734371164e-18
relative error = 2.3821489145204805600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0647
y[1] (analytic) = 2.2972662531587410980932690098782
y[1] (numeric) = 2.2972662531587411035787974099232
absolute error = 5.4855284000450e-18
relative error = 2.3878505125395885000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0648
y[1] (analytic) = 2.2977941176470588235294117647059
y[1] (numeric) = 2.2977941176470588290293213671477
absolute error = 5.4999096024418e-18
relative error = 2.3935606589826713600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0649
y[1] (analytic) = 2.2983222247759135830843484256493
y[1] (numeric) = 2.2983222247759135885986655204038
absolute error = 5.5143170947545e-18
relative error = 2.3992793679276829500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 2.2988505747126436781609195402299
y[1] (numeric) = 2.2988505747126436836896704677669
absolute error = 5.5287509275370e-18
relative error = 2.4050066534785950000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0651
y[1] (analytic) = 2.2993791676247413198436422166015
y[1] (numeric) = 2.2993791676247413253868533680515
absolute error = 5.5432111514500e-18
relative error = 2.4107425297656050000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0652
y[1] (analytic) = 2.2999080036798528058877644894204
y[1] (numeric) = 2.2999080036798528114454623066815
absolute error = 5.5576978172611e-18
relative error = 2.4164870109451262800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.2MB, time=6.79
NO POLE
x[1] = 0.0653
y[1] (analytic) = 2.3004370830457786979526109960893
y[1] (numeric) = 2.3004370830457787035248219719344
absolute error = 5.5722109758451e-18
relative error = 2.4222401111998649700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0654
y[1] (analytic) = 2.3009664058904739990796134376438
y[1] (numeric) = 2.3009664058904740046663641158283
absolute error = 5.5867506781845e-18
relative error = 2.4280018447389837000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0655
y[1] (analytic) = 2.301495972382048331415420023015
y[1] (numeric) = 2.301495972382048337016736998384
absolute error = 5.6013169753690e-18
relative error = 2.4337722257978305000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0656
y[1] (analytic) = 2.3020257826887661141804788213628
y[1] (numeric) = 2.3020257826887661197963887399595
absolute error = 5.6159099185967e-18
relative error = 2.4395512686384064800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0657
y[1] (analytic) = 2.3025558369790467418834906746489
y[1] (numeric) = 2.3025558369790467475140202338225
absolute error = 5.6305295591736e-18
relative error = 2.4453389875490944800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0658
y[1] (analytic) = 2.3030861354214647627821280515891
y[1] (numeric) = 2.3030861354214647684273040001036
absolute error = 5.6451759485145e-18
relative error = 2.4511353968449959000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0659
y[1] (analytic) = 2.3036166781847500575904169546188
y[1] (numeric) = 2.3036166781847500632502660927611
absolute error = 5.6598491381423e-18
relative error = 2.4569405108675724299999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 2.3041474654377880184331797235023
y[1] (numeric) = 2.3041474654377880241077289031919
absolute error = 5.6745491796896e-18
relative error = 2.4627543439852864000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0661
y[1] (analytic) = 2.3046784973496197280479373127449
y[1] (numeric) = 2.3046784973496197337372134376425
absolute error = 5.6892761248976e-18
relative error = 2.4685769105930686400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0662
y[1] (analytic) = 2.3052097740894421392346703550023
y[1] (numeric) = 2.3052097740894421449387003806197
absolute error = 5.7040300256174e-18
relative error = 2.4744082251128281200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0663
y[1] (analytic) = 2.3057412958266082545538390592576
y[1] (numeric) = 2.305741295826608260272649993067
absolute error = 5.7188109338094e-18
relative error = 2.4802483019931367799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0664
y[1] (analytic) = 2.3062730627306273062730627306273
y[1] (numeric) = 2.3062730627306273120066816321717
absolute error = 5.7336189015444e-18
relative error = 2.4860971557096518400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0665
y[1] (analytic) = 2.306805074971164936562860438293
y[1] (numeric) = 2.306805074971164942311314419296
absolute error = 5.7484539810030e-18
relative error = 2.4919548007648005000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0666
y[1] (analytic) = 2.3073373327180433779418550992155
y[1] (numeric) = 2.3073373327180433837051713236923
absolute error = 5.7633162244768e-18
relative error = 2.4978212516882451200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0667
y[1] (analytic) = 2.3078698361412416339718439879991
y[1] (numeric) = 2.3078698361412416397500496723667
absolute error = 5.7782056843676e-18
relative error = 2.5036965230364810800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=164.0MB, alloc=4.2MB, time=6.95
x[1] = 0.0668
y[1] (analytic) = 2.3084025854108956602031394275162
y[1] (numeric) = 2.3084025854108956659962618407048
absolute error = 5.7931224131886e-18
relative error = 2.5095806293933015200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0669
y[1] (analytic) = 2.3089355806972985453705841607019
y[1] (numeric) = 2.3089355806972985511786506242661
absolute error = 5.8080664635642e-18
relative error = 2.5154735853696550200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 2.3094688221709006928406466512702
y[1] (numeric) = 2.3094688221709006986636845395003
absolute error = 5.8230378882301e-18
relative error = 2.5213754056036333000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0671
y[1] (analytic) = 2.3100023100023100023100023100023
y[1] (numeric) = 2.3100023100023100081480390500363
absolute error = 5.8380367400340e-18
relative error = 2.5272861047607186000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0672
y[1] (analytic) = 2.3105360443622920517560073937153
y[1] (numeric) = 2.3105360443622920576090704656508
absolute error = 5.8530630719355e-18
relative error = 2.5332056975336844000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0673
y[1] (analytic) = 2.3110700254217702796394730760342
y[1] (numeric) = 2.3110700254217702855075900130408
absolute error = 5.8681169370066e-18
relative error = 2.5391341986427558200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0674
y[1] (analytic) = 2.3116042533518261673601479426722
y[1] (numeric) = 2.3116042533518261732433463311041
absolute error = 5.8831983884319e-18
relative error = 2.5450716228356399400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0675
y[1] (analytic) = 2.3121387283236994219653179190751
y[1] (numeric) = 2.3121387283236994278636253985839
absolute error = 5.8983074795088e-18
relative error = 2.5510179848875560000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0676
y[1] (analytic) = 2.3126734505087881591119333950046
y[1] (numeric) = 2.3126734505087881650253776586522
absolute error = 5.9134442636476e-18
relative error = 2.5569732996012222400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0677
y[1] (analytic) = 2.3132084200786490862826740689336
y[1] (numeric) = 2.3132084200786490922112828633059
absolute error = 5.9286087943723e-18
relative error = 2.5629375818071452900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0678
y[1] (analytic) = 2.3137436372049976862563627950023
y[1] (numeric) = 2.3137436372049976922001639203226
absolute error = 5.9438011253203e-18
relative error = 2.5689108463634336600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0679
y[1] (analytic) = 2.3142791020597084008331404767415
y[1] (numeric) = 2.3142791020597084067921617869844
absolute error = 5.9590213102429e-18
relative error = 2.5748931081559570900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 2.3148148148148148148148148148148
y[1] (numeric) = 2.3148148148148148207890842178204
absolute error = 5.9742694030056e-18
relative error = 2.5808843820984192000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0681
y[1] (analytic) = 2.3153507756425098402407964806668
y[1] (numeric) = 2.3153507756425098462303419382551
absolute error = 5.9895454575883e-18
relative error = 2.5868846831323867700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0682
y[1] (analytic) = 2.3158869847151459008800370541918
y[1] (numeric) = 2.3158869847151459068848865822773
absolute error = 6.0048495280855e-18
relative error = 2.5928940262273189000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0683
y[1] (analytic) = 2.3164234422052351169793838313644
y[1] (numeric) = 2.3164234422052351229995655000714
absolute error = 6.0201816687070e-18
relative error = 2.5989124263808119000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=167.8MB, alloc=4.2MB, time=7.12
x[1] = 0.0684
y[1] (analytic) = 2.3169601482854494902687673772011
y[1] (numeric) = 2.3169601482854494963043093109785
absolute error = 6.0355419337774e-18
relative error = 2.6049398986183258400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0685
y[1] (analytic) = 2.3174971031286210892236384704519
y[1] (numeric) = 2.3174971031286210952745688481889
absolute error = 6.0509303777370e-18
relative error = 2.6109764579935155000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0686
y[1] (analytic) = 2.3180343069077422345850718590635
y[1] (numeric) = 2.3180343069077422406514189142054
absolute error = 6.0663470551419e-18
relative error = 2.6170221195882156600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0687
y[1] (analytic) = 2.3185717597959656851379550197079
y[1] (numeric) = 2.3185717597959656912197470403719
absolute error = 6.0817920206640e-18
relative error = 2.6230768985123832000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0688
y[1] (analytic) = 2.319109461966604823747680890538
y[1] (numeric) = 2.31910946196660482984494621963
absolute error = 6.0972653290920e-18
relative error = 2.6291408099044704000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0689
y[1] (analytic) = 2.3196474135931338436557643238228
y[1] (numeric) = 2.3196474135931338497685313591533
absolute error = 6.1127670353305e-18
relative error = 2.6352138689309785500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 2.3201856148491879350348027842227
y[1] (numeric) = 2.3201856148491879411630999786244
absolute error = 6.1282971944017e-18
relative error = 2.6412960907871327000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0691
y[1] (analytic) = 2.320724065908563471803202599211
