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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_iolevel,
> INFO,
> glob_max_terms,
> ALWAYS,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_iter,
> glob_warned,
> glob_smallish_float,
> glob_max_hours,
> glob_dump,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> centuries_in_millinium,
> glob_percent_done,
> glob_max_sec,
> glob_dump_analytic,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_abserr,
> glob_hmin_init,
> glob_disp_incr,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_relerr,
> glob_log10_relerr,
> glob_large_float,
> days_in_year,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_optimal_done,
> glob_not_yet_start_msg,
> djd_debug,
> glob_start,
> glob_last_good_h,
> glob_hmin,
> min_in_hour,
> glob_html_log,
> glob_warned2,
> years_in_century,
> glob_display_flag,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_tmp3_g,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_poles,
> array_y_higher_work,
> array_fact_2,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher,
> 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 glob_iolevel, INFO, glob_max_terms, ALWAYS, DEBUGL, DEBUGMASSIVE,
glob_max_iter, glob_hmax, glob_h, glob_reached_optimal_h, glob_log10normmin,
glob_iter, glob_warned, glob_smallish_float, glob_max_hours, glob_dump,
glob_small_float, glob_max_rel_trunc_err, glob_log10_abserr,
glob_look_poles, centuries_in_millinium, glob_percent_done, glob_max_sec,
glob_dump_analytic, hours_in_day, glob_optimal_expect_sec, glob_log10relerr,
glob_abserr, glob_hmin_init, glob_disp_incr, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_curr_iter_when_opt,
glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_relerr,
glob_log10_relerr, glob_large_float, days_in_year, glob_initial_pass,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_clock_start_sec,
glob_max_trunc_err, glob_optimal_done, glob_not_yet_start_msg, djd_debug,
glob_start, glob_last_good_h, glob_hmin, min_in_hour, glob_html_log,
glob_warned2, years_in_century, glob_display_flag, glob_max_opt_iter,
glob_max_minutes, glob_almost_1, sec_in_min, djd_debug2, array_const_1,
array_const_0D0, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_type_pole, array_fact_1, array_m1,
array_tmp1_g, array_last_rel_error, array_norms, array_tmp3_g,
array_1st_rel_error, array_pole, array_y, array_x, array_poles,
array_y_higher_work, array_fact_2, array_complex_pole, array_y_set_initial,
array_real_pole, array_y_higher_work2, array_y_higher, 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
> glob_iolevel,
> INFO,
> glob_max_terms,
> ALWAYS,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_iter,
> glob_warned,
> glob_smallish_float,
> glob_max_hours,
> glob_dump,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> centuries_in_millinium,
> glob_percent_done,
> glob_max_sec,
> glob_dump_analytic,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_abserr,
> glob_hmin_init,
> glob_disp_incr,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_relerr,
> glob_log10_relerr,
> glob_large_float,
> days_in_year,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_optimal_done,
> glob_not_yet_start_msg,
> djd_debug,
> glob_start,
> glob_last_good_h,
> glob_hmin,
> min_in_hour,
> glob_html_log,
> glob_warned2,
> years_in_century,
> glob_display_flag,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_tmp3_g,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_poles,
> array_y_higher_work,
> array_fact_2,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher,
> 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 glob_iolevel, INFO, glob_max_terms, ALWAYS, DEBUGL, DEBUGMASSIVE,
glob_max_iter, glob_hmax, glob_h, glob_reached_optimal_h, glob_log10normmin,
glob_iter, glob_warned, glob_smallish_float, glob_max_hours, glob_dump,
glob_small_float, glob_max_rel_trunc_err, glob_log10_abserr,
glob_look_poles, centuries_in_millinium, glob_percent_done, glob_max_sec,
glob_dump_analytic, hours_in_day, glob_optimal_expect_sec, glob_log10relerr,
glob_abserr, glob_hmin_init, glob_disp_incr, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_curr_iter_when_opt,
glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_relerr,
glob_log10_relerr, glob_large_float, days_in_year, glob_initial_pass,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_clock_start_sec,
glob_max_trunc_err, glob_optimal_done, glob_not_yet_start_msg, djd_debug,
glob_start, glob_last_good_h, glob_hmin, min_in_hour, glob_html_log,
glob_warned2, years_in_century, glob_display_flag, glob_max_opt_iter,
glob_max_minutes, glob_almost_1, sec_in_min, djd_debug2, array_const_1,
array_const_0D0, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_type_pole, array_fact_1, array_m1,
array_tmp1_g, array_last_rel_error, array_norms, array_tmp3_g,
array_1st_rel_error, array_pole, array_y, array_x, array_poles,
array_y_higher_work, array_fact_2, array_complex_pole, array_y_set_initial,
array_real_pole, array_y_higher_work2, array_y_higher, 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
> glob_iolevel,
> INFO,
> glob_max_terms,
> ALWAYS,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_iter,
> glob_warned,
> glob_smallish_float,
> glob_max_hours,
> glob_dump,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> centuries_in_millinium,
> glob_percent_done,
> glob_max_sec,
> glob_dump_analytic,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_abserr,
> glob_hmin_init,
> glob_disp_incr,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_relerr,
> glob_log10_relerr,
> glob_large_float,
> days_in_year,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_optimal_done,
> glob_not_yet_start_msg,
> djd_debug,
> glob_start,
> glob_last_good_h,
> glob_hmin,
> min_in_hour,
> glob_html_log,
> glob_warned2,
> years_in_century,
> glob_display_flag,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_tmp3_g,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_poles,
> array_y_higher_work,
> array_fact_2,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher,
> 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 glob_iolevel, INFO, glob_max_terms, ALWAYS, DEBUGL, DEBUGMASSIVE,
glob_max_iter, glob_hmax, glob_h, glob_reached_optimal_h, glob_log10normmin,
glob_iter, glob_warned, glob_smallish_float, glob_max_hours, glob_dump,
glob_small_float, glob_max_rel_trunc_err, glob_log10_abserr,
glob_look_poles, centuries_in_millinium, glob_percent_done, glob_max_sec,
glob_dump_analytic, hours_in_day, glob_optimal_expect_sec, glob_log10relerr,
glob_abserr, glob_hmin_init, glob_disp_incr, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_curr_iter_when_opt,
glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_relerr,
glob_log10_relerr, glob_large_float, days_in_year, glob_initial_pass,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_clock_start_sec,
glob_max_trunc_err, glob_optimal_done, glob_not_yet_start_msg, djd_debug,
glob_start, glob_last_good_h, glob_hmin, min_in_hour, glob_html_log,
glob_warned2, years_in_century, glob_display_flag, glob_max_opt_iter,
glob_max_minutes, glob_almost_1, sec_in_min, djd_debug2, array_const_1,
array_const_0D0, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_type_pole, array_fact_1, array_m1,
array_tmp1_g, array_last_rel_error, array_norms, array_tmp3_g,
array_1st_rel_error, array_pole, array_y, array_x, array_poles,
array_y_higher_work, array_fact_2, array_complex_pole, array_y_set_initial,
array_real_pole, array_y_higher_work2, array_y_higher, 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
> glob_iolevel,
> INFO,
> glob_max_terms,
> ALWAYS,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_iter,
> glob_warned,
> glob_smallish_float,
> glob_max_hours,
> glob_dump,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> centuries_in_millinium,
> glob_percent_done,
> glob_max_sec,
> glob_dump_analytic,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_abserr,
> glob_hmin_init,
> glob_disp_incr,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_relerr,
> glob_log10_relerr,
> glob_large_float,
> days_in_year,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_optimal_done,
> glob_not_yet_start_msg,
> djd_debug,
> glob_start,
> glob_last_good_h,
> glob_hmin,
> min_in_hour,
> glob_html_log,
> glob_warned2,
> years_in_century,
> glob_display_flag,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_tmp3_g,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_poles,
> array_y_higher_work,
> array_fact_2,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher,
> 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 glob_iolevel, INFO, glob_max_terms, ALWAYS, DEBUGL, DEBUGMASSIVE,
glob_max_iter, glob_hmax, glob_h, glob_reached_optimal_h, glob_log10normmin,
glob_iter, glob_warned, glob_smallish_float, glob_max_hours, glob_dump,
glob_small_float, glob_max_rel_trunc_err, glob_log10_abserr,
glob_look_poles, centuries_in_millinium, glob_percent_done, glob_max_sec,
glob_dump_analytic, hours_in_day, glob_optimal_expect_sec, glob_log10relerr,
glob_abserr, glob_hmin_init, glob_disp_incr, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_curr_iter_when_opt,
glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_relerr,
glob_log10_relerr, glob_large_float, days_in_year, glob_initial_pass,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_clock_start_sec,
glob_max_trunc_err, glob_optimal_done, glob_not_yet_start_msg, djd_debug,
glob_start, glob_last_good_h, glob_hmin, min_in_hour, glob_html_log,
glob_warned2, years_in_century, glob_display_flag, glob_max_opt_iter,
glob_max_minutes, glob_almost_1, sec_in_min, djd_debug2, array_const_1,
array_const_0D0, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_type_pole, array_fact_1, array_m1,
array_tmp1_g, array_last_rel_error, array_norms, array_tmp3_g,
array_1st_rel_error, array_pole, array_y, array_x, array_poles,
array_y_higher_work, array_fact_2, array_complex_pole, array_y_set_initial,
array_real_pole, array_y_higher_work2, array_y_higher, 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
> glob_iolevel,
> INFO,
> glob_max_terms,
> ALWAYS,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_iter,
> glob_warned,
> glob_smallish_float,
> glob_max_hours,
> glob_dump,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> centuries_in_millinium,
> glob_percent_done,
> glob_max_sec,
> glob_dump_analytic,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_abserr,
> glob_hmin_init,
> glob_disp_incr,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_relerr,
> glob_log10_relerr,
> glob_large_float,
> days_in_year,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_optimal_done,
> glob_not_yet_start_msg,
> djd_debug,
> glob_start,
> glob_last_good_h,
> glob_hmin,
> min_in_hour,
> glob_html_log,
> glob_warned2,
> years_in_century,
> glob_display_flag,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_tmp3_g,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_poles,
> array_y_higher_work,
> array_fact_2,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher,
> 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 glob_iolevel, INFO, glob_max_terms, ALWAYS, DEBUGL, DEBUGMASSIVE,
glob_max_iter, glob_hmax, glob_h, glob_reached_optimal_h, glob_log10normmin,
glob_iter, glob_warned, glob_smallish_float, glob_max_hours, glob_dump,
glob_small_float, glob_max_rel_trunc_err, glob_log10_abserr,
glob_look_poles, centuries_in_millinium, glob_percent_done, glob_max_sec,
glob_dump_analytic, hours_in_day, glob_optimal_expect_sec, glob_log10relerr,
glob_abserr, glob_hmin_init, glob_disp_incr, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_curr_iter_when_opt,
glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_relerr,
glob_log10_relerr, glob_large_float, days_in_year, glob_initial_pass,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_clock_start_sec,
glob_max_trunc_err, glob_optimal_done, glob_not_yet_start_msg, djd_debug,
glob_start, glob_last_good_h, glob_hmin, min_in_hour, glob_html_log,
glob_warned2, years_in_century, glob_display_flag, glob_max_opt_iter,
glob_max_minutes, glob_almost_1, sec_in_min, djd_debug2, array_const_1,
array_const_0D0, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_type_pole, array_fact_1, array_m1,
array_tmp1_g, array_last_rel_error, array_norms, array_tmp3_g,
array_1st_rel_error, array_pole, array_y, array_x, array_poles,
array_y_higher_work, array_fact_2, array_complex_pole, array_y_set_initial,
array_real_pole, array_y_higher_work2, array_y_higher, 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
> glob_iolevel,
> INFO,
> glob_max_terms,
> ALWAYS,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_iter,
> glob_warned,
> glob_smallish_float,
> glob_max_hours,
> glob_dump,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> centuries_in_millinium,
> glob_percent_done,
> glob_max_sec,
> glob_dump_analytic,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_abserr,
> glob_hmin_init,
> glob_disp_incr,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_relerr,
> glob_log10_relerr,
> glob_large_float,
> days_in_year,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_optimal_done,
> glob_not_yet_start_msg,
> djd_debug,
> glob_start,
> glob_last_good_h,
> glob_hmin,
> min_in_hour,
> glob_html_log,
> glob_warned2,
> years_in_century,
> glob_display_flag,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_tmp3_g,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_poles,
> array_y_higher_work,
> array_fact_2,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cos $eq_no = 1
> array_tmp1_g[1] := sin(array_x[1]);
> array_tmp1[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre sin $eq_no = 1 iii = 1
> #emit pre sin 1 $eq_no = 1
> array_tmp3[1] := sin(array_x[1]);
> array_tmp3_g[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] + array_tmp3[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_tmp4[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre cos $eq_no = 1
> array_tmp1_g[2] := (att(1,array_tmp1,array_x,1));
> array_tmp1[2] := (-att(1,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp3[2] := att(1,array_tmp3_g,array_x,1);
> array_tmp3_g[2] := -att(1,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp2[2] + array_tmp3[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_tmp4[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre cos $eq_no = 1
> array_tmp1_g[3] := (att(2,array_tmp1,array_x,1));
> array_tmp1[3] := (-att(2,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp3[3] := att(2,array_tmp3_g,array_x,1);
> array_tmp3_g[3] := -att(2,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp2[3] + array_tmp3[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_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre cos $eq_no = 1
> array_tmp1_g[4] := (att(3,array_tmp1,array_x,1));
> array_tmp1[4] := (-att(3,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp3[4] := att(3,array_tmp3_g,array_x,1);
> array_tmp3_g[4] := -att(3,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp2[4] + array_tmp3[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_tmp4[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre cos $eq_no = 1
> array_tmp1_g[5] := (att(4,array_tmp1,array_x,1));
> array_tmp1[5] := (-att(4,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp3[5] := att(4,array_tmp3_g,array_x,1);
> array_tmp3_g[5] := -att(4,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp2[5] + array_tmp3[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_tmp4[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit cos $eq_no = 1
> array_tmp1_g[kkk] := (att(kkk-1,array_tmp1,array_x,1));
> array_tmp1[kkk] := (-att(kkk-1,array_tmp1_g,array_x,1));
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit sin $eq_no = 1
> array_tmp3[kkk] := att(kkk-1,array_tmp3_g,array_x,1);
> array_tmp3_g[kkk] := -att(kkk-1,array_tmp3,array_x,1);
> #emit add $eq_no = 1
> array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[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_tmp4[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 glob_iolevel, INFO, glob_max_terms, ALWAYS, DEBUGL, DEBUGMASSIVE,
glob_max_iter, glob_hmax, glob_h, glob_reached_optimal_h, glob_log10normmin,
glob_iter, glob_warned, glob_smallish_float, glob_max_hours, glob_dump,
glob_small_float, glob_max_rel_trunc_err, glob_log10_abserr,
glob_look_poles, centuries_in_millinium, glob_percent_done, glob_max_sec,
glob_dump_analytic, hours_in_day, glob_optimal_expect_sec, glob_log10relerr,
glob_abserr, glob_hmin_init, glob_disp_incr, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_curr_iter_when_opt,
glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_relerr,
glob_log10_relerr, glob_large_float, days_in_year, glob_initial_pass,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_clock_start_sec,
glob_max_trunc_err, glob_optimal_done, glob_not_yet_start_msg, djd_debug,
glob_start, glob_last_good_h, glob_hmin, min_in_hour, glob_html_log,
glob_warned2, years_in_century, glob_display_flag, glob_max_opt_iter,
glob_max_minutes, glob_almost_1, sec_in_min, djd_debug2, array_const_1,
array_const_0D0, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_type_pole, array_fact_1, array_m1,
array_tmp1_g, array_last_rel_error, array_norms, array_tmp3_g,
array_1st_rel_error, array_pole, array_y, array_x, array_poles,
array_y_higher_work, array_fact_2, array_complex_pole, array_y_set_initial,
array_real_pole, array_y_higher_work2, array_y_higher, glob_last;
array_tmp1_g[1] := sin(array_x[1]);
array_tmp1[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := sin(array_x[1]);
array_tmp3_g[1] := cos(array_x[1]);
array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1_g[2] := att(1, array_tmp1, array_x, 1);
array_tmp1[2] := -att(1, array_tmp1_g, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
array_tmp3[2] := att(1, array_tmp3_g, array_x, 1);
array_tmp3_g[2] := -att(1, array_tmp3, array_x, 1);
array_tmp4[2] := array_tmp2[2] + array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1_g[3] := att(2, array_tmp1, array_x, 1);
array_tmp1[3] := -att(2, array_tmp1_g, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
array_tmp3[3] := att(2, array_tmp3_g, array_x, 1);
array_tmp3_g[3] := -att(2, array_tmp3, array_x, 1);
array_tmp4[3] := array_tmp2[3] + array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1_g[4] := att(3, array_tmp1, array_x, 1);
array_tmp1[4] := -att(3, array_tmp1_g, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
array_tmp3[4] := att(3, array_tmp3_g, array_x, 1);
array_tmp3_g[4] := -att(3, array_tmp3, array_x, 1);
array_tmp4[4] := array_tmp2[4] + array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1_g[5] := att(4, array_tmp1, array_x, 1);
array_tmp1[5] := -att(4, array_tmp1_g, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
array_tmp3[5] := att(4, array_tmp3_g, array_x, 1);
array_tmp3_g[5] := -att(4, array_tmp3, array_x, 1);
array_tmp4[5] := array_tmp2[5] + array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp1[kkk] := -att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
array_tmp3[kkk] := att(kkk - 1, array_tmp3_g, array_x, 1);
array_tmp3_g[kkk] := -att(kkk - 1, array_tmp3, array_x, 1);
array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[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_tmp4[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)
> if (nnn <= glob_max_terms) then # if number 13
> ret := array_fact_1[nnn];
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_1`
factorial_1 := proc(nnn)
local ret;
if nnn <= glob_max_terms then ret := array_fact_1[nnn]
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> ret := array_fact_2[mmm,nnn];
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_3`
factorial_3 := proc(mmm, nnn)
local ret;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
ret := array_fact_2[mmm, nnn]
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 + sin(x) - cos(x);
> end;
exact_soln_y := proc(x) 2.0 + sin(x) - cos(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
> glob_iolevel,
> INFO,
> glob_max_terms,
> ALWAYS,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_max_iter,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_log10normmin,
> glob_iter,
> glob_warned,
> glob_smallish_float,
> glob_max_hours,
> glob_dump,
> glob_small_float,
> glob_max_rel_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> centuries_in_millinium,
> glob_percent_done,
> glob_max_sec,
> glob_dump_analytic,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_abserr,
> glob_hmin_init,
> glob_disp_incr,
> glob_subiter_method,
> glob_normmax,
> MAX_UNCHANGED,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_relerr,
> glob_log10_relerr,
> glob_large_float,
> days_in_year,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_optimal_done,
> glob_not_yet_start_msg,
> djd_debug,
> glob_start,
> glob_last_good_h,
> glob_hmin,
> min_in_hour,
> glob_html_log,
> glob_warned2,
> years_in_century,
> glob_display_flag,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_almost_1,
> sec_in_min,
> djd_debug2,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_norms,
> array_tmp3_g,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_poles,
> array_y_higher_work,
> array_fact_2,
> array_complex_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work2,
> array_y_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_iolevel := 5;
> INFO := 2;
> glob_max_terms := 30;
> ALWAYS := 1;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_max_iter := 1000;
> glob_hmax := 1.0;
> glob_h := 0.1;
> glob_reached_optimal_h := false;
> glob_log10normmin := 0.1;
> glob_iter := 0;
> glob_warned := false;
> glob_smallish_float := 0.1e-100;
> glob_max_hours := 0.0;
> glob_dump := false;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_look_poles := false;
> centuries_in_millinium := 10.0;
> glob_percent_done := 0.0;
> glob_max_sec := 10000.0;
> glob_dump_analytic := false;
> hours_in_day := 24.0;
> glob_optimal_expect_sec := 0.1;
> glob_log10relerr := 0.0;
> glob_abserr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_disp_incr := 0.1;
> glob_subiter_method := 3;
> glob_normmax := 0.0;
> MAX_UNCHANGED := 10;
> glob_current_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_unchanged_h_cnt := 0;
> glob_optimal_start := 0.0;
> glob_no_eqs := 0;
> glob_relerr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> days_in_year := 365.0;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> glob_clock_sec := 0.0;
> glob_log10abserr := 0.0;
> glob_orig_start_sec := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_optimal_done := false;
> glob_not_yet_start_msg := true;
> djd_debug := true;
> glob_start := 0;
> glob_last_good_h := 0.1;
> glob_hmin := 0.00000000001;
> min_in_hour := 60.0;
> glob_html_log := true;
> glob_warned2 := false;
> years_in_century := 100.0;
> glob_display_flag := true;
> glob_max_opt_iter := 10;
> glob_max_minutes := 0.0;
> glob_almost_1 := 0.9990;
> sec_in_min := 60.0;
> djd_debug2 := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/addpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 10.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"2.0 + sin(x) - cos(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
> max_terms := 30;
> Digits := 32;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_tmp3_g:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> 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_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[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_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=max_terms do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[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_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[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_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while iiif <= glob_max_terms do # do number 2
> jjjf := 0;
> while jjjf <= glob_max_terms do # do number 3
> temp1 := iiif !;
> temp2 := jjjf !;
> array_fact_1[iiif] := temp1;
> array_fact_2[iiif,jjjf] := temp1/temp2;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 10.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-16T20:11:45-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"add")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 091 | ")
> ;
> logitem_str(html_log_file,"add diffeq.mxt")
> ;
> logitem_str(html_log_file,"add maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly for speeding factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `iiif` is implicitly declared local to procedure `mainprog`
Warning, `jjjf` is implicitly declared local to procedure `mainprog`
Warning, `temp1` is implicitly declared local to procedure `mainprog`
Warning, `temp2` is implicitly declared local to procedure `mainprog`
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, iiif,
jjjf, temp1, temp2;
global glob_iolevel, INFO, glob_max_terms, ALWAYS, DEBUGL, DEBUGMASSIVE,
glob_max_iter, glob_hmax, glob_h, glob_reached_optimal_h, glob_log10normmin,
glob_iter, glob_warned, glob_smallish_float, glob_max_hours, glob_dump,
glob_small_float, glob_max_rel_trunc_err, glob_log10_abserr,
glob_look_poles, centuries_in_millinium, glob_percent_done, glob_max_sec,
glob_dump_analytic, hours_in_day, glob_optimal_expect_sec, glob_log10relerr,
glob_abserr, glob_hmin_init, glob_disp_incr, glob_subiter_method,
glob_normmax, MAX_UNCHANGED, glob_current_iter, glob_curr_iter_when_opt,
glob_unchanged_h_cnt, glob_optimal_start, glob_no_eqs, glob_relerr,
glob_log10_relerr, glob_large_float, days_in_year, glob_initial_pass,
glob_not_yet_finished, glob_clock_start_sec, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_clock_start_sec,
glob_max_trunc_err, glob_optimal_done, glob_not_yet_start_msg, djd_debug,
glob_start, glob_last_good_h, glob_hmin, min_in_hour, glob_html_log,
glob_warned2, years_in_century, glob_display_flag, glob_max_opt_iter,
glob_max_minutes, glob_almost_1, sec_in_min, djd_debug2, array_const_1,
array_const_0D0, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_type_pole, array_fact_1, array_m1,
array_tmp1_g, array_last_rel_error, array_norms, array_tmp3_g,
array_1st_rel_error, array_pole, array_y, array_x, array_poles,
array_y_higher_work, array_fact_2, array_complex_pole, array_y_set_initial,
array_real_pole, array_y_higher_work2, array_y_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_iolevel := 5;
INFO := 2;
glob_max_terms := 30;
ALWAYS := 1;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_max_iter := 1000;
glob_hmax := 1.0;
glob_h := 0.1;
glob_reached_optimal_h := false;
glob_log10normmin := 0.1;
glob_iter := 0;
glob_warned := false;
glob_smallish_float := 0.1*10^(-100);
glob_max_hours := 0.;
glob_dump := false;
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_look_poles := false;
centuries_in_millinium := 10.0;
glob_percent_done := 0.;
glob_max_sec := 10000.0;
glob_dump_analytic := false;
hours_in_day := 24.0;
glob_optimal_expect_sec := 0.1;
glob_log10relerr := 0.;
glob_abserr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_disp_incr := 0.1;
glob_subiter_method := 3;
glob_normmax := 0.;
MAX_UNCHANGED := 10;
glob_current_iter := 0;
glob_curr_iter_when_opt := 0;
glob_unchanged_h_cnt := 0;
glob_optimal_start := 0.;
glob_no_eqs := 0;
glob_relerr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
days_in_year := 365.0;
glob_initial_pass := true;
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
glob_clock_sec := 0.;
glob_log10abserr := 0.;
glob_orig_start_sec := 0.;
glob_optimal_clock_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_optimal_done := false;
glob_not_yet_start_msg := true;
djd_debug := true;
glob_start := 0;
glob_last_good_h := 0.1;
glob_hmin := 0.1*10^(-10);
min_in_hour := 60.0;
glob_html_log := true;
glob_warned2 := false;
years_in_century := 100.0;
glob_display_flag := true;
glob_max_opt_iter := 10;
glob_max_minutes := 0.;
glob_almost_1 := 0.9990;
sec_in_min := 60.0;
djd_debug2 := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/addpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 10.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "2.0 + sin(x) - cos(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;
max_terms := 30;
Digits := 32;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_tmp3_g := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
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_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[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_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[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_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_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_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[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_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp3_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp3_g[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
temp1 := iiif!;
temp2 := jjjf!;
array_fact_1[iiif] := temp1;
array_fact_2[iiif, jjjf] := temp1/temp2;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
x_end := 10.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-16T20:11:45-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "add");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 091 | ");
logitem_str(html_log_file,
"add diffeq.mxt");
logitem_str(html_log_file,
"add maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly for speeding factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/addpostode.ode#################
diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
max_terms := 30;
Digits := 32;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 10.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 + sin(x) - cos(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 1.0010004998332916750013886904514
y[1] (numeric) = 1.0010004998332916750499902761907
absolute error = 4.86015857393e-20
relative error = 4.8553008462427531968680029819310e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 1.0020019986660002667555301523823
y[1] (numeric) = 1.0020019986660002668526846789349
absolute error = 9.71545265526e-20
relative error = 9.6960411937246795574820344852769e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 1.0030044954966270260120659087596
y[1] (numeric) = 1.0030044954966270261577246826464
absolute error = 1.456587738868e-19
relative error = 1.4522245367871317936552784177578e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 1.004007989322675205685636470564
y[1] (numeric) = 1.0040079893226752058797507498018
absolute error = 1.941142792378e-19
relative error = 1.9333937707881543234807905606074e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 1.005012479140651063352544880757
y[1] (numeric) = 1.0050124791406510635950658749072
absolute error = 2.425209941502e-19
relative error = 2.4131142566266512137649542904813e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 1.0060179639460648647444155135024
y[1] (numeric) = 1.0060179639460648650352943837195
absolute error = 2.908788702171e-19
relative error = 2.8913884308401350038852734365429e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 1.0070244427334318882378446350663
y[1] (numeric) = 1.007024442733431888577032494147
absolute error = 3.391878590807e-19
relative error = 3.3682187312159012878917235137481e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 1.0080319144962734303390382368304
y[1] (numeric) = 1.0080319144962734307264861492625
absolute error = 3.874479124321e-19
relative error = 3.8436075967467034710225718950539e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 1.0090403782271178121624316558638
y[1] (numeric) = 1.0090403782271178125980906378749
absolute error = 4.356589820111e-19
relative error = 4.3175574675866992847694940602208e-17 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.20
NO POLE
x[1] = 0.01
y[1] (analytic) = 1.0100498329175013869022845045169
y[1] (numeric) = 1.0100498329175013873861055241235
absolute error = 4.838210196066e-19
relative error = 4.7900707850136085279700333655114e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 1.0110602775579695482962434375271
y[1] (numeric) = 1.0110602775579695488281774145838
absolute error = 5.319339770567e-19
relative error = 5.2611499913881380939530032949371e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 1.0120717111380777400798642931584
y[1] (numeric) = 1.0120717111380777406598620994068
absolute error = 5.799978062484e-19
