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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_initial_pass,
> glob_log10normmin,
> glob_max_hours,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_finished,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_orig_start_sec,
> glob_smallish_float,
> centuries_in_millinium,
> glob_log10abserr,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_disp_incr,
> glob_optimal_start,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> sec_in_min,
> glob_dump,
> glob_html_log,
> glob_max_sec,
> glob_max_iter,
> glob_relerr,
> glob_last_good_h,
> glob_hmin,
> glob_optimal_done,
> min_in_hour,
> djd_debug2,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_warned2,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_no_eqs,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10_relerr,
> glob_look_poles,
> glob_display_flag,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmax,
> glob_h,
> glob_current_iter,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_fact_1,
> array_norms,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y,
> array_x,
> array_type_pole,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher_work2,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_start, glob_initial_pass, glob_log10normmin, glob_max_hours,
glob_log10_abserr, glob_dump_analytic, glob_not_yet_finished, days_in_year,
djd_debug, glob_max_opt_iter, glob_normmax, glob_hmin_init,
glob_not_yet_start_msg, glob_clock_sec, glob_almost_1, glob_orig_start_sec,
glob_smallish_float, centuries_in_millinium, glob_log10abserr, glob_iter,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_disp_incr,
glob_optimal_start, glob_large_float, glob_reached_optimal_h,
years_in_century, sec_in_min, glob_dump, glob_html_log, glob_max_sec,
glob_max_iter, glob_relerr, glob_last_good_h, glob_hmin, glob_optimal_done,
min_in_hour, djd_debug2, glob_subiter_method, glob_max_minutes,
glob_log10relerr, MAX_UNCHANGED, glob_warned2, glob_warned,
glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_clock_start_sec,
glob_optimal_expect_sec, glob_percent_done, glob_log10_relerr,
glob_look_poles, glob_display_flag, glob_curr_iter_when_opt,
glob_max_trunc_err, glob_abserr, glob_hmax, glob_h, glob_current_iter,
hours_in_day, array_const_1D0, array_const_1, array_const_0D0,
array_last_rel_error, array_pole, array_fact_1, array_norms,
array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y,
array_x, array_type_pole, array_y_init, array_real_pole, array_y_higher,
array_fact_2, array_complex_pole, array_poles, array_y_higher_work,
array_y_set_initial, array_y_higher_work2, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_initial_pass,
> glob_log10normmin,
> glob_max_hours,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_finished,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_orig_start_sec,
> glob_smallish_float,
> centuries_in_millinium,
> glob_log10abserr,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_disp_incr,
> glob_optimal_start,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> sec_in_min,
> glob_dump,
> glob_html_log,
> glob_max_sec,
> glob_max_iter,
> glob_relerr,
> glob_last_good_h,
> glob_hmin,
> glob_optimal_done,
> min_in_hour,
> djd_debug2,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_warned2,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_no_eqs,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10_relerr,
> glob_look_poles,
> glob_display_flag,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmax,
> glob_h,
> glob_current_iter,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_fact_1,
> array_norms,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y,
> array_x,
> array_type_pole,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher_work2,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_start, glob_initial_pass, glob_log10normmin, glob_max_hours,
glob_log10_abserr, glob_dump_analytic, glob_not_yet_finished, days_in_year,
djd_debug, glob_max_opt_iter, glob_normmax, glob_hmin_init,
glob_not_yet_start_msg, glob_clock_sec, glob_almost_1, glob_orig_start_sec,
glob_smallish_float, centuries_in_millinium, glob_log10abserr, glob_iter,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_disp_incr,
glob_optimal_start, glob_large_float, glob_reached_optimal_h,
years_in_century, sec_in_min, glob_dump, glob_html_log, glob_max_sec,
glob_max_iter, glob_relerr, glob_last_good_h, glob_hmin, glob_optimal_done,
min_in_hour, djd_debug2, glob_subiter_method, glob_max_minutes,
glob_log10relerr, MAX_UNCHANGED, glob_warned2, glob_warned,
glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_clock_start_sec,
glob_optimal_expect_sec, glob_percent_done, glob_log10_relerr,
glob_look_poles, glob_display_flag, glob_curr_iter_when_opt,