y[1] (numeric) = 2.3207240659085634779470584606552
absolute error = 6.1438558614442e-18
relative error = 2.6473874906963057799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0692
y[1] (analytic) = 2.3212627669452181987000928505107
y[1] (numeric) = 2.3212627669452182048595359422253
absolute error = 6.1594430917146e-18
relative error = 2.6534880839106496800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0693
y[1] (analytic) = 2.3218017181332714186208497794288
y[1] (numeric) = 2.3218017181332714247959087200157
absolute error = 6.1750589405869e-18
relative error = 2.6595978857107778300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0694
y[1] (analytic) = 2.3223409196470041802136553646075
y[1] (numeric) = 2.3223409196470041864043588281604
absolute error = 6.1907034635529e-18
relative error = 2.6657169114058787400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0695
y[1] (analytic) = 2.3228803716608594657375145180023
y[1] (numeric) = 2.3228803716608594719438912342253
absolute error = 6.2063767162230e-18
relative error = 2.6718451763340015000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0696
y[1] (analytic) = 2.323420074349442379182156133829
y[1] (numeric) = 2.3234200743494423854042348881548
absolute error = 6.2220787543258e-18
relative error = 2.6779826958618243200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0697
y[1] (analytic) = 2.3239600278875203346502440158029
y[1] (numeric) = 2.3239600278875203408880536495119
absolute error = 6.2378096337090e-18
relative error = 2.6841294853849827000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0698
y[1] (analytic) = 2.3245002324500232450023245002324
y[1] (numeric) = 2.3245002324500232512558939105714
absolute error = 6.2535694103390e-18
relative error = 2.6902855603278378000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0699
y[1] (analytic) = 2.3250406882120437107649383864218
y[1] (numeric) = 2.3250406882120437170342965267235
absolute error = 6.2693581403017e-18
relative error = 2.6964509361437611700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.2MB, time=7.29
NO POLE
x[1] = 0.07
y[1] (analytic) = 2.3255813953488372093023255813953
y[1] (numeric) = 2.3255813953488372155875014611982
absolute error = 6.2851758798029e-18
relative error = 2.7026256283152470000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0701
y[1] (analytic) = 2.3261223540358222842521516631775
y[1] (numeric) = 2.3261223540358222905531743483452
absolute error = 6.3010226851677e-18
relative error = 2.7088096523535942300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0702
y[1] (analytic) = 2.3266635644485807352256863657515
y[1] (numeric) = 2.3266635644485807415425849785935
absolute error = 6.3168986128420e-18
relative error = 2.7150030237994916000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0703
y[1] (analytic) = 2.3272050267628578077728647893879
y[1] (numeric) = 2.3272050267628578141056685087797
absolute error = 6.3328037193918e-18
relative error = 2.7212057582226564600000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0704
y[1] (analytic) = 2.3277467411545623836126629422719
y[1] (numeric) = 2.3277467411545623899614010037758
absolute error = 6.3487380615039e-18
relative error = 2.7274178712220754400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0705
y[1] (analytic) = 2.3282887077997671711292200232829
y[1] (numeric) = 2.3282887077997671774939217192693
absolute error = 6.3647016959864e-18
relative error = 2.7336393784261588000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0706
y[1] (analytic) = 2.328830926874708896134140661388
y[1] (numeric) = 2.3288309268747089025148353411564
absolute error = 6.3806946797684e-18
relative error = 2.7398702954925509600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0707
y[1] (analytic) = 2.3293733985557884928954111344048
y[1] (numeric) = 2.3293733985557884992921282043056
absolute error = 6.3967170699008e-18
relative error = 2.7461106381084134400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0708
y[1] (analytic) = 2.3299161230195712954333643988816
y[1] (numeric) = 2.3299161230195713018461333224378
absolute error = 6.4127689235562e-18
relative error = 2.7523604219903210400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0709
y[1] (analytic) = 2.330459100442787229084129573526
y[1] (numeric) = 2.3304591004427872355129798715555
absolute error = 6.4288502980295e-18
relative error = 2.7586196628844584500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 2.3310023310023310023310023310023
y[1] (numeric) = 2.3310023310023310087759635817406
absolute error = 6.4449612507383e-18
relative error = 2.7648883765667307000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0711
y[1] (analytic) = 2.3315458148752622989041734670086
y[1] (numeric) = 2.3315458148752623053652753062311
absolute error = 6.4611018392225e-18
relative error = 2.7711665788425302500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0712
y[1] (analytic) = 2.3320895522388059701492537313433
y[1] (numeric) = 2.3320895522388059766265258524886
absolute error = 6.4772721211453e-18
relative error = 2.7774542855471046400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0713
y[1] (analytic) = 2.3326335432703522276650338231864
y[1] (numeric) = 2.3326335432703522341585059774797
absolute error = 6.4934721542933e-18
relative error = 2.7837515125455377100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0714
y[1] (analytic) = 2.3331777881474568362109192720485
y[1] (numeric) = 2.3331777881474568427206212686251
absolute error = 6.5097019965766e-18
relative error = 2.7900582757327307600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0715
y[1] (analytic) = 2.3337222870478413068844807467911
y[1] (numeric) = 2.3337222870478413134104424528203
absolute error = 6.5259617060292e-18
relative error = 2.7963745910335122000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.2MB, time=7.45
NO POLE
x[1] = 0.0716
y[1] (analytic) = 2.3342670401493930905695611577965
y[1] (numeric) = 2.3342670401493930971118124986058
absolute error = 6.5422513408093e-18
relative error = 2.8027004744027041199999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0717
y[1] (analytic) = 2.3348120476301657716553817417698
y[1] (numeric) = 2.3348120476301657782139527009697
absolute error = 6.5585709591999e-18
relative error = 2.8090359418253171700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0718
y[1] (analytic) = 2.3353573096683792620270901447922
y[1] (numeric) = 2.3353573096683792686020107644005
absolute error = 6.5749206196083e-18
relative error = 2.8153810093162740599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0719
y[1] (analytic) = 2.3359028264424199953281943471152
y[1] (numeric) = 2.3359028264424200019194947276825
absolute error = 6.5913003805673e-18
relative error = 2.8217356929208611300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 2.3364485981308411214953271028037
y[1] (numeric) = 2.3364485981308411281030374035386
absolute error = 6.6077103007349e-18
relative error = 2.8281000087145372000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0721
y[1] (analytic) = 2.3369946249123627015657863986913
y[1] (numeric) = 2.336994624912362708189936837586
absolute error = 6.6241504388947e-18
relative error = 2.8344739728030421300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0722
y[1] (analytic) = 2.3375409069658719027582982702197
y[1] (numeric) = 2.3375409069658719093989191241763
absolute error = 6.6406208539566e-18
relative error = 2.8408576013226334800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0723
y[1] (analytic) = 2.3380874444704231938274491465981
y[1] (numeric) = 2.3380874444704232004845707515544
absolute error = 6.6571216049563e-18
relative error = 2.8472509104398095100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0724
y[1] (analytic) = 2.3386342376052385406922357343312
y[1] (numeric) = 2.3386342376052385473658884853877
absolute error = 6.6736527510565e-18
relative error = 2.8536539163517593999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0725
y[1] (analytic) = 2.3391812865497076023391812865497
y[1] (numeric) = 2.3391812865497076090293956380964
absolute error = 6.6902143515467e-18
relative error = 2.8600666352862142500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0726
y[1] (analytic) = 2.3397285914833879270004679457183
y[1] (numeric) = 2.3397285914833879337072744115616
absolute error = 6.7068064658433e-18
relative error = 2.8664890835014264200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0727
y[1] (analytic) = 2.3402761525860051486075356892113
y[1] (numeric) = 2.3402761525860051553309648427017
absolute error = 6.7234291534904e-18
relative error = 2.8729212772864479200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0728
y[1] (analytic) = 2.3408239700374531835205992509363
y[1] (numeric) = 2.3408239700374531902606817250961
absolute error = 6.7400824741598e-18
relative error = 2.8793632329610665600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0729
y[1] (analytic) = 2.3413720440177944275345352376493
y[1] (numeric) = 2.3413720440177944342913017253007
absolute error = 6.7567664876514e-18
relative error = 2.8858149668759129400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 2.3419203747072599531615925058548
y[1] (numeric) = 2.3419203747072599599350737597484
absolute error = 6.7734812538936e-18
relative error = 2.8922764954125672000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0731
y[1] (analytic) = 2.3424689622862497071913797142188
y[1] (numeric) = 2.342468962286249713981606547162
absolute error = 6.7902268329432e-18
relative error = 2.8987478349834520800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.2MB, time=7.62
NO POLE
x[1] = 0.0732
y[1] (analytic) = 2.3430178069353327085285848172446
y[1] (numeric) = 2.3430178069353327153355881022309
absolute error = 6.8070032849863e-18
relative error = 2.9052290020321528400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0733
y[1] (analytic) = 2.3435669088352472463088821185845
y[1] (numeric) = 2.3435669088352472531326927889225
absolute error = 6.8238106703380e-18
relative error = 2.9117200130332246000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0734
y[1] (analytic) = 2.3441162681669010782934833567745
y[1] (numeric) = 2.3441162681669010851341324062177
absolute error = 6.8406490494432e-18
relative error = 2.9182208844924691200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0735
y[1] (analytic) = 2.3446658851113716295427901524033
y[1] (numeric) = 2.3446658851113716364003086352799
absolute error = 6.8575184828766e-18