relative error = 5.7307975301097062559702192033067e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 1.0130841326463924664310841539349
y[1] (numeric) = 1.0130841326463924670590966130528
absolute error = 6.280124591179e-19
relative error = 6.1990158455783639281512590537907e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 1.0140975410704923034036328825821
y[1] (numeric) = 1.0140975410704923040796107702326
absolute error = 6.759778876505e-19
relative error = 6.6658073831530096211096146436941e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 1.0151119353969689113483726998476
y[1] (numeric) = 1.0151119353969689120722667437284
absolute error = 7.238940438808e-19
relative error = 7.1311745891128207321537447524197e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 1.0161273146114280483215533829469
y[1] (numeric) = 1.0161273146114280490933142628396
absolute error = 7.717608798927e-19
relative error = 7.5951199106169590243721189517064e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 1.017143677698490584478969676463
y[1] (numeric) = 1.0171436776984905852985480242823
absolute error = 8.195783478193e-19
relative error = 8.0576457956635464378573301412830e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 1.0181610236417935174550065216268
y[1] (numeric) = 1.01816102364179351832235292147
absolute error = 8.673463998432e-19
relative error = 8.5187546930528281096940803234863e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 1.0191793514239909887255567250185
y[1] (numeric) = 1.0191793514239909896406217132147
absolute error = 9.150649881962e-19
relative error = 8.9784490523446824709798700311564e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 1.0201986600267553009537947038555
y[1] (numeric) = 1.0201986600267553019165287690153
absolute error = 9.627340651598e-19
relative error = 9.4367313238242416564348172235775e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 1.0212189484307779363177889621797
y[1] (numeric) = 1.0212189484307779373281425452447
absolute error = 1.0103535830650e-18
relative error = 9.8936039584608781701029650606907e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 1.0222402156157705758189349704154
y[1] (numeric) = 1.0222402156157705768768584647077
absolute error = 1.0579234942923e-18
relative error = 1.0349069407869409218581886363376e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 1.0232624605604661195701891399502
y[1] (numeric) = 1.0232624605604661206756328912218
absolute error = 1.1054437512716e-18
relative error = 1.0803130124270572361306264600406e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 1.0242856822426197080630836045889
y[1] (numeric) = 1.0242856822426197092159979110719
absolute error = 1.1529143064830e-18
relative error = 1.1255788560460541383845359061697e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 1.0253098796390097444125005419541
y[1] (numeric) = 1.0253098796390097456128356544096
absolute error = 1.2003351124555e-18
relative error = 1.1707047169760160655027173395863e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=0.47
NO POLE
x[1] = 0.026
y[1] (analytic) = 1.0263350517254389175781837901389
y[1] (numeric) = 1.0263350517254389188258899119076
absolute error = 1.2477061217687e-18
relative error = 1.2156908405993731889859019781722e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 1.0273611974767352265619645381911
y[1] (numeric) = 1.0273611974767352278569918252424
absolute error = 1.2950272870513e-18
relative error = 1.2605374723436799049481617245903e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 1.0283883158667530055796768932843
y[1] (numeric) = 1.0283883158667530069219754542665
absolute error = 1.3422985609822e-18
relative error = 1.3052448576789547599919475479875e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 1.0294164058683739502067381527475
y[1] (numeric) = 1.0294164058683739515962580490379
absolute error = 1.3895198962904e-18
relative error = 1.3498132421138726100874720328095e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 1.0304454664535081444963676354597
y[1] (numeric) = 1.0304454664535081459330588812138
absolute error = 1.4366912457541e-18
relative error = 1.3942428711912052825790087817659e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 1.0314754965930950890694169544723
y[1] (numeric) = 1.0314754965930950905532295166748
absolute error = 1.4838125622025e-18
relative error = 1.4385339904859092792092618303722e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 1.0325064952571047301747836411203
y[1] (numeric) = 1.0325064952571047317056674396341
absolute error = 1.5308837985138e-18
relative error = 1.4826868455995467598762441069822e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 1.0335384614145384897193790602884
y[1] (numeric) = 1.0335384614145384912972839679054
absolute error = 1.5779049076170e-18
relative error = 1.5267016821584188635492042557121e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 1.0345713940334302962666205869552
y[1] (numeric) = 1.0345713940334302978914964294462
absolute error = 1.6248758424910e-18
relative error = 1.5705787458091027473523439684382e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 1.035605292080847617002417045606
y[1] (numeric) = 1.0356052920808476186742136017708
absolute error = 1.6717965561648e-18
relative error = 1.6143182822150798875982138460455e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 1.0366401545228924906676154466153
y[1] (numeric) = 1.036640154522892492386282448333
absolute error = 1.7186670017177e-18
relative error = 1.6579205370533869953210049504656e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 1.0376759803247025614558760872396
y[1] (numeric) = 1.037675980324702563221363219519
absolute error = 1.7654871322794e-18
relative error = 1.7013857560111930961325936981645e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 1.0387127684504521138759421194306
y[1] (numeric) = 1.03871276845045211568819902046
absolute error = 1.8122569010294e-18
relative error = 1.7447141847817257285853740087596e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 1.0397505178633531085772687222844
y[1] (numeric) = 1.0397505178633531104362449834827
absolute error = 1.8589762611983e-18
relative error = 1.7879060690620514857903292130173e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 1.0407892275256562191379760535868
y[1] (numeric) = 1.0407892275256562210436212196535
absolute error = 1.9056451660667e-18
relative error = 1.8309616545485665555254517341284e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 1.0418288963986518698140891925851
y[1] (numeric) = 1.0418288963986518717663527615507
absolute error = 1.9522635689656e-18
relative error = 1.8738811869339567262485809848803e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.2MB, time=0.75
NO POLE
x[1] = 0.042
y[1] (analytic) = 1.0428695234426712742490273248348
y[1] (numeric) = 1.0428695234426712762478587481114
absolute error = 1.9988314232766e-18
relative error = 1.9166649119039865748757359760380e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 1.0439111076170874751423034597174
y[1] (numeric) = 1.0439111076170874771876521421493
absolute error = 2.0453486824319e-18
relative error = 1.9593130751341190983727928952620e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 1.0449536478803163848763950120176
y[1] (numeric) = 1.0449536478803163869682103119318
absolute error = 2.0918152999142e-18
relative error = 2.0018259222860627433565749150902e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 1.0459971431898178271007446207744
y[1] (numeric) = 1.0459971431898178292389758500314
absolute error = 2.1382312292570e-18
relative error = 2.0442036990047244284907369195445e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 1.0470415925020965792718496214939
y[1] (numeric) = 1.047041592502096581456446045538
absolute error = 2.1845964240441e-18
relative error = 2.0864466509144197146111679078411e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 1.0480869947727034161483976317188
y[1] (numeric) = 1.0480869947727034183793084696295
absolute error = 2.2309108379107e-18
relative error = 2.1285550236166352635720167451329e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 1.0491333489562361542404047549093
y[1] (numeric) = 1.0491333489562361565175791794513
absolute error = 2.2771744245420e-18
relative error = 2.1705290626854248430874002957074e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 1.0501806540063406972113119535802
y[1] (numeric) = 1.0501806540063406995346990912549
absolute error = 2.3233871376747e-18
relative error = 2.2123690136655974220266464450648e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 1.051228908875712082231994189689
y[1] (numeric) = 1.051228908875712084601543120785
absolute error = 2.3695489310960e-18
relative error = 2.2540751220685411186828029835850e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 1.0522781125160955272856359783499
y[1] (numeric) = 1.052278112516095529701295736994
absolute error = 2.4156597586441e-18
relative error = 2.2956476333695008227959274795104e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 1.0533282638782874794224260500869
y[1] (numeric) = 1.0533282638782874818841456242951
absolute error = 2.4617195742082e-18
relative error = 2.3370867930044006911649001659531e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 1.054379361912136663963022867019
y[1] (numeric) = 1.0543793619121366664707511987475
absolute error = 2.5077283317285e-18
relative error = 2.3783928463666889658717152701411e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 1.055431405566545134649741789598
y[1] (numeric) = 1.0554314055665451372034277747942
absolute error = 2.5536859851962e-18
relative error = 2.4195660388042050281341867920531e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 1.0564843937894693247444137428009
y[1] (numeric) = 1.0564843937894693273440062314544
absolute error = 2.5995924886535e-18
relative error = 2.4606066156160686007483170628704e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 1.0575383255279210990718642840042
y[1] (numeric) = 1.0575383255279211017173120801983
absolute error = 2.6454477961941e-18
relative error = 2.5015148220500638081355314567691e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 1.0585931997279688070079610291504
y[1] (numeric) = 1.0585931997279688096992128911132
absolute error = 2.6912518619628e-18
relative error = 2.5422909032991921990026835972884e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 1.0596490153347383364111764492458
y[1] (numeric) = 1.0596490153347383391481810894011
absolute error = 2.7370046401553e-18
relative error = 2.5829351044984386646763074109857e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.2MB, time=1.01
NO POLE
x[1] = 0.059
y[1] (analytic) = 1.0607057712924141684966121057147
y[1] (numeric) = 1.0607057712924141712793181907336
absolute error = 2.7827060850189e-18
relative error = 2.6234476707224087788726973994943e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 1.0617634665442404336514294506742
y[1] (numeric) = 1.0617634665442404364797856015265
absolute error = 2.8283561508523e-18
relative error = 2.6638288469821362577804639374556e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 1.0628221000325219681906313767867
y[1] (numeric) = 1.0628221000325219710645861687921
absolute error = 2.8739547920054e-18
relative error = 2.7040788782219131807077673329741e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 1.0638816706986253720521377609965
y[1] (numeric) = 1.0638816706986253749716397238758
absolute error = 2.9195019628793e-18
relative error = 2.7441980093163308704779569517355e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 1.0649421774829800674300973071622
y[1] (numeric) = 1.0649421774829800703950949250893
absolute error = 2.9649976179271e-18
relative error = 2.7841864850680934423201520168553e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 1.0660036193250793583453770543635
y[1] (numeric) = 1.0660036193250793613558187660166
absolute error = 3.0104417116531e-18
relative error = 2.8240445502043472984502239511345e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 1.0670659951634814911521699804788
y[1] (numeric) = 1.0670659951634814942080041790918
absolute error = 3.0558341986130e-18
relative error = 2.8637724493739735466463258350602e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 1.0681293039358107159796601945154
y[1] (numeric) = 1.0681293039358107190808352279301
absolute error = 3.1011750334147e-18
relative error = 2.9033704271454622210835771373597e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 1.0691935445787583491076842761166
y[1] (numeric) = 1.0691935445787583522541484468337
absolute error = 3.1464641707171e-18
relative error = 2.9428387280029325692326339195700e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 1.0702587160280838362753263866704
y[1] (numeric) = 1.0702587160280838394670279519015
absolute error = 3.1917015652311e-18
relative error = 2.9821775963442366515054123383781e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 1.0713248172186158169213838435158
y[1] (numeric) = 1.0713248172186158201582710152351
absolute error = 3.2368871717193e-18
relative error = 3.0213872764778648381827941459066e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 1.0723918470842531893556389168682
y[1] (numeric) = 1.0723918470842531926376598618643
absolute error = 3.2820209449961e-18
relative error = 3.0604680126202468313019825013437e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 1.0734598045579661768598716782817
y[1] (numeric) = 1.0734598045579661801869745182096
absolute error = 3.3271028399279e-18
relative error = 3.0994200488931660498731106539668e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 1.0745286885717973947175477997241
y[1] (numeric) = 1.0745286885717973980896806111567
absolute error = 3.3721328114326e-18
relative error = 3.1382436293205421322037073494324e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 1.0755984980568629181711142736652
y[1] (numeric) = 1.0755984980568629215882250881455
absolute error = 3.4171108144803e-18
relative error = 3.1769389978263524664497796020253e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 1.0766692319433533513058350969725
y[1] (numeric) = 1.0766692319433533547678719010656
absolute error = 3.4620368040931e-18
relative error = 3.2155063982317344249273323429671e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=1.29
NO POLE
x[1] = 0.075
y[1] (analytic) = 1.0777408891605348968590980348673
y[1] (numeric) = 1.0777408891605349003660087702121
absolute error = 3.5069107353448e-18
relative error = 3.2539460742520163421069622243640e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 1.0788134686367504269541226557232
y[1] (numeric) = 1.0788134686367504305058552190848
absolute error = 3.5517325633616e-18
relative error = 3.2922582694946974292464157518001e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 1.079886969299420554756998903089
y[1] (numeric) = 1.0798869692994205583535011464107
absolute error = 3.5965022433217e-18
relative error = 3.3304432274564254337699182068528e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 1.080961390075044707055984547986
y[1] (numeric) = 1.0809613900750447106972042784416
absolute error = 3.6412197304556e-18
relative error = 3.3685011915206442432366602397496e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 1.0820367298892021977619889422729
y[1] (numeric) = 1.0820367298892022014478739223183
absolute error = 3.6858849800454e-18
relative error = 3.4064324049543357219872590537156e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 1.083112987666553302329169572681
y[1] (numeric) = 1.083112987666553306059667520107
absolute error = 3.7304979474260e-18
relative error = 3.4442371109065395960583821905963e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 1.0841901623308403330945669950168
y[1] (numeric) = 1.0841901623308403368696255830014
absolute error = 3.7750585879846e-18
relative error = 3.4819155524053186334253705777983e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 1.0852682528048887155357028089837
y[1] (numeric) = 1.0852682528048887193552696661441
absolute error = 3.8195668571604e-18
relative error = 3.5194679723549306815640594643352e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 1.0863472580106080654450644161152
y[1] (numeric) = 1.0863472580106080693090871265606
absolute error = 3.8640227104454e-18
relative error = 3.5568946135340346476563149353386e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 1.0874271768689932670203993864259
y[1] (numeric) = 1.0874271768689932709288254898092
absolute error = 3.9084261033833e-18
relative error = 3.5941957185921644836562949364733e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 1.0885080083001255518697413435729
y[1] (numeric) = 1.0885080083001255558225183351439
absolute error = 3.9527769915710e-18
relative error = 3.6313715300486173506406502314808e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 1.0895897512231735789300883635951
y[1] (numeric) = 1.0895897512231735829271636942527
absolute error = 3.9970753306576e-18
relative error = 3.6684222902890585912360323357993e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 1.0906724045563945152986539686397
y[1] (numeric) = 1.0906724045563945193399750449845
absolute error = 4.0413210763448e-18
relative error = 3.7053482415634351752816445939712e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 1.0917559672171351179756098845156
y[1] (numeric) = 1.0917559672171351220611240689023
absolute error = 4.0855141843867e-18
relative error = 3.7421496259833566812827132846907e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 1.0928404381218328165172388194208
y[1] (numeric) = 1.0928404381218328206468934300111
absolute error = 4.1296546105903e-18
relative error = 3.7788266855201371142642320644515e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 1.093925816186016796598414610782
y[1] (numeric) = 1.0939258161860168007721569215973
absolute error = 4.1737423108153e-18
relative error = 3.8153796620022132263743983305888e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 1.0950121003243090844833261778163
y[1] (numeric) = 1.09501210032430908870110341879
absolute error = 4.2177772409737e-18
relative error = 3.8518087971124003245294326721349e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=1.56
NO POLE
x[1] = 0.092
y[1] (analytic) = 1.09609928945042563240336080918
y[1] (numeric) = 1.0960992894504256366651201662109
absolute error = 4.2617593570309e-18
relative error = 3.8881143323865376971138813923543e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 1.0971873824771774048410614079145
y[1] (numeric) = 1.0971873824771774091467500229191
absolute error = 4.3056886150046e-18
relative error = 3.9242965092101418059401890710582e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 1.0982763783164714657190714098198
y[1] (numeric) = 1.0982763783164714700686363807853
absolute error = 4.3495649709655e-18
relative error = 3.9603555688167231694460470675891e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 1.0993662758793120664929801864023
y[1] (numeric) = 1.0993662758793120708863685674397
absolute error = 4.3933883810374e-18
relative error = 3.9962917522855723775853688778230e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 1.1004570740758017351469808396437
y[1] (numeric) = 1.1004570740758017395841396410405
absolute error = 4.4371588013968e-18
relative error = 4.0321053005391098262173530425341e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 1.1015487718151423660912513930206
y[1] (numeric) = 1.101548771815142370572127581294
absolute error = 4.4808761882734e-18
relative error = 4.0677964543410731774406514645179e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 1.1026413680056363109599694814882
y[1] (numeric) = 1.1026413680056363154845099794378
absolute error = 4.5245404979496e-18
relative error = 4.1033654542938136494051832342233e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 1.103734861554687470308869742501
y[1] (numeric) = 1.1037348615546874748770214292622
absolute error = 4.5681516867612e-18
relative error = 4.1388125408367005829678735740665e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 1.1048292513688023862112522106067
y[1] (numeric) = 1.1048292513688023908229619217038
absolute error = 4.6117097110971e-18
relative error = 4.1741379542436353923978362985597e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.1059245363535913357513491196942
y[1] (numeric) = 1.1059245363535913404065636470934
absolute error = 4.6552145273992e-18
relative error = 4.2093419346207661701641414836099e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.1070207154137694254139566196207
y[1] (numeric) = 1.1070207154137694301126227117834
absolute error = 4.6986660921627e-18
relative error = 4.2444247219045822657480699274196e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.108117787453157686369237017678
y[1] (numeric) = 1.1081177874531576911113013796139
absolute error = 4.7420643619359e-18
relative error = 4.2793865558595740592214298144830e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.1092157513746841706515962601848
y[1] (numeric) = 1.1092157513746841754370055535056
absolute error = 4.7854092933208e-18
relative error = 4.3142276760766329770474592704220e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.1103146060803850482315404754227
y[1] (numeric) = 1.110314606080385053060241318395
absolute error = 4.8287008429723e-18
relative error = 4.3489483219702052441359562145781e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.1114143504714057049794145061465
y[1] (numeric) = 1.1114143504714057098513534737454
absolute error = 4.8719389675989e-18
relative error = 4.3835487327768173222828419824057e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.1125149834480018415199244680247
y[1] (numeric) = 1.1125149834480018464350480919872
absolute error = 4.9151236239625e-18
relative error = 4.4180291475528063121893619235542e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=26.7MB, alloc=4.3MB, time=1.83
x[1] = 0.108
y[1] (analytic) = 1.1136165039095405729763454795783
y[1] (numeric) = 1.1136165039095405779346002484567
absolute error = 4.9582547688784e-18
relative error = 4.4523898051722486241653638355340e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.1147189107545015296033148195015
y[1] (numeric) = 1.114718910754501534604647178717
absolute error = 5.0013323592155e-18
relative error = 4.4866309443250855856936688318968e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.1158222028804779583071098786636
y[1] (numeric) = 1.1158222028804779633514662305598
absolute error = 5.0443563518962e-18
relative error = 4.5207528035149965599537091497659e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.1169263791841778250523093866049
y[1] (numeric) = 1.1169263791841778301396360905014
absolute error = 5.0873267038965e-18
relative error = 4.5547556210574690134244333076405e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.1180314385614249181537355059585
y[1] (numeric) = 1.1180314385614249232839788782046
absolute error = 5.1302433722461e-18
relative error = 4.5886396350778853218968351349533e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.1191373799071599524525735029468
y[1] (numeric) = 1.1191373799071599576256798169749
absolute error = 5.1731063140281e-18
relative error = 4.6224050835092688153589030013276e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.1202442021154416743755648179252
y[1] (numeric) = 1.1202442021154416795914803043051
absolute error = 5.2159154863799e-18
relative error = 4.6560522040911197124675518682833e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.1213519040794479678761684768732
y[1] (numeric) = 1.1213519040794479731348393233654
absolute error = 5.2586708464922e-18
relative error = 4.6895812343665689274464925853115e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.1224604846914769612565849027618
y[1] (numeric) = 1.1224604846914769665579572543715
absolute error = 5.3013723516097e-18
relative error = 4.7229924116810686398585637933088e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 1.1235699428429481348695353048669
y[1] (numeric) = 1.1235699428429481402135552638976
absolute error = 5.3440199590307e-18
relative error = 4.7562859731801169971149760053450e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.124680277424403429698688944341
y[1] (numeric) = 1.1246802774244034350853025704487
absolute error = 5.3866136261077e-18
relative error = 4.7894621558078908452869175747090e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.125791487325508356816629695709
y[1] (numeric) = 1.1257914873255083622457830059561
absolute error = 5.4291533102471e-18
relative error = 4.8225211963050925519010982110171e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.1269035714350531077192524464134
y[1] (numeric) = 1.1269035714350531131908914153225
absolute error = 5.4716389689091e-18
relative error = 4.8554633312069924999301683580684e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 1.1280165286409536655354790001047
y[1] (numeric) = 1.128016528640953671049549559713
absolute error = 5.5140705596083e-18
relative error = 4.8882887968421091942263045355612e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.1291303578302529171111822740552
y[1] (numeric) = 1.1291303578302529226676303139681
absolute error = 5.5564480399129e-18
relative error = 4.9209978293296627725874272983942e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.1302450578891217659662067068628
y[1] (numeric) = 1.1302450578891217715649780743081
absolute error = 5.5987713674453e-18
relative error = 4.9535906645782877513052793565219e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.1313606277028602461233719195179
y[1] (numeric) = 1.1313606277028602517644124194004
absolute error = 5.6410404998825e-18
relative error = 4.9860675382845821298442123204332e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.3MB, time=2.10
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.1324770661558986368083458009238
y[1] (numeric) = 1.132477066155898642491601195879
absolute error = 5.6832553949552e-18
relative error = 5.0184286859305226839300367494601e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 1.133594372131798578019272318088
y[1] (numeric) = 1.1335943721317985837446883285364
absolute error = 5.7254160104484e-18
relative error = 5.0506743427822243136391295256822e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.1347125445132541869650384814514
y[1] (numeric) = 1.134712544513254192732560785653
absolute error = 5.7675223042016e-18
relative error = 5.0828047438883597850430912766014e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.1358315821820931753710640271808
y[1] (numeric) = 1.1358315821820931811806382612894
absolute error = 5.8095742341086e-18
relative error = 5.1148201240782422284809942629778e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.1369514840192779676514965107286
y[1] (numeric) = 1.1369514840192779735030682688459
absolute error = 5.8515717581173e-18
relative error = 5.1467207179599245630501166376116e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.1380722489049068199466936395565
y[1] (numeric) = 1.1380722489049068258402084737869
absolute error = 5.8935148342304e-18
relative error = 5.1785067599191065731084808612174e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.139193875718214940024873807636
y[1] (numeric) = 1.1391938757182149459602772281407
absolute error = 5.9354034205047e-18
relative error = 5.2101784841168251299728472547510e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.1403163633375756080468149301671
y[1] (numeric) = 1.1403163633375756140240524052186
absolute error = 5.9772374750515e-18
relative error = 5.2417361244881283357984795291748e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.1414397106405012981924808139097
y[1] (numeric) = 1.1414397106405013042114977699467
absolute error = 6.0190169560370e-18
relative error = 5.2731799147407631534091501905513e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.1425639165036448011484534365966
y[1] (numeric) = 1.142563916503644807209195258278
absolute error = 6.0607418216814e-18
relative error = 5.3045100883527386588336995654687e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.1436889798028003474550486480861
y[1] (numeric) = 1.1436889798028003535574606783462
absolute error = 6.1024120302601e-18
relative error = 5.3357268785717455164507277571195e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.1448148994129047317119919462362
y[1] (numeric) = 1.144814899412904737856019486339
absolute error = 6.1440275401028e-18
relative error = 5.3668305184127502210739945279772e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 1.1459416742080384376415301219145
y[1] (numeric) = 1.1459416742080384438271184315086
absolute error = 6.1855883095941e-18
relative error = 5.3978212406569182005553530167961e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.1470693030614267640078537101284
y[1] (numeric) = 1.1470693030614267702349480073015
absolute error = 6.2270942971731e-18
relative error = 5.4286992778496772052402504405046e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.148197784845440951391704327946
y[1] (numeric) = 1.1481977848454409576602497892798
absolute error = 6.2685454613338e-18
relative error = 5.4594648622994945901480116704824e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.149327118431599309819040124694
y[1] (numeric) = 1.149327118431599316128981885319
absolute error = 6.3099417606250e-18
relative error = 5.4901182260762325132926735219253e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.150457302690568347242631715862
y[1] (numeric) = 1.1504573026905683535939148695126
memory used=34.3MB, alloc=4.3MB, time=2.38
absolute error = 6.3512831536506e-18
relative error = 5.5206596010098662693710731108787e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 1.1515883364921638988754601192109
y[1] (numeric) = 1.1515883364921639052680297182801
absolute error = 6.3925695990692e-18
relative error = 5.5510892186886080853155523515074e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 1.1527202187053522573747873597812
y[1] (numeric) = 1.1527202187053522638085884153754
absolute error = 6.4338010555942e-18
relative error = 5.5814073104574814998522692796160e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.1538529481982513038757695598249
y[1] (numeric) = 1.1538529481982513103507470418191
absolute error = 6.4749774819942e-18
relative error = 5.6116141074171699272348553037569e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.1549865238381316398734814801429
y[1] (numeric) = 1.1549865238381316463895803172358
absolute error = 6.5160988370929e-18
relative error = 5.6417098404224448944123123299076e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.1561209444914177199522206308969
y[1] (numeric) = 1.1561209444914177265093857106656
absolute error = 6.5571650797687e-18
relative error = 5.6716947400803498483846443120322e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.157256209023688985360958222686
y[1] (numeric) = 1.1572562090236889919591343916415
absolute error = 6.5981761689555e-18
relative error = 5.7015690367494374053118170848548e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.158392316299680998433803382532
y[1] (numeric) = 1.1583923162996810050729354461743
absolute error = 6.6391320636423e-18
relative error = 5.7313329605379809995471444515799e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.1595292651832865778543462144042
y[1] (numeric) = 1.1595292651832865845343789372773
absolute error = 6.6800327228731e-18
relative error = 5.7609867413024616115423443632377e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.1606670545375569347627444400333
y[1] (numeric) = 1.1606670545375569414836225457806
absolute error = 6.7208781057473e-18
relative error = 5.7905306086465000283932747248620e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.161805683224702809704417513025
y[1] (numeric) = 1.1618056832247028164660856844445
absolute error = 6.7616681714195e-18
relative error = 5.8199647919192848008085970770471e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.1629451501060956104192112576717
y[1] (numeric) = 1.1629451501060956172216141367713
absolute error = 6.8024028790996e-18
relative error = 5.8492895202142732680334677268884e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.164085454042268550469895243394
y[1] (numeric) = 1.1640854540422685573129774314469
absolute error = 6.8430821880529e-18
relative error = 5.8785050223679060882539895519001e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.1652265938929177887088542664086
y[1] (numeric) = 1.1652265938929177955925603240088
absolute error = 6.8837060576002e-18
relative error = 5.9076115269583352006431811064152e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.1663685685169035695818344720268