glob_max_trunc_err, glob_abserr, glob_hmax, glob_h, glob_current_iter,
hours_in_day, array_const_1D0, array_const_1, array_const_0D0,
array_last_rel_error, array_pole, array_fact_1, array_norms,
array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y,
array_x, array_type_pole, array_y_init, array_real_pole, array_y_higher,
array_fact_2, array_complex_pole, array_poles, array_y_higher_work,
array_y_set_initial, array_y_higher_work2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_initial_pass,
> glob_log10normmin,
> glob_max_hours,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_finished,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_orig_start_sec,
> glob_smallish_float,
> centuries_in_millinium,
> glob_log10abserr,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_disp_incr,
> glob_optimal_start,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> sec_in_min,
> glob_dump,
> glob_html_log,
> glob_max_sec,
> glob_max_iter,
> glob_relerr,
> glob_last_good_h,
> glob_hmin,
> glob_optimal_done,
> min_in_hour,
> djd_debug2,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_warned2,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_no_eqs,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10_relerr,
> glob_look_poles,
> glob_display_flag,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmax,
> glob_h,
> glob_current_iter,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_fact_1,
> array_norms,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y,
> array_x,
> array_type_pole,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher_work2,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_start, glob_initial_pass, glob_log10normmin, glob_max_hours,
glob_log10_abserr, glob_dump_analytic, glob_not_yet_finished, days_in_year,
djd_debug, glob_max_opt_iter, glob_normmax, glob_hmin_init,
glob_not_yet_start_msg, glob_clock_sec, glob_almost_1, glob_orig_start_sec,
glob_smallish_float, centuries_in_millinium, glob_log10abserr, glob_iter,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_disp_incr,
glob_optimal_start, glob_large_float, glob_reached_optimal_h,
years_in_century, sec_in_min, glob_dump, glob_html_log, glob_max_sec,
glob_max_iter, glob_relerr, glob_last_good_h, glob_hmin, glob_optimal_done,
min_in_hour, djd_debug2, glob_subiter_method, glob_max_minutes,
glob_log10relerr, MAX_UNCHANGED, glob_warned2, glob_warned,
glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_clock_start_sec,
glob_optimal_expect_sec, glob_percent_done, glob_log10_relerr,
glob_look_poles, glob_display_flag, glob_curr_iter_when_opt,
glob_max_trunc_err, glob_abserr, glob_hmax, glob_h, glob_current_iter,
hours_in_day, array_const_1D0, array_const_1, array_const_0D0,
array_last_rel_error, array_pole, array_fact_1, array_norms,
array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y,
array_x, array_type_pole, array_y_init, array_real_pole, array_y_higher,
array_fact_2, array_complex_pole, array_poles, array_y_higher_work,
array_y_set_initial, array_y_higher_work2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_initial_pass,
> glob_log10normmin,
> glob_max_hours,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_finished,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_orig_start_sec,
> glob_smallish_float,
> centuries_in_millinium,
> glob_log10abserr,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_disp_incr,
> glob_optimal_start,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> sec_in_min,
> glob_dump,
> glob_html_log,
> glob_max_sec,
> glob_max_iter,
> glob_relerr,
> glob_last_good_h,
> glob_hmin,
> glob_optimal_done,
> min_in_hour,
> djd_debug2,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_warned2,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_no_eqs,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10_relerr,
> glob_look_poles,
> glob_display_flag,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmax,
> glob_h,
> glob_current_iter,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_fact_1,
> array_norms,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y,
> array_x,
> array_type_pole,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher_work2,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_start, glob_initial_pass, glob_log10normmin, glob_max_hours,
glob_log10_abserr, glob_dump_analytic, glob_not_yet_finished, days_in_year,
djd_debug, glob_max_opt_iter, glob_normmax, glob_hmin_init,
glob_not_yet_start_msg, glob_clock_sec, glob_almost_1, glob_orig_start_sec,
glob_smallish_float, centuries_in_millinium, glob_log10abserr, glob_iter,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_disp_incr,
glob_optimal_start, glob_large_float, glob_reached_optimal_h,
years_in_century, sec_in_min, glob_dump, glob_html_log, glob_max_sec,
glob_max_iter, glob_relerr, glob_last_good_h, glob_hmin, glob_optimal_done,