relative error = 2.9247316329468699000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0736
y[1] (analytic) = 2.3452157598499061913696060037523
y[1] (numeric) = 2.3452157598499061982440250350955
absolute error = 6.8744190313432e-18
relative error = 2.9312522749647404800000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0737
y[1] (analytic) = 2.3457658925639221205723668777856
y[1] (numeric) = 2.3457658925639221274637176334639
absolute error = 6.8913507556783e-18
relative error = 2.9377828271456592900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0738
y[1] (analytic) = 2.3463162834350070389488503050211
y[1] (numeric) = 2.3463162834350070458571640218695
absolute error = 6.9083137168484e-18
relative error = 2.9443233061207880800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0739
y[1] (analytic) = 2.3468669326449190330908237502934
y[1] (numeric) = 2.3468669326449190400161317262442
absolute error = 6.9253079759508e-18
relative error = 2.9508737285526358799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 2.3474178403755868544600938967136
y[1] (numeric) = 2.3474178403755868614024274909281
absolute error = 6.9423335942145e-18
relative error = 2.9574341111353770000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0741
y[1] (analytic) = 2.3479690068091101197464193472646
y[1] (numeric) = 2.3479690068091101267058099802647
absolute error = 6.9593906330001e-18
relative error = 2.9640044705947425900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0742
y[1] (analytic) = 2.348520432127759511507750117426
y[1] (numeric) = 2.3485204321277595184842292712263
absolute error = 6.9764791538003e-18
relative error = 2.9705848236881677400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0743
y[1] (analytic) = 2.3490721165139769790932581630256
y[1] (numeric) = 2.3490721165139769860868573812657
absolute error = 6.9935992182401e-18
relative error = 2.9771751872048105700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0744
y[1] (analytic) = 2.3496240601503759398496240601504
y[1] (numeric) = 2.3496240601503759468603749482278
absolute error = 7.0107508880774e-18
relative error = 2.9837755779657414400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0745
y[1] (analytic) = 2.3501762632197414806110458284371
y[1] (numeric) = 2.3501762632197414876389800536402
absolute error = 7.0279342252031e-18
relative error = 2.9903860128239190500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0746
y[1] (analytic) = 2.3507287259050305594734367653973
y[1] (numeric) = 2.3507287259050305665185860570385
absolute error = 7.0451492916412e-18
relative error = 2.9970065086641664800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=183.1MB, alloc=4.2MB, time=7.79
x[1] = 0.0747
y[1] (analytic) = 2.3512814483893722078532800376205
y[1] (numeric) = 2.3512814483893722149156761871702
absolute error = 7.0623961495497e-18
relative error = 3.0036370824034874100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0748
y[1] (analytic) = 2.3518344308560677328316086547507
y[1] (numeric) = 2.3518344308560677399112835159709
absolute error = 7.0796748612202e-18
relative error = 3.0102777509908290400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0749
y[1] (analytic) = 2.352387673488590919783580334039
y[1] (numeric) = 2.3523876734885909268805658231178
absolute error = 7.0969854890788e-18
relative error = 3.0169285314073978800000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 2.3529411764705882352941176470588
y[1] (numeric) = 2.3529411764705882424084457427449
absolute error = 7.1143280956861e-18
relative error = 3.0235894406665925000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0751
y[1] (analytic) = 2.3534949399858790303600847258178
y[1] (numeric) = 2.3534949399858790374917874695556
absolute error = 7.1317027437378e-18
relative error = 3.0302604958141912200000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0752
y[1] (analytic) = 2.354048964218455743879472693032
y[1] (numeric) = 2.3540489642184557510285821890966
absolute error = 7.1491094960646e-18
relative error = 3.0369417139282420800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0753
y[1] (analytic) = 2.3546032493524841064280668707323
y[1] (numeric) = 2.3546032493524841135946152863652
absolute error = 7.1665484156329e-18
relative error = 3.0436331121192926300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0754
y[1] (analytic) = 2.3551577955723033443240697126707
y[1] (numeric) = 2.3551577955723033515080892782157
absolute error = 7.1840195655450e-18
relative error = 3.0503347075304070000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0755
y[1] (analytic) = 2.3557126030624263839811542991755
y[1] (numeric) = 2.3557126030624263911826773082148
absolute error = 7.2015230090393e-18
relative error = 3.0570465173371828500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0756
y[1] (analytic) = 2.356267672007540056550424128181
y[1] (numeric) = 2.3562676720075400637694829376718
absolute error = 7.2190588094908e-18
relative error = 3.0637685587478955199999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0757
y[1] (analytic) = 2.3568230025925053028517558331369
y[1] (numeric) = 2.3568230025925053100883828635484
absolute error = 7.2366270304115e-18
relative error = 3.0705008490035994500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0758
y[1] (analytic) = 2.3573785950023573785950023573786
y[1] (numeric) = 2.3573785950023573858492300928289
absolute error = 7.2542277354503e-18
relative error = 3.0772434053780172600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0759
y[1] (analytic) = 2.3579344494223060598915350153266
y[1] (numeric) = 2.3579344494223060671633960037204
absolute error = 7.2718609883938e-18
relative error = 3.0839962451778105800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 2.3584905660377358490566037735849
y[1] (numeric) = 2.3584905660377358563461306267514
absolute error = 7.2895268531665e-18
relative error = 3.0907593857425960000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0761
y[1] (analytic) = 2.3590469450342061807029959896202
y[1] (numeric) = 2.359046945034206188010221383451
absolute error = 7.3072253938308e-18
relative error = 3.0975328444448761200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0762
y[1] (analytic) = 2.3596035865974516281264747522416
y[1] (numeric) = 2.3596035865974516354514314268295
absolute error = 7.3249566745879e-18
relative error = 3.1043166386903520200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.2MB, time=7.96
NO POLE
x[1] = 0.0763
y[1] (analytic) = 2.3601604909133821099834788765636
y[1] (numeric) = 2.3601604909133821173261996363412
absolute error = 7.3427207597776e-18
relative error = 3.1111107859177691200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0764
y[1] (analytic) = 2.360717658168083097261567516525
y[1] (numeric) = 2.360717658168083104622085230404
absolute error = 7.3605177138790e-18
relative error = 3.1179153035991444000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0765
y[1] (analytic) = 2.361275088547815820543093270366
y[1] (numeric) = 2.3612750885478158279214408718765
absolute error = 7.3783476015105e-18
relative error = 3.1247302092396967500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0766
y[1] (analytic) = 2.3618327822390174775625885687293
y[1] (numeric) = 2.3618327822390174849587990561599
absolute error = 7.3962104874306e-18
relative error = 3.1315555203781160400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0767
y[1] (analytic) = 2.3623907394283014410583510512639
y[1] (numeric) = 2.3623907394283014484724574878015
absolute error = 7.4141064365376e-18
relative error = 3.1383912545863660800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0768
y[1] (analytic) = 2.3629489603024574669187145557656
y[1] (numeric) = 2.3629489603024574743507500696362
absolute error = 7.4320355138706e-18
relative error = 3.1452374294700379200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0769
y[1] (analytic) = 2.3635074450484519026234932640038
y[1] (numeric) = 2.3635074450484519100734910486132
absolute error = 7.4499977846094e-18
relative error = 3.1520940626682371400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 2.3640661938534278959810874704492
y[1] (numeric) = 2.3640661938534279034490807845242
absolute error = 7.4679933140750e-18
relative error = 3.1589611718537250000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0771
y[1] (analytic) = 2.3646252069047056041617403641523
y[1] (numeric) = 2.3646252069047056116477625318821
absolute error = 7.4860221677298e-18
relative error = 3.1658387747329324200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0772
y[1] (analytic) = 2.3651844843897824030274361400189
y[1] (numeric) = 2.365184484389782410531520551197
absolute error = 7.5040844111781e-18
relative error = 3.1727268890461006800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0773
y[1] (analytic) = 2.3657440264963330967589306837
y[1] (numeric) = 2.3657440264963331042811107938663
absolute error = 7.5221801101663e-18
relative error = 3.1796255325672950100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0774
y[1] (analytic) = 2.3663038334122101277804070042593
y[1] (numeric) = 2.3663038334122101353207163348428
absolute error = 7.5403093305835e-18
relative error = 3.1865347231045871000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0775
y[1] (analytic) = 2.3668639053254437869822485207101
y[1] (numeric) = 2.3668639053254437945407206591714
absolute error = 7.5584721384613e-18
relative error = 3.1934544784998992499999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0776
y[1] (analytic) = 2.3674242424242424242424242424242
y[1] (numeric) = 2.3674242424242424318190928423993
absolute error = 7.5766685999751e-18
relative error = 3.2003848166294822400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0777
y[1] (analytic) = 2.3679848448969926592469808193228
y[1] (numeric) = 2.3679848448969926668418796007659
absolute error = 7.5948987814431e-18
relative error = 3.2073257554034211299999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0778
y[1] (analytic) = 2.3685457129322595926101373756514
y[1] (numeric) = 2.3685457129322596002233001249793
absolute error = 7.6131627493279e-18
relative error = 3.2142773127662393799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.2MB, time=8.13
NO POLE
x[1] = 0.0779
y[1] (analytic) = 2.3691068467187870172944799810471
y[1] (numeric) = 2.3691068467187870249259405512833
absolute error = 7.6314605702362e-18
relative error = 3.2212395066967000200000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 2.3696682464454976303317535545024