y[1] (numeric) = 1.1663685685169035765061089191444
absolute error = 6.9242744471176e-18
relative error = 5.9366092623039079368456788772407e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 1.167511376772251364267603813932
y[1] (numeric) = 1.1675113767722513712323911299685
absolute error = 6.9647873160365e-18
relative error = 5.9654984564618372322061737619661e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.1686550175161530126523857108703
y[1] (numeric) = 1.1686550175161530196576303347145
absolute error = 7.0052446238442e-18
relative error = 5.9942793372273989573863542594513e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=2.65
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.1697994896049678661379239264173
y[1] (numeric) = 1.1697994896049678731835702565008
absolute error = 7.0456463300835e-18
relative error = 6.0229521321322850233977767560849e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 1.1709447918942239312820358638504
y[1] (numeric) = 1.1709447918942239383680282582029
absolute error = 7.0859923943525e-18
relative error = 6.0515170684431428644840625058322e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.1720909232386190142705106356677
y[1] (numeric) = 1.1720909232386190213967934119729
absolute error = 7.1262827763052e-18
relative error = 6.0799743731608119520318145625975e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.1732378824920218662192074359532
y[1] (numeric) = 1.1732378824920218733857248716046
absolute error = 7.1665174356514e-18
relative error = 6.1083242730189740768335681982791e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.1743856685074733293052089135833
y[1] (numeric) = 1.1743856685074733365119052457396
absolute error = 7.2066963321563e-18
relative error = 6.1365669944825620239138295340286e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.1755342801371874837258834152173
y[1] (numeric) = 1.1755342801371874909727028408583
absolute error = 7.2468194256410e-18
relative error = 6.1647027637469491233582375027713e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 1.1766837162325527954847091391059
y[1] (numeric) = 1.1766837162325528027715958150882
absolute error = 7.2868866759823e-18
relative error = 6.1927318067365546058566690447690e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.177833975644133265002712413988
y[1] (numeric) = 1.177833975644133272329610457101
absolute error = 7.3268980431130e-18
relative error = 6.2206543491038875862435451269853e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.1789850572216695765543714917343
y[1] (numeric) = 1.1789850572216695839212249787563
absolute error = 7.3668534870220e-18
relative error = 6.2484706162284329651077253381199e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.1801369598140802485268364179298
y[1] (numeric) = 1.1801369598140802559335893856833
absolute error = 7.4067529677535e-18
relative error = 6.2761808332147871893715844375641e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.1812896822694627845013147212693
y[1] (numeric) = 1.1812896822694627919479111666777
absolute error = 7.4465964454084e-18
relative error = 6.3037852248926732608184872209685e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 1.1824432234350948251554718404793
y[1] (numeric) = 1.1824432234350948326418557206222
absolute error = 7.4863838801429e-18
relative error = 6.3312840158145936518505597321742e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.1835975821574353009856943864583
y[1] (numeric) = 1.183597582157435308511809618628
absolute error = 7.5261152321697e-18
relative error = 6.3586774302556996140405702571396e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.1847527572821255858480635174716
y[1] (numeric) = 1.1847527572821255934138539792289
absolute error = 7.5657904617573e-18
relative error = 6.3859656922120635232917521769851e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.1859087476539906513168848865206
y[1] (numeric) = 1.1859087476539906589222944157513
absolute error = 7.6054095292307e-18
relative error = 6.4131490254001478343816548147468e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.1870655521170402218596208024551
y[1] (numeric) = 1.1870655521170402295045931974259
absolute error = 7.6449723949708e-18
relative error = 6.4402276532551879886718739228687e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.1882231695144699308270694299911
y[1] (numeric) = 1.1882231695144699385115484494057
absolute error = 7.6844790194146e-18
relative error = 6.4672017989302640317895098064740e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=2.91
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.1893815986886624772576350385519
y[1] (numeric) = 1.1893815986886624849815644016074
absolute error = 7.7239293630555e-18
relative error = 6.4940716852954677256707971281107e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 1.1905408384811887834945324957586
y[1] (numeric) = 1.1905408384811887912578558822019
absolute error = 7.7633233864433e-18
relative error = 6.5208375349368285333848089598689e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.1917008877328091536147683884622
y[1] (numeric) = 1.1917008877328091614174294386461
absolute error = 7.8026610501839e-18
relative error = 6.5474995701550001294088610653622e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.1928617452834744326687403424319
y[1] (numeric) = 1.1928617452834744405106826573716
absolute error = 7.8419423149397e-18
relative error = 6.5740580129645473997856209924408e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.1940234099723271667292953011982
y[1] (numeric) = 1.1940234099723271746104624426275
absolute error = 7.8811671414293e-18
relative error = 6.6005130850926573525931738667351e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 1.1951858806377027637490867150877
y[1] (numeric) = 1.1951858806377027716694222055156
absolute error = 7.9203354904279e-18
relative error = 6.6268650079784492345408476031543e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.1963491561171306552250697831901
y[1] (numeric) = 1.1963491561171306631845171059574
absolute error = 7.9594473227673e-18
relative error = 6.6531140027719603269133192293001e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.1975132352473354586689730838595
y[1] (numeric) = 1.1975132352473354666674756831949
absolute error = 7.9985025993354e-18
relative error = 6.6792602903327261285100509609752e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.1986781168642381408825841233728
y[1] (numeric) = 1.1986781168642381489200854044501
absolute error = 8.0375012810773e-18
relative error = 6.7053040912297096263524765196222e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.1998437998029571820366855275606
y[1] (numeric) = 1.1998437998029571901131288565546
absolute error = 8.0764433289940e-18
relative error = 6.7312456257392367293966875033310e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.2010102828978097405524777975666
y[1] (numeric) = 1.2010102828978097486678065017103
absolute error = 8.1153287041437e-18
relative error = 6.7570851138451145808322961353678e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.2021775649823128187843237484144
y[1] (numeric) = 1.2021775649823128269384811160553
absolute error = 8.1541573676409e-18
relative error = 6.7828227752369251838262608110993e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.2033456448891844295026489477312
y[1] (numeric) = 1.203345644889184437695578228388
absolute error = 8.1929292806568e-18
relative error = 6.8084588293094152922102857031230e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.204514521450344763175831671826
y[1] (numeric) = 1.2045145214503447714074760762458
absolute error = 8.2316444044198e-18
relative error = 6.8339934951619788881533163928551e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.2056841934969173560499150973315
y[1] (numeric) = 1.2056841934969173643202177975461
absolute error = 8.2703027002146e-18
relative error = 6.8594269915969875167121825074027e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.2068546598592302590249736487914
y[1] (numeric) = 1.2068546598592302673338777781743
absolute error = 8.3089041293829e-18
relative error = 6.8847595371194621038424370004288e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=4.3MB, time=3.18
x[1] = 0.191
y[1] (analytic) = 1.2080259193668172073269646259269
y[1] (numeric) = 1.2080259193668172156744132792502
absolute error = 8.3474486533233e-18
relative error = 6.9099913499360904609555491927512e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.2091979708484187909738954388276
y[1] (numeric) = 1.2091979708484187993598316723188
absolute error = 8.3859362334912e-18
relative error = 6.9351226479542565124939544843659e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 1.210370813131983626035135984996
y[1] (numeric) = 1.2103708131319836344595028163952
absolute error = 8.4243668313992e-18
relative error = 6.9601536487814942739140026254559e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.2115444450446695266827049090327
y[1] (numeric) = 1.2115444450446695351454453176493
absolute error = 8.4627404086166e-18
relative error = 6.9850845697242081601321313020442e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 1.2127188654128446780333576937721
y[1] (numeric) = 1.2127188654128446865344146205418
absolute error = 8.5010569267697e-18
relative error = 7.0099156277870664109816136950370e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.2138940730620888097803037408782
y[1] (numeric) = 1.2138940730620888183196200884205
absolute error = 8.5393163475423e-18
relative error = 7.0346470396725688091255661414343e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.2150700668171943706133788092841
y[1] (numeric) = 1.2150700668171943791908974419587
absolute error = 8.5775186326746e-18
relative error = 7.0592790217793061184776413516637e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.2162468455021677034264983913951
y[1] (numeric) = 1.2162468455021677120421621353598
absolute error = 8.6156637439647e-18
relative error = 7.0838117902023733527617265349028e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.2174244079402302213112168197067
y[1] (numeric) = 1.217424407940230229964968462974
absolute error = 8.6537516432673e-18
relative error = 7.1082455607314867175149050094798e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.2186027529538195843352161103702
y[1] (numeric) = 1.2186027529538195930269984028646
absolute error = 8.6917822924944e-18
relative error = 7.1325805488507586971687076519045e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.2197818793645908771045477653193
y[1] (numeric) = 1.2197818793645908858343034189348
absolute error = 8.7297556536155e-18
relative error = 7.1568169697380705421403339110991e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.2209617859934177871084499708124
y[1] (numeric) = 1.2209617859934177958761216594696
absolute error = 8.7676716886572e-18
relative error = 7.1809550382639629761733609164967e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.2221424716603937838455618476712
y[1] (numeric) = 1.2221424716603937926510922073748
absolute error = 8.8055303597036e-18
relative error = 7.2049949689911939160812200410231e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.2233239351848332987303556271016
y[1] (numeric) = 1.2233239351848333075736872559973
absolute error = 8.8433316288957e-18
relative error = 7.2289369761734873047996172189516e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 1.2245061753852729057786068457593
y[1] (numeric) = 1.2245061753852729146596823041919
absolute error = 8.8810754584326e-18
relative error = 7.2527812737557651627877261988441e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.2256891910794725030707218746935
y[1] (numeric) = 1.2256891910794725119894836852637
absolute error = 8.9187618105702e-18
relative error = 7.2765280753723446192859323415348e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.2268729810844164949917413189339
y[1] (numeric) = 1.2268729810844165039481319665564
absolute error = 8.9563906476225e-18
relative error = 7.3001775943472705710094706568946e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=3.45
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.2280575442163149752468370478219
y[1] (numeric) = 1.2280575442163149842407989797822
absolute error = 8.9939619319603e-18
relative error = 7.3237300436925352391175347309572e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 1.2292428792906049106511198406818
y[1] (numeric) = 1.2292428792906049196825954666943
absolute error = 9.0314756260125e-18
relative error = 7.3471856361084291257313997934764e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.2304289851219513256925738581282
y[1] (numeric) = 1.2304289851219513347615055503935
absolute error = 9.0689316922653e-18
relative error = 7.3705445839821892011972976656421e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.2316158605242484878669333761701
y[1] (numeric) = 1.2316158605242484969732634694327
absolute error = 9.1063300932626e-18
relative error = 7.3938070993876352067813055483992e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.232803504310621093783316448335
y[1] (numeric) = 1.2328035043106211029269872399413
absolute error = 9.1436707916063e-18
relative error = 7.4169733940847329160151732263122e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.2339919152934254560394293902803
y[1] (numeric) = 1.2339919152934254652203831402357
absolute error = 9.1809537499554e-18
relative error = 7.4400436795181934319108564386365e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.2351810922842506908651552117814
y[1] (numeric) = 1.2351810922842507000833341428085
absolute error = 9.2181789310271e-18
relative error = 7.4630181668177057313170585508077e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.2363710340939199065333383526129
y[1] (numeric) = 1.236371034093919915788684650209
absolute error = 9.2553462975961e-18
relative error = 7.4858970667967179560826402529753e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.2375617395324913925365773116322
y[1] (numeric) = 1.2375617395324914018290331241274
absolute error = 9.2924558124952e-18
relative error = 7.5086805899522821435124703891341e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.238753207409259809528835992376
y[1] (numeric) = 1.2387532074092598188583434309908
absolute error = 9.3295074386148e-18
relative error = 7.5313689464640178158414615289573e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 1.2399454365327573800306838236542
y[1] (numeric) = 1.2399454365327573893971849625573
absolute error = 9.3665011389031e-18
relative error = 7.5539623461936520338879109526180e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.241138425710755079896973950002
y[1] (numeric) = 1.2411384257107550893004108263687
absolute error = 9.4034368763667e-18
relative error = 7.5764609986848903316674074668044e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.2423321737502638305457680244123
y[1] (numeric) = 1.2423321737502638399860826384821
absolute error = 9.4403146140698e-18
relative error = 7.5988651131621674200965503448417e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 1.2435266794575356919473153745203
y[1] (numeric) = 1.2435266794575357014244496896549
absolute error = 9.4771343151346e-18
relative error = 7.6211748985303760172477918917031e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.2447219416380650563718935533623
y[1] (numeric) = 1.2447219416380650658857894961037
absolute error = 9.5138959427414e-18
relative error = 7.6433905633743621534732297188860e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.245917959096589842895316526968
y[1] (numeric) = 1.2459179590965898524459159870965
absolute error = 9.5505994601285e-18
relative error = 7.6655123159582687817163705203693e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.2471147306370926926609159933758
y[1] (numeric) = 1.2471147306370927022481608239683
absolute error = 9.5872448305925e-18
relative error = 7.6875403642252098244531857964951e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=3.72
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.2483122550628021648968005711917
y[1] (numeric) = 1.2483122550628021745206325886798
absolute error = 9.6238320174881e-18
relative error = 7.7094749157965514686631008649003e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 1.2495105311761939336871968405306
y[1] (numeric) = 1.2495105311761939433475578247585
absolute error = 9.6603609842279e-18
relative error = 7.7313161779712035016244209979055e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.2507095577789919854966754650988
y[1] (numeric) = 1.250709557778991995193507159382
absolute error = 9.6968316942832e-18
relative error = 7.7530643577257201707716176928532e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.2519093336721698174460648712927
y[1] (numeric) = 1.2519093336721698271793089824758
absolute error = 9.7332441111831e-18
relative error = 7.7747196617130484355067980001667e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.2531098576559516363388542084982
y[1] (numeric) = 1.2531098576559516461084524070133
absolute error = 9.7695981985151e-18
relative error = 7.7962822962624863227829372540115e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.2543111285298135584368865642885
y[1] (numeric) = 1.2543111285298135682427804842139
absolute error = 9.8058939199254e-18
relative error = 7.8177524673794082342534760415076e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.2555131450924848099841426589281
y[1] (numeric) = 1.2555131450924848198262738980462
absolute error = 9.8421312391181e-18
relative error = 7.8391303807441215729334000894629e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.256715906141948928477414495497
y[1] (numeric) = 1.256715906141948938355724615353
absolute error = 9.8783101198560e-18
relative error = 7.8604162417120089646597620037657e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.2579194104754449646826676950638
y[1] (numeric) = 1.2579194104754449745970982210238
absolute error = 9.9144305259600e-18
relative error = 7.8816102553125625834173010871928e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.2591236568894686853958905006441
y[1] (numeric) = 1.2591236568894686953463829219539
absolute error = 9.9504924213098e-18
relative error = 7.9027126262494623397563943415002e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.2603286441797737769472266891962
y[1] (numeric) = 1.2603286441797737869337224590398
absolute error = 9.9864957698436e-18
relative error = 7.9237235588998660323480279836185e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.2615343711413730494471888876213
y[1] (numeric) = 1.2615343711413730594696294231794
absolute error = 1.00224405355581e-17
relative error = 7.9446432573139472201851562159863e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.2627408365685396417737480466553
y[1] (numeric) = 1.2627408365685396518320747291636
absolute error = 1.00583266825083e-17
relative error = 7.9654719252142831983932324807551e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.2639480392548082272990940856621
y[1] (numeric) = 1.2639480392548082373932482604703
absolute error = 1.00941541748082e-17
relative error = 7.9862097659959643694560574590182e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.2651559779929762203548619816704
y[1] (numeric) = 1.2651559779929762304847849583008
absolute error = 1.01299229766304e-17
relative error = 8.0068569827258393582018872301655e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.2663646515751049834346168375264
y[1] (numeric) = 1.2663646515751049936002498897324
absolute error = 1.01656330522060e-17
relative error = 8.0274137781420071651216881668508e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=57.2MB, alloc=4.3MB, time=3.99
x[1] = 0.241
y[1] (analytic) = 1.267574058792521035132390726779
y[1] (numeric) = 1.2675740587925210453336750926039
absolute error = 1.02012843658249e-17
relative error = 8.0478803546536336030855173127793e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.2687841984358172588160633768609
y[1] (numeric) = 1.2687841984358172690529402586966
absolute error = 1.02368768818357e-17
relative error = 8.0682569143404593285834658180841e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.2699950692948541120343780172857
y[1] (numeric) = 1.2699950692948541223067885819318
absolute error = 1.02724105646461e-17
relative error = 8.0885436589527101870882930916869e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.2712066701587608366563829859464
y[1] (numeric) = 1.2712066701587608469642683646688
absolute error = 1.03078853787224e-17
relative error = 8.1087407899103058733668381260003e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.2724189998159366697420889541739
y[1] (numeric) = 1.2724189998159366800853902427636
absolute error = 1.03433012885897e-17
relative error = 8.1288485083026290299030699534799e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.2736320570540520551431308999993
y[1] (numeric) = 1.2736320570540520655217891588314
absolute error = 1.03786582588321e-17
relative error = 8.1488670148883014419581439930631e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 1.2748458406600498558322232290596
y[1] (numeric) = 1.2748458406600498662461794831521
absolute error = 1.04139562540925e-17
relative error = 8.1687965100946535160590520507862e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.2760603494201465669601957137912
y[1] (numeric) = 1.2760603494201465774093909528644
absolute error = 1.04491952390732e-17
relative error = 8.1886371940178294771627911987643e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.2772755821198335296393971939789
y[1] (numeric) = 1.277275582119833540123772372514
absolute error = 1.04843751785351e-17
relative error = 8.2083892664218016355616303040201e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.2784915375438781454522532553552
y[1] (numeric) = 1.2784915375438781559717492926533
absolute error = 1.05194960372981e-17
relative error = 8.2280529267383346265533941829828e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.2797082144763250916837633777947
y[1] (numeric) = 1.2797082144763251022383211580362
absolute error = 1.05545577802415e-17
relative error = 8.2476283740669555931669194561756e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.280925611700497537276722320708
y[1] (numeric) = 1.2809256117004975478662826930117
absolute error = 1.05895603723037e-17
relative error = 8.2671158071743837876100376882568e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.2821437279989983595084497905146
y[1] (numeric) = 1.2821437279989983701329535689964
absolute error = 1.06245037784818e-17
relative error = 8.2865154244938911477349039092622e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.2833625621537113613878117135658
y[1] (numeric) = 1.2833625621537113720471996773983
absolute error = 1.06593879638325e-17
relative error = 8.3058274241256851929154370392234e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.2845821129458024897713157175993
y[1] (numeric) = 1.2845821129458025004655286110711
absolute error = 1.06942128934718e-17
relative error = 8.3250520038363612892158103502892e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.2858023791557210541970627057309
y[1] (numeric) = 1.2858023791557210649260412383055
absolute error = 1.07289785325746e-17
relative error = 8.3441893610582859531916363201211e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.2870233595632009464353356891324
y[1] (numeric) = 1.2870233595632009571990205355076
absolute error = 1.07636848463752e-17
relative error = 8.3632396928896886398306319856922e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=4.26
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.2882450529472618607546063279096
y[1] (numeric) = 1.288245052947261871552938128077
absolute error = 1.07983318001674e-17
relative error = 8.3822031960944481882973028487773e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.2894674580862105149017389142753
y[1] (numeric) = 1.2894674580862105257346582735796
absolute error = 1.08329193593043e-17
relative error = 8.4010800671016534964656945560325e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.2906905737576418717951708179151
y[1] (numeric) = 1.2906905737576418826626183071134
absolute error = 1.08674474891983e-17
relative error = 8.4198705020053273082887382740355e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.2919143987384403619298477004668
y[1] (numeric) = 1.2919143987384403728317638557879
absolute error = 1.09019161553211e-17
relative error = 8.4385746965641572228201988069355e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.2931389318047811064926910942802
y[1] (numeric) = 1.2931389318047811174290164174846
absolute error = 1.09363253232044e-17
relative error = 8.4571928462017751930257707654302e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.2943641717321311411873752300938
y[1] (numeric) = 1.2943641717321311521580501885324
absolute error = 1.09706749584386e-17
relative error = 8.4757251460054959111383373859341e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.2955901172952506407671892889484
y[1] (numeric) = 1.2955901172952506517721543156228
absolute error = 1.10049650266744e-17
relative error = 8.4941717907273063398963694945628e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.2968167672681941442747605455841
y[1] (numeric) = 1.2968167672681941553139560392058
absolute error = 1.10391954936217e-17
relative error = 8.5125329747827732267572172314840e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.2980441204243117809874131636941
y[1] (numeric) = 1.2980441204243117920607794887439
absolute error = 1.10733663250498e-17
relative error = 8.5308088922509639238346785112317e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.299272175536250497066936697781
y[1] (numeric) = 1.2992721755362505081744141845692
absolute error = 1.11074774867882e-17
relative error = 8.5489997368748350526907563955832e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.3005009313759552829125376519503
y[1] (numeric) = 1.3005009313759552940540665966759
absolute error = 1.11415289447256e-17
relative error = 8.5671057020602404720926168956034e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.3017303867146704012157467427893
y[1] (numeric) = 1.3017303867146704123912674075997
absolute error = 1.11755206648104e-17
relative error = 8.5851269808761027539608675393962e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.3029605403229406157160538115283
y[1] (numeric) = 1.3029605403229406269255064245794
absolute error = 1.12094526130511e-17
relative error = 8.6030637660545125106750224421785e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.3041913909706124206560416299516
y[1] (numeric) = 1.3041913909706124318993663854672
absolute error = 1.12433247555156e-17
relative error = 8.6209162499899892839533402969393e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.3054229374268352709347891450256
y[1] (numeric) = 1.3054229374268352822119262033574
absolute error = 1.12771370583318e-17
relative error = 8.6386846247397480098658725834619e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 1.3066551784600628129583140089445
y[1] (numeric) = 1.306655178460062824269203496632
absolute error = 1.13108894876875e-17
relative error = 8.6563690820234337984760357631860e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.3078881128380541161858235442537
y[1] (numeric) = 1.3078881128380541275304055540839
absolute error = 1.13445820098302e-17
relative error = 8.6739698132227872825539254380963e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=4.53
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.3091217393278749053705425979014
y[1] (numeric) = 1.3091217393278749167487571889686
absolute error = 1.13782145910672e-17
relative error = 8.6914870093815465387132534232432e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.3103560566958987934938860434939
y[1] (numeric) = 1.3103560566958988049056732412601
absolute error = 1.14117871977662e-17
relative error = 8.7089208612057366490724204154724e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 1.3115910637078085153917429976859
y[1] (numeric) = 1.3115910637078085268370427940404
absolute error = 1.14452997963545e-17
relative error = 8.7262715590628957212363234963453e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.3128267591285971620716391245223
y[1] (numeric) = 1.3128267591285971735503914778418
absolute error = 1.14787523533195e-17
relative error = 8.7435392929823009956339639749498e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 1.3140631417225694157195427106736
y[1] (numeric) = 1.3140631417225694272316875458822
absolute error = 1.15121448352086e-17
relative error = 8.7607242526547425588883747527846e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.3153002102533427853950795048613
y[1] (numeric) = 1.3153002102533427969405567134908
absolute error = 1.15454772086295e-17
relative error = 8.7778266274326079157937078965990e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.3165379634838488434139206263616
y[1] (numeric) = 1.316537963483848854992670066611
absolute error = 1.15787494402494e-17
relative error = 8.7948466063291360186358732780024e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.3177764001763344624161071603012
y[1] (numeric) = 1.3177764001763344740280686570977
absolute error = 1.16119614967965e-17
relative error = 8.8117843780194263144910572541453e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.3190155190923630531190743715266
y[1] (numeric) = 1.3190155190923630647641877165854
absolute error = 1.16451133450588e-17
relative error = 8.8286401308394005655562637364702e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.3202553189928158027541377841232
y[1] (numeric) = 1.3202553189928158144323427360072
absolute error = 1.16782049518840e-17
relative error = 8.8454140527856091138963503119239e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.3214957986378929141852026902012
y[1] (numeric) = 1.3214957986378929258964389743821
absolute error = 1.17112362841809e-17
relative error = 8.8621063315161787342815363046644e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.3227369567871148457084579693452
y[1] (numeric) = 1.3227369567871148574526652782631
absolute error = 1.17442073089179e-17
relative error = 8.8787171543495681366334340739142e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.3239787921993235515318144191325
y[1] (numeric) = 1.3239787921993235633089324122567
absolute error = 1.17771179931242e-17
relative error = 8.8952467082653751710222741312371e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 1.3252213036326837229328471173895
y[1] (numeric) = 1.3252213036326837347428154212785
absolute error = 1.18099683038890e-17
relative error = 8.9116951799036356993544790645230e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.3264644898446840300940006583437
y[1] (numeric) = 1.3264644898446840419367588667058
absolute error = 1.18427582083621e-17
relative error = 8.9280627555651872190428830660972e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.3277083495921383646138154275725
y[1] (numeric) = 1.3277083495921383764893031013259
absolute error = 1.18754876737534e-17
relative error = 8.9443496212112073136943090923521e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.3MB, time=4.81
x[1] = 0.291
y[1] (analytic) = 1.3289528816311870826929324046229
y[1] (numeric) = 1.3289528816311870946010890719565
absolute error = 1.19081566673336e-17
relative error = 8.9605559624636630158641414015320e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.3301980847172982489936333074044
y[1] (numeric) = 1.330198084717298260934398463838
absolute error = 1.19407651564336e-17
relative error = 8.9766819646047856922159414421096e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.3314439576052688811716722189159
y[1] (numeric) = 1.3314439576052688931449853273609
absolute error = 1.19733131084450e-17
relative error = 8.9927278125773803772650340065718e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 1.3326904990492261950791541645798
y[1] (numeric) = 1.3326904990492262070849546553997
absolute error = 1.20058004908199e-17
relative error = 9.0086936909846134402127571960181e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.3339377078026288506372154374088
y[1] (numeric) = 1.3339377078026288626754427084795
absolute error = 1.20382272710707e-17
relative error = 9.0245797840898067516822571952572e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.3351855826182681983772597984274
y[1] (numeric) = 1.3351855826182682104478532151982
absolute error = 1.20705934167708e-17
relative error = 9.0403862758169123673297516993459e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.336434122248269526649504011218
y[1] (numeric) = 1.3364341222482695387524029067721
absolute error = 1.21028988955541e-17