min_in_hour, djd_debug2, glob_subiter_method, glob_max_minutes,
glob_log10relerr, MAX_UNCHANGED, glob_warned2, glob_warned,
glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_clock_start_sec,
glob_optimal_expect_sec, glob_percent_done, glob_log10_relerr,
glob_look_poles, glob_display_flag, glob_curr_iter_when_opt,
glob_max_trunc_err, glob_abserr, glob_hmax, glob_h, glob_current_iter,
hours_in_day, array_const_1D0, array_const_1, array_const_0D0,
array_last_rel_error, array_pole, array_fact_1, array_norms,
array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y,
array_x, array_type_pole, array_y_init, array_real_pole, array_y_higher,
array_fact_2, array_complex_pole, array_poles, array_y_higher_work,
array_y_set_initial, array_y_higher_work2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_initial_pass,
> glob_log10normmin,
> glob_max_hours,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_finished,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_orig_start_sec,
> glob_smallish_float,
> centuries_in_millinium,
> glob_log10abserr,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_disp_incr,
> glob_optimal_start,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> sec_in_min,
> glob_dump,
> glob_html_log,
> glob_max_sec,
> glob_max_iter,
> glob_relerr,
> glob_last_good_h,
> glob_hmin,
> glob_optimal_done,
> min_in_hour,
> djd_debug2,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_warned2,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_no_eqs,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10_relerr,
> glob_look_poles,
> glob_display_flag,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmax,
> glob_h,
> glob_current_iter,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_fact_1,
> array_norms,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y,
> array_x,
> array_type_pole,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher_work2,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_start, glob_initial_pass, glob_log10normmin, glob_max_hours,
glob_log10_abserr, glob_dump_analytic, glob_not_yet_finished, days_in_year,
djd_debug, glob_max_opt_iter, glob_normmax, glob_hmin_init,
glob_not_yet_start_msg, glob_clock_sec, glob_almost_1, glob_orig_start_sec,
glob_smallish_float, centuries_in_millinium, glob_log10abserr, glob_iter,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_disp_incr,
glob_optimal_start, glob_large_float, glob_reached_optimal_h,
years_in_century, sec_in_min, glob_dump, glob_html_log, glob_max_sec,
glob_max_iter, glob_relerr, glob_last_good_h, glob_hmin, glob_optimal_done,
min_in_hour, djd_debug2, glob_subiter_method, glob_max_minutes,
glob_log10relerr, MAX_UNCHANGED, glob_warned2, glob_warned,
glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_clock_start_sec,
glob_optimal_expect_sec, glob_percent_done, glob_log10_relerr,
glob_look_poles, glob_display_flag, glob_curr_iter_when_opt,
glob_max_trunc_err, glob_abserr, glob_hmax, glob_h, glob_current_iter,
hours_in_day, array_const_1D0, array_const_1, array_const_0D0,
array_last_rel_error, array_pole, array_fact_1, array_norms,
array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y,
array_x, array_type_pole, array_y_init, array_real_pole, array_y_higher,
array_fact_2, array_complex_pole, array_poles, array_y_higher_work,
array_y_set_initial, array_y_higher_work2, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_initial_pass,
> glob_log10normmin,
> glob_max_hours,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_finished,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_orig_start_sec,
> glob_smallish_float,
> centuries_in_millinium,
> glob_log10abserr,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_disp_incr,
> glob_optimal_start,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> sec_in_min,
> glob_dump,
> glob_html_log,
> glob_max_sec,
> glob_max_iter,
> glob_relerr,
> glob_last_good_h,
> glob_hmin,
> glob_optimal_done,
> min_in_hour,
> djd_debug2,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_warned2,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_no_eqs,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10_relerr,
> glob_look_poles,
> glob_display_flag,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmax,
> glob_h,
> glob_current_iter,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_fact_1,
> array_norms,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y,
> array_x,
> array_type_pole,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher_work2,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre add $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_y[1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp2[1] := (array_tmp1[1] - (array_const_1D0[1]));