y[1] (numeric) = 2.3696682464454976379815458654214
absolute error = 7.6497923109190e-18
relative error = 3.2282123552078180000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0781
y[1] (analytic) = 2.3702299123014932448447499407443
y[1] (numeric) = 2.3702299123014932525129079790169
absolute error = 7.6681580382726e-18
relative error = 3.2351958763472099399999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0782
y[1] (analytic) = 2.3707918444760550023707918444761
y[1] (numeric) = 2.3707918444760550100573496638145
absolute error = 7.6865578193384e-18
relative error = 3.2421900881969371199999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0783
y[1] (analytic) = 2.3713540431586435854873132558691
y[1] (numeric) = 2.3713540431586435931923049771724
absolute error = 7.7049917213033e-18
relative error = 3.2491950088736016100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0784
y[1] (analytic) = 2.3719165085388994307400379506641
y[1] (numeric) = 2.3719165085388994384634977621644
absolute error = 7.7234598115003e-18
relative error = 3.2562106565285264800000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0785
y[1] (analytic) = 2.3724792408066429418742586002372
y[1] (numeric) = 2.3724792408066429496162207576459
absolute error = 7.7419621574087e-18
relative error = 3.2632370493477670500000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0786
y[1] (analytic) = 2.3730422401518747033697199810157
y[1] (numeric) = 2.37304224015187471113021880767
absolute error = 7.7604988266543e-18
relative error = 3.2702742055521220199999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0787
y[1] (analytic) = 2.3736055067647756942796107286969
y[1] (numeric) = 2.3736055067647757020586806157071
absolute error = 7.7790698870102e-18
relative error = 3.2773221433973972600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0788
y[1] (analytic) = 2.3741690408357075023741690408357
y[1] (numeric) = 2.3741690408357075101718444472322
absolute error = 7.7976754063965e-18
relative error = 3.2843808811742058000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0789
y[1] (analytic) = 2.3747328425552125385894086915222
y[1] (numeric) = 2.3747328425552125464057241444035
absolute error = 7.8163154528813e-18
relative error = 3.2914504372083154300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 2.3752969121140142517814726840855
y[1] (numeric) = 2.3752969121140142596164627787661
absolute error = 7.8349900946806e-18
relative error = 3.2985308298605326000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0791
y[1] (analytic) = 2.3758612497030173437871228320266
y[1] (numeric) = 2.3758612497030173516408222321855
absolute error = 7.8536994001589e-18
relative error = 3.3056220775268810100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0792
y[1] (analytic) = 2.3764258555133079847908745247148
y[1] (numeric) = 2.3764258555133079926633179625443
absolute error = 7.8724434378295e-18
relative error = 3.3127241986386536000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0793
y[1] (analytic) = 2.3769907297361540289992869027811
y[1] (numeric) = 2.3769907297361540368905091791358
absolute error = 7.8912222763547e-18
relative error = 3.3198372116624222900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0794
y[1] (analytic) = 2.3775558725630052306229196386115
y[1] (numeric) = 2.377555872563005238532955623158
absolute error = 7.9100359845465e-18
relative error = 3.3269611351002579000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.2MB, time=8.29
NO POLE
x[1] = 0.0795
y[1] (analytic) = 2.378121284185493460166468489893
y[1] (numeric) = 2.3781212841854934680953531212596
absolute error = 7.9288846313666e-18
relative error = 3.3340959874896553000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0796
y[1] (analytic) = 2.3786869647954329210275927687916
y[1] (numeric) = 2.3786869647954329289753610547185
absolute error = 7.9477682859269e-18
relative error = 3.3412417874036687600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0797
y[1] (analytic) = 2.3792529145848203664049488460623
y[1] (numeric) = 2.3792529145848203743716358635522
absolute error = 7.9666870174899e-18
relative error = 3.3483985534510049700000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0798
y[1] (analytic) = 2.3798191337458353165159447881961
y[1] (numeric) = 2.3798191337458353245015856836651
absolute error = 7.9856408954690e-18
relative error = 3.3555663042760738000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0799
y[1] (analytic) = 2.3803856224708402761247322066175
y[1] (numeric) = 2.3803856224708402841293621960466
absolute error = 8.0046299894291e-18
relative error = 3.3627450585591649100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 2.3809523809523809523809523809524
y[1] (numeric) = 2.3809523809523809604046067500389
absolute error = 8.0236543690865e-18
relative error = 3.3699348350163300000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0801
y[1] (analytic) = 2.3815194093831864729697547035008
y[1] (numeric) = 2.3815194093831864810124688078105
absolute error = 8.0427141043097e-18
relative error = 3.3771356523996430300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0802
y[1] (analytic) = 2.3820867079561696045736064792758
y[1] (numeric) = 2.3820867079561696126354157443952
absolute error = 8.0618092651194e-18
relative error = 3.3843475294971241200000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0803
y[1] (analytic) = 2.3826542768644269716464141053133
y[1] (numeric) = 2.3826542768644269797273540270024
absolute error = 8.0809399216891e-18
relative error = 3.3915704851329152700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0804
y[1] (analytic) = 2.3832221163012392755004766444233
y[1] (numeric) = 2.3832221163012392836005827887689
absolute error = 8.1001061443456e-18
relative error = 3.3988045381674137599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0805
y[1] (analytic) = 2.3837902264600715137067938021454
y[1] (numeric) = 2.3837902264600715218261018057146
absolute error = 8.1193080035692e-18
relative error = 3.4060497074972794000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0806
y[1] (analytic) = 2.3843586075345731998092513113972
y[1] (numeric) = 2.3843586075345732079477968813909
absolute error = 8.1385455699937e-18
relative error = 3.4133060120553577800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0807
y[1] (analytic) = 2.3849272597185785833532077271643
y[1] (numeric) = 2.3849272597185785915110266415718
absolute error = 8.1578189144075e-18
relative error = 3.4205734708110647500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0808
y[1] (analytic) = 2.3854961832061068702290076335878
y[1] (numeric) = 2.3854961832061068784061357413412
absolute error = 8.1771281077534e-18
relative error = 3.4278521027702252800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0809
y[1] (analytic) = 2.3860653781913624433309472679551
y[1] (numeric) = 2.3860653781913624515274204890844
absolute error = 8.1964732211293e-18
relative error = 3.4351419269752896300000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=198.3MB, alloc=4.2MB, time=8.46
x[1] = 0.081
y[1] (analytic) = 2.3866348448687350835322195704057
y[1] (numeric) = 2.386634844868735091748073896194
absolute error = 8.2158543257883e-18
relative error = 3.4424429625052977000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0811
y[1] (analytic) = 2.387204583432800190976366674624
y[1] (numeric) = 2.3872045834328001992116381677633
absolute error = 8.2352714931393e-18
relative error = 3.4497552284760527700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0812
y[1] (analytic) = 2.3877745940783190066857688634193
y[1] (numeric) = 2.3877745940783190149404936581667
absolute error = 8.2547247947474e-18
relative error = 3.4570787440402111200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0813
y[1] (analytic) = 2.3883448770002388344877000238834
y[1] (numeric) = 2.3883448770002388427619143262175
absolute error = 8.2742143023341e-18
relative error = 3.4644135283872876700000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0814
y[1] (analytic) = 2.388915432393693263258480649785
y[1] (numeric) = 2.3889154323936932715522207375625
absolute error = 8.2937400877775e-18
relative error = 3.4717596007436615000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0815
y[1] (analytic) = 2.3894862604540023894862604540024
y[1] (numeric) = 2.3894862604540023977995626771158
absolute error = 8.3133022231134e-18
relative error = 3.4791169803729579000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0816
y[1] (analytic) = 2.3900573613766730401529636711281
y[1] (numeric) = 2.3900573613766730484858644516629
absolute error = 8.3329007805348e-18
relative error = 3.4864856865757603200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0817
y[1] (analytic) = 2.3906287353573989959359311498924
y[1] (numeric) = 2.3906287353573990042884669822853
absolute error = 8.3525358323929e-18
relative error = 3.4938657386899500700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0818
y[1] (analytic) = 2.3912003825920612147297943567671
y[1] (numeric) = 2.3912003825920612231020018079643
absolute error = 8.3722074511972e-18
relative error = 3.5012571560906690400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0819
y[1] (analytic) = 2.3917723032767280554891174360201
y[1] (numeric) = 2.391772303276728063881033145636
absolute error = 8.3919157096159e-18
relative error = 3.5086599581904077900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 2.3923444976076555023923444976077
y[1] (numeric) = 2.3923444976076555108040051780841
absolute error = 8.4116606804764e-18
relative error = 3.5160741644391351999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0821
y[1] (analytic) = 2.3929169657812873893275903326155
y[1] (numeric) = 2.3929169657812873977590327693812
absolute error = 8.4314424367657e-18
relative error = 3.5234997943243860299999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0822
y[1] (analytic) = 2.3934897079942556247008137865007
y[1] (numeric) = 2.3934897079942556331520748381313
absolute error = 8.4512610516306e-18
relative error = 3.5309368673712646800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0823
y[1] (analytic) = 2.3940627244433804165669140531482
y[1] (numeric) = 2.3940627244433804250380306515263
absolute error = 8.4711165983781e-18
relative error = 3.5383854031425323700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0824
y[1] (analytic) = 2.3946360153256704980842911877395
y[1] (numeric) = 2.3946360153256705065753003382155
absolute error = 8.4910091504760e-18