relative error = 9.0561133497500919281177187062590e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.3376833254440933094975855021482
y[1] (numeric) = 1.3376833254440933216327291772633
absolute error = 1.21351436751151e-17
relative error = 9.0717611891337522283503386593102e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 1.3389331909565364551979842717762
y[1] (numeric) = 1.3389331909565364673653119949852
absolute error = 1.21673277232090e-17
relative error = 9.0873299768725858507607211796498e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.340183717535733555463010518117
y[1] (numeric) = 1.3401837175357335676624615257686
absolute error = 1.21994510076516e-17
relative error = 9.1028198955314675955188439993034e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.3414349039311581353061087688842
y[1] (numeric) = 1.3414349039311581475376222652041
absolute error = 1.22315134963199e-17
relative error = 9.1182311273358785612124521375783e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.3426867488916239035682286575105
y[1] (numeric) = 1.3426867488916239158317438146616
absolute error = 1.22635151571511e-17
relative error = 9.1335638541711414454611503377188e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 1.343939251165286004104011816676
y[1] (numeric) = 1.3439392511652860163994677748198
absolute error = 1.22954559581438e-17
relative error = 9.1488182575833023184246800864170e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.3451924094996422676265437032665
y[1] (numeric) = 1.3451924094996422799538795706236
absolute error = 1.23273358673571e-17
relative error = 9.1639945187784515650803953702389e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.3464462226415344642094185101101
y[1] (numeric) = 1.3464462226415344765685733630211
absolute error = 1.23591548529110e-17
relative error = 9.1790928186230193207643462345082e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.3477006893371495564448646625341
y[1] (numeric) = 1.3477006893371495688357775455208
absolute error = 1.23909128829867e-17
relative error = 9.1941133376440002445598743062092e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.3489558083320209532566777417204
y[1] (numeric) = 1.3489558083320209656792876675464
absolute error = 1.24226099258260e-17
relative error = 9.2090562560285150299594104133948e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=5.08
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.3502115783710297643667070220308
y[1] (numeric) = 1.3502115783710297768209529717627
absolute error = 1.24542459497319e-17
relative error = 9.2239217536242682739133234716941e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.35146799819840605541364115592
y[1] (numeric) = 1.3514679981984060678994620789886
absolute error = 1.24858209230686e-17
relative error = 9.2387100099395649839259970663412e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.3527250665577301037228378877568
y[1] (numeric) = 1.3527250665577301162401727020176
absolute error = 1.25173348142608e-17
relative error = 9.2534212041428146582613266339898e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 1.353982782191933654725942026825
y[1] (numeric) = 1.3539827821919336672747296186199
absolute error = 1.25487875917949e-17
relative error = 9.2680555150634465252682582940260e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.3552411438433011790290352599955
y[1] (numeric) = 1.3552411438433011916092144842134
absolute error = 1.25801792242179e-17
relative error = 9.2826131211911276888006410312201e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.3565001502534711301280607360196
y[1] (numeric) = 1.3565001502534711427395704161579
absolute error = 1.26115096801383e-17
relative error = 9.2970942006764651121103797131505e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.3577598001634372027702647061278
y[1] (numeric) = 1.3577598001634372154130436343534
absolute error = 1.26427789282256e-17
relative error = 9.3114989313306776802973581300740e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.3590200923135495919603968595948
y[1] (numeric) = 1.3590200923135496046343837968054
absolute error = 1.26739869372106e-17
relative error = 9.3258274906258638269059591121424e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.3602810254435162526104103481761
y[1] (numeric) = 1.3602810254435162653155440240613
absolute error = 1.27051336758852e-17
relative error = 9.3400800556949051719786820402345e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.3615425982924041598314018498212
y[1] (numeric) = 1.361542598292404172567620962924
absolute error = 1.27362191131028e-17
relative error = 9.3542568033318164303035529474944e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.3628048095986405698665313798287
y[1] (numeric) = 1.3628048095986405826337745976065
absolute error = 1.27672432177778e-17
relative error = 9.3683579099914380196827575564381e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.3640676581000142816636609166273
y[1] (numeric) = 1.3640676581000142944618668755135
absolute error = 1.27982059588862e-17
relative error = 9.3823835517899418217675984496762e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.3653311425336768990864502696511
y[1] (numeric) = 1.3653311425336769119155575751163
absolute error = 1.28291073054652e-17
relative error = 9.3963339045046067359555647974552e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.3665952616361440937626479783166
y[1] (numeric) = 1.3665952616361441066225952049301
absolute error = 1.28599472266135e-17
relative error = 9.4102091435741127103499170649557e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.367860014143296868568314393917
y[1] (numeric) = 1.3678600141432968814590400854083
absolute error = 1.28907256914913e-17
relative error = 9.4240094440986188205823572121713e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 1.3691253987903828217467134603159
y[1] (numeric) = 1.3691253987903828346681561296359
absolute error = 1.29214426693200e-17
relative error = 9.4377349808396267840955727334424e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.370391414312017411660609074653
y[1] (numeric) = 1.3703914143120174246127072040356
absolute error = 1.29520981293826e-17
relative error = 9.4513859282203610085309391820247e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=5.36
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.3716580594421852221767012758721
y[1] (numeric) = 1.3716580594421852351593933168958
absolute error = 1.29826920410237e-17
relative error = 9.4649624603258598807872950451218e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.3729253329142412286809368767401
y[1] (numeric) = 1.3729253329142412416941612503893
absolute error = 1.30132243736492e-17
relative error = 9.4784647509028529893318520184161e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.3741932334609120647234285241509
y[1] (numeric) = 1.374193233460912077767123620878
absolute error = 1.30436950967271e-17
relative error = 9.4918929733604444343196925164192e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 1.3754617598142972892917155429035
y[1] (numeric) = 1.37546175981429730236581972269
absolute error = 1.30741041797865e-17
relative error = 9.5052473007694886331885359346455e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.3767309107058706547110992897953
y[1] (numeric) = 1.3767309107058706678155508822137
absolute error = 1.31044515924184e-17
relative error = 9.5185279058632819359030853106665e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.378000684866481375170785117804
y[1] (numeric) = 1.3780006848664813883055224220793
absolute error = 1.31347373042753e-17
relative error = 9.5317349610373844946486813053540e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.37927108102635539587456242432
y[1] (numeric) = 1.3792710810263554090395237093915
absolute error = 1.31649612850715e-17
relative error = 9.5448686383499555215176669957504e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.3805420979150966628147536328562
y[1] (numeric) = 1.3805420979150966760098771374393
absolute error = 1.31951235045831e-17
relative error = 9.5579291095218742673781305035956e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.3818137342616883931681623343915
y[1] (numeric) = 1.3818137342616884063933862670392
absolute error = 1.32252239326477e-17
relative error = 9.5709165459366480923595019155259e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.3830859887944943463127501925045
y[1] (numeric) = 1.3830859887944943595680127316697
absolute error = 1.32552625391652e-17
relative error = 9.5838311186411212201677145182607e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.3843588602412600954637715957301
y[1] (numeric) = 1.3843588602412601087490108898268
absolute error = 1.32852392940967e-17
relative error = 9.5966729983448119487491353768959e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.3856323473291142999280944211053
y[1] (numeric) = 1.3856323473291143132432485885709
absolute error = 1.33151541674656e-17
relative error = 9.6094423554208460655229561822285e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.3869064487845699779754346546935
y[1] (numeric) = 1.3869064487845699913204417840505
absolute error = 1.33450071293570e-17
relative error = 9.6221393599056641881891734789601e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.3881811633335257803252319979572
y[1] (numeric) = 1.388181163333525793700030147875
absolute error = 1.33747981499178e-17
relative error = 9.6347641814992397776225053697591e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.3894564897012672642478929732087
y[1] (numeric) = 1.3894564897012672776524201725659
absolute error = 1.34045271993572e-17
relative error = 9.6473169895655886259243063088954e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.3907324266124681682791274270042
y[1] (numeric) = 1.3907324266124681817133216749503
absolute error = 1.34341942479461e-17
relative error = 9.6597979531324893705314956292770e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=80.1MB, alloc=4.3MB, time=5.63
x[1] = 0.341
y[1] (analytic) = 1.3920089727911916875461037172489
y[1] (numeric) = 1.3920089727911917010099029832662
absolute error = 1.34637992660173e-17
relative error = 9.6722072408917850213275672021184e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.3932861269608917497041472579648
y[1] (numeric) = 1.3932861269608917631974894819307
absolute error = 1.34933422239659e-17
relative error = 9.6845450211998311318078153057974e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.3945638878444142914827064851298
y[1] (numeric) = 1.3945638878444143050055295773788
absolute error = 1.35228230922490e-17
relative error = 9.6968114620774443011290222127661e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 1.3958422541639985358393096977274
y[1] (numeric) = 1.3958422541639985493915515391131
absolute error = 1.35522418413857e-17
relative error = 9.7090067312100706127696476348781e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 1.3971212246412782697202356201573
y[1] (numeric) = 1.3971212246412782833018340621145
absolute error = 1.35815984419572e-17
relative error = 9.7211309959480294425723339047988e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.3984007979972831224266199254425
y[1] (numeric) = 1.3984007979972831360375127900493
absolute error = 1.36108928646068e-17
relative error = 9.7331844233066891245275549520575e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 1.3996809729524398445847193532324
y[1] (numeric) = 1.3996809729524398582248444332728
absolute error = 1.36401250800404e-17
relative error = 9.7451671799670035706251776804424e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.4009617482265735877190544524466
y[1] (numeric) = 1.4009617482265736013883495114721
absolute error = 1.36692950590255e-17
relative error = 9.7570794322749799356903375044649e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.4022431225389091844271513755194
y[1] (numeric) = 1.4022431225389091981255541479116
absolute error = 1.36984027723922e-17
relative error = 9.7689213462425801540593482566805e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.4035250946080724291546025496139
y[1] (numeric) = 1.4035250946080724428820507406467
absolute error = 1.37274481910328e-17
relative error = 9.7806930875476247063376596124550e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.4048076631520913595691654498493
y[1] (numeric) = 1.4048076631520913733255967357512
absolute error = 1.37564312859019e-17
relative error = 9.7923948215340574762759034935224e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.4060908268883975385326181005498
y[1] (numeric) = 1.4060908268883975523179701285662
absolute error = 1.37853520280164e-17
relative error = 9.8040267132121426701309679794613e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.4073745845338273366690893327673
y[1] (numeric) = 1.4073745845338273504832997212229
absolute error = 1.38142103884556e-17
relative error = 9.8155889272587363316508955481398e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.4086589348046232155285812298538
y[1] (numeric) = 1.4086589348046232293715875682149
absolute error = 1.38430063383611e-17
relative error = 9.8270816280174189994543983461122e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.4099438764164350113444005976677
y[1] (numeric) = 1.4099438764164350252161404466046
absolute error = 1.38717398489369e-17
relative error = 9.8385049794987740825865938548433e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.4112294080843212193832157020904
y[1] (numeric) = 1.4112294080843212332836265935399
absolute error = 1.39004108914495e-17
relative error = 9.8498591453806692966169984022787e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.412515528522750278886453923903
y[1] (numeric) = 1.4125155285227502928154733611309
absolute error = 1.39290194372279e-17
relative error = 9.8611442890084703357549636356735e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=5.90
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.413802236445601858601755389732
y[1] (numeric) = 1.4138022364456018725593208473956
absolute error = 1.39575654576636e-17
relative error = 9.8723605733952579345817228651935e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.415089530566168142903197047719
y[1] (numeric) = 1.4150895305661681568892459719296
absolute error = 1.39860489242106e-17
relative error = 9.8835081612220482890522983930427e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.416377409597155118499001067796
y[1] (numeric) = 1.4163774095971551325134708761812
absolute error = 1.40144698083852e-17
relative error = 9.8945872148378756012937703236379e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 1.417665872250683861725440858965
y[1] (numeric) = 1.4176658722506838757682689407318
absolute error = 1.40428280817668e-17
relative error = 9.9055978962605840783518514965693e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 1.4189549172382918264256574097853
y[1] (numeric) = 1.4189549172382918404967811257824
absolute error = 1.40711237159971e-17
relative error = 9.9165403671764925312857943630642e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.4202445432709341324120980733571
y[1] (numeric) = 1.4202445432709341465114547561374
absolute error = 1.40993566827803e-17
relative error = 9.9274147889407693975299442047768e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.4215347490589848545112893344707
y[1] (numeric) = 1.4215347490589848686388162883542
absolute error = 1.41275269538835e-17
relative error = 9.9382213225779508969194717144988e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.4228255333122383121896545142567
y[1] (numeric) = 1.4228255333122383263452890153933
absolute error = 1.41556345011366e-17
relative error = 9.9489601287821094234938123908587e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.4241168947399103597590867866264
y[1] (numeric) = 1.4241168947399103739427660830582
absolute error = 1.41836792964318e-17
relative error = 9.9596313679167446008100201985582e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.4254088320506396771609873010365
y[1] (numeric) = 1.4254088320506396913726486127609
absolute error = 1.42116613117244e-17
relative error = 9.9702352000155913922750962731383e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.4267013439524890613274776276481
y[1] (numeric) = 1.4267013439524890755670581466806
absolute error = 1.42395805190325e-17
relative error = 9.9807717847826572427839883568106e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.4279944291529467181184951637757
y[1] (numeric) = 1.4279944291529467323859320542124
absolute error = 1.42674368904367e-17
relative error = 9.9912412815922634359594099798087e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.4292880863589275548334795646363
y[1] (numeric) = 1.4292880863589275691287099627171
absolute error = 1.42952303980808e-17
relative error = 1.0001643849489790282060267355203e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 1.4305823142767744732963576868232
y[1] (numeric) = 1.4305823142767744876193187009944
absolute error = 1.43229610141712e-17
relative error = 1.0011979647191513935139223084067e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.4318771116122596635125339596239
y[1] (numeric) = 1.4318771116122596778631626706013
absolute error = 1.43506287109774e-17
relative error = 1.0022248833085216697633459897990e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.4331724770705858978965925273021
y[1] (numeric) = 1.4331724770705859122748259881337
absolute error = 1.43782334608316e-17
relative error = 1.0032451565230170407580436186685e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.4344684093563878260694169347483
y[1] (numeric) = 1.4344684093563878404751921708773
absolute error = 1.44057752361290e-17
relative error = 1.0042588001357612256824088653210e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.3MB, time=6.17
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.4357649071737332702234325594867
y[1] (numeric) = 1.4357649071737332846566865688147
absolute error = 1.44332540093280e-17
relative error = 1.0052658298871152726466789283909e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.437061969226124521054676424906
y[1] (numeric) = 1.4370619692261245355153461778558
absolute error = 1.44606697529498e-17
relative error = 1.0062662614846768125475997933401e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.43835959421649963426039846275
y[1] (numeric) = 1.4383595942164996487484209023284
absolute error = 1.44880224395784e-17
relative error = 1.0072601106033075581858255468158e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 1.4396577808472337276008977273755
y[1] (numeric) = 1.4396577808472337421162097692368
absolute error = 1.45153120418613e-17
relative error = 1.0082473928852097079501608562417e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 1.4409565278201402785242965000503
y[1] (numeric) = 1.4409565278201402930668350325593
absolute error = 1.45425385325090e-17
relative error = 1.0092281239399190877445267513929e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 1.4422558338364724223529546586246
y[1] (numeric) = 1.4422558338364724369226565429195
absolute error = 1.45697018842949e-17
relative error = 1.0102023193443264922274563976901e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.4435556975969242510302261262689
y[1] (numeric) = 1.4435556975969242656270281963246
absolute error = 1.45968020700557e-17
relative error = 1.0111699946427339743190028488731e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.4448561178016321124262586526316
y[1] (numeric) = 1.4448561178016321270500977153227
absolute error = 1.46238390626911e-17
relative error = 1.0121311653468628086726946301756e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.4461570931501759102015376217236
y[1] (numeric) = 1.4461570931501759248523504568878
absolute error = 1.46508128351642e-17
relative error = 1.0130858469359102405786174543553e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.4474586223415804042268740230953
y[1] (numeric) = 1.4474586223415804189045973835966
absolute error = 1.46777233605013e-17
relative error = 1.0140340548565648998858071770592e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.448760704074316511558536166426
y[1] (numeric) = 1.4487607040743165262631067782178
absolute error = 1.47045706117918e-17
relative error = 1.0149758045230294560029216093414e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.4500633370463026079672241645024
y[1] (numeric) = 1.4500633370463026226985787266908
absolute error = 1.47313545621884e-17
relative error = 1.0159111113170642601269622647643e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.4513665199549058300195856557195
y[1] (numeric) = 1.4513665199549058447776608406267
absolute error = 1.47580751849072e-17
relative error = 1.0168399905880242816807289236249e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.4526702514969433777109706846986
y[1] (numeric) = 1.4526702514969433924957031379262
absolute error = 1.47847324532276e-17
relative error = 1.0177624576528824961712235182205e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.4539745303686838176481231083739
y[1] (numeric) = 1.4539745303686838324594494488662
absolute error = 1.48113263404923e-17
relative error = 1.0186785277962604416570522787457e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.4552793552658483867805053449661
y[1] (numeric) = 1.4552793552658484016183621650735
absolute error = 1.48378568201074e-17
relative error = 1.0195882162704658979540623312816e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=91.5MB, alloc=4.3MB, time=6.45
x[1] = 0.391
y[1] (analytic) = 1.4565847248836122966789527346269
y[1] (numeric) = 1.4565847248836123115432766001693
absolute error = 1.48643238655424e-17
relative error = 1.0204915382955239122123696450477e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.457890637916606038360353233208
y[1] (numeric) = 1.4578906379166060532510806835384
absolute error = 1.48907274503304e-17
relative error = 1.0213885090592217892709046575571e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.4591970930589166876570476145846
y[1] (numeric) = 1.4591970930589167025741151626524
absolute error = 1.49170675480678e-17
relative error = 1.0222791437171199867455494940330e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.4605040890040892111296448122411
y[1] (numeric) = 1.4605040890040892260729889446555
absolute error = 1.49433441324144e-17
relative error = 1.0231634573925907499479683772807e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 1.4618116244451277725219464874132
y[1] (numeric) = 1.4618116244451277874915036645067
absolute error = 1.49695571770935e-17
relative error = 1.0240414651768569488647842594215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 1.4631196980744970397566743689696
y[1] (numeric) = 1.4631196980744970547523810248619
absolute error = 1.49957066558923e-17
relative error = 1.0249131821290516190725171982237e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.464428308584123492470693369417
y[1] (numeric) = 1.4644283085841235074924859120783
absolute error = 1.50217925426613e-17
relative error = 1.0257786232762093042455178654027e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 1.4657374546653967300884229419116
y[1] (numeric) = 1.4657374546653967451362377532262
absolute error = 1.50478148113146e-17
relative error = 1.0266378036133192530744573916613e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.4670471350091707804321286049769
y[1] (numeric) = 1.4670471350091707955059020408067
absolute error = 1.50737734358298e-17
relative error = 1.0274907381033514700567602465766e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.4683573483057654088677850247439
y[1] (numeric) = 1.4683573483057654239674534149922
absolute error = 1.50996683902483e-17
relative error = 1.0283374416773102712674852145680e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.4696680932449674279852015089605
y[1] (numeric) = 1.4696680932449674431107011576357
absolute error = 1.51254996486752e-17
relative error = 1.0291779292342607384457569616607e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.4709793685160320078111002327536
y[1] (numeric) = 1.470979368516032022962367418033
absolute error = 1.51512671852794e-17
relative error = 1.0300122156413690285645287175207e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.4722911728076839865538369831752
y[1] (numeric) = 1.4722911728076840017308079574682
absolute error = 1.51769709742930e-17
relative error = 1.0308403157338953223633344044295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.473603504808119181878453677919
y[1] (numeric) = 1.4736035048081191970810646679316
absolute error = 1.52026109900126e-17
relative error = 1.0316622443153161443276653058236e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.4749163632050057027107513832682
y[1] (numeric) = 1.4749163632050057179389385900661
absolute error = 1.52281872067979e-17
relative error = 1.0324780161572633652883798830174e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.4762297466854852615690720273063
y[1] (numeric) = 1.4762297466854852768227716263791
absolute error = 1.52536995990728e-17
relative error = 1.0332876459996332763950758936451e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.4775436539361744874224764767218
y[1] (numeric) = 1.4775436539361745027016246180468
absolute error = 1.52791481413250e-17
relative error = 1.0340911485505939559929385887688e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.3MB, time=6.73
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.4788580836431662390740061191368
y[1] (numeric) = 1.4788580836431662543785389272426
absolute error = 1.53045328081058e-17
relative error = 1.0348885384866065142511544509600e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.4801730344920309190677145678075
y[1] (numeric) = 1.4801730344920309343975681418381
absolute error = 1.53298535740306e-17
relative error = 1.0356798304524939083321826171949e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.4814885051678177881181555817741
y[1] (numeric) = 1.4814885051678178034732659955528
absolute error = 1.53551104137787e-17
relative error = 1.0364650390614625320247811387183e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.482804494355056280061012772083
y[1] (numeric) = 1.4828044943550562954413160741761
absolute error = 1.53803033020931e-17
relative error = 1.0372441788951240798751973511214e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 1.4841210007377573173235561435591
y[1] (numeric) = 1.4841210007377573327289883573402
absolute error = 1.54054322137811e-17
relative error = 1.0380172645035715872252389298721e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 1.4854380229994146269136100017834
y[1] (numeric) = 1.4854380229994146423441071254971
absolute error = 1.54304971237137e-17
relative error = 1.0387843104053746686527866670269e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.4867555598230060569257162364162
y[1] (numeric) = 1.4867555598230060723812142432421
absolute error = 1.54554980068259e-17
relative error = 1.0395453310876357019668132003137e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.4880736098909948935631764748125
y[1] (numeric) = 1.4880736098909949090436113129295
absolute error = 1.54804348381170e-17
relative error = 1.0403003410060460983496830266370e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.4893921718853311786746560839983
y[1] (numeric) = 1.4893921718853311941799636766484
absolute error = 1.55053075926501e-17
relative error = 1.0410493545848889438313492313539e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.4907112444874530278040324845124
y[1] (numeric) = 1.4907112444874530433341487300648
absolute error = 1.55301162455524e-17
relative error = 1.0417923862170956744962263890202e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.4920308263782879487521697263753
y[1] (numeric) = 1.4920308263782879643070304983906
absolute error = 1.55548607720153e-17
relative error = 1.0425294502642894274530188583833e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.4933509162382541606493007655212
y[1] (numeric) = 1.4933509162382541762288419128155
absolute error = 1.55795411472943e-17
relative error = 1.0432605610568151489230344527313e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.4946715127472619135366983684206
y[1] (numeric) = 1.4946715127472619291408557151296
absolute error = 1.56041573467090e-17
relative error = 1.0439857328937766116551126344619e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.4959926145847148084563150633318
y[1] (numeric) = 1.4959926145847148240850244089749
absolute error = 1.56287093456431e-17
relative error = 1.0447049800430736135310596935894e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 1.497314220429511118047072048652
y[1] (numeric) = 1.4973142204295111337002691681967
absolute error = 1.56531971195447e-17
relative error = 1.0454183167414593911687338934644e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.4986363289600451076464764621894
y[1] (numeric) = 1.4986363289600451233240971061155
absolute error = 1.56776206439261e-17
relative error = 1.0461257571945647408744734466442e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.4999589388542083568962459098485
y[1] (numeric) = 1.4999589388542083725982258042121
absolute error = 1.57019798943636e-17
relative error = 1.0468273155769223855959510523327e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=7.00
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.5012820487893910818506186482142
y[1] (numeric) = 1.5012820487893910975768934947123
absolute error = 1.57262748464981e-17
relative error = 1.0475230060320448732928244363225e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.5026056574424834575860273128356
y[1] (numeric) = 1.5026056574424834733365327888702
absolute error = 1.57505054760346e-17
relative error = 1.0482128426724292287741766706214e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.5039297634898769413108135826447
y[1] (numeric) = 1.5039297634898769570854853413872
absolute error = 1.57746717587425e-17
relative error = 1.0488968395796151448837036030736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.5052543656074655959736606709065
y[1] (numeric) = 1.505254365607465611772434341362
absolute error = 1.57987736704555e-17
relative error = 1.0495750108042166617751380431038e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.5065794624706474143694200343783
y[1] (numeric) = 1.50657946247064743019223122145
absolute error = 1.58228111870717e-17
relative error = 1.0502473703659673217349187697546e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 1.5079050527543256437410081949612
y[1] (numeric) = 1.5079050527543256595877924795146
absolute error = 1.58467842845534e-17
relative error = 1.0509139322537455571415507847585e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.5092311351329101108760490720573
y[1] (numeric) = 1.5092311351329101267467420109852
absolute error = 1.58706929389279e-17
relative error = 1.0515747104256665687213479466554e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.5105577082803185476969367291028
y[1] (numeric) = 1.510557708280318563591473855389
absolute error = 1.58945371262862e-17
relative error = 1.0522297188090350622870047824589e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.511884770869977917342992944321
y[1] (numeric) = 1.5118847708699779332613097671053
absolute error = 1.59183168227843e-17
relative error = 1.0528789713004705678289118395580e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.5132123215748257407433935236517
y[1] (numeric) = 1.5132123215748257566854255282941
absolute error = 1.59420320046424e-17
relative error = 1.0535224817658936832229915915506e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.5145403590673114236795367830388
y[1] (numeric) = 1.5145403590673114396452194311841
absolute error = 1.59656826481453e-17
relative error = 1.0541602640405919825613781146244e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.5158688820193975843355271378195
y[1] (numeric) = 1.515868882019397600324795867462
absolute error = 1.59892687296425e-17
relative error = 1.0547923319292661466382253539367e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.5171978891025613813354462488422
y[1] (numeric) = 1.51719788910256139734823647439
absolute error = 1.60127902255478e-17
relative error = 1.0554186992060432535456608170670e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.5185273789877958422660836881512
y[1] (numeric) = 1.5185273789877958583023308004909
absolute error = 1.60362471123397e-17
relative error = 1.0560393796145430389122032480548e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.5198573503456111926837986016201
y[1] (numeric) = 1.5198573503456112087434379681814
absolute error = 1.60596393665613e-17