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre add $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D0[2] + array_y[2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp2[2] := (array_tmp1[2] - (array_const_1D0[2]));
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre add $eq_no = 1 i = 3
> array_tmp1[3] := array_const_0D0[3] + array_y[3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp2[3] := (array_tmp1[3] - (array_const_1D0[3]));
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add $eq_no = 1 i = 4
> array_tmp1[4] := array_const_0D0[4] + array_y[4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp2[4] := (array_tmp1[4] - (array_const_1D0[4]));
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add $eq_no = 1 i = 5
> array_tmp1[5] := array_const_0D0[5] + array_y[5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp2[5] := (array_tmp1[5] - (array_const_1D0[5]));
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit add $eq_no = 1
> array_tmp1[kkk] := array_const_0D0[kkk] + array_y[kkk];
> #emit sub $eq_no = 1
> array_tmp2[kkk] := (array_tmp1[kkk] - (array_const_1D0[kkk]));
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_start, glob_initial_pass, glob_log10normmin, glob_max_hours,
glob_log10_abserr, glob_dump_analytic, glob_not_yet_finished, days_in_year,
djd_debug, glob_max_opt_iter, glob_normmax, glob_hmin_init,
glob_not_yet_start_msg, glob_clock_sec, glob_almost_1, glob_orig_start_sec,
glob_smallish_float, centuries_in_millinium, glob_log10abserr, glob_iter,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_disp_incr,
glob_optimal_start, glob_large_float, glob_reached_optimal_h,
years_in_century, sec_in_min, glob_dump, glob_html_log, glob_max_sec,
glob_max_iter, glob_relerr, glob_last_good_h, glob_hmin, glob_optimal_done,
min_in_hour, djd_debug2, glob_subiter_method, glob_max_minutes,
glob_log10relerr, MAX_UNCHANGED, glob_warned2, glob_warned,
glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_clock_start_sec,
glob_optimal_expect_sec, glob_percent_done, glob_log10_relerr,
glob_look_poles, glob_display_flag, glob_curr_iter_when_opt,
glob_max_trunc_err, glob_abserr, glob_hmax, glob_h, glob_current_iter,
hours_in_day, array_const_1D0, array_const_1, array_const_0D0,
array_last_rel_error, array_pole, array_fact_1, array_norms,
array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y,
array_x, array_type_pole, array_y_init, array_real_pole, array_y_higher,
array_fact_2, array_complex_pole, array_poles, array_y_higher_work,
array_y_set_initial, array_y_higher_work2, glob_last;
array_tmp1[1] := array_const_0D0[1] + array_y[1];
array_tmp2[1] := array_tmp1[1] - array_const_1D0[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D0[2] + array_y[2];
array_tmp2[2] := array_tmp1[2] - array_const_1D0[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_const_0D0[3] + array_y[3];
array_tmp2[3] := array_tmp1[3] - array_const_1D0[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_const_0D0[4] + array_y[4];
array_tmp2[4] := array_tmp1[4] - array_const_1D0[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_const_0D0[5] + array_y[5];
array_tmp2[5] := array_tmp1[5] - array_const_1D0[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_const_0D0[kkk] + array_y[kkk];
array_tmp2[kkk] := array_tmp1[kkk] - array_const_1D0[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 17
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 13
> if array_fact_1[nnn] = 0 then # if number 14
> ret := nnn!;
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> if array_fact_2[mmm,nnn] = 0 then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 1.0 + exp(x);
> end;
exact_soln_y := proc(x) 1.0 + exp(x) end proc
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_initial_pass,
> glob_log10normmin,
> glob_max_hours,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_finished,
> days_in_year,
> djd_debug,
> glob_max_opt_iter,
> glob_normmax,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_almost_1,
> glob_orig_start_sec,
> glob_smallish_float,
> centuries_in_millinium,
> glob_log10abserr,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_disp_incr,
> glob_optimal_start,
> glob_large_float,
> glob_reached_optimal_h,
> years_in_century,
> sec_in_min,
> glob_dump,
> glob_html_log,
> glob_max_sec,
> glob_max_iter,
> glob_relerr,
> glob_last_good_h,
> glob_hmin,
> glob_optimal_done,
> min_in_hour,
> djd_debug2,
> glob_subiter_method,
> glob_max_minutes,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_warned2,
> glob_warned,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_no_eqs,
> glob_clock_start_sec,
> glob_optimal_expect_sec,
> glob_percent_done,
> glob_log10_relerr,
> glob_look_poles,
> glob_display_flag,
> glob_curr_iter_when_opt,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmax,
> glob_h,
> glob_current_iter,
> hours_in_day,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1D0,