relative error = 3.5458454212387775999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0825
y[1] (analytic) = 2.3952095808383233532934131736527
y[1] (numeric) = 2.3952095808383233618043519552059
absolute error = 8.5109387815532e-18
relative error = 3.5533169412984610000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.2MB, time=8.63
NO POLE
x[1] = 0.0826
y[1] (analytic) = 2.3957834211787254432199329180642
y[1] (numeric) = 2.3957834211787254517508384834641
absolute error = 8.5309055653999e-18
relative error = 3.5607999829979182600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0827
y[1] (analytic) = 2.3963575365444524323028995926192
y[1] (numeric) = 2.3963575365444524408538091685875
absolute error = 8.5509095759683e-18
relative error = 3.5682945660515715900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0828
y[1] (analytic) = 2.3969319271332694151486097794823
y[1] (numeric) = 2.3969319271332694237195606668549
absolute error = 8.5709508873726e-18
relative error = 3.5758007102118487199999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0829
y[1] (analytic) = 2.3975065931431311436106449292736
y[1] (numeric) = 2.3975065931431311522016745031636
absolute error = 8.5910295738900e-18
relative error = 3.5833184352695189999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 2.3980815347721822541966426858513
y[1] (numeric) = 2.3980815347721822628077883958118
absolute error = 8.6111457099605e-18
relative error = 3.5908477610535285000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0831
y[1] (analytic) = 2.3986567522187574958023506836172
y[1] (numeric) = 2.3986567522187575044336500538045
absolute error = 8.6312993701873e-18
relative error = 3.5983887074310853700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0832
y[1] (analytic) = 2.3992322456813819577735124760077
y[1] (numeric) = 2.3992322456813819664250031053456
absolute error = 8.6514906293379e-18
relative error = 3.6059412943080367200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0833
y[1] (analytic) = 2.3998080153587712982961363090953
y[1] (numeric) = 2.3998080153587713069678558714389
absolute error = 8.6717195623436e-18
relative error = 3.6135055416285781200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0834
y[1] (analytic) = 2.4003840614498319731156985117619
y[1] (numeric) = 2.4003840614498319818076847560624
absolute error = 8.6919862443005e-18
relative error = 3.6210814693755883000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0835
y[1] (analytic) = 2.4009603841536614645858343337335
y[1] (numeric) = 2.4009603841536614732981250842032
absolute error = 8.7122907504697e-18
relative error = 3.6286690975706300500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0836
y[1] (analytic) = 2.4015369836695485110470701248799
y[1] (numeric) = 2.4015369836695485197797032811575
absolute error = 8.7326331562776e-18
relative error = 3.6362684462739926400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0837
y[1] (analytic) = 2.402113860196973336536151813596
y[1] (numeric) = 2.4021138601969733452891653509124
absolute error = 8.7530135373164e-18
relative error = 3.6438795355848173199999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0838
y[1] (analytic) = 2.4026910139356078808265257087938
y[1] (numeric) = 2.4026910139356078895999576781385
absolute error = 8.7734319693447e-18
relative error = 3.6515023856412641400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0839
y[1] (analytic) = 2.4032684450853160298005287190579
y[1] (numeric) = 2.4032684450853160385944172473453
absolute error = 8.7938885282874e-18
relative error = 3.6591370166203871400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 2.4038461538461538461538461538462
y[1] (numeric) = 2.4038461538461538549682294440829
absolute error = 8.8143832902367e-18
relative error = 3.6667834487384671999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0841
y[1] (analytic) = 2.4044241404183698004327963452753
y[1] (numeric) = 2.4044241404183698092677126767275
absolute error = 8.8349163314522e-18
relative error = 3.6744417022509699800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=206.0MB, alloc=4.2MB, time=8.80
NO POLE
x[1] = 0.0842
y[1] (analytic) = 2.4050024050024050024050024050024
y[1] (numeric) = 2.4050024050024050112604901333634
absolute error = 8.8554877283610e-18
relative error = 3.6821117974525038000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0843
y[1] (analytic) = 2.4055809477988934327640125090209
y[1] (numeric) = 2.4055809477988934416401100665797
absolute error = 8.8760975575588e-18
relative error = 3.6897937546771931600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0844
y[1] (analytic) = 2.4061597690086621751684311838306
y[1] (numeric) = 2.4061597690086621840651770796403
absolute error = 8.8967458958097e-18
relative error = 3.6974875942985113200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0845
y[1] (analytic) = 2.4067388688327316486161251504212
y[1] (numeric) = 2.4067388688327316575335579704682
absolute error = 8.9174328200470e-18
relative error = 3.7051933367295285000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0846
y[1] (analytic) = 2.4073182474723158401540683678382
y[1] (numeric) = 2.4073182474723158490922267752117
absolute error = 8.9381584073735e-18
relative error = 3.7129110024229519000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0847
y[1] (analytic) = 2.407897905128822537924392005779
y[1] (numeric) = 2.4078979051288225468833147408406
absolute error = 8.9589227350616e-18
relative error = 3.7206406118710824799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0848
y[1] (analytic) = 2.4084778420038535645472061657033
y[1] (numeric) = 2.4084778420038535735269320462576
absolute error = 8.9797258805543e-18
relative error = 3.7283821856061453600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0849
y[1] (analytic) = 2.4090580582992050108407612623464
y[1] (numeric) = 2.4090580582992050198413291838116
absolute error = 9.0005679214652e-18
relative error = 3.7361357442002045200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 2.4096385542168674698795180722892
y[1] (numeric) = 2.409638554216867478900967007868
absolute error = 9.0214489355788e-18
relative error = 3.7439013082652019999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0851
y[1] (analytic) = 2.4102193299590262713906965533864
y[1] (numeric) = 2.4102193299590262804330655542378
absolute error = 9.0423690008514e-18
relative error = 3.7516788984532458599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0852
y[1] (analytic) = 2.4108003857280617164898746383799
y[1] (numeric) = 2.4108003857280617255532028337911
absolute error = 9.0633281954112e-18
relative error = 3.7594685354565657600000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0853
y[1] (analytic) = 2.4113817217265493127562093079334
y[1] (numeric) = 2.4113817217265493218405359054919
absolute error = 9.0843265975585e-18
relative error = 3.7672702400075099500000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0854
y[1] (analytic) = 2.411963338157260009647853352629
y[1] (numeric) = 2.4119633381572600187532176383957
absolute error = 9.1053642857667e-18
relative error = 3.7750840328788738200000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0855
y[1] (analytic) = 2.4125452352231604342581423401689
y[1] (numeric) = 2.4125452352231604433845836788512
absolute error = 9.1264413386823e-18
relative error = 3.7829099348838133500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0856
y[1] (analytic) = 2.4131274131274131274131274131274
y[1] (numeric) = 2.4131274131274131365606852482529
absolute error = 9.1475578351255e-18
relative error = 3.7907479668760072000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=209.8MB, alloc=4.2MB, time=8.97
x[1] = 0.0857
y[1] (analytic) = 2.4137098720733767801110306541154
y[1] (numeric) = 2.4137098720733767892797445082057
absolute error = 9.1687138540903e-18
relative error = 3.7985981497496112900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0858
y[1] (analytic) = 2.4142926122646064703042008691453
y[1] (numeric) = 2.4142926122646064794941103438908
absolute error = 9.1899094747455e-18
relative error = 3.8064605044395861000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0859
y[1] (analytic) = 2.414875633904853900024148756339
y[1] (numeric) = 2.4148756339048539092352935327735
absolute error = 9.2111447764345e-18
relative error = 3.8143350519215264500000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 2.4154589371980676328502415458937
y[1] (numeric) = 2.4154589371980676420826613845699
absolute error = 9.2324198386762e-18
relative error = 3.8222218132119468000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0861
y[1] (analytic) = 2.4160425223483933317226383184344
y[1] (numeric) = 2.4160425223483933409763730595996
absolute error = 9.2537347411652e-18
relative error = 3.8301208093682762800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0862
y[1] (analytic) = 2.4166263895601739971000483325278
y[1] (numeric) = 2.4166263895601740063751378963001
absolute error = 9.2750895637723e-18
relative error = 3.8380320614889777400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0863
y[1] (analytic) = 2.4172105390379502054628958182258
y[1] (numeric) = 2.4172105390379502147593802047707
absolute error = 9.2964843865449e-18
relative error = 3.8459555907136251299999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0864
y[1] (analytic) = 2.4177949709864603481624758220503
y[1] (numeric) = 2.4177949709864603574803951117577
absolute error = 9.3179192897074e-18
relative error = 3.8538914182229806400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0865
y[1] (analytic) = 2.4183796856106408706166868198307
y[1] (numeric) = 2.4183796856106408799560811734924
absolute error = 9.3393943536617e-18
relative error = 3.8618395652391129500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0866
y[1] (analytic) = 2.4189646831156265118529269472666
y[1] (numeric) = 2.4189646831156265212138366062541
absolute error = 9.3609096589875e-18
relative error = 3.8698000530254325000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0867
y[1] (analytic) = 2.4195499637067505443987418340189
y[1] (numeric) = 2.419549963706750553781207120462
absolute error = 9.3824652864431e-18
relative error = 3.8777729028869332300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0868
y[1] (analytic) = 2.4201355275895450145208131655373
y[1] (numeric) = 2.4201355275895450239248744825026
absolute error = 9.4040613169653e-18
relative error = 3.8857581361700619600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0869
y[1] (analytic) = 2.4207213749697409828128782377148