relative error = 1.0566543868679112662119331453036e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.5211878018460361856041833617815
y[1] (numeric) = 1.5211878018460362016871503266021
absolute error = 1.60829669648206e-17
relative error = 1.0572637346488795716815168274941e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
memory used=102.9MB, alloc=4.4MB, time=7.27
y[1] (analytic) = 1.5225187321586194314731997213019
y[1] (numeric) = 1.5225187321586194475794296050915
absolute error = 1.61062298837896e-17
relative error = 1.0578674366097465319270376371786e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.5238501399524307286184574960732
y[1] (numeric) = 1.5238501399524307447478855962789
absolute error = 1.61294281002057e-17
relative error = 1.0584655063725101163298352555163e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.5251820238960623941793053267576
y[1] (numeric) = 1.5251820238960624103318669176282
absolute error = 1.61525615908706e-17
relative error = 1.0590579575288358817759722982342e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.5265143826576305955144025888017
y[1] (numeric) = 1.5265143826576306116900329214526
absolute error = 1.61756303326509e-17
relative error = 1.0596448036401370483441632434048e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 1.5278472149047766820854410434621
y[1] (numeric) = 1.5278472149047766982840753459397
absolute error = 1.61986343024776e-17
relative error = 1.0602260582375825078850289477263e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.529180519304668517815684346229
y[1] (numeric) = 1.5291805193046685340372578235759
absolute error = 1.62215734773469e-17
relative error = 1.0608017348221901509558903153077e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 1.5305142945240018139219930542221
y[1] (numeric) = 1.5305142945240018301664408885418
absolute error = 1.62444478343197e-17
relative error = 1.0613718468648351133903820723684e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.531848539229001462219002300643
y[1] (numeric) = 1.5318485392290014784862596511646
absolute error = 1.62672573505216e-17
relative error = 1.0619364078062909650552368609589e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.533183252085422868894118832218
y[1] (numeric) = 1.5331832520854228851841208353609
absolute error = 1.62900020031429e-17
relative error = 1.0624954310572710274376219591845e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.5345184317585532887520036347454
y[1] (numeric) = 1.5345184317585533050646854041845
absolute error = 1.63126817694391e-17
relative error = 1.0630489299985024018556982120245e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.5358540769132131599272059023764
y[1] (numeric) = 1.5358540769132131762625025291068
absolute error = 1.63352966267304e-17
relative error = 1.0635969179807348427038819103619e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.5371901862137574390636136381059
y[1] (numeric) = 1.5371901862137574554214601905079
absolute error = 1.63578465524020e-17
relative error = 1.0641394083248019677831987355461e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.5385267583240769369593857061348
y[1] (numeric) = 1.5385267583240769533397172300388
absolute error = 1.63803315239040e-17
relative error = 1.0646764143216564900288433675119e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.5398637919075996546760296912822
y[1] (numeric) = 1.5398637919075996710787812100336
absolute error = 1.64027515187514e-17
relative error = 1.0652079492324120978817801251268e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.541201285627292120110289456482
y[1] (numeric) = 1.5412012856272921365353959710061
absolute error = 1.64251065145241e-17
relative error = 1.0657340262883854545812189160645e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.5425392381456607250275058265862
y[1] (numeric) = 1.5425392381456607414749023154534
absolute error = 1.64473964888672e-17
relative error = 1.0662546586911577631784626235792e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.5438776481247530625551133652274
y[1] (numeric) = 1.5438776481247530790247347847182
absolute error = 1.64696214194908e-17
relative error = 1.0667698596126039600333920473339e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=7.56
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.5452165142261592651349357513541
y[1] (numeric) = 1.545216514226159281626717035524
absolute error = 1.64917812841699e-17
relative error = 1.0672796421949285615955550092947e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.5465558351110133429329418032552
y[1] (numeric) = 1.5465558351110133594468178639997
absolute error = 1.65138760607445e-17
relative error = 1.0677840195507145892726863535903e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.5478956094399945227051237404285
y[1] (numeric) = 1.5478956094399945392410294675485
absolute error = 1.65359057271200e-17
relative error = 1.0682830047629919526474423407647e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.5492358358733285871181588175286
y[1] (numeric) = 1.5492358358733286036760290787952
absolute error = 1.65578702612666e-17
relative error = 1.0687766108852412599084102975101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.5505765130707892145235150098411
y[1] (numeric) = 1.5505765130707892311032846510611
absolute error = 1.65797696412200e-17
relative error = 1.0692648509414817771615821876157e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.5519176396916993191836609762924
y[1] (numeric) = 1.551917639691699335785264821373
absolute error = 1.66016038450806e-17
relative error = 1.0697477379262626049565396878657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 1.5532592143949323919490400738935
y[1] (numeric) = 1.5532592143949324085724129249078
absolute error = 1.66233728510143e-17
relative error = 1.0702252848047572363203213376281e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.5546012358389138413844677467584
y[1] (numeric) = 1.5546012358389138580295443840105
absolute error = 1.66450766372521e-17
relative error = 1.0706975045127807604812687554657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.5559437026816223353436111634097
y[1] (numeric) = 1.5559437026816223520103263454997
absolute error = 1.66667151820900e-17
relative error = 1.0711644099568265827578551851500e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.5572866135805911429902095280037
y[1] (numeric) = 1.5572866135805911596784979918935
absolute error = 1.66882884638898e-17
relative error = 1.0716260140141610705963706440191e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.5586299671929094772646930443682
y[1] (numeric) = 1.5586299671929094939744895054463
absolute error = 1.67097964610781e-17
relative error = 1.0720823295328025463436458300966e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.5599737621752238377948580663431
y[1] (numeric) = 1.55997376217522385452609721849
absolute error = 1.67312391521469e-17
relative error = 1.0725333693316032753008999318699e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.561317997183739354249255523863
y[1] (numeric) = 1.5613179971837393710018720395164
absolute error = 1.67526165156534e-17
relative error = 1.0729791462002801115180144807557e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.5626626708742211301319492715041
y[1] (numeric) = 1.5626626708742211469058778017244
absolute error = 1.67739285302203e-17
relative error = 1.0734196728994773007868368890130e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.5640077819019955870173005648492
y[1] (numeric) = 1.5640077819019956038124757393849
absolute error = 1.67951751745357e-17
relative error = 1.0738549621608037019314066820957e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.5653533289219518092234344299993
y[1] (numeric) = 1.565353328921951826039790857352
absolute error = 1.68163564273527e-17
relative error = 1.0742850266868509676330481544054e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.5666993105885428889230432528748
y[1] (numeric) = 1.5666993105885429057605155203651
absolute error = 1.68374722674903e-17
relative error = 1.0747098791512949239571454166058e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=7.84
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.5680457255557872716901824776192
y[1] (numeric) = 1.5680457255557872885487051514517
absolute error = 1.68585226738325e-17
relative error = 1.0751295321988819494314435299900e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.5693925724772701024817128674168
y[1] (numeric) = 1.5693925724772701193612204927459
absolute error = 1.68795076253291e-17
relative error = 1.0755439984455240595074726192544e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.5707398500061445720520433463986
y[1] (numeric) = 1.5707398500061445889524704473935
absolute error = 1.69004271009949e-17
relative error = 1.0759532904782919510713521471201e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.5720875567951332637998280080022
y[1] (numeric) = 1.5720875567951332807211090879129
absolute error = 1.69212810799107e-17
relative error = 1.0763574208555228910799819474070e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.5734356914965295010452704432042
y[1] (numeric) = 1.5734356914965295179873399844264
absolute error = 1.69420695412222e-17
relative error = 1.0767564021067948946854114183725e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.5747842527621986947366881114299
y[1] (numeric) = 1.5747842527621987116994805755711
absolute error = 1.69627924641412e-17
relative error = 1.0771502467330473964536252720864e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 1.576133239243579691584989047691
y[1] (numeric) = 1.5761332392435797085684388756358
absolute error = 1.69834498279448e-17
relative error = 1.0775389672065747169342038747554e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 1.5774826495916861226247127715853
y[1] (numeric) = 1.5774826495916861396287543835606
absolute error = 1.70040416119753e-17
relative error = 1.0779225759710642437209073945451e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.5788324824571077522002868372293
y[1] (numeric) = 1.5788324824571077692248546328706
absolute error = 1.70245677956413e-17
relative error = 1.0783010854417107277620667600468e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.5801827364900118273761500379826
y[1] (numeric) = 1.580182736490011844421178396399
absolute error = 1.70450283584164e-17
relative error = 1.0786745080051784170285435527337e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.5815334103401444277693928559493
y[1] (numeric) = 1.5815334103401444448348161357894
absolute error = 1.70654232798401e-17
relative error = 1.0790428560197027928739910895230e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.5828845026568318158035653237315
y[1] (numeric) = 1.582884502656831832889317863249
absolute error = 1.70857525395175e-17
relative error = 1.0794061418151162768046713971080e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.5842360120889817873823020447383
y[1] (numeric) = 1.5842360120889818044883181618576
absolute error = 1.71060161171193e-17
relative error = 1.0797643776928930433385119327639e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.5855879372850850229814136985378
y[1] (numeric) = 1.5855879372850850401076276909197
absolute error = 1.71262139923819e-17
relative error = 1.0801175759262002105181570623683e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.5869402768932164391580939392736
y[1] (numeric) = 1.5869402768932164563044400843811
absolute error = 1.71463461451075e-17
relative error = 1.0804657487599490677117041936149e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.5882930295610365404758901780513
y[1] (numeric) = 1.5882930295610365576423027332152
absolute error = 1.71664125551639e-17
relative error = 1.0808089084108274513554300339950e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.5896461939357927718440863244369
y[1] (numeric) = 1.5896461939357927890304995269216
absolute error = 1.71864132024847e-17
relative error = 1.0811470670673574150080912419394e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=8.11
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.590999768664320871270145147797
y[1] (numeric) = 1.5909997686643208884764932148663
absolute error = 1.72063480670693e-17
relative error = 1.0814802368899403301282139912399e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.5923537523930462230238575061512
y[1] (numeric) = 1.5923537523930462402500746351341
absolute error = 1.72262171289829e-17
relative error = 1.0818084300109020514612671623088e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.5937081437679852112118452785009
y[1] (numeric) = 1.5937081437679852284578656468571
absolute error = 1.72460203683562e-17
relative error = 1.0821316585345193217484506166111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.5950629414347465737610644262422
y[1] (numeric) = 1.5950629414347465910268221916284
absolute error = 1.72657577653862e-17
relative error = 1.0824499345371152972527750833433e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.5964181440385327568099542002762
y[1] (numeric) = 1.5964181440385327740953835006115
absolute error = 1.72854293003353e-17
relative error = 1.0827632700670483899434781557172e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.5977737502241412695058781027767
y[1] (numeric) = 1.5977737502241412868109130563088
absolute error = 1.73050349535321e-17
relative error = 1.0830716771448078548786411251538e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 1.5991297586359660392075018062899
y[1] (numeric) = 1.5991297586359660565320765116608
absolute error = 1.73245747053709e-17
relative error = 1.0833751677630278865600250809274e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.6004861679179987670907528278995
y[1] (numeric) = 1.6004861679179987844348013642116
absolute error = 1.73440485363121e-17
relative error = 1.0836737538865581648001408119349e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 1.6018429767138302841570063526118
y[1] (numeric) = 1.6018429767138303015204627794934
absolute error = 1.73634564268816e-17
relative error = 1.0839674474524719013207803527577e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 1.6032001836666519076421411978863
y[1] (numeric) = 1.6032001836666519250249395555581
absolute error = 1.73827983576718e-17
relative error = 1.0842562603701739320792538909084e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 1.6045577874192567978251095103709
y[1] (numeric) = 1.6045577874192568152271838197115
absolute error = 1.74020743093406e-17
relative error = 1.0845402045213839012329539929692e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 1.6059157866140413152346633863834
y[1] (numeric) = 1.6059157866140413326559476489955
absolute error = 1.74212842626121e-17
relative error = 1.0848192917602256730637897810643e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 1.6072741798930063782528812095264
y[1] (numeric) = 1.6072741798930063956933094078027
absolute error = 1.74404281982763e-17
relative error = 1.0850935339132543565950640432201e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 1.6086329658977588211141361020228
y[1] (numeric) = 1.608632965897758838573642199212
absolute error = 1.74595060971892e-17
relative error = 1.0853629427795083411145307675281e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 1.6099921432695127522981484909158
y[1] (numeric) = 1.6099921432695127697766664311888
absolute error = 1.74785179402730e-17
relative error = 1.0856275301305675604057091399533e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 1.6113517106490909133157643961943
y[1] (numeric) = 1.6113517106490909308132281047104
absolute error = 1.74974637085161e-17
relative error = 1.0858873077105993300991566831765e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=118.2MB, alloc=4.4MB, time=8.39
x[1] = 0.508
y[1] (analytic) = 1.6127116666769260378861006551804
y[1] (numeric) = 1.6127116666769260554024440381526
absolute error = 1.75163433829722e-17
relative error = 1.0861422872363484254230920815376e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 1.6140720099930622115036979061422
y[1] (numeric) = 1.6140720099930622290388548509042
absolute error = 1.75351569447620e-17
relative error = 1.0863924803972885703240522748723e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 1.6154327392371562313943217640991
y[1] (numeric) = 1.6154327392371562489482261391709
absolute error = 1.75539043750718e-17
relative error = 1.0866378988555815390201560695738e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 1.6167938530484789668580522331254
y[1] (numeric) = 1.6167938530484789844306378882797
absolute error = 1.75725856551543e-17
relative error = 1.0868785542461728116119773879600e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 1.6181553500659167199983010121804
y[1] (numeric) = 1.6181553500659167375895017785085
absolute error = 1.75912007663281e-17
relative error = 1.0871144581768066833967793744768e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 1.6195172289279725868353959655585
y[1] (numeric) = 1.6195172289279726044451456555367
absolute error = 1.76097496899782e-17
relative error = 1.0873456222281033185507080852321e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 1.6208794882727678188033716444903
y[1] (numeric) = 1.6208794882727678364316040520459
absolute error = 1.76282324075556e-17
relative error = 1.0875720579535801627471195693356e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.515
y[1] (analytic) = 1.6222421267380431846286043632159
y[1] (numeric) = 1.6222421267380432022752532637934
absolute error = 1.76466489005775e-17
relative error = 1.0877937768797105054911642450489e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 1.6236051429611603325889299510095
y[1] (numeric) = 1.6236051429611603502539291016371
absolute error = 1.76649991506276e-17
relative error = 1.0880107905059881774733377961925e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 1.6249685355791031531518819211518
y[1] (numeric) = 1.6249685355791031708351650605073
absolute error = 1.76832831393555e-17
relative error = 1.0882231103049368063546306681805e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 1.626332303228479141990687418724
y[1] (numeric) = 1.6263323032284791596921882672014
absolute error = 1.77015008484774e-17
relative error = 1.0884307477221992291966112202111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 1.6276964445455207633766579313432
y[1] (numeric) = 1.6276964445455207810963101911186
absolute error = 1.77196522597754e-17
relative error = 1.0886337141765407120376107864105e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 1.6290609581660868139466113705593
y[1] (numeric) = 1.6290609581660868316843487256573
absolute error = 1.77377373550980e-17
relative error = 1.0888320210599260820902364435927e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 1.6304258427256637868439617566073
y[1] (numeric) = 1.6304258427256638045997178729677
absolute error = 1.77557561163604e-17
relative error = 1.0890256797375844716716069691259e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 1.6317910968593672362321123655388
y[1] (numeric) = 1.6317910968593672540058208910825
absolute error = 1.77737085255437e-17
relative error = 1.0892147015480065913212364123297e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 1.6331567192019431421787878254514
y[1] (numeric) = 1.6331567192019431599703823901469
absolute error = 1.77915945646955e-17
relative error = 1.0893990978030280038929441725151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 1.6345227083877692759099402776
y[1] (numeric) = 1.6345227083877692937193544935296
absolute error = 1.78094142159296e-17
relative error = 1.0895788797878571820599623987407e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=8.67
NO POLE
x[1] = 0.525
y[1] (analytic) = 1.6358890630508565654318643485952
y[1] (numeric) = 1.6358890630508565832590318100219
absolute error = 1.78271674614267e-17
relative error = 1.0897540587611648158601162280346e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 1.6372557818248504615201553116912
y[1] (numeric) = 1.6372557818248504793650095951245
absolute error = 1.78448542834333e-17
relative error = 1.0899246459550629937655260051098e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 1.6386228633430323040741444483139
y[1] (numeric) = 1.6386228633430323219366191125766
absolute error = 1.78624746642627e-17
relative error = 1.0900906525752129041284083524709e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 1.6399903062383206888354452555126
y[1] (numeric) = 1.6399903062383207067154738418069
absolute error = 1.78800285862943e-17
relative error = 1.0902520898008285976748833354965e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 1.6413581091432728344692437808992
y[1] (numeric) = 1.6413581091432728523667598128737
absolute error = 1.78975160319745e-17
relative error = 1.0904089687847784692740197291132e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 1.6427262706900859500069660039019
y[1] (numeric) = 1.6427262706900859679219029877174
absolute error = 1.79149369838155e-17
relative error = 1.0905613006535586533218687137487e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 1.6440947895105986026489548207758
y[1] (numeric) = 1.6440947895105986205812462451725
absolute error = 1.79322914243967e-17
relative error = 1.0907090965074249495883566186996e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 1.6454636642362920859257888308122
y[1] (numeric) = 1.6454636642362921038753681671756
absolute error = 1.79495793363634e-17
relative error = 1.0908523674203602582044972251146e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 1.6468328934982917882168747625375
y[1] (numeric) = 1.6468328934982918061836754649654
absolute error = 1.79668007024279e-17
relative error = 1.0909911244401881652687876565435e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 1.6482024759273685616249450214265
y[1] (numeric) = 1.6482024759273685796089005267952
absolute error = 1.79839555053687e-17
relative error = 1.0911253785885709382312651756363e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 1.6495724101539400912050914847445
y[1] (numeric) = 1.6495724101539401092061352127755
absolute error = 1.80010437280310e-17
relative error = 1.0912551408610865915778861593953e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 1.6509426948080722645469663145997
y[1] (numeric) = 1.6509426948080722825650316679263
absolute error = 1.80180653533266e-17
relative error = 1.0913804222272694770643481243442e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 1.6523133285194805417087802071188
y[1] (numeric) = 1.6523133285194805597438005713528
absolute error = 1.80350203642340e-17
relative error = 1.0915012336306630263274988885471e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 1.6536843099175313255017281438619
y[1] (numeric) = 1.65368430991753134355363688766
absolute error = 1.80519087437981e-17
relative error = 1.0916175859888482919545288654207e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.539
y[1] (analytic) = 1.655055637631243332123472361165
y[1] (numeric) = 1.6550556376312433501922028362953
absolute error = 1.80687304751303e-17
relative error = 1.0917294901934967632950923936213e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 1.6564273102892889621393119040404
y[1] (numeric) = 1.6564273102892889802247974454497
absolute error = 1.80854855414093e-17
relative error = 1.0918369571104654268542391105178e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 1.6577993265199956718096677835831
y[1] (numeric) = 1.6577993265199956899118417094627
absolute error = 1.81021739258796e-17
relative error = 1.0919399975797528629123531181781e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=8.94
NO POLE
x[1] = 0.542
y[1] (analytic) = 1.6591716849513473447625124105066
y[1] (numeric) = 1.6591716849513473628813080223597
absolute error = 1.81187956118531e-17
relative error = 1.0920386224156426455664888882848e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 1.6605443842109856640093716324991
y[1] (numeric) = 1.6605443842109856821447222152071
absolute error = 1.81353505827080e-17
relative error = 1.0921328424066836788979097943404e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 1.6619174229262114843035273595079
y[1] (numeric) = 1.6619174229262115024553661813973
absolute error = 1.81518388218894e-17
relative error = 1.0922226683157731655269262188656e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 1.6632907997239862048390484188659
y[1] (numeric) = 1.6632907997239862230073087317749
absolute error = 1.81682603129090e-17
relative error = 1.0923081108801852972247122702308e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 1.6646645132309331422892769413433
y[1] (numeric) = 1.6646645132309331604738919806886
absolute error = 1.81846150393453e-17
relative error = 1.0923891808116300812092587416279e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 1.6660385620733389041833972397522
y[1] (numeric) = 1.6660385620733389223843002245959
absolute error = 1.82009029848437e-17
relative error = 1.0924658887963061138664915259217e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 1.6674129448771547626197138036502
y[1] (numeric) = 1.6674129448771547808368379367664
absolute error = 1.82171241331162e-17
relative error = 1.0925382454949293440413262422603e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 1.6687876602679980283142646969791
y[1] (numeric) = 1.6687876602679980465475431649206
absolute error = 1.82332784679415e-17
relative error = 1.0926062615427859025411978206931e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 1.6701627068711534249833963101395
y[1] (numeric) = 1.670162706871153443232762283305
absolute error = 1.82493659731655e-17
relative error = 1.0926699475498088584523548855921e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 1.6715380833115744640589250840425
y[1] (numeric) = 1.671538083311574482324311716743
absolute error = 1.82653866327005e-17
relative error = 1.0927293141005770609161980388366e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 1.6729137882138848197345114910892
y[1] (numeric) = 1.6729137882138848380158519216151
absolute error = 1.82813404305259e-17
relative error = 1.0927843717544038866147583774486e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 1.6742898202023797043418712268203
y[1] (numeric) = 1.6742898202023797226390985775083
absolute error = 1.82972273506880e-17
relative error = 1.0928351310453720308020671778758e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 1.6756661779010272440554482361388
y[1] (numeric) = 1.6756661779010272623684956134386
absolute error = 1.83130473772998e-17
relative error = 1.0928816024823683611514524947010e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 1.6770428599334698549241738695469
y[1] (numeric) = 1.6770428599334698732529743640882
absolute error = 1.83288004945413e-17
relative error = 1.0929237965491486477222398129598e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 1.6784198649230256192289361377532
y[1] (numeric) = 1.6784198649230256375734228244126
absolute error = 1.83444866866594e-17
relative error = 1.0929617237043783748881088920262e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 1.6797971914926896621643827072954
y[1] (numeric) = 1.6797971914926896805244886452632
absolute error = 1.83601059379678e-17
relative error = 1.0929953943816735840671298044109e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
memory used=129.7MB, alloc=4.4MB, time=9.22
y[1] (analytic) = 1.68117483826513552884368095549
y[1] (numeric) = 1.6811748382651355472193391883374
absolute error = 1.83756582328474e-17
relative error = 1.0930248189896714874446061629494e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 1.6825528038627165616248580800645
y[1] (numeric) = 1.6825528038627165800160016358103
absolute error = 1.83911435557458e-17
relative error = 1.0930500079120474743817561386061e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 1.6839310869074672777573439372457
y[1] (numeric) = 1.6839310869074672961639058284234
absolute error = 1.84065618911777e-17
relative error = 1.0930709715075857095320799476448e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.561
y[1] (analytic) = 1.6853096860211047473473389618768
y[1] (numeric) = 1.6853096860211047657692521856016
absolute error = 1.84219132237248e-17
relative error = 1.0930877201102199443708620814373e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 1.68668859982502997164062920431
y[1] (numeric) = 1.6866885998250299900778267423457
absolute error = 1.84371975380357e-17
relative error = 1.0931002640290743556319778555876e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.563
y[1] (analytic) = 1.6880678269403292616214702013744
y[1] (numeric) = 1.6880678269403292800738850202005
absolute error = 1.84524148188261e-17
relative error = 1.0931086135485221815665652756652e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 1.68944736598777561692616108265
y[1] (numeric) = 1.6894473659877756353937261335289
absolute error = 1.84675650508789e-17
relative error = 1.0931127789282383771833513158264e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 1.6908272155878301050699299985895
y[1] (numeric) = 1.6908272155878301235525782176331
absolute error = 1.84826482190436e-17
relative error = 1.0931127704032108362536607901094e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.566
y[1] (analytic) = 1.6922073743606432409857516437158
y[1] (numeric) = 1.692207374360643259483415951953
absolute error = 1.84976643082372e-17
relative error = 1.0931085981838404235683162060147e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 1.6935878409260563668737173361942
y[1] (numeric) = 1.6935878409260563853863306396378
absolute error = 1.85126133034436e-17
relative error = 1.0931002724559521713740991307921e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 1.6949686139036030323595778045237
y[1] (numeric) = 1.6949686139036030508870729942374
absolute error = 1.85274951897137e-17
relative error = 1.0930878033808479415363639166134e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 1.6963496919125103749610785229188
y[1] (numeric) = 1.6963496919125103935033884750845
absolute error = 1.85423099521657e-17
relative error = 1.0930712010953708414530590369902e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 1.6977310735717005008607071291628
y[1] (numeric) = 1.6977310735717005194177647051477
absolute error = 1.85570575759849e-17
relative error = 1.0930504757119400945131017549661e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 1.6991127574997918659834721523
y[1] (numeric) = 1.6991127574997918845552101987235
absolute error = 1.85717380464235e-17
relative error = 1.0930256373185859595996018103207e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 1.7004947423151006573783319725013
y[1] (numeric) = 1.7004947423151006759646833213026
absolute error = 1.85863513488013e-17
relative error = 1.0929966959790376244425108551046e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 1.701877026635642174901892631793
y[1] (numeric) = 1.7018770266356421935027901002978
absolute error = 1.86008974685048e-17
relative error = 1.0929636617327168743198483988153e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 1.7032596090791322132029928120624
y[1] (numeric) = 1.7032596090791322318183692030502
absolute error = 1.86153763909878e-17
relative error = 1.0929265445948200745820142714936e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=9.50
NO POLE
x[1] = 0.575
y[1] (analytic) = 1.7046424882629884440067939958724
y[1] (numeric) = 1.7046424882629884626365820976439
absolute error = 1.86297881017715e-17
relative error = 1.0928853545563706383032538356849e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 1.7060256628043317986969935261099
y[1] (numeric) = 1.7060256628043318173411261125542
absolute error = 1.86441325864443e-17
relative error = 1.0928401015842538688638623545457e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 1.7074091313199878511947779823704
y[1] (numeric) = 1.7074091313199878698531878130319
absolute error = 1.86584098306615e-17
relative error = 1.0927907956212459903400421133654e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 1.708792892426488201133133995239
y[1] (numeric) = 1.708792892426488219805753815385
absolute error = 1.86726198201460e-17
relative error = 1.0927374465861017708954043110080e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 1.7101769447400718573251333242747
y[1] (numeric) = 1.7101769447400718760118958649625
absolute error = 1.86867625406878e-17
relative error = 1.0926800643735717649207791568226e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 1.7115612868766866215248087315265
y[1] (numeric) = 1.7115612868766866402256467096707
absolute error = 1.87008379781442e-17