> array_const_1,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_pole,
> array_fact_1,
> array_norms,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y,
> array_x,
> array_type_pole,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_fact_2,
> array_complex_pole,
> array_poles,
> array_y_higher_work,
> array_y_set_initial,
> array_y_higher_work2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGL := 3;
> INFO := 2;
> glob_start := 0;
> glob_initial_pass := true;
> glob_log10normmin := 0.1;
> glob_max_hours := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_not_yet_finished := true;
> days_in_year := 365.0;
> djd_debug := true;
> glob_max_opt_iter := 10;
> glob_normmax := 0.0;
> glob_hmin_init := 0.001;
> glob_not_yet_start_msg := true;
> glob_clock_sec := 0.0;
> glob_almost_1 := 0.9990;
> glob_orig_start_sec := 0.0;
> glob_smallish_float := 0.1e-100;
> centuries_in_millinium := 10.0;
> glob_log10abserr := 0.0;
> glob_iter := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_disp_incr := 0.1;
> glob_optimal_start := 0.0;
> glob_large_float := 9.0e100;
> glob_reached_optimal_h := false;
> years_in_century := 100.0;
> sec_in_min := 60.0;
> glob_dump := false;
> glob_html_log := true;
> glob_max_sec := 10000.0;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_hmin := 0.00000000001;
> glob_optimal_done := false;
> min_in_hour := 60.0;
> djd_debug2 := true;
> glob_subiter_method := 3;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> MAX_UNCHANGED := 10;
> glob_warned2 := false;
> glob_warned := false;
> glob_unchanged_h_cnt := 0;
> glob_small_float := 0.1e-50;
> glob_no_eqs := 0;
> glob_clock_start_sec := 0.0;
> glob_optimal_expect_sec := 0.1;
> glob_percent_done := 0.0;
> glob_log10_relerr := 0.1e-10;
> glob_look_poles := false;
> glob_display_flag := true;
> glob_curr_iter_when_opt := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_hmax := 1.0;
> glob_h := 0.1;
> glob_current_iter := 0;
> hours_in_day := 24.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/diff0postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = y - 1.0;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 1.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.01 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"1.0 + exp(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= 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_m1:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> 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_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_norms[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_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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=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 <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while iiif <= glob_max_terms do # do number 2
> jjjf := 0;
> while jjjf <= glob_max_terms do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 1.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.01 ;
> 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 ) = y - 1.0;");
> 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,"2012-06-17T20:05:52-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"diff0")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = y - 1.0;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 092 | ")
> ;
> logitem_str(html_log_file,"diff0 diffeq.mxt")
> ;
> logitem_str(html_log_file,"diff0 maple results")
> ;
> logitem_str(html_log_file,"Mostly affecting speed of factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp;
global DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_max_terms, DEBUGL, INFO,
glob_start, glob_initial_pass, glob_log10normmin, glob_max_hours,
glob_log10_abserr, glob_dump_analytic, glob_not_yet_finished, days_in_year,
djd_debug, glob_max_opt_iter, glob_normmax, glob_hmin_init,
glob_not_yet_start_msg, glob_clock_sec, glob_almost_1, glob_orig_start_sec,
glob_smallish_float, centuries_in_millinium, glob_log10abserr, glob_iter,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_disp_incr,
glob_optimal_start, glob_large_float, glob_reached_optimal_h,
years_in_century, sec_in_min, glob_dump, glob_html_log, glob_max_sec,
glob_max_iter, glob_relerr, glob_last_good_h, glob_hmin, glob_optimal_done,
min_in_hour, djd_debug2, glob_subiter_method, glob_max_minutes,
glob_log10relerr, MAX_UNCHANGED, glob_warned2, glob_warned,
glob_unchanged_h_cnt, glob_small_float, glob_no_eqs, glob_clock_start_sec,
glob_optimal_expect_sec, glob_percent_done, glob_log10_relerr,
glob_look_poles, glob_display_flag, glob_curr_iter_when_opt,
glob_max_trunc_err, glob_abserr, glob_hmax, glob_h, glob_current_iter,
hours_in_day, array_const_1D0, array_const_1, array_const_0D0,
array_last_rel_error, array_pole, array_fact_1, array_norms,