y[1] (numeric) = 2.4207213749697409922385760693852
absolute error = 9.4256978316704e-18
relative error = 3.8937557742630422400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 2.4213075060532687651331719128329
y[1] (numeric) = 2.4213075060532687745805468246868
absolute error = 9.4473749118539e-18
relative error = 3.9017658385956607000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0871
y[1] (analytic) = 2.4218939210462581738919835311213
y[1] (numeric) = 2.4218939210462581833610761701131
absolute error = 9.4690926389918e-18
relative error = 3.9097883506397142200000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0872
y[1] (analytic) = 2.4224806201550387596899224806202
y[1] (numeric) = 2.4224806201550387691807735753605
absolute error = 9.4908510947403e-18
relative error = 3.9178233319087958399999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.2MB, time=9.13
NO POLE
x[1] = 0.0873
y[1] (analytic) = 2.4230676035861400533074872788951
y[1] (numeric) = 2.4230676035861400628201376398321
absolute error = 9.5126503609370e-18
relative error = 3.9258708039586999000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0874
y[1] (analytic) = 2.4236548715462918080465341735337
y[1] (numeric) = 2.4236548715462918175810246931342
absolute error = 9.5344905196005e-18
relative error = 3.9339307883871663000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0875
y[1] (analytic) = 2.4242424242424242424242424242424
y[1] (numeric) = 2.4242424242424242519806140771739
absolute error = 9.5563716529315e-18
relative error = 3.9420033068342437500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0876
y[1] (analytic) = 2.4248302618816682832201745877789
y[1] (numeric) = 2.4248302618816682927984684310916
absolute error = 9.5782938433127e-18
relative error = 3.9500883809821574799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0877
y[1] (analytic) = 2.4254183846713558088770312878972
y[1] (numeric) = 2.4254183846713558184772884612071
absolute error = 9.6002571733099e-18
relative error = 3.9581860325556717699999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0878
y[1] (analytic) = 2.4260067928190198932557011159631
y[1] (numeric) = 2.426006792819019902877962841635
absolute error = 9.6222617256719e-18
relative error = 3.9662962833219571800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0879
y[1] (analytic) = 2.4265954865323950497452074739141
y[1] (numeric) = 2.4265954865323950593895150572452
absolute error = 9.6443075833311e-18
relative error = 3.9744191550907463100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 2.4271844660194174757281553398058
y[1] (numeric) = 2.4271844660194174853945501692099
absolute error = 9.6663948294041e-18
relative error = 3.9825546697144892000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0881
y[1] (analytic) = 2.4277737314882252974022821073076
y[1] (numeric) = 2.4277737314882253070908056544996
absolute error = 9.6885235471920e-18
relative error = 3.9907028490883848000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0882
y[1] (analytic) = 2.4283632831471588149587178241865
y[1] (numeric) = 2.4283632831471588246694116443674
absolute error = 9.7106938201809e-18
relative error = 3.9988637151504946200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0883
y[1] (analytic) = 2.4289531212047607481175613310663
y[1] (numeric) = 2.4289531212047607578504670631086
absolute error = 9.7329057320423e-18
relative error = 4.0070372898818149100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0884
y[1] (analytic) = 2.4295432458697764820213799805637
y[1] (numeric) = 2.4295432458697764917765393471972
absolute error = 9.7551593666335e-18
relative error = 4.0152235953063485999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0885
y[1] (analytic) = 2.4301336573511543134872417982989
y[1] (numeric) = 2.4301336573511543232646966062974
absolute error = 9.7774548079985e-18
relative error = 4.0234226534913827500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0886
y[1] (analytic) = 2.4307243558580456976178901312591
y[1] (numeric) = 2.4307243558580457074176822716269
absolute error = 9.7997921403678e-18
relative error = 4.0316344865473129200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0887
y[1] (analytic) = 2.4313153415998054947726720155604
y[1] (numeric) = 2.4313153415998055045948434637196
absolute error = 9.8221714481592e-18
relative error = 4.0398591166278789600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0888
y[1] (analytic) = 2.4319066147859922178988326848249
y[1] (numeric) = 2.4319066147859922277434255008032
absolute error = 9.8445928159783e-18
relative error = 4.0480965659302769600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.2MB, time=9.30
NO POLE
x[1] = 0.0889
y[1] (analytic) = 2.4324981756263682802237898321576
y[1] (numeric) = 2.4324981756263682900908461607765
absolute error = 9.8670563286189e-18
relative error = 4.0563468566952297900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 2.43309002433090024330900243309
y[1] (numeric) = 2.4330900243309002531985645041533
absolute error = 9.8895620710633e-18
relative error = 4.0646100112070163000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0891
y[1] (analytic) = 2.4336821611097590654660501338525
y[1] (numeric) = 2.4336821611097590753781602623356
absolute error = 9.9121101284831e-18
relative error = 4.0728860517937057900000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0892
y[1] (analytic) = 2.4342745861733203505355404089581
y[1] (numeric) = 2.4342745861733203604702409951976
absolute error = 9.9347005862395e-18
relative error = 4.0811750008271866000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0893
y[1] (analytic) = 2.4348672997321645970294618943268
y[1] (numeric) = 2.4348672997321646069867954242102
absolute error = 9.9573335298834e-18
relative error = 4.0894768807231123799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0894
y[1] (analytic) = 2.4354603019970774476376035070628
y[1] (numeric) = 2.4354603019970774576176125522196
absolute error = 9.9800090451568e-18
relative error = 4.0977917139413820800000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0895
y[1] (analytic) = 2.4360535931790499390986601705238
y[1] (numeric) = 2.4360535931790499491013873885158
absolute error = 1.00027272179920e-17
relative error = 4.1061195229857159999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0896
y[1] (analytic) = 2.4366471734892787524366471734893
y[1] (numeric) = 2.4366471734892787624621353080026
absolute error = 1.00254881345133e-17
relative error = 4.1144603304042583200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0897
y[1] (analytic) = 2.4372410431391664635632464050695
y[1] (numeric) = 2.4372410431391664736115382861061
absolute error = 1.00482918810366e-17
relative error = 4.1228141587893169799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0898
y[1] (analytic) = 2.4378352023403217942467089224768
y[1] (numeric) = 2.4378352023403218043178474665472
absolute error = 1.00711385440704e-17
relative error = 4.1311810307776780800000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0899
y[1] (analytic) = 2.4384296513045598634479395269446
y[1] (numeric) = 2.4384296513045598735419677372603
absolute error = 1.00940282103157e-17
relative error = 4.1395609690504685700000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 2.4390243902439024390243902439024
y[1] (numeric) = 2.4390243902439024491413512105696
absolute error = 1.01169609666672e-17
relative error = 4.1479539963335520000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0901
y[1] (analytic) = 2.439619419370578189802390827031
y[1] (numeric) = 2.4396194193705781999423277272443
absolute error = 1.01399369002133e-17
relative error = 4.1563601353974316700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0902
y[1] (analytic) = 2.4402147388970229380185456320156
y[1] (numeric) = 2.4402147388970229481815017302523
absolute error = 1.01629560982367e-17
relative error = 4.1647794090573996600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0903
y[1] (analytic) = 2.4408103490358799121308274347083
y[1] (numeric) = 2.4408103490358799223168460829231
absolute error = 1.01860186482148e-17
relative error = 4.1732118401736035600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=221.2MB, alloc=4.2MB, time=9.46
x[1] = 0.0904
y[1] (analytic) = 2.44140625
y[1] (numeric) = 2.4414062500000000102091246378203
absolute error = 1.02091246378203e-17
relative error = 4.1816574516511948800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0905
y[1] (analytic) = 2.4420024420024420024420024420024
y[1] (numeric) = 2.4420024420024420126742765969241
absolute error = 1.02322741549217e-17
relative error = 4.1901162664404361500000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0906
y[1] (analytic) = 2.442598925256472887151929653151
y[1] (numeric) = 2.4425989252564728974073969407344
absolute error = 1.02554672875834e-17
relative error = 4.1985883075366439599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0907
y[1] (analytic) = 2.44319569997556804300024431957
y[1] (numeric) = 2.4431956999755680532789484436369
absolute error = 1.02787041240669e-17
relative error = 4.2070735979805821700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0908
y[1] (analytic) = 2.4437927663734115347018572825024
y[1] (numeric) = 2.443792766373411545003842035333
absolute error = 1.03019847528306e-17
relative error = 4.2155721608582815200000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0909
y[1] (analytic) = 2.4443901246638963578587142507944
y[1] (numeric) = 2.444390124663896368184023513325
absolute error = 1.03253092625306e-17
relative error = 4.2240840193012684600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 2.4449877750611246943765281173594
y[1] (numeric) = 2.4449877750611247047252058593807
absolute error = 1.03486777420213e-17
relative error = 4.2326091964867117000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0911
y[1] (analytic) = 2.4455857177794081682562973832233
y[1] (numeric) = 2.4455857177794081786283876635789
absolute error = 1.03720902803556e-17
relative error = 4.2411477156374048400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0912
y[1] (analytic) = 2.446183953033268101761252446184
y[1] (numeric) = 2.4461839530332681121567994129696
absolute error = 1.03955469667856e-17
relative error = 4.2496996000219532799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0913
y[1] (analytic) = 2.446782481037435771959872767311
y[1] (numeric) = 2.446782481037435782378920658074
absolute error = 1.04190478907630e-17