relative error = 1.0926186588544605812928602369738e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 1.7129459174519904724792368898212
y[1] (numeric) = 1.712945917451990491194083008261
absolute error = 1.87148461184398e-17
relative error = 1.0925532398756734039372904148698e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.582
y[1] (analytic) = 1.7143308350813529502704442738558
y[1] (numeric) = 1.714330835081352968999231221422
absolute error = 1.87287869475662e-17
relative error = 1.0924838172602449971934163799238e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 1.7157160383798565409457516923026
y[1] (numeric) = 1.7157160383798565596884121438854
absolute error = 1.87426604515828e-17
relative error = 1.0924104008074328928410508626315e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 1.7171015259622980614351728306998
y[1] (numeric) = 1.7171015259622980801916394473159
absolute error = 1.87564666166161e-17
relative error = 1.0923330002927229776798705029188e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 1.7184872964431900447544818878432
y[1] (numeric) = 1.718487296443190063524687316703
absolute error = 1.87702054288598e-17
relative error = 1.0922516254678818139053230859181e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 1.7198733484367621254925651027264
y[1] (numeric) = 1.7198733484367621442764419773017
absolute error = 1.87838768745753e-17
relative error = 1.0921662860610321705553069077543e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.587
y[1] (analytic) = 1.7212596805569624255816706847957
y[1] (numeric) = 1.7212596805569624443791516248865
absolute error = 1.87974809400908e-17
relative error = 1.0920769917766470598661466487796e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 1.7226462914174589403491713773808
y[1] (numeric) = 1.7226462914174589591601889891835
absolute error = 1.88110176118027e-17
relative error = 1.0919837522956775227446470750313e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 1.7240331796316409248494536026609
y[1] (numeric) = 1.7240331796316409436739404788348
absolute error = 1.88244868761739e-17
relative error = 1.0918865772755001906485923089377e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 1.7254203438126202804745468563851
y[1] (numeric) = 1.7254203438126202993124355761205
absolute error = 1.88378887197354e-17
relative error = 1.0917854763500565612552188933640e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 1.7268077825732329418421067418394
y[1] (numeric) = 1.7268077825732329606933298709247
absolute error = 1.88512231290853e-17
relative error = 1.0916804591298412383813656750662e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=9.78
NO POLE
x[1] = 0.592
y[1] (analytic) = 1.7281954945260402639593647551891
y[1] (numeric) = 1.7281954945260402828238548460783
absolute error = 1.88644900908892e-17
relative error = 1.0915715352019714394023445632580e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 1.7295834782833304096616576583645
y[1] (numeric) = 1.7295834782833304285393472502446
absolute error = 1.88776895918801e-17
relative error = 1.0914587141302274601149355784200e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 1.7309717324571197373241490010745
y[1] (numeric) = 1.7309717324571197562149706199329
absolute error = 1.88908216188584e-17
relative error = 1.0913420054550989219363838776984e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 1.7323602556591541888453550803433
y[1] (numeric) = 1.7323602556591542077492412390356
absolute error = 1.89038861586923e-17
relative error = 1.0912214186938540857427920034159e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 1.7337490465009106779010873541604
y[1] (numeric) = 1.7337490465009106968179705524776
absolute error = 1.89168831983172e-17
relative error = 1.0910969633405513524575381739868e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 1.7351381035935984784674230554155
y[1] (numeric) = 1.7351381035935984973972357801514
absolute error = 1.89298127247359e-17
relative error = 1.0909686488660970117474415745747e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 1.7365274255481606136113154832642
y[1] (numeric) = 1.7365274255481606325539902082833
absolute error = 1.89426747250191e-17
relative error = 1.0908364847183201861538093713722e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 1.7379170109752752445474551814312
y[1] (numeric) = 1.7379170109752752635029243677359
absolute error = 1.89554691863047e-17
relative error = 1.0907004803219785634792512495164e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 1.7393068584853570599599929467033
y[1] (numeric) = 1.7393068584853570789281890425014
absolute error = 1.89681960957981e-17
relative error = 1.0905606450788217909714409377216e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 1.7406969666885586655877353460065
y[1] (numeric) = 1.7406969666885586845685907867791
absolute error = 1.89808554407726e-17
relative error = 1.0904169883676605049907156255483e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 1.7420873341947719740714231569872
y[1] (numeric) = 1.742087334194771993064870365556
absolute error = 1.89934472085688e-17
relative error = 1.0902695195443778213064256513845e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 1.7434779596136295950617028849348
y[1] (numeric) = 1.7434779596136296140676742715297
absolute error = 1.90059713865949e-17
relative error = 1.0901182479419925841150149385390e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 1.7448688415545062255864012481898
y[1] (numeric) = 1.7448688415545062446048292105164
absolute error = 1.90184279623266e-17
relative error = 1.0899631828706995802432510408580e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 1.7462599786265200406757122648785
y[1] (numeric) = 1.7462599786265200597065291881862
absolute error = 1.90308169233077e-17
relative error = 1.0898043336179498380355794698357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 1.7476513694385340842439063159053
y[1] (numeric) = 1.7476513694385341032870445730541
absolute error = 1.90431382571488e-17
relative error = 1.0896417094484220157945423788066e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 1.7490430125991576602261703026051
y[1] (numeric) = 1.7490430125991576792815622541339
absolute error = 1.90553919515288e-17
relative error = 1.0894753196041542039743822367199e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 1.7504349067167477239691877623366
y[1] (numeric) = 1.7504349067167477430367657565306
absolute error = 1.90675779941940e-17
relative error = 1.0893051733045381787685343561038e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=10.05
NO POLE
x[1] = 0.609
y[1] (analytic) = 1.7518270503994102738740675515486
y[1] (numeric) = 1.7518270503994102929537639245069
absolute error = 1.90796963729583e-17
relative error = 1.0891312797463766627371611914386e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 1.7532194422550017432902294535079
y[1] (numeric) = 1.7532194422550017623819765292113
absolute error = 1.90917470757034e-17
relative error = 1.0889536481039404999772071345493e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 1.7546120808911303926588548169201
y[1] (numeric) = 1.7546120808911304117625849072987
absolute error = 1.91037300903786e-17
relative error = 1.0887722875290029485595471478307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 1.7560049649151577019045100821067
y[1] (numeric) = 1.7560049649151577210201554871075
absolute error = 1.91156454050008e-17
relative error = 1.0885872071508853850718082974410e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.613
y[1] (analytic) = 1.7573980929341997630735508032326
y[1] (numeric) = 1.7573980929341997822010438108873
absolute error = 1.91274930076547e-17
relative error = 1.0883984160765143573239365505026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 1.7587914635551286732179135282956
y[1] (numeric) = 1.7587914635551286923571864147883
absolute error = 1.91392728864927e-17
relative error = 1.0882059233904614930237347065415e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 1.7601850753845739275229026532015
y[1] (numeric) = 1.7601850753845739466738876829365
absolute error = 1.91509850297350e-17
relative error = 1.0880097381549947648627623716341e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 1.7615789270289238126775791222552
y[1] (numeric) = 1.7615789270289238318402085479246
absolute error = 1.91626294256694e-17
relative error = 1.0878098694101126648572585325252e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 1.7629730170943268004863576047939
y[1] (numeric) = 1.7629730170943268196605636674454
absolute error = 1.91742060626515e-17
relative error = 1.0876063261736010875447915929044e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 1.7643673441866929417204185364825
y[1] (numeric) = 1.7643673441866929609061334655871
absolute error = 1.91857149291046e-17
relative error = 1.0873991174410731215283358724342e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 1.7657619069116952602075411739744
y[1] (numeric) = 1.7657619069116952794046971874943
absolute error = 1.91971560135199e-17
relative error = 1.0871882521860258228544428078041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 1.7671567038747711471589635732215
y[1] (numeric) = 1.7671567038747711663674928776779
absolute error = 1.92085293044564e-17
relative error = 1.0869737393598799229343101240671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 1.7685517336811237557318751646895
y[1] (numeric) = 1.7685517336811237749517099552302
absolute error = 1.92198347905407e-17
relative error = 1.0867555878920138732590807120416e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 1.7699469949357233958261473631013
y[1] (numeric) = 1.7699469949357234150572198235687
absolute error = 1.92310724604674e-17
relative error = 1.0865338066898318067508635405445e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 1.7713424862433089291139074150959
y[1] (numeric) = 1.7713424862433089483561497180946
absolute error = 1.92422423029987e-17
relative error = 1.0863084046387861920113735235007e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 1.7727382062083891643005604553429
y[1] (numeric) = 1.7727382062083891835539047623078
absolute error = 1.92533443069649e-17
relative error = 1.0860793906024513263230776194930e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=144.9MB, alloc=4.4MB, time=10.32
x[1] = 0.625
y[1] (analytic) = 1.774134153435244252615864510209
y[1] (numeric) = 1.774134153435244271880242971473
absolute error = 1.92643784612640e-17
relative error = 1.0858467734225459288852076035598e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 1.7755303265279270835336629580165
y[1] (numeric) = 1.7755303265279271028090077128782
absolute error = 1.92753447548617e-17
relative error = 1.0856105619189783313184439202190e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 1.7769267240902646807188787262776
y[1] (numeric) = 1.7769267240902647000051219030694
absolute error = 1.92862431767918e-17
relative error = 1.0853707648899141405707209746883e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 1.7783233447258595982003742790276
y[1] (numeric) = 1.7783233447258596174974479951835
absolute error = 1.92970737161559e-17
relative error = 1.0851273911118043940446441504043e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 1.7797201870380913167682812215125
y[1] (numeric) = 1.7797201870380913360761175836358
absolute error = 1.93078363621233e-17
relative error = 1.0848804493394249930753281355666e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 1.7811172496301176405944031250175
y[1] (numeric) = 1.7811172496301176599129342289491
absolute error = 1.93185311039316e-17
relative error = 1.0846299483059554245299557700198e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 1.782514531104876094074294951552
y[1] (numeric) = 1.7825145311048761134034528824378
absolute error = 1.93291579308858e-17
relative error = 1.0843758967229731331953913384464e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
y[1] (analytic) = 1.7839120300650853188896222364242
y[1] (numeric) = 1.7839120300650853382293390687836
absolute error = 1.93397168323594e-17
relative error = 1.0841183032805602048195776483094e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 1.7853097451132464712894029664678
y[1] (numeric) = 1.785309745113246490639610764261
absolute error = 1.93502077977932e-17
relative error = 1.0838571766472808892683215289319e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 1.7867076748516446195887348727894
y[1] (numeric) = 1.7867076748516446389493656894858
absolute error = 1.93606308166964e-17
relative error = 1.0835925254702881271985066564691e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 1.7881058178823501418836106394315
y[1] (numeric) = 1.7881058178823501612545965180774
absolute error = 1.93709858786459e-17
relative error = 1.0833243583753290808077254443673e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 1.789504172807220123980423313248
y[1] (numeric) = 1.7895041728072201433616962865347
absolute error = 1.93812729732867e-17
relative error = 1.0830526839668122764069082960953e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 1.7909027382278997575387639856055
y[1] (numeric) = 1.7909027382278997769302560759371
absolute error = 1.93914920903316e-17
relative error = 1.0827775108278355135408307641833e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 1.7923015127458237384261136032289
y[1] (numeric) = 1.7923015127458237578277568227905
absolute error = 1.94016432195616e-17
relative error = 1.0824988475202528661932443274213e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 1.7937004949622176652830305536155
y[1] (numeric) = 1.7937004949622176846947569044412
absolute error = 1.94117263508257e-17
relative error = 1.0822167025847080862255938744815e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 1.7950996834780994382974354599476
y[1] (numeric) = 1.795099683478099457719176933988
absolute error = 1.94217414740404e-17
relative error = 1.0819310845406513038778022299389e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 1.796499076894280658186594411333
y[1] (numeric) = 1.7964990768942806776182829905239
absolute error = 1.94316885791909e-17
relative error = 1.0816420018864504434795041906861e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=10.60
NO POLE
x[1] = 0.642
y[1] (analytic) = 1.7978986738113680253854016465109
y[1] (numeric) = 1.7978986738113680448269693028407
absolute error = 1.94415676563298e-17
relative error = 1.0813494630993632316750174343257e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 1.7992984728297647394395625028518
y[1] (numeric) = 1.7992984728297647588909411984302
absolute error = 1.94513786955784e-17
relative error = 1.0810534766356540003993197346292e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 1.8006984725496718986022772375908
y[1] (numeric) = 1.8006984725496719180633989247161
absolute error = 1.94611216871253e-17
relative error = 1.0807540509305601659348199652817e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 1.8020986715710898996330261247216
y[1] (numeric) = 1.8020986715710899191038227459493
absolute error = 1.94707966212277e-17
relative error = 1.0804511943984088515165602109730e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 1.803499068493819837797056028887
y[1] (numeric) = 1.8034990684938198572774595170977
absolute error = 1.94804034882107e-17
relative error = 1.0801449154326222324744487684757e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 1.804899661917464907064168456894
y[1] (numeric) = 1.8048996619174649265541107353613
absolute error = 1.94899422784673e-17
relative error = 1.0798352224057618004233655144937e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 1.806300450441431800505408888182
y[1] (numeric) = 1.8063004504414318200048218706408
absolute error = 1.94994129824588e-17
relative error = 1.0795221236695947262057694324600e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 1.8077014326649321108862569876724
y[1] (numeric) = 1.807701432664932130395072578387
absolute error = 1.95088155907146e-17
relative error = 1.0792056275551268822524458852727e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 1.809102607186983731454917107926
y[1] (numeric) = 1.8091026071869837509730672017579
absolute error = 1.95181500938319e-17
relative error = 1.0788857423726303425075199201078e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 1.8105039726064122569243082924329
y[1] (numeric) = 1.8105039726064122764517247749092
absolute error = 1.95274164824763e-17
relative error = 1.0785624764117206225302318594391e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 1.8119055275218523846463527981641
y[1] (numeric) = 1.8119055275218524041829675455454
absolute error = 1.95366147473813e-17
relative error = 1.0782358379413730088804658147876e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 1.813307270531749315977161963211
y[1] (numeric) = 1.8133072705317493355229068425597
absolute error = 1.95457448793487e-17
relative error = 1.0779058352099886024497641248629e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 1.8147092002343601578317180544448
y[1] (numeric) = 1.8147092002343601773865249236933
absolute error = 1.95548068692485e-17
relative error = 1.0775724764454326590426351045453e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 1.8161113152277553244266505406306
y[1] (numeric) = 1.8161113152277553439904512486491
absolute error = 1.95638007080185e-17
relative error = 1.0772357698550563888495287391148e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.656
y[1] (analytic) = 1.8175136141098199392097050483358
y[1] (numeric) = 1.8175136141098199587824314350009
absolute error = 1.95727263866651e-17
relative error = 1.0768957236257848339265452021728e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 1.8189160954782552369745030712827
y[1] (numeric) = 1.8189160954782552565560869675451
absolute error = 1.95815838962624e-17
relative error = 1.0765523459241110309074520962571e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 1.8203187579305799661591903184999
y[1] (numeric) = 1.8203187579305799857495635464528
absolute error = 1.95903732279529e-17
relative error = 1.0762056448961782507151217859682e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=10.87
NO POLE
x[1] = 0.659
y[1] (analytic) = 1.821721600064131791327571402743
y[1] (numeric) = 1.8217216000641318109266657756904
absolute error = 1.95990943729474e-17
relative error = 1.0758556286678180965322485850612e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 1.8231246204760686958313283881661
y[1] (numeric) = 1.8231246204760687154390757106907
absolute error = 1.96077473225246e-17
relative error = 1.0755023053445721226292377239004e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 1.8245278177633703846519205351419
y[1] (numeric) = 1.8245278177633704042682526031737
absolute error = 1.96163320680318e-17
relative error = 1.0751456830117737944043910474509e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 1.8259311905228396874207624004491
y[1] (numeric) = 1.8259311905228397070456110013331
absolute error = 1.96248486008840e-17
relative error = 1.0747857697345425947336538110394e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 1.8273347373511039616162772727633
y[1] (numeric) = 1.8273347373511039812495741853281
absolute error = 1.96332969125648e-17
relative error = 1.0744225735578768116932444519260e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 1.828738456844616495936422746518
y[1] (numeric) = 1.8287384568446165155780997411439
absolute error = 1.96416769946259e-17
relative error = 1.0740561025066694929620299587046e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 1.8301423475996579138452850617248
y[1] (numeric) = 1.830142347599657933495273900412
absolute error = 1.96499888386872e-17
relative error = 1.0736863645857572599451886498612e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.666
y[1] (analytic) = 1.8315464082123375772923386632766
y[1] (numeric) = 1.8315464082123375969505710997134
absolute error = 1.96582324364368e-17
relative error = 1.0733133677799635857275649593284e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 1.8329506372785949906029672605899
y[1] (numeric) = 1.8329506372785950102693750402211
absolute error = 1.96664077796312e-17
relative error = 1.0729371200541529330453750283377e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.668
y[1] (analytic) = 1.8343550333942012045388424971846
y[1] (numeric) = 1.8343550333942012242133573572794
absolute error = 1.96745148600948e-17
relative error = 1.0725576293532466299677467103407e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 1.8357595951547602205267561699361
y[1] (numeric) = 1.835759595154760240209309839657
absolute error = 1.96825536697209e-17
relative error = 1.0721749036023205290533978315881e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 1.8371643211557103950545017692885
y[1] (numeric) = 1.8371643211557104147450259697589
absolute error = 1.96905242004704e-17
relative error = 1.0717889507065771712591564886198e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 1.8385692099923258442324009446607
y[1] (numeric) = 1.8385692099923258639308273890337
absolute error = 1.96984264443730e-17
relative error = 1.0713997785514541977943680417101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 1.8399742602597178485190703336388
y[1] (numeric) = 1.8399742602597178682253307271651
absolute error = 1.97062603935263e-17
relative error = 1.0710073950026182777262905083736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 1.8413794705528362576100240293031
y[1] (numeric) = 1.8413794705528362773240500693994
absolute error = 1.97140260400963e-17
relative error = 1.0706118079060352371388856327977e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 1.8427848394664708954877067972054
y[1] (numeric) = 1.8427848394664709152094301735229
absolute error = 1.97217233763175e-17
relative error = 1.0702130250880183043575520109848e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 1.8441903655952529656315529920803
y[1] (numeric) = 1.8441903655952529853609053865728
absolute error = 1.97293523944925e-17
relative error = 1.0698110543552491649795705330526e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=11.15
NO POLE
x[1] = 0.676
y[1] (analytic) = 1.8455960475336564563866659643483
y[1] (numeric) = 1.8455960475336564761235790513406
absolute error = 1.97369130869923e-17
relative error = 1.0694059034948369907848878331746e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 1.8470018838759995464897125878487
y[1] (numeric) = 1.8470018838759995662341180341049
absolute error = 1.97444054462562e-17
relative error = 1.0689975802743556837408293503945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 1.8484078732164460107506273830248
y[1] (numeric) = 1.8484078732164460305024568478166
absolute error = 1.97518294647918e-17
relative error = 1.0685860924418865008520511359623e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 1.8498140141490066258887205539746
y[1] (numeric) = 1.8498140141490066456479056891497
absolute error = 1.97591851351751e-17
relative error = 1.0681714477260660307137607486377e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.68
y[1] (analytic) = 1.8512203052675405765217841033759
y[1] (numeric) = 1.8512203052675405962882565534264
absolute error = 1.97664724500505e-17
relative error = 1.0677536538361286891078264388488e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 1.8526267451657568613067900362969
y[1] (numeric) = 1.8526267451657568810804814384275
absolute error = 1.97736914021306e-17
relative error = 1.0673327184619383645018604680064e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 1.8540333324372156992307745123115
y[1] (numeric) = 1.8540333324372157190116164965078
absolute error = 1.97808419841963e-17
relative error = 1.0669086492740362387898488332512e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.683
y[1] (analytic) = 1.8554400656753299360505016551511
y[1] (numeric) = 1.8554400656753299558384258442486
absolute error = 1.97879241890975e-17
relative error = 1.0664814539237208656064282843526e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 1.8568469434733664508795005803499
y[1] (numeric) = 1.8568469434733664706744385901014
absolute error = 1.97949380097515e-17
relative error = 1.0660511400430041558798514709058e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.685
y[1] (analytic) = 1.8582539644244475629210690539577
y[1] (numeric) = 1.8582539644244475827229524931025
absolute error = 1.98018834391448e-17
relative error = 1.0656177152447506673306619380324e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 1.8596611271215524383458370494408
y[1] (numeric) = 1.8596611271215524581545975197726
absolute error = 1.98087604703318e-17
relative error = 1.0651811871226497005898476281905e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 1.8610684301575184973124833253188
y[1] (numeric) = 1.8610684301575185171280524217543
absolute error = 1.98155690964355e-17
relative error = 1.0647415632512951224101477959758e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 1.8624758721250428211301980029421
y[1] (numeric) = 1.8624758721250428409525073135894
absolute error = 1.98223093106473e-17
relative error = 1.0642988511862166390105303281926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 1.863883451616683559561483982062
y[1] (numeric) = 1.8638834516166835793904650882889
absolute error = 1.98289811062269e-17
relative error = 1.0638530584639164270663941278177e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 1.8652911672248613382638898915109
y[1] (numeric) = 1.8652911672248613580994743680137
absolute error = 1.98355844765028e-17
relative error = 1.0634041926019378990261936546307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 1.8666990175418606663692671333771
y[1] (numeric) = 1.8666990175418606862113865482483
absolute error = 1.98421194148712e-17
relative error = 1.0629522610988485775166927639631e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.692
y[1] (analytic) = 1.8681070011598313441991434415318
y[1] (numeric) = 1.8681070011598313640477293563293
memory used=160.2MB, alloc=4.4MB, time=11.42
absolute error = 1.98485859147975e-17
relative error = 1.0624972714343623579721939564053e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 1.8695151166707898711148052392565
y[1] (numeric) = 1.8695151166707898909697892090715
absolute error = 1.98549839698150e-17
relative error = 1.0620392310693115792234918873430e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 1.8709233626666208535006809460012
y[1] (numeric) = 1.870923362666620873361994519527
absolute error = 1.98613135735258e-17
relative error = 1.0615781474457369405022433614742e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 1.8723317377390784128796172500113
y[1] (numeric) = 1.8723317377390784327471919696114
absolute error = 1.98675747196001e-17
relative error = 1.0611140279868916884738734366817e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 1.8737402404797875941586402316607
y[1] (numeric) = 1.8737402404797876140324076334376
absolute error = 1.98737674017769e-17
relative error = 1.0606468800973206324192721511687e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 1.8751488694802457740037930918506
y[1] (numeric) = 1.8751488694802457938836847057142
absolute error = 1.98798916138636e-17
relative error = 1.0601767111628802709033267569261e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 1.8765576233318240693426421107517
y[1] (numeric) = 1.8765576233318240892285894604875
absolute error = 1.98859473497358e-17
relative error = 1.0597035285507696146347043986278e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 1.877966500625768745993042334501
y[1] (numeric) = 1.8779665006257687658849769378389
absolute error = 1.98919346033379e-17
relative error = 1.0592273396096035983447798329859e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 1.8793754999532026274167543612068
y[1] (numeric) = 1.8793754999532026473146077298894
absolute error = 1.98978533686826e-17
relative error = 1.0587481516694277602988316459204e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 1.8807846199051265035965034727604
y[1] (numeric) = 1.8807846199051265235002071126113
absolute error = 1.99037036398509e-17
relative error = 1.0582659720417595678193320364376e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 1.8821938590724205400350722355133
y[1] (numeric) = 1.8821938590724205599445576465063
absolute error = 1.99094854109930e-17
relative error = 1.0577808080196775005227981073580e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 1.8836032160458456868750175708468
y[1] (numeric) = 1.8836032160458457067902162471737
absolute error = 1.99151986763269e-17
relative error = 1.0572926668777877535005592606892e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 1.8850126894160450881376031760309
y[1] (numeric) = 1.88501268941604510805844660617
absolute error = 1.99208434301391e-17
relative error = 1.0568015558723026206340575402425e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 1.8864222777735454910795380565594
y[1] (numeric) = 1.8864222777735455110059577233446
absolute error = 1.99264196667852e-17
relative error = 1.0563074822411133506343805483645e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 1.8878319797087586556661118133413
y[1] (numeric) = 1.8878319797087586755980391940302
absolute error = 1.99319273806889e-17
relative error = 1.0558104532037780479557508408348e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 1.8892417938119827641593172117281
y[1] (numeric) = 1.8892417938119827840966837780703
absolute error = 1.99373665663422e-17
relative error = 1.0553104759615732694530948566324e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 1.8906517186734038308195504443729
y[1] (numeric) = 1.8906517186734038507622876626792
absolute error = 1.99427372183063e-17
relative error = 1.0548075576975825379748941864858e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=11.70
NO POLE
x[1] = 0.709
y[1] (analytic) = 1.8920617528830971117194793863404
y[1] (numeric) = 1.8920617528830971316675187175507
absolute error = 1.99480393312103e-17
relative error = 1.0543017055766683078768368254414e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 1.8934718950310285146686700287132
y[1] (numeric) = 1.8934718950310285346219429284655
absolute error = 1.99532728997523e-17
relative error = 1.0537929267455709294880948477937e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 1.8948821437070560092475611661898
y[1] (numeric) = 1.8948821437070560292059990848882
absolute error = 1.99584379186984e-17
relative error = 1.0532812283328964687380944779909e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 1.8962924975009310369493773048126
y[1] (numeric) = 1.8962924975009310569129116876965
absolute error = 1.99635343828839e-17
relative error = 1.0527666174492207183243806581947e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 1.8977029550022999214285696480353
y[1] (numeric) = 1.8977029550022999413971319352475
absolute error = 1.99685622872122e-17
relative error = 1.0522491011870716667266751987557e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 1.8991135148007052788543749128016
y[1] (numeric) = 1.8991135148007052988278965394571
absolute error = 1.99735216266555e-17
relative error = 1.0517286866210069466653172092627e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 1.9005241754855874283680816221979
y[1] (numeric) = 1.9005241754855874483464940184522
absolute error = 1.99784123962543e-17
relative error = 1.0512053808076279179384466470764e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 1.9019349356462858026425934175282
y[1] (numeric) = 1.9019349356462858226258280086461
absolute error = 1.99832345911179e-17
relative error = 1.0506791907856463848292623028976e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 1.9033457938720403585428788303669
y[1] (numeric) = 1.903345793872040378530867036791
absolute error = 1.99879882064241e-17
relative error = 1.0501501235759091042438948526697e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 1.9047567487519929878858968542578
y[1] (numeric) = 1.9047567487519930078785700916771
absolute error = 1.99926732374193e-17
relative error = 1.0496181861814433031393260496228e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 1.9061677988751889282985875562496
y[1] (numeric) = 1.906167798875188948295877235668
absolute error = 1.99972896794184e-17
relative error = 1.0490833855874916191779194641489e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 1.9075789428305781741725168703962
y[1] (numeric) = 1.9075789428305781941743543982014
absolute error = 2.00018375278052e-17
relative error = 1.0485457287615732146558899319253e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 1.9089901792070168877137646186948
y[1] (numeric) = 1.9089901792070169077200813967263