array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y,
array_x, array_type_pole, array_y_init, array_real_pole, array_y_higher,
array_fact_2, array_complex_pole, array_poles, array_y_higher_work,
array_y_set_initial, array_y_higher_work2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGL := 3;
INFO := 2;
glob_start := 0;
glob_initial_pass := true;
glob_log10normmin := 0.1;
glob_max_hours := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_not_yet_finished := true;
days_in_year := 365.0;
djd_debug := true;
glob_max_opt_iter := 10;
glob_normmax := 0.;
glob_hmin_init := 0.001;
glob_not_yet_start_msg := true;
glob_clock_sec := 0.;
glob_almost_1 := 0.9990;
glob_orig_start_sec := 0.;
glob_smallish_float := 0.1*10^(-100);
centuries_in_millinium := 10.0;
glob_log10abserr := 0.;
glob_iter := 0;
glob_optimal_clock_start_sec := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_optimal_start := 0.;
glob_large_float := 0.90*10^101;
glob_reached_optimal_h := false;
years_in_century := 100.0;
sec_in_min := 60.0;
glob_dump := false;
glob_html_log := true;
glob_max_sec := 10000.0;
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_hmin := 0.1*10^(-10);
glob_optimal_done := false;
min_in_hour := 60.0;
djd_debug2 := true;
glob_subiter_method := 3;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
MAX_UNCHANGED := 10;
glob_warned2 := false;
glob_warned := false;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1*10^(-50);
glob_no_eqs := 0;
glob_clock_start_sec := 0.;
glob_optimal_expect_sec := 0.1;
glob_percent_done := 0.;
glob_log10_relerr := 0.1*10^(-10);
glob_look_poles := false;
glob_display_flag := true;
glob_curr_iter_when_opt := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_hmax := 1.0;
glob_h := 0.1;
glob_current_iter := 0;
hours_in_day := 24.0;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/diff0postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y - 1.0;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 1.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.01 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "1.0 + exp(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_1st_rel_error := 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_m1 := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_y_higher := 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_poles := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
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_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_norms[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_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_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 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 <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 1.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.01;
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 ) = y - 1.0;");
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, "2012-06-17T20:05:52-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "diff0");
logitem_str(html_log_file, "diff ( y , x , 1 ) = y - 1.0;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 092 | ");
logitem_str(html_log_file,
"diff0 diffeq.mxt");
logitem_str(html_log_file,
"diff0 maple results");
logitem_str(html_log_file, "Mostly affecting speed of factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/diff0postode.ode#################
diff ( y , x , 1 ) = y - 1.0;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 1.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.01 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
1.0 + exp(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 1.1
y[1] (analytic) = 4.0041660239464331120584079535887
y[1] (numeric) = 4.0041660239464331120584079535887
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.101
y[1] (analytic) = 4.0071716925542110543346489259728
y[1] (numeric) = 4.0071716925542110544817441244636
absolute error = 1.470951984908e-19
relative error = 3.6707985026975487257384879981583e-18 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.102
y[1] (analytic) = 4.0101803683339321484713436721111
y[1] (numeric) = 4.0101803683339321487658284066339
absolute error = 2.944847345228e-19
relative error = 7.3434286609194714131903402268726e-18 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.103
y[1] (analytic) = 4.0131920542942724249125763295557
y[1] (numeric) = 4.0131920542942724253547453793789
absolute error = 4.421690498232e-19
relative error = 1.1017889097783442152150097090399e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.104
y[1] (analytic) = 4.0162067534469180949724617336901
y[1] (numeric) = 4.0162067534469180955626103203984
absolute error = 5.901485867083e-19
relative error = 1.4694178435953370791570473766388e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.105