relative error = 4.2582648729548381000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0914
y[1] (analytic) = 2.4473813020068526676456191874694
y[1] (numeric) = 2.4473813020068526780882123294089
absolute error = 1.04425931419395e-17
relative error = 4.2668435577964797000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0915
y[1] (analytic) = 2.4479804161566707466340269277846
y[1] (numeric) = 2.4479804161566707571002097379521
absolute error = 1.04661828101675e-17
relative error = 4.2754356779534237500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0916
y[1] (analytic) = 2.448579823702252693437806072478
y[1] (numeric) = 2.4485798237022527039276230579785
absolute error = 1.04898169855005e-17
relative error = 4.2840412568784041999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0917
y[1] (analytic) = 2.4491795248591721773205975998041
y[1] (numeric) = 2.4491795248591721878340933579978
absolute error = 1.05134957581937e-17
relative error = 4.2926603180704877099999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0918
y[1] (analytic) = 2.4497795198432141107300342969133
y[1] (numeric) = 2.4497795198432141212672535156175
absolute error = 1.05372192187042e-17
relative error = 4.3012928850750544400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0919
y[1] (analytic) = 2.4503798088703749081107571673609
y[1] (numeric) = 2.4503798088703749186717446250528
absolute error = 1.05609874576919e-17
relative error = 4.3099389814840643900000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.2MB, time=9.63
NO POLE
x[1] = 0.092
y[1] (analytic) = 2.4509803921568627450980392156863
y[1] (numeric) = 2.4509803921568627556828397817057
absolute error = 1.05848005660194e-17
relative error = 4.3185986309359152000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0921
y[1] (analytic) = 2.4515812699190978180926697720029
y[1] (numeric) = 2.4515812699190978287013284067564
absolute error = 1.06086586347535e-17
relative error = 4.3272718571159526500000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0922
y[1] (analytic) = 2.4521824423737126042177538008828
y[1] (numeric) = 2.4521824423737126148503155560473
absolute error = 1.06325617551645e-17
relative error = 4.3359586837560831000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0923
y[1] (analytic) = 2.4527839097375521216580819229826
y[1] (numeric) = 2.4527839097375521323145919417104
absolute error = 1.06565100187278e-17
relative error = 4.3446591346353240600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0924
y[1] (analytic) = 2.4533856722276741903827281648675
y[1] (numeric) = 2.4533856722276742010632316819911
absolute error = 1.06805035171236e-17
relative error = 4.3533732335795793600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0925
y[1] (analytic) = 2.4539877300613496932515337423313
y[1] (numeric) = 2.4539877300613497039560760845691
absolute error = 1.07045423422378e-17
relative error = 4.3621010044619035000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0926
y[1] (analytic) = 2.4545900834560628375061364752086
y[1] (numeric) = 2.4545900834560628482347630613711
absolute error = 1.07286265861625e-17
relative error = 4.3708424712026025000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0927
y[1] (analytic) = 2.4551927326295114166462067272281
y[1] (numeric) = 2.4551927326295114273989630684243
absolute error = 1.07527563411962e-17
relative error = 4.3795976577692122600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0928
y[1] (analytic) = 2.4557956777996070726915520628684
y[1] (numeric) = 2.4557956777996070834684837627133
absolute error = 1.07769316998449e-17
relative error = 4.3883665881768432799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0929
y[1] (analytic) = 2.4563989191844755588307541144682
y[1] (numeric) = 2.4563989191844755696319068692903
absolute error = 1.08011527548221e-17
relative error = 4.3971492864880769100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 2.4570024570024570024570024570025
y[1] (numeric) = 2.4570024570024570132824220560518
absolute error = 1.08254195990493e-17
relative error = 4.4059457768130650999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0931
y[1] (analytic) = 2.4576062914721061685917915949865
y[1] (numeric) = 2.4576062914721061794415239206435
absolute error = 1.08497323256570e-17
relative error = 4.4147560833098333000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0932
y[1] (analytic) = 2.4582104228121927236971484759095
y[1] (numeric) = 2.4582104228121927345712395038943
absolute error = 1.08740910279848e-17
relative error = 4.4235802301842166400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0933
y[1] (analytic) = 2.4588148512417014998770592574379
y[1] (numeric) = 2.4588148512417015107755550570197
absolute error = 1.08984957995818e-17
relative error = 4.4324182416899180600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0934
y[1] (analytic) = 2.4594195769798327594687653713724
y[1] (numeric) = 2.45941957697983277039171210558
absolute error = 1.09229467342076e-17
relative error = 4.4412701421288101599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0935
y[1] (analytic) = 2.4600246002460024600246002460025
y[1] (numeric) = 2.4600246002460024709720441718351
absolute error = 1.09474439258326e-17
relative error = 4.4501359558509518999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.2MB, time=9.80
NO POLE
x[1] = 0.0936
y[1] (analytic) = 2.4606299212598425196850393700787
y[1] (numeric) = 2.4606299212598425306570268387171
absolute error = 1.09719874686384e-17
relative error = 4.4590157072546457600000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0937
y[1] (analytic) = 2.4612355402412010829436377061285
y[1] (numeric) = 2.4612355402412010939402151631467
absolute error = 1.09965774570182e-17
relative error = 4.4679094207864946600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0938
y[1] (analytic) = 2.4618414574101427868045297882816
y[1] (numeric) = 2.4618414574101427978257437738596
absolute error = 1.10212139855780e-17
relative error = 4.4768171209417836000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0939
y[1] (analytic) = 2.4624476729869490273331691701551
y[1] (numeric) = 2.4624476729869490383790663192914
absolute error = 1.10458971491363e-17
relative error = 4.4857388322642514300000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 2.4630541871921182266009852216749
y[1] (numeric) = 2.4630541871921182376716122644
absolute error = 1.10706270427251e-17
relative error = 4.4946745793463906000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0941
y[1] (analytic) = 2.4636610002463661000246366100025
y[1] (numeric) = 2.4636610002463661111200403715929
absolute error = 1.10954037615904e-17
relative error = 4.5036243868295433599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0942
y[1] (analytic) = 2.4642681123706259241005421389847
y[1] (numeric) = 2.4642681123706259352207695401774
absolute error = 1.11202274011927e-17
relative error = 4.5125882794039976600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0943
y[1] (analytic) = 2.4648755237860488045353709637663
y[1] (numeric) = 2.4648755237860488156804690209735
absolute error = 1.11450980572072e-17
relative error = 4.5215662818089610400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0944
y[1] (analytic) = 2.4654832347140039447731755424063
y[1] (numeric) = 2.4654832347140039559431913679312
absolute error = 1.11700158255249e-17
relative error = 4.5305584188328994400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0945
y[1] (analytic) = 2.4660912453760789149198520345253
y[1] (numeric) = 2.4660912453760789261148328367781
absolute error = 1.11949808022528e-17
relative error = 4.5395647153135104000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0946
y[1] (analytic) = 2.4666995559940799210656142081894
y[1] (numeric) = 2.466699555994079932285607291904
absolute error = 1.12199930837146e-17
relative error = 4.5485851961378988400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0947
y[1] (analytic) = 2.467308166790032075006168270417
y[1] (numeric) = 2.4673081667900320862512210368678
absolute error = 1.12450527664508e-17
relative error = 4.5576198862425092400000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0948
y[1] (analytic) = 2.4679170779861796643632773938796
y[1] (numeric) = 2.4679170779861796756334373410995
absolute error = 1.12701599472199e-17
relative error = 4.5666688106135034799999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0949
y[1] (analytic) = 2.4685262898049864231054060725747
y[1] (numeric) = 2.4685262898049864344007207955733
absolute error = 1.12953147229986e-17
relative error = 4.5757319942867328599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 2.4691358024691358024691358024691
y[1] (numeric) = 2.4691358024691358137896529934513
absolute error = 1.13205171909822e-17
relative error = 4.5848094623477910000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0951
y[1] (analytic) = 2.4697456162015312422820449493702
y[1] (numeric) = 2.4697456162015312536278123979555
absolute error = 1.13457674485853e-17
relative error = 4.5939012399321879700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.2MB, time=9.96
NO POLE
x[1] = 0.0952
y[1] (analytic) = 2.4703557312252964426877470355731
y[1] (numeric) = 2.4703557312252964540588126290157
absolute error = 1.13710655934426e-17
relative error = 4.6030073522255644800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0953
y[1] (analytic) = 2.4709661477637756362737830491722
y[1] (numeric) = 2.4709661477637756476701947725812
absolute error = 1.13964117234090e-17
relative error = 4.6121278244636223000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0954
y[1] (analytic) = 2.4715768660405338606030647553139
y[1] (numeric) = 2.4715768660405338720248706918742
absolute error = 1.14218059365603e-17
relative error = 4.6212626819322973800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0955
y[1] (analytic) = 2.4721878862793572311495673671199
y[1] (numeric) = 2.4721878862793572425968156983139
absolute error = 1.14472483311940e-17
relative error = 4.6304119499679730000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0956
y[1] (analytic) = 2.4727992087042532146389713155292
y[1] (numeric) = 2.4727992087042532261117103213586
absolute error = 1.14727390058294e-17
relative error = 4.6395756539574093600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0957
y[1] (analytic) = 2.4734108335394509027949542418996
y[1] (numeric) = 2.4734108335394509142932323011083
absolute error = 1.14982780592087e-17
relative error = 4.6487538193380774100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0958