absolute error = 2.00063167780315e-17
relative error = 1.0480052226534766371359662917970e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 1.9104015065932688100866447096893
y[1] (numeric) = 1.9104015065932688300973721353076
absolute error = 2.00107274256183e-17
relative error = 1.0474618741953627523391359818166e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 1.9118129235780066726498463711394
y[1] (numeric) = 1.9118129235780066926649158372943
absolute error = 2.00150694661549e-17
relative error = 1.0469156903017574933003861242939e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 1.9132244287498136082835851807292
y[1] (numeric) = 1.9132244287498136283029280760285
absolute error = 2.00193428952993e-17
relative error = 1.0463666778696127047771929560664e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 1.9146360206971845628063525677838
y[1] (numeric) = 1.9146360206971845828299002765617
absolute error = 2.00235477087779e-17
relative error = 1.0458148437783302725935402067195e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.4MB, time=11.98
NO POLE
x[1] = 0.726
y[1] (analytic) = 1.9160476980085277064798523693599
y[1] (numeric) = 1.9160476980085277265075362717459
absolute error = 2.00276839023860e-17
relative error = 1.0452601948898280129678203152954e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 1.9174594592721658456007129358939
y[1] (numeric) = 1.9174594592721658656324644078813
absolute error = 2.00317514719874e-17
relative error = 1.0447027380485584471998132557526e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 1.918871303076337834177563194811
y[1] (numeric) = 1.9188713030763378542133136083257
absolute error = 2.00357504135147e-17
relative error = 1.0441424800815640862694083344269e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 1.9202832280091999856920609951387
y[1] (numeric) = 1.9202832280092000057317417181073
absolute error = 2.00396807229686e-17
relative error = 1.0435794277984805084157745812439e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 1.9216952326588274849424619722112
y[1] (numeric) = 1.9216952326588275049860043686303
absolute error = 2.00435423964191e-17
relative error = 1.0430135879916384062000189281959e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 1.9231073156132157999683170890175
y[1] (numeric) = 1.9231073156132158200156525190219
absolute error = 2.00473354300044e-17
relative error = 1.0424449674360456974138018813221e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 1.9245194754602820940548869296097
y[1] (numeric) = 1.924519475460282114105946749541
absolute error = 2.00510598199313e-17
relative error = 1.0418735728894477672822708690512e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 1.925931710787866637815860740276
y[1] (numeric) = 1.9259317107878666578705763027517
absolute error = 2.00547155624757e-17
relative error = 1.0412994110923927484547210246665e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 1.9273440201837342213529681358789
y[1] (numeric) = 1.9273440201837342414112707898606
absolute error = 2.00583026539817e-17
relative error = 1.0407224887682239851926628229554e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 1.9287564022355755664910713118613
y[1] (numeric) = 1.9287564022355755865528924027236
absolute error = 2.00618210908623e-17
relative error = 1.0401428126231555952002921105206e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 1.9301688555310087390873255269487
y[1] (numeric) = 1.9301688555310087591525963965478
absolute error = 2.00652708695991e-17
relative error = 1.0395603893462959998119408926140e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 1.9315813786575805614129955475034
y[1] (numeric) = 1.9315813786575805814816475342456
absolute error = 2.00686519867422e-17
relative error = 1.0389752256096818137006245893576e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 1.9329939702027680246065156718319
y[1] (numeric) = 1.9329939702027680446784801107424
absolute error = 2.00719644389105e-17
relative error = 1.0383873280683323873540828049949e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 1.934406628753979701196380881504
y[1] (numeric) = 1.9344066287539797212715891042955
absolute error = 2.00752082227915e-17
relative error = 1.0377967033602783704367188445932e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 1.9358193528985571576924565969094
y[1] (numeric) = 1.9358193528985571777708399320509
absolute error = 2.00783833351415e-17
relative error = 1.0372033581066109202686865591995e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 1.93723214122377636724429444586
y[1] (numeric) = 1.9372321412237763873257842186455
absolute error = 2.00814897727855e-17
relative error = 1.0366072989115153155982355975935e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 1.9386449923168491223650413870404
y[1] (numeric) = 1.9386449923168491424495689196572
absolute error = 2.00845275326168e-17
relative error = 1.0360085323622890548071599358790e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=12.25
NO POLE
x[1] = 0.743
y[1] (analytic) = 1.9400579047649244477195294645134
y[1] (numeric) = 1.9400579047649244678070260761113
absolute error = 2.00874966115979e-17
relative error = 1.0354070650294269890088118888701e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 1.9414708771550900129751334053113
y[1] (numeric) = 1.9414708771550900330655304120709
absolute error = 2.00903970067596e-17
relative error = 1.0348029034666134753844454373548e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 1.9428839080743735457139832093709
y[1] (numeric) = 1.9428839080743735658072119245723
absolute error = 2.00932287152014e-17
relative error = 1.0341960542107815803088803897529e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 1.9442969961097442444051188197175
y[1] (numeric) = 1.9442969961097442645011105538092
absolute error = 2.00959917340917e-17
relative error = 1.0335865237821618420688097773340e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 1.9457101398481141914351739008624
y[1] (numeric) = 1.94571013984811421153385996153
absolute error = 2.00986860606676e-17
relative error = 1.0329743186843103668155148905779e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 1.9471233378763397661961756948473
y[1] (numeric) = 1.9471233378763397862974873870818
absolute error = 2.01013116922345e-17
relative error = 1.0323594454041266339072870239411e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 1.9485365887812230582290478672513
y[1] (numeric) = 1.9485365887812230783329164934183
absolute error = 2.01038686261670e-17
relative error = 1.0317419104119380433439956724788e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 1.9499498911495132804214031997798
y[1] (numeric) = 1.9499498911495133005277600596879
absolute error = 2.01063568599081e-17
relative error = 1.0311217201614970161840402180681e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.751
y[1] (analytic) = 1.9513632435679081822582129317562
y[1] (numeric) = 1.9513632435679082023669893227257
absolute error = 2.01087763909695e-17
relative error = 1.0304988810900345803126497376172e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 1.9527766446230554631239394999668
y[1] (numeric) = 1.9527766446230554832350667168987
absolute error = 2.01111272169319e-17
relative error = 1.0298733996183138249587675129595e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 1.9541900929015541856547193748448
y[1] (numeric) = 1.9541900929015542057681287102889
absolute error = 2.01134093354441e-17
relative error = 1.0292452821506218177119558705642e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 1.9556035869899561891391826409251
y[1] (numeric) = 1.9556035869899562092548053851494
absolute error = 2.01156227442243e-17
relative error = 1.0286145350748741543594742953238e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 1.9570171254747675029664959208726
y[1] (numeric) = 1.9570171254747675230842633619314
absolute error = 2.01177674410588e-17
relative error = 1.0279811647625863004694334887794e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 1.9584307069424497601202151951542
y[1] (numeric) = 1.9584307069424497802400586189574
absolute error = 2.01198434238032e-17
relative error = 1.0273451775689728099266544541331e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 1.9598443299794216107165350236238
y[1] (numeric) = 1.9598443299794216308383857140051
absolute error = 2.01218506903813e-17
relative error = 1.0267065798329288569973804610422e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 1.961257993172060135585520630885
y[1] (numeric) = 1.961257993172060155709309869671
absolute error = 2.01237892387860e-17
relative error = 1.0260653778771139223409937775217e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 1.9626716951067022598939092743208
y[1] (numeric) = 1.9626716951067022800195683413993
absolute error = 2.01256590670785e-17
relative error = 1.0254215780079485990052825956000e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=12.52
NO POLE
x[1] = 0.76
y[1] (analytic) = 1.9640854343696461668080672721027
y[1] (numeric) = 1.9640854343696461869355274454921
absolute error = 2.01274601733894e-17
relative error = 1.0247751865157082471721269626665e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 1.9654992095471527111956890283452
y[1] (numeric) = 1.9654992095471527313248815842624
absolute error = 2.01291925559172e-17
relative error = 1.0241262096744840601815990637070e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 1.9669130192254468333648243538186
y[1] (numeric) = 1.9669130192254468534956805667483
absolute error = 2.01308562129297e-17
relative error = 1.0234746537422918345555168794866e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 1.9683268619907189728388203433154
y[1] (numeric) = 1.9683268619907189929712714860786
absolute error = 2.01324511427632e-17
relative error = 1.0228205249610685976977617006516e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 1.9697407364291264821657640348435
y[1] (numeric) = 1.9697407364291265022997413786663
absolute error = 2.01339773438228e-17
relative error = 1.0221638295567251910787699212477e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 1.9711546411267950407610120413229
y[1] (numeric) = 1.9711546411267950608964468559051
absolute error = 2.01354348145822e-17
relative error = 1.0215045737391733568889389250939e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 1.9725685746698200687813933123724
y[1] (numeric) = 1.9725685746698200889182168659565
absolute error = 2.01368235535841e-17
relative error = 1.0208427637023832205702989319218e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 1.9739825356442681410296711521034
y[1] (numeric) = 1.9739825356442681611678147115429
absolute error = 2.01381435594395e-17
relative error = 1.0201784056243848961357521484111e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 1.9753965226361784008878505885746
y[1] (numeric) = 1.9753965226361784210272454194033
absolute error = 2.01393948308287e-17
relative error = 1.0195115056673562375735399245505e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 1.9768105342315639742779171617202
y[1] (numeric) = 1.9768105342315639944184945282204
absolute error = 2.01405773665002e-17
relative error = 1.0188420699776040757957870194559e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
y[1] (analytic) = 1.9782245690164133836485931691279
y[1] (numeric) = 1.9782245690164134037902843343995
absolute error = 2.01416911652716e-17
relative error = 1.0181701046856467302586950181106e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 1.9796386255766919619866973830316
y[1] (numeric) = 1.9796386255766919821294336090607
absolute error = 2.01427362260291e-17
relative error = 1.0174956159062255400023707558075e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 1.9810527024983432668516942272738
y[1] (numeric) = 1.9810527024983432869954067750014
absolute error = 2.01437125477276e-17
relative error = 1.0168186097383467248249887032090e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 1.9824667983672904944320183798085
y[1] (numeric) = 1.9824667983672905145766385091991
absolute error = 2.01446201293906e-17
relative error = 1.0161390922653130710288802621231e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 1.9838809117694378936217607445362
y[1] (numeric) = 1.983880911769437913767219714647
absolute error = 2.01454589701108e-17
relative error = 1.0154570695547908577756540199537e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 1.9852950412906721801163017159054
y[1] (numeric) = 1.9852950412906722002625307849545
absolute error = 2.01462290690491e-17
relative error = 1.0147725476587959961815288103912e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=179.2MB, alloc=4.4MB, time=12.80
x[1] = 0.776
y[1] (analytic) = 1.9867091855168639505254776407612
y[1] (numeric) = 1.9867091855168639706724080661969
absolute error = 2.01469304254357e-17
relative error = 1.0140855326137860209482574368578e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 1.9881233430338690965028663643972
y[1] (numeric) = 1.9881233430338691166504294029662
absolute error = 2.01475630385690e-17
relative error = 1.0133960304406411227622632596339e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 1.9895375124275302188897777316379
y[1] (numeric) = 1.9895375124275302390379046394545
absolute error = 2.01481269078166e-17
relative error = 1.0127040471447509038239440134987e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 1.9909516922836780418725348990842
y[1] (numeric) = 1.9909516922836780620211569316986
absolute error = 2.01486220326144e-17
relative error = 1.0120095887160054215503357337646e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 1.9923658811881328271516323013533
y[1] (numeric) = 1.9923658811881328473006807138208
absolute error = 2.01490484124675e-17
relative error = 1.0113126611288767045130822274158e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 1.9937800777267057881213561022777
y[1] (numeric) = 1.993780077726705808270762149227
absolute error = 2.01494060469493e-17
relative error = 1.0106132703424097295209947171574e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 1.9951942804852005040584529515565
y[1] (numeric) = 1.9951942804852005242081478872588
absolute error = 2.01496949357023e-17
relative error = 1.0099114223002987302296726278194e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 1.9966084880494143343184328583116
y[1] (numeric) = 1.9966084880494143544683479367492
absolute error = 2.01499150784376e-17
relative error = 1.0092071229308981590540793246719e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 1.9980226990051398325380919853615
y[1] (numeric) = 1.9980226990051398526881584602965
absolute error = 2.01500664749350e-17
relative error = 1.0085003781472637198210932950494e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
y[1] (analytic) = 1.9994369119381661608428411618081
y[1] (numeric) = 1.9994369119381661809929902868512
absolute error = 2.01501491250431e-17
relative error = 1.0077911938471933134864264400021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 2.000851125434280504057425906727
y[1] (numeric) = 2.0008511254342805242075889354064
absolute error = 2.01501630286794e-17
relative error = 1.0070795759132678970038049680528e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 2.0022653380792694839186237533582
y[1] (numeric) = 2.002265338079269504068731939188
absolute error = 2.01501081858298e-17
relative error = 1.0063655302128622893768209684487e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 2.0036795484589205732885046612169
y[1] (numeric) = 2.0036795484589205934384892577662
absolute error = 2.01499845965493e-17
relative error = 1.0056490625982159077592079333464e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 2.0050937551590235103668403029842
y[1] (numeric) = 2.0050937551590235305166325639457
absolute error = 2.01497922609615e-17
relative error = 1.0049301789064434422303213003085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 2.0065079567653717129012480138842
y[1] (numeric) = 2.0065079567653717330507791931427
absolute error = 2.01495311792585e-17
relative error = 1.0042088849595655057586250781787e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 2.0079221518637636923936551935216
y[1] (numeric) = 2.0079221518637637125428565452231
absolute error = 2.01492013517015e-17
relative error = 1.0034851865645741013545138795041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 2.0093363390400044683016699538344
y[1] (numeric) = 2.0093363390400044884504727324549
absolute error = 2.01488027786205e-17
relative error = 1.0027590895134531062643304145212e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.4MB, time=13.08
NO POLE
x[1] = 0.793
y[1] (analytic) = 2.0107505168799069822334438119084
y[1] (numeric) = 2.0107505168799070023817792723222
absolute error = 2.01483354604138e-17
relative error = 1.0020305995831888072061487094501e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 2.0121646839692935121346122329074
y[1] (numeric) = 2.0121646839692935322824116304563
absolute error = 2.01477993975489e-17
relative error = 1.0012997225358500516151903686426e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 2.0135788388939970864658988362986
y[1] (numeric) = 2.0135788388939971066130934268604
absolute error = 2.01471945905618e-17
relative error = 1.0005664641185886838678105967050e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 2.0149929802398628983699690878851
y[1] (numeric) = 2.0149929802398629185164901279426
absolute error = 2.01465210400575e-17
relative error = 9.9983083006369961607571902570525e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.797
y[1] (analytic) = 2.016407106592749719826119310911
y[1] (numeric) = 2.0164071065927497399718980576202
absolute error = 2.01457787467092e-17
relative error = 9.9909282608861625746308343314551e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 2.0178212165385313157913868616656
y[1] (numeric) = 2.017821216538531335936354572925
absolute error = 2.01449677112594e-17
relative error = 9.9835245789600020600918384700300e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 2.0192353086630978583266673285979
y[1] (numeric) = 2.019235308663097878470755263117
absolute error = 2.01440879345191e-17
relative error = 9.9760973117373654988250282817004e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 2.0206493815523573407064246289391
y[1] (numeric) = 2.0206493815523573608495640463072
absolute error = 2.01431394173681e-17
relative error = 9.9686465159498370786413949376571e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 2.0220634337922369915105798932418
y[1] (numeric) = 2.0220634337922370116527020539967
absolute error = 2.01421221607549e-17
relative error = 9.9611722481820335980437000558652e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 2.0234774639686846886971650460656
y[1] (numeric) = 2.0234774639686847088382012117624
absolute error = 2.01410361656968e-17
relative error = 9.9536745648720021611301113068386e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 2.024891470667670373654327010272
y[1] (numeric) = 2.0248914706676703937942084435516
absolute error = 2.01398814332796e-17
relative error = 9.9461535223114194665134491601533e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 2.0263054524751874652302684830429
y[1] (numeric) = 2.0263054524751874853689264477012
absolute error = 2.01386579646583e-17
relative error = 9.9386091766462845688652701583856e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 2.0277194079772542737397112538008
y[1] (numeric) = 2.027719407977254293877077014857
absolute error = 2.01373657610562e-17
relative error = 9.9310415838768204724637160145667e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 2.0291333357599154149454680576827
y[1] (numeric) = 2.0291333357599154350814728814484
absolute error = 2.01360048237657e-17
relative error = 9.9234507998582147228559565625234e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 2.0305472344092432240137089831167
y[1] (numeric) = 2.0305472344092432441482841372641
absolute error = 2.01345751541474e-17
relative error = 9.9158368803005204784671248234229e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 2.0319611025113391694415084783495
y[1] (numeric) = 2.0319611025113391895745852319808
absolute error = 2.01330767536313e-17
relative error = 9.9081998807695922627493404444883e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 2.0333749386523352669552590294994
y[1] (numeric) = 2.0333749386523352870867686532149
absolute error = 2.01315096237155e-17
relative error = 9.9005398566867891088303761974401e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.4MB, time=13.35
NO POLE
x[1] = 0.81
y[1] (analytic) = 2.0347887414183954933785376118344
y[1] (numeric) = 2.0347887414183955135084113778019
absolute error = 2.01298737659675e-17
relative error = 9.8928568633299574915152385357159e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 2.0362025093957172004680110465319
y[1] (numeric) = 2.0362025093957172205961802285547
absolute error = 2.01281691820228e-17
relative error = 9.8851509558330849387800494634881e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 2.0376162411705325287159664271275
y[1] (numeric) = 2.0376162411705325488423623007136
absolute error = 2.01263958735861e-17
relative error = 9.8774221891872318546575151746059e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 2.0390299353291098211180528132436
y[1] (numeric) = 2.0390299353291098412426066556745
absolute error = 2.01245538424309e-17
relative error = 9.8696706182406755437539515841414e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 2.0404435904577550369048204239738
y[1] (numeric) = 2.0404435904577550570274635143726
absolute error = 2.01226430903988e-17
relative error = 9.8618962976989073715560667617884e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 2.0418572051428131652356435994983
y[1] (numeric) = 2.0418572051428131853563072188994
absolute error = 2.01206636194011e-17
relative error = 9.8540992821257571197165755149162e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 2.0432707779706696388536138371308
y[1] (numeric) = 2.0432707779706696589722292685477
absolute error = 2.01186154314169e-17
relative error = 9.8462796259428004883732577888675e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 2.044684307527751747699989247016
y[1] (numeric) = 2.0446843075277517678164877755105
absolute error = 2.01164985284945e-17
relative error = 9.8384373834303837478700352485953e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 2.0460977924005300524867868131501
y[1] (numeric) = 2.0460977924005300726010997259008
absolute error = 2.01143129127507e-17
relative error = 9.8305726087276185463236931043820e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 2.0475112311755197982261038872473
y[1] (numeric) = 2.0475112311755198183381624736186
absolute error = 2.01120585863713e-17
relative error = 9.8226853558329635596053503513680e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 2.0489246224392823277147553862508
y[1] (numeric) = 2.0489246224392823478244909378612
absolute error = 2.01097355516104e-17
relative error = 9.8147756786042188007366192274054e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.821
y[1] (analytic) = 2.0503379647784264949728132089662
y[1] (numeric) = 2.0503379647784265150801570197575
absolute error = 2.01073438107913e-17
relative error = 9.8068436307593010484595307940601e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 2.0517512567796100786346344333989
y[1] (numeric) = 2.0517512567796100987395177997044
absolute error = 2.01048833663055e-17
relative error = 9.7988892658760907657016029640137e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 2.053164497029541195290964903882
y[1] (numeric) = 2.0531644970295412153933191244955
absolute error = 2.01023542206135e-17
relative error = 9.7909126373931570752764640760869e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 2.0545776841149797127807048660105
y[1] (numeric) = 2.0545776841149797328804612422552
absolute error = 2.00997563762447e-17
relative error = 9.7829137986100424233350248515213e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 2.0559908166227386634309233577349
y[1] (numeric) = 2.0559908166227386835280131935315
absolute error = 2.00970898357966e-17
relative error = 9.7748928026872063230432332335624e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 2.0574038931396856572437081167145
y[1] (numeric) = 2.0574038931396856773380627186504
absolute error = 2.00943546019359e-17
relative error = 9.7668497026468935431752162477058e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.4MB, time=13.62
NO POLE
x[1] = 0.827
y[1] (analytic) = 2.0588169122527442950284378172016
y[1] (numeric) = 2.0588169122527443151199884945993
absolute error = 2.00915506773977e-17
relative error = 9.7587845513730765770146354555396e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 2.0602298725488955814780635042998
y[1] (numeric) = 2.060229872548895601566741569286
absolute error = 2.00886780649862e-17
relative error = 9.7506974016121271344838885875012e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 2.0616427726151793381879861494345
y[1] (numeric) = 2.0616427726151793582737229170082
absolute error = 2.00857367675737e-17
relative error = 9.7425883059726609968168264704175e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 2.0630556110386956166161173082736
y[1] (numeric) = 2.0630556110386956366988440963754
absolute error = 2.00827267881018e-17
relative error = 9.7344573169264505937248126502264e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 2.0644683864066061109827099211583
y[1] (numeric) = 2.0644683864066061310623580507384
absolute error = 2.00796481295801e-17
relative error = 9.7263044868081235700672369818420e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 2.0658810973061355711085463563275
y[1] (numeric) = 2.0658810973061355911850471514152
absolute error = 2.00765007950877e-17
relative error = 9.7181298678162186421366242819442e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 2.0672937423245732151900708578699
y[1] (numeric) = 2.0672937423245732352633556456416
absolute error = 2.00732847877717e-17
relative error = 9.7099335120127866476771801325205e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 2.0687063200492741425100536233841
y[1] (numeric) = 2.0687063200492741625800537342321
absolute error = 2.00700001108480e-17
relative error = 9.7017154713241057286826406355792e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 2.0701188290676607460823738008042
y[1] (numeric) = 2.0701188290676607661490205684057
absolute error = 2.00666467676015e-17
relative error = 9.6934757975411044364772238220713e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.836
y[1] (analytic) = 2.0715312679672241252295087597243
y[1] (numeric) = 2.0715312679672241452927335211097
absolute error = 2.00632247613854e-17
relative error = 9.6852145423193493302194266596304e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 2.0729436353355254980913170598497
y[1] (numeric) = 2.0729436353355255181510511554715
absolute error = 2.00597340956218e-17
relative error = 9.6769317571796604359561423387776e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 2.0743559297601976140637026079107
y[1] (numeric) = 2.0743559297601976341198773817119
absolute error = 2.00561747738012e-17
relative error = 9.6686274935081945853296969078305e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 2.0757681498289461661657475644911
y[1] (numeric) = 2.0757681498289461862182943639743
absolute error = 2.00525467994832e-17
relative error = 9.6603018025571071891257858892507e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 2.0771802941295512033339016337587
y[1] (numeric) = 2.0771802941295512233827518100543
absolute error = 2.00488501762956e-17
relative error = 9.6519547354444417088711425941452e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 2.078592361249868542641815442023
y[1] (numeric) = 2.0785923612498685626869003499579
absolute error = 2.00450849079349e-17
relative error = 9.6435863431546937810551408800027e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 2.0800043497778311814444057854063
y[1] (numeric) = 2.0800043497778312014856567835728
absolute error = 2.00412509981665e-17
relative error = 9.6351966765392294791006126857187e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 2.0814162583014507094447406026813
y[1] (numeric) = 2.0814162583014507294820890535056
absolute error = 2.00373484508243e-17
relative error = 9.6267857863164142705770927572464e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.4MB, time=13.90
NO POLE
x[1] = 0.844
y[1] (analytic) = 2.0828280854088187206823316065058
y[1] (numeric) = 2.0828280854088187407157088763167
absolute error = 2.00333772698109e-17
relative error = 9.6183537230720301795160167558448e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 2.0842398296881082254414225848812
y[1] (numeric) = 2.0842398296881082454707600439786
absolute error = 2.00293374590974e-17
relative error = 9.6099005372594999932888202951726e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 2.0856514897275750620778614646634
y[1] (numeric) = 2.0856514897275750821030904873871
absolute error = 2.00252290227237e-17
relative error = 9.6014262792003509455336400344427e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 2.087063064115559308763144310372
y[1] (numeric) = 2.0870630641155593287841962751702
absolute error = 2.00210519647982e-17
relative error = 9.5929309990843896822148296056369e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 2.0884745514404866951442195143717
y[1] (numeric) = 2.0884745514404867151610258038695
absolute error = 2.00168062894978e-17
relative error = 9.5844147469700208107614401228303e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 2.0898859502908700139176405187379
y[1] (numeric) = 2.0898859502908700339301325198063
absolute error = 2.00124920010684e-17
relative error = 9.5758775727848040497762389074764e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 2.091297259255310532316655494774
y[1] (numeric) = 2.0912972592553105523247645985982
absolute error = 2.00081091038242e-17
relative error = 9.5673195263254359570172996828914e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 2.0927084769224994035098224932056
y[1] (numeric) = 2.0927084769224994235134800953536
absolute error = 2.00036576021480e-17
relative error = 9.5587406572582102187529977121203e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 2.0941196018812190779097386665558
y[1] (numeric) = 2.0941196018812190979088761670474
absolute error = 1.99991375004916e-17
relative error = 9.5501410151195244653786118940135e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.853
y[1] (analytic) = 2.09553063272034471439047225509
y[1] (numeric) = 2.0955306327203447343850210584648
absolute error = 1.99945488033748e-17
relative error = 9.5415206493157175824179868335431e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 2.0969415680288455914122861190142
y[1] (numeric) = 2.0969415680288456114021776344006
absolute error = 1.99898915153864e-17
relative error = 9.5328796091238620769296988198735e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 2.098352406395786518052241692323
y[1] (numeric) = 2.0983524063957865380374073335067
absolute error = 1.99851656411837e-17
relative error = 9.5242179436918390260589649036426e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 2.0997631464103292449392723278092
y[1] (numeric) = 2.0997631464103292649196435133018
absolute error = 1.99803711854926e-17
relative error = 9.5155357020386990924879162411161e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 2.1011737866617338750923150982807
y[1] (numeric) = 2.1011737866617338950678232513882
absolute error = 1.99755081531075e-17
relative error = 9.5068329330549275200953430359092e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 2.1025843257393602746600902159687
y[1] (numeric) = 2.1025843257393602946306667648602
absolute error = 1.99705765488915e-17
relative error = 9.4981096855028513608722678537263e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 2.1039947622326694835611173304674
y[1] (numeric) = 2.1039947622326695035266937082435
absolute error = 1.99655763777761e-17
relative error = 9.4893660080168080340460028660289e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=198.3MB, alloc=4.4MB, time=14.17
x[1] = 0.86
y[1] (analytic) = 2.1054050947312251260225580653047
y[1] (numeric) = 2.1054050947312251459830657100662
absolute error = 1.99605076447615e-17
relative error = 9.4806019491035987989288161869072e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 2.10681532182469482101647425442
y[1] (numeric) = 2.1068153218246948409718446093363
absolute error = 1.99553703549163e-17
relative error = 9.4718175571426562238349788048478e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 2.1082254421028515925920914424073
y[1] (numeric) = 2.1082254421028516125422559557855
absolute error = 1.99501645133782e-17
relative error = 9.4630128803866859199646993121055e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 2.10963545415557528010265731638
y[1] (numeric) = 2.1096354541555753000475474417326
absolute error = 1.99448901253526e-17
relative error = 9.4541879669613108705826773363005e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 2.1110453565728539483254848427125
y[1] (numeric) = 2.1110453565728539682650320388267
absolute error = 1.99395471961142e-17
relative error = 9.4453428648661388810887708438773e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 2.1124551479447852974737699887376
y[1] (numeric) = 2.1124551479447853174079057197433
absolute error = 1.99341357310057e-17
relative error = 9.4364776219744535398735698170222e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 2.1138648268615780730987740176954
y[1] (numeric) = 2.1138648268615780930274297531342
absolute error = 1.99286557354388e-17
relative error = 9.4275922860339950631441012272745e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 2.1152743919135534758809604548718
y[1] (numeric) = 2.1152743919135534958040676697652
absolute error = 1.99231072148934e-17
relative error = 9.4186869046668876539181248786263e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 2.1166838416911465713086769339058
y[1] (numeric) = 2.1166838416911465912261671088235
absolute error = 1.99174901749177e-17
relative error = 9.4097615253699929317447005268154e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 2.1180931747849076992429722447002
y[1] (numeric) = 2.1180931747849077191547768658295
absolute error = 1.99118046211293e-17
relative error = 9.4008161955157346581258909142575e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 2.11950238978550388336713901824
y[1] (numeric) = 2.1195023897855039032731895774534
absolute error = 1.99060505592134e-17
relative error = 9.3918509623515525072934719644085e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 2.1209114852837202405195725988876
y[1] (numeric) = 2.1209114852837202604198005938117
absolute error = 1.99002279949241e-17
relative error = 9.3828658730008202288316231913989e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
y[1] (analytic) = 2.1223204598704613899085367714184
y[1] (numeric) = 2.1223204598704614098028737055024
absolute error = 1.98943369340840e-17
relative error = 9.3738609744629597180731796212174e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 2.1237293121367528622074271281457
y[1] (numeric) = 2.1237293121367528820958045107299
absolute error = 1.98883773825842e-17
relative error = 9.3648363136137435532129011291231e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 2.1251380406737425085291229809903
y[1] (numeric) = 2.1251380406737425284114723273744
absolute error = 1.98823493463841e-17
relative error = 9.3557919372055027874568663413689e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.875
y[1] (analytic) = 2.1265466440727019092780188442585
y[1] (numeric) = 2.1265466440727019291542716757705
absolute error = 1.98762528315120e-17
relative error = 9.3467278918677106791733769146842e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 2.1279551209250277828783266362175
y[1] (numeric) = 2.1279551209250278027484144802817
absolute error = 1.98700878440642e-17
relative error = 9.3376442241068597659464824324706e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.4MB, time=14.45
NO POLE
x[1] = 0.877
y[1] (analytic) = 2.12936346982224339437723987128
y[1] (numeric) = 2.1293634698222434142410942614858
absolute error = 1.98638543902058e-17
relative error = 9.3285409803071383487536827856851e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 2.1307716893559999639215512397536
y[1] (numeric) = 2.1307716893559999837791037159237
absolute error = 1.98575524761701e-17
relative error = 9.3194182067304478131885451502903e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 2.1321797781180780751063150986534
y[1] (numeric) = 2.1321797781180780949574972069125
absolute error = 1.98511821082591e-17
relative error = 9.3102759495169363421157163187213e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 2.1335877347003890831941465250339
y[1] (numeric) = 2.1335877347003891030388898178771
absolute error = 1.98447432928432e-17
relative error = 9.3011142546851561129555387877220e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 2.1349955576949765232037487126573
y[1] (numeric) = 2.1349955576949765430419847490185
absolute error = 1.98382360363612e-17
relative error = 9.2919331681323609391332227346811e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 2.1364032456940175178662606235886
y[1] (numeric) = 2.136403245694017537697920968909
absolute error = 1.98316603453204e-17
relative error = 9.2827327356348500902032743699341e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 2.1378107972898241854480169384879
y[1] (numeric) = 2.1378107972898242052730331647843
absolute error = 1.98250162262964e-17
relative error = 9.2735130028481709682879552159973e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 2.1392182110748450474383124829557
y[1] (numeric) = 2.139218211074845067256616168889
absolute error = 1.98183036859333e-17
relative error = 9.2642740153075085110346341659894e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 2.1406254856416664361007634422855
y[1] (numeric) = 2.1406254856416664559122861732293
absolute error = 1.98115227309438e-17
relative error = 9.2550158184280268828683489280639e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 2.1420326195830139018868578133794
y[1] (numeric) = 2.1420326195830139216915311814882
absolute error = 1.98046733681088e-17
relative error = 9.2457384575049769333436305059721e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 2.1434396114917536207102876803934
y[1] (numeric) = 2.1434396114917536405080432846709
absolute error = 1.97977556042775e-17
relative error = 9.2364419777140370366042619593060e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 2.1448464599608938010806560398966
y[1] (numeric) = 2.1448464599608938208714254862645
absolute error = 1.97907694463679e-17
relative error = 9.2271264241118396145686123011478e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 2.1462531635835860910951510419567
y[1] (numeric) = 2.1462531635835861108788659433227
absolute error = 1.97837149013660e-17
relative error = 9.2177918416358904117831402217537e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 2.147659720953126985286780655593
y[1] (numeric) = 2.1476597209531270050633726319193
absolute error = 1.97765919763263e-17
relative error = 9.2084382751050939241201950299832e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 2.1490661306629592313277609104797
y[1] (numeric) = 2.1490661306629592510971615888516
absolute error = 1.97694006783719e-17
relative error = 9.1990657692200911605750962732603e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 2.1504723913066732365866510116304
y[1] (numeric) = 2.1504723913066732563487920263244
absolute error = 1.97621410146940e-17
relative error = 9.1896743685633175925834515669051e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 2.1518785014780084745378287700424
y[1] (numeric) = 2.1518785014780084942926417625948
absolute error = 1.97548129925524e-17
relative error = 9.1802641175995261050716189223913e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.4MB, time=14.73
NO POLE
x[1] = 0.894
y[1] (analytic) = 2.1532844597708548910218999399466
y[1] (numeric) = 2.1532844597708549107693165592213
absolute error = 1.97474166192747e-17
relative error = 9.1708350606757046857611721336537e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 2.1546902647792543103556352023665
y[1] (numeric) = 2.1546902647792543300955871046243
absolute error = 1.97399519022578e-17
relative error = 9.1613872420220623890177762285070e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 2.1560959150974018412900286851716
y[1] (numeric) = 2.1560959150974018610224475341376
absolute error = 1.97324188489660e-17
relative error = 9.1519207057514350292340642047350e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 2.1575014093196472828150720616783
y[1] (numeric) = 2.1575014093196473025398895286109
absolute error = 1.97248174669326e-17
relative error = 9.1424354958603159528394004426080e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 2.1589067460404965298098384231462
y[1] (numeric) = 2.1589067460404965495269861869051
absolute error = 1.97171477637589e-17
relative error = 9.1329316562286789764527968638883e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 2.1603119238546129785364702751998
y[1] (numeric) = 2.1603119238546129982458800223145
absolute error = 1.97094097471147e-17
relative error = 9.1234092306204968637819671593287e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 2.1617169413568189319766661643065
y[1] (numeric) = 2.1617169413568189516782695890443
absolute error = 1.97016034247378e-17
relative error = 9.1138682626837956858724243463448e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 2.1631217971420970050092605979399
y[1] (numeric) = 2.1631217971420970247029894023747
absolute error = 1.96937288044348e-17
relative error = 9.1043087959513104510665015113794e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 2.1645264898055915294274920809681
y[1] (numeric) = 2.1645264898055915491132779750482
absolute error = 1.96857858940801e-17
relative error = 9.0947308738403070869564005991180e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 2.1659310179426099587945542511125
y[1] (numeric) = 2.1659310179426099784723289527293
absolute error = 1.96777747016168e-17
relative error = 9.0851345396532828293369591960860e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 2.1673353801486242731360252580467
y[1] (numeric) = 2.1673353801486242928057204931024
absolute error = 1.96696952350557e-17
relative error = 9.0755198365777877261234242222254e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 2.1687395750192723834677706938194
y[1] (numeric) = 2.1687395750192724031293181962962
absolute error = 1.96615475024768e-17
relative error = 9.0658868076874000664495850865474e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 2.1701436011503595361579155468202
y[1] (numeric) = 2.1701436011503595558112470588476
absolute error = 1.96533315120274e-17
relative error = 9.0562354959411317921783191525947e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 2.1715474571378597171214808174275
y[1] (numeric) = 2.1715474571378597367665280893513
absolute error = 1.96450472719238e-17
relative error = 9.0465659441844945035497345643049e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 2.1729511415779170558462806008247
y[1] (numeric) = 2.1729511415779170754829753912747
absolute error = 1.96366947904500e-17
relative error = 9.0368781951491812026057585457501e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 2.1743546530668472292486756112001
y[1] (numeric) = 2.1743546530668472488769496871587
absolute error = 1.96282740759586e-17
relative error = 9.0271722914537615425361329370351e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 2.1757579902011388653577792916969
y[1] (numeric) = 2.1757579902011388849775644285672
absolute error = 1.96197851368703e-17
relative error = 9.0174482756037314082999653917441e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.4MB, time=15.00
NO POLE
x[1] = 0.911
y[1] (analytic) = 2.1771611515774549468267128260225
y[1] (numeric) = 2.1771611515774549664379408076965
absolute error = 1.96112279816740e-17
relative error = 9.0077061899918383676080994863773e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 2.1785641357926342142695055405796
y[1] (numeric) = 2.1785641357926342338721081595066
absolute error = 1.96026026189270e-17
relative error = 8.9979460768984522373486220232263e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 2.1799669414436925694222373603363
y[1] (numeric) = 2.1799669414436925890161464175908
absolute error = 1.95939090572545e-17
relative error = 8.9881679784916135823292647368653e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 2.181369567127824478127020157408
y[1] (numeric) = 2.1813695671278244977121674627581
absolute error = 1.95851473053501e-17
relative error = 8.9783719368275409211046063837622e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 2.1827720114424043731374150084886
y[1] (numeric) = 2.1827720114424043927137323804641
absolute error = 1.95763173719755e-17
relative error = 8.9685579938507699340221647174658e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 2.1841742729849880567438825558292
y[1] (numeric) = 2.18417427298498807631130182179
absolute error = 1.95674192659608e-17
relative error = 8.9587261913945673002771003657854e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 2.1855763503533141032178638464317
y[1] (numeric) = 2.1855763503533141227763168426357
absolute error = 1.95584529962040e-17
relative error = 8.9488765711809773652820871073582e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 2.1869782421453052610730892054928
y[1] (numeric) = 2.1869782421453052806225077771641
absolute error = 1.95494185716713e-17
relative error = 8.9390091748212348873098028553119e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 2.1883799469590698551427128829064
y[1] (numeric) = 2.1883799469590698746830288843036
absolute error = 1.95403160013972e-17
relative error = 8.9291240438160852607017960802631e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.92
y[1] (analytic) = 2.1897814633929031884708713958072
y[1] (numeric) = 2.1897814633929032080020166902916
absolute error = 1.95311452944844e-17
relative error = 8.9192212195560126285347902538688e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 2.1911827900452889440172636757135
y[1] (numeric) = 2.1911827900452889635391701358168
absolute error = 1.95219064601033e-17
relative error = 8.9093007433212850204079764015653e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 2.1925839255149005861733513158053
y[1] (numeric) = 2.1925839255149006056859508232982
absolute error = 1.95125995074929e-17
relative error = 8.8993626562826382810914919670155e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 2.1939848684006027620887774022554
y[1] (numeric) = 2.1939848684006027815920018482157
absolute error = 1.95032244459603e-17
relative error = 8.8894069995013197158789429892126e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 2.1953856173014527028066026033113
y[1] (numeric) = 2.1953856173014527223003838881916
absolute error = 1.94937812848803e-17
relative error = 8.8794338139291775625214500787606e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 2.196786170816701624205957381007
y[1] (numeric) = 2.1967861708167016436902274147032
absolute error = 1.94842700336962e-17
relative error = 8.8694431404092968144575218200437e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 2.1981865275457961277507093829716
y[1] (numeric) = 2.1981865275457961472254000848907
absolute error = 1.94746907019191e-17
relative error = 8.8594350196759506715882242923538e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
memory used=213.6MB, alloc=4.4MB, time=15.28
y[1] (analytic) = 2.1995866860883796010427452657818
y[1] (numeric) = 2.1995866860883796205077885649104
absolute error = 1.94650432991286e-17
relative error = 8.8494094923551890964672648853322e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 2.2009866450442936181784663966953
y[1] (numeric) = 2.2009866450442936376337942316673
absolute error = 1.94553278349720e-17
relative error = 8.8393665989647440459258063902409e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 2.2023864030135793399070980773845
y[1] (numeric) = 2.2023864030135793593526423965491
absolute error = 1.94455443191646e-17
relative error = 8.8293063799144349546382630182350e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 2.2037859585964789135894121314776
y[1] (numeric) = 2.2037859585964789330251048929678
absolute error = 1.94356927614902e-17
relative error = 8.8192288755066638561644798034953e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 2.2051853103934368729554628973044
y[1] (numeric) = 2.2051853103934368923812360691045
absolute error = 1.94257731718001e-17
relative error = 8.8091341259362288315109423807762e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 2.2065844570051015376599368682224
y[1] (numeric) = 2.2065844570051015570757224282363
absolute error = 1.94157855600139e-17
relative error = 8.7990221712909543335111689874289e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 2.2079833970323264126337164252946
y[1] (numeric) = 2.207983397032326432039446361414
absolute error = 1.94057299361194e-17
relative error = 8.7888930515519119261846196612322e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 2.2093821290761715872302583108701
y[1] (numeric) = 2.2093821290761716066258646210421
absolute error = 1.93956063101720e-17
relative error = 8.7787468065934142992469267672959e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 2.2107806517379051341653876968046
y[1] (numeric) = 2.2107806517379051535508023891002
absolute error = 1.93854146922956e-17
relative error = 8.7685834761836882177264332822856e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 2.2121789636190045082491089076461
y[1] (numeric) = 2.2121789636190045276242640003276
absolute error = 1.93751550926815e-17
relative error = 8.7584030999846412498619064512871e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 2.213577063321157944908034067088
y[1] (numeric) = 2.2135770633211579642728615886777
absolute error = 1.93648275215897e-17
relative error = 8.7482057175527140118898389754816e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.938
y[1] (analytic) = 2.2149749494462658584970311453817
y[1] (numeric) = 2.214974949446265877851463134729
absolute error = 1.93544319893473e-17
relative error = 8.7379913683384203278719821584208e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 2.2163726205964422403986930961723
y[1] (numeric) = 2.2163726205964422597426616025225
absolute error = 1.93439685063502e-17
relative error = 8.7277600916873784595171893606383e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 2.2177700753740160569092299834102
y[1] (numeric) = 2.2177700753740160762426670664718
absolute error = 1.93334370830616e-17
relative error = 8.7175119268398959540763748231147e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 2.2191673123815326469093862125574
y[1] (numeric) = 2.2191673123815326662322239425707
absolute error = 1.93228377300133e-17
relative error = 8.7072469129318182017343726501087e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 2.2205643302217551193189851952934
y[1] (numeric) = 2.2205643302217551386311556530976
absolute error = 1.93121704578042e-17
relative error = 8.6969650889941132527230416774146e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 2.2219611274976657503337039932866
y[1] (numeric) = 2.2219611274976657696351392703885
absolute error = 1.93014352771019e-17
relative error = 8.6866664939538537666720438545447e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.4MB, time=15.55
NO POLE
x[1] = 0.944
y[1] (analytic) = 2.2233577028124673804426807043785
y[1] (numeric) = 2.22335770281246739973331290302
absolute error = 1.92906321986415e-17
relative error = 8.6763511666339363038957953092364e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 2.2247540547695848112255575736859
y[1] (numeric) = 2.2247540547695848305053188069118
absolute error = 1.92797612332259e-17
relative error = 8.6660191457534763038747307903806e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 2.2261501819726662019275630326955
y[1] (numeric) = 2.2261501819726662211963854244219
absolute error = 1.92688223917264e-17
relative error = 8.6556704699283367346536805887473e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 2.227546083025584465811236091387
y[1] (numeric) = 2.2275460830255844850690517764685
absolute error = 1.92578156850815e-17
relative error = 8.6453051776708470839991047898234e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 2.2289417565324386662833967317729
y[1] (numeric) = 2.228941756532438685530137856071
absolute error = 1.92467411242981e-17
relative error = 8.6349233073906005423470256267521e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 2.2303372010975554127959661760054
y[1] (numeric) = 2.230337201097555432031564896456
absolute error = 1.92355987204506e-17
relative error = 8.6245248973943070205129984511777e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 2.2317324153254902565192411283421
y[1] (numeric) = 2.2317324153254902757436296130238
absolute error = 1.92243884846817e-17
relative error = 8.6141099858864088466487933361173e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 2.2331273978210290857862263178169
y[1] (numeric) = 2.2331273978210291049993367460183
absolute error = 1.92131104282014e-17
relative error = 8.6036786109688884962606116647209e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 2.2345221471891895213066298973958
y[1] (numeric) = 2.2345221471891895405083944596835
absolute error = 1.92017645622877e-17
relative error = 8.5932308106418382151113615450588e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 2.2359166620352223111491264857409
y[1] (numeric) = 2.2359166620352223303394773840276
absolute error = 1.91903508982867e-17
relative error = 8.5827666228037595452612931353228e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 2.237310940964612725490492869436
y[1] (numeric) = 2.2373109409646127446693623170479
absolute error = 1.91788694476119e-17
relative error = 8.5722860852515045385784949038468e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 2.2387049825830819511302216166523
y[1] (numeric) = 2.238704982583081970297541838397
absolute error = 1.91673202217447e-17
relative error = 8.5617892356807535917180253752990e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 2.2400987854965884857692180877586
y[1] (numeric) = 2.2400987854965885049249213199931
absolute error = 1.91557032322345e-17
relative error = 8.5512761116863133088584781408162e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 2.241492348311329532051186564295
y[1] (numeric) = 2.2414923483113295511952050549932
absolute error = 1.91440184906982e-17
relative error = 8.5407467507621459480965085034402e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 2.2428856696337423913653114550392
y[1] (numeric) = 2.2428856696337424104975774638598
absolute error = 1.91322660088206e-17
relative error = 8.5302011903018003985609802365744e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 2.244278748070505857408839776601
y[1] (numeric) = 2.244278748070505876529285574955
absolute error = 1.91204457983540e-17
relative error = 8.5196394675984854598475115775134e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 2.2456715822285416095081713460785
y[1] (numeric) = 2.2456715822285416286167292171974
absolute error = 1.91085578711189e-17
relative error = 8.5090616198456330476894601387157e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.4MB, time=15.83
NO POLE
x[1] = 0.961
y[1] (analytic) = 2.2470641707150156056970633648027
y[1] (numeric) = 2.2470641707150156247936656038056
absolute error = 1.90966022390029e-17
relative error = 8.4984676841366586256991973889628e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 2.2484565121373394755505563150798
y[1] (numeric) = 2.2484565121373394946351352290416
absolute error = 1.90845789139618e-17
relative error = 8.4878576974657013403167426217829e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 2.2498486051031719127732283361244
y[1] (numeric) = 2.2498486051031719318457162441433
absolute error = 1.90724879080189e-17
relative error = 8.4772316967275617155700916839713e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 2.2512404482204200675403854910427
y[1] (numeric) = 2.251240448220420086600714724308
absolute error = 1.90603292332653e-17
relative error = 8.4665897187180841388131573306756e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 2.252632040097240938590795583793
y[1] (numeric) = 2.2526320400972409576388984856525
absolute error = 1.90481029018595e-17
relative error = 8.4559318001342275390414814590953e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 2.2540233793420427650695734335048
y[1] (numeric) = 2.2540233793420427841053823595328
absolute error = 1.90358089260280e-17
relative error = 8.4452579775745798107910916808065e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 2.255414464563486418119825763388
y[1] (numeric) = 2.2554144645634864371432730814527
absolute error = 1.90234473180647e-17
relative error = 8.4345682875393386353965429984707e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 2.2568052943704867922216641127026
y[1] (numeric) = 2.2568052943704868112326822030337
absolute error = 1.90110180903311e-17
relative error = 8.4238627664306472091914528091911e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 2.2581958673722141962771944328918
y[1] (numeric) = 2.2581958673722142152757156881485
absolute error = 1.89985212552567e-17
relative error = 8.4131414505530176478779547813231e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 2.2595861821780957444400922830064
y[1] (numeric) = 2.2595861821780957634260491083445
absolute error = 1.89859568253381e-17
relative error = 8.4024043761131778498145526533435e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 2.2609762373978167466883727949588
y[1] (numeric) = 2.2609762373978167656616976080985
absolute error = 1.89733248131397e-17
relative error = 8.3916515792206269301945362845676e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 2.2623660316413220991389648359541
y[1] (numeric) = 2.2623660316413221180995900672477
absolute error = 1.89606252312936e-17
relative error = 8.3808830958878353404285829848280e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.973
y[1] (analytic) = 2.2637555635188176741026990536402
y[1] (numeric) = 2.2637555635188176930505571461396
absolute error = 1.89478580924994e-17
relative error = 8.3700989620304004193892607542312e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 2.2651448316407717098783197491032
y[1] (numeric) = 2.2651448316407717288133431586276
absolute error = 1.89350234095244e-17
relative error = 8.3592992134673783027527808447425e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 2.2665338346179162002841307838144
y[1] (numeric) = 2.2665338346179162192062519790173
absolute error = 1.89221211952029e-17
relative error = 8.3484838859212178692225365141888e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 2.2679225710612482839258859889952
y[1] (numeric) = 2.2679225710612483028350374514326
absolute error = 1.89091514624374e-17
relative error = 8.3376530150185330382959646158556e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 2.2693110395820316331995348096295
y[1] (numeric) = 2.2693110395820316520956490338271
absolute error = 1.88961142241976e-17
relative error = 8.3268066362899031110487903698382e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.4MB, time=16.10
NO POLE
x[1] = 0.978
y[1] (analytic) = 2.2706992387917978430274341804908
y[1] (numeric) = 2.2706992387917978619104436740114
absolute error = 1.88830094935206e-17
relative error = 8.3159447851702026494303135112605e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 2.2720871673023478193266378980882
y[1] (numeric) = 2.2720871673023478381964751815995
absolute error = 1.88698372835113e-17
relative error = 8.3050674969990185032904628520747e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 2.2734748237257531672078750203593
y[1] (numeric) = 2.273474823725753186064472627701
absolute error = 1.88565976073417e-17
relative error = 8.2941748070205817996995901492825e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 2.2748622066743575789038290952446
y[1] (numeric) = 2.2748622066743575977471195734964
absolute error = 1.88432904782518e-17
relative error = 8.2832667503844038493803107116583e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 2.2762493147607782214253302899831
y[1] (numeric) = 2.2762493147607782402552461995315
absolute error = 1.88299159095484e-17
relative error = 8.2723433621449874844103739844036e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 2.2776361465979071239440727650492
y[1] (numeric) = 2.2776361465979071427605466796554
absolute error = 1.88164739146062e-17
relative error = 8.2614046772625495949956873836677e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 2.2790227007989125649004699101316
y[1] (numeric) = 2.2790227007989125837034344169988
absolute error = 1.88029645068672e-17
relative error = 8.2504507306029954178293200136754e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 2.2804089759772404588352603344138
y[1] (numeric) = 2.2804089759772404776246480342547
absolute error = 1.87893876998409e-17
relative error = 8.2394815569382440545485948114954e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 2.2817949707466157429434777796658
y[1] (numeric) = 2.2817949707466157617192212867696
absolute error = 1.87757435071038e-17
relative error = 8.2284971909462463476608278881981e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 2.2831806837210437633493984022915
y[1] (numeric) = 2.2831806837210437821114303445919
absolute error = 1.87620319423004e-17
relative error = 8.2174976672116599878919010673392e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 2.2845661135148116611010791495028
y[1] (numeric) = 2.284566113514811679849332168645
absolute error = 1.87482530191422e-17
relative error = 8.2064830202256470415219862484499e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 2.2859512587424897578831012351944
y[1] (numeric) = 2.2859512587424897766175079866025
absolute error = 1.87344067514081e-17
relative error = 8.1954532843862849656323514065563e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 2.2873361180189329414461330028935
y[1] (numeric) = 2.2873361180189329601666261558377
absolute error = 1.87204931529442e-17
relative error = 8.1844084939987141291719369216824e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 2.2887206899592820507519267463355
y[1] (numeric) = 2.2887206899592820694584389839998
absolute error = 1.87065122376643e-17
relative error = 8.1733486832755909577032843910522e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.992
y[1] (analytic) = 2.2901049731789652608323643427861
y[1] (numeric) = 2.2901049731789652795248283623354
absolute error = 1.86924640195493e-17
relative error = 8.1622738863370594169468632365480e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 2.2914889662936994673611668401773
y[1] (numeric) = 2.2914889662936994860395153528248
absolute error = 1.86783485126475e-17
relative error = 8.1511841372111156657161503626302e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 2.2928726679194916709368834264655
y[1] (numeric) = 2.2928726679194916896010491575396
memory used=228.8MB, alloc=4.4MB, time=16.38
absolute error = 1.86641657310741e-17
relative error = 8.1400794698336227873589379814008e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 2.2942560766726403610757754983354
y[1] (numeric) = 2.2942560766726403797256911873474
absolute error = 1.86499156890120e-17
relative error = 8.1289599180488924051358103968777e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 2.2956391911697368999132118364837
y[1] (numeric) = 2.2956391911697369185488102371951
absolute error = 1.86355984007114e-17
relative error = 8.1178255156097417675354680729632e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.997
y[1] (analytic) = 2.2970220100276669056121911862009
y[1] (numeric) = 2.2970220100276669242334050666905
absolute error = 1.86212138804896e-17
relative error = 8.1066762961776379983773275417900e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 2.298404531863611635477608834845
y[1] (numeric) = 2.2984045318636116540843709775758
absolute error = 1.86067621427308e-17
relative error = 8.0955122933228421260601720136354e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 2.2997867552950493687748840720538
y[1] (numeric) = 2.2997867552950493873671272739409
absolute error = 1.85922432018871e-17
relative error = 8.0843335405250746788923275776135e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 2.3011686789397567892515657141873
y[1] (numeric) = 2.3011686789397568078292227866645
absolute error = 1.85776570724772e-17
relative error = 8.0731400711731796861942755625510e-16 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;
Iterations = 1000
Total Elapsed Time = 16 Seconds
Elapsed Time(since restart) = 16 Seconds
Expected Time Remaining = 2 Minutes 27 Seconds
Optimized Time Remaining = 2 Minutes 27 Seconds
Time to Timeout = 14 Minutes 43 Seconds
Percent Done = 10.01 %
> quit
memory used=230.3MB, alloc=4.4MB, time=16.48