y[1] (analytic) = 2.4740227610094012864918357248887
y[1] (numeric) = 2.4740227610094012980157013151857
absolute error = 1.15238655902970e-17
relative error = 4.6579464715980473999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0959
y[1] (analytic) = 2.4746349913387775303142786439
y[1] (numeric) = 2.4746349913387775418637803421833
absolute error = 1.15495016982833e-17
relative error = 4.6671536362762815300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 2.4752475247524752475247524752475
y[1] (numeric) = 2.4752475247524752590999389578282
absolute error = 1.15751864825807e-17
relative error = 4.6763753389626028000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0961
y[1] (analytic) = 2.4758603614756127754394652141619
y[1] (numeric) = 2.4758603614756127870403852569892
absolute error = 1.16009200428273e-17
relative error = 4.6856116052979464700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0962
y[1] (analytic) = 2.4764735017335314512134720158494
y[1] (numeric) = 2.476473501733531462840174494736
absolute error = 1.16267024788866e-17
relative error = 4.6948624609744090800000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0963
y[1] (analytic) = 2.4770869457517958880356700520188
y[1] (numeric) = 2.4770869457517958996882039428667
absolute error = 1.16525338908479e-17
relative error = 4.7041279317352972300000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0964
y[1] (analytic) = 2.4777006937561942517343904856293
y[1] (numeric) = 2.4777006937561942634128048646564
absolute error = 1.16784143790271e-17
relative error = 4.7134080433753375600000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0965
y[1] (analytic) = 2.4783147459727385377942998760843
y[1] (numeric) = 2.4783147459727385494986439200515
absolute error = 1.17043440439672e-17
relative error = 4.7227028217407651999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0966
y[1] (analytic) = 2.4789291026276648487853247397124
y[1] (numeric) = 2.4789291026276648605156477261514
absolute error = 1.17303229864390e-17
relative error = 4.7320122927294926000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=236.5MB, alloc=4.2MB, time=10.13
x[1] = 0.0967
y[1] (analytic) = 2.4795437639474336722043144061493
y[1] (numeric) = 2.4795437639474336839606657135904
absolute error = 1.17563513074411e-17
relative error = 4.7413364822909956299999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0968
y[1] (analytic) = 2.4801587301587301587301587301587
y[1] (numeric) = 2.4801587301587301705125878383602
absolute error = 1.17824291082015e-17
relative error = 4.7506754164268448000000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0969
y[1] (analytic) = 2.4807740014884644008930786405358
y[1] (numeric) = 2.4807740014884644127016351307129
absolute error = 1.18085564901771e-17
relative error = 4.7600291211903890100000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 2.4813895781637717121588089330025
y[1] (numeric) = 2.4813895781637717239935424880573
absolute error = 1.18347335550548e-17
relative error = 4.7693976226870844000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0971
y[1] (analytic) = 2.4820054604120129064283941424671
y[1] (numeric) = 2.4820054604120129182893545472194
absolute error = 1.18609604047523e-17
relative error = 4.7787809470747016700000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0972
y[1] (analytic) = 2.4826216484607745779543197616683
y[1] (numeric) = 2.4826216484607745898415569030863
absolute error = 1.18872371414180e-17
relative error = 4.7881791205631704000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0973
y[1] (analytic) = 2.4832381425378693816737025080705
y[1] (numeric) = 2.4832381425378693935872663755028
absolute error = 1.19135638674323e-17
relative error = 4.7975921694149872100000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0974
y[1] (analytic) = 2.4838549428713363139592647789369
y[1] (numeric) = 2.4838549428713363258992054643445
absolute error = 1.19399406854076e-17
relative error = 4.8070201199450997600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0975
y[1] (analytic) = 2.4844720496894409937888198757764
y[1] (numeric) = 2.4844720496894410057551875739658
absolute error = 1.19663676981894e-17
relative error = 4.8164629985212335000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0976
y[1] (analytic) = 2.4850894632206759443339960238569
y[1] (numeric) = 2.4850894632206759563268410327133
absolute error = 1.19928450088564e-17
relative error = 4.8259208315638153599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0977
y[1] (analytic) = 2.4857071836937608749689286602038
y[1] (numeric) = 2.4857071836937608869883013809253
absolute error = 1.20193727207215e-17
relative error = 4.8353936455462594500000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0978
y[1] (analytic) = 2.4863252113376429636996519144704
y[1] (numeric) = 2.4863252113376429757456028518022
absolute error = 1.20459509373318e-17
relative error = 4.8448814669948499600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0979
y[1] (analytic) = 2.4869435463814971400149216612783
y[1] (numeric) = 2.4869435463814971520875014237483
absolute error = 1.20725797624700e-17
relative error = 4.8543843224891870000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 2.4875621890547263681592039800995
y[1] (numeric) = 2.4875621890547263802584632802539
absolute error = 1.20992593001544e-17
relative error = 4.8639022386620688000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0981
y[1] (analytic) = 2.4881811395869619308285643194825
y[1] (numeric) = 2.4881811395869619429545539741221
absolute error = 1.21259896546396e-17
relative error = 4.8734352421996552399999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0982
y[1] (analytic) = 2.4888003982080637132901941264311
y[1] (numeric) = 2.4888003982080637254429650568483
absolute error = 1.21527709304172e-17
relative error = 4.8829833598416309599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.2MB, time=10.30
NO POLE
x[1] = 0.0983
y[1] (analytic) = 2.4894199651481204879263131690316
y[1] (numeric) = 2.4894199651481205001059164012481
absolute error = 1.21796032322165e-17
relative error = 4.8925466183813680500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0984
y[1] (analytic) = 2.490039840637450199203187250996
y[1] (numeric) = 2.4900398406374502114096739160006
absolute error = 1.22064866650046e-17
relative error = 4.9021250446658473600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0985
y[1] (analytic) = 2.49066002490660024906600249066
y[1] (numeric) = 2.4906600249066002612994238246476
absolute error = 1.22334213339876e-17
relative error = 4.9117186655960214000000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0986
y[1] (analytic) = 2.4912805181863477827603388141505
y[1] (numeric) = 2.4912805181863477950207461587613
absolute error = 1.22604073446108e-17
relative error = 4.9213275081267751199999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0987
y[1] (analytic) = 2.491901320707699975080986792923
y[1] (numeric) = 2.4919013207076999873684315954826
absolute error = 1.22874448025596e-17
relative error = 4.9309515992671674800000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0988
y[1] (analytic) = 2.492522432701894317048853439681
y[1] (numeric) = 2.4925224327018943293633872534407
absolute error = 1.23145338137597e-17
relative error = 4.9405909660803916399999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0989
y[1] (analytic) = 2.4931438544003989030167040638245
y[1] (numeric) = 2.4931438544003989153583785482027
absolute error = 1.23416744843782e-17
relative error = 4.9502456356840960200000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 2.4937655860349127182044887780549
y[1] (numeric) = 2.4937655860349127305733556988787
absolute error = 1.23688669208238e-17
relative error = 4.9599156352503437999999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0991
y[1] (analytic) = 2.4943876278373659266650037415814
y[1] (numeric) = 2.4943876278373659390611149713291
absolute error = 1.23961112297477e-17
relative error = 4.9696009920058529300000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0992
y[1] (analytic) = 2.4950099800399201596806387225549
y[1] (numeric) = 2.4950099800399201721040462405986
absolute error = 1.24234075180437e-17
relative error = 4.9793017332319149600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0993
y[1] (analytic) = 2.4956326428749688045919640628899
y[1] (numeric) = 2.4956326428749688170427199557395
absolute error = 1.24507558928496e-17
relative error = 4.9890178862648347200000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0994
y[1] (analytic) = 2.4962556165751372940589116325512
y[1] (numeric) = 2.4962556165751373065370680940983
absolute error = 1.24781564615471e-17
relative error = 4.9987494784957682599999999999999e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0995
y[1] (analytic) = 2.4968789013732833957553058676654
y[1] (numeric) = 2.4968789013732834082609151994285
absolute error = 1.25056093317631e-17
relative error = 5.0084965373711215500000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0996
y[1] (analytic) = 2.4975024975024975024975024975025
y[1] (numeric) = 2.4975024975024975150306171088719
absolute error = 1.25331146113694e-17
relative error = 5.0182590903923077600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0997
y[1] (analytic) = 2.4981264051961029228078940794404
y[1] (numeric) = 2.4981264051961029353685664879246
absolute error = 1.25606724084842e-17
relative error = 5.0280371651162252600000000000000e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0998
y[1] (analytic) = 2.4987506246876561719140429785107
y[1] (numeric) = 2.4987506246876561845023258099829
absolute error = 1.25882828314722e-17
relative error = 5.0378307891551744400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.2MB, time=10.47
NO POLE
x[1] = 0.0999
y[1] (analytic) = 2.4993751562109472631842039490127
y[1] (numeric) = 2.4993751562109472758001499379581
absolute error = 1.26159459889454e-17
relative error = 5.0476399901770545400000000000001e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 2.5
y[1] (numeric) = 2.5000000000000000126436619897637
absolute error = 1.26436619897637e-17
relative error = 5.0574647959054800000000000000000e-16 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = y * y;
Iterations = 1000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Expected Time Remaining = 10 Seconds
Optimized Time Remaining = 10 Seconds
Time to Timeout = 14 Minutes 49 Seconds
Percent Done = 50.05 %
> quit
memory used=244.6MB, alloc=4.2MB, time=10.49