y[1] (analytic) = 4.0192244688065685625216077057034
y[1] (numeric) = 4.0192244688065685632600314937879
absolute error = 7.384237880845e-19
relative error = 1.8372295297648820989301585251733e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.106
y[1] (analytic) = 4.0222452033909394386867701481565
y[1] (numeric) = 4.0222452033909394395737652456057
absolute error = 8.869950974492e-19
relative error = 2.2052238304651888308906884668416e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.107
y[1] (analytic) = 4.0252689602207655595667156480479
y[1] (numeric) = 4.0252689602207655606025786069387
absolute error = 1.0358629588908e-18
relative error = 2.5734006078291677122671742214075e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.108
y[1] (analytic) = 4.0282957423198040069673093034912
y[1] (numeric) = 4.0282957423198040081523371205813
absolute error = 1.1850278170901e-18
relative error = 2.9417597239463590140614131475007e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.109
y[1] (analytic) = 4.0313255527148371321588485093454
y[1] (numeric) = 4.0313255527148371334933386266664
absolute error = 1.3344901173210e-18
relative error = 3.3103010408631155614908669826062e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.11
y[1] (analytic) = 4.0343583944356755826586664593838
y[1] (numeric) = 4.0343583944356755841429167648347
absolute error = 1.4842503054509e-18
relative error = 3.6790244205820398642420307030134e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.111
y[1] (analytic) = 4.0373942705151613320420321478555
y[1] (numeric) = 4.0373942705151613336763409757974
absolute error = 1.6343088279419e-18
relative error = 4.0479297250634041076260307306446e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.112
y[1] (analytic) = 4.0404331839891707127843766815947
y[1] (numeric) = 4.0404331839891707145690428134457
absolute error = 1.7846661318510e-18
relative error = 4.4170168162240876060825681814729e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.113
y[1] (analytic) = 4.0434751378966174521378787451541
y[1] (numeric) = 4.0434751378966174540732014099853
absolute error = 1.9353226648312e-18
relative error = 4.7862855559387436984331512932035e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.114
y[1] (analytic) = 4.0465201352794557110454450958028
y[1] (numeric) = 4.0465201352794557131317239709351
absolute error = 2.0862788751323e-18
relative error = 5.1557358060402188470416617956270e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.115
y[1] (analytic) = 4.0495681791826831260951250026217
y[1] (numeric) = 4.0495681791826831283326602142231
absolute error = 2.2375352116014e-18
relative error = 5.5253674283192278623864754388392e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.116
y[1] (analytic) = 4.052619272654343854518000584364
y[1] (numeric) = 4.0526192726543438569070927080478
absolute error = 2.3890921236838e-18
relative error = 5.8951802845250164446104863086939e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.117
y[1] (analytic) = 4.0556734187455316222325980442257
y[1] (numeric) = 4.0556734187455316247735481056496
absolute error = 2.5409500614239e-18
relative error = 6.2651742363660195698706435564084e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.118
y[1] (analytic) = 4.058730620510392774938867846191
y[1] (numeric) = 4.0587306205103927776319773216563
absolute error = 2.6931094754653e-18
relative error = 6.6353491455085446732445742562119e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.119
y[1] (analytic) = 4.0617908810061293322647849271863
y[1] (numeric) = 4.0617908810061293351103557442388
absolute error = 2.8455708170525e-18
relative error = 7.0057048735793987585843932032327e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.12
y[1] (analytic) = 4.0648542032930020449686230918988
y[1] (numeric) = 4.0648542032930020479669576299298
absolute error = 2.9983345380310e-18
relative error = 7.3762412821645662896470197692446e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.121
y[1] (analytic) = 4.0679205904343334551999607927883
y[1] (numeric) = 4.0679205904343334583513618836362
absolute error = 3.1514010908479e-18
relative error = 7.7469582328091210019058489560630e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.122
y[1] (analytic) = 4.0709900454965109598224785565521
y[1] (numeric) = 4.0709900454965109631272494851056
absolute error = 3.3047709285535e-18
relative error = 8.1178555870195933458217610577738e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.123
y[1] (analytic) = 4.0740625715489898768016113800976
y[1] (numeric) = 4.0740625715489898802600558848987
absolute error = 3.4584445048011e-18
relative error = 8.4889332062619078524990006397978e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.124
y[1] (analytic) = 4.0771381716642965146601224839288
y[1] (numeric) = 4.0771381716642965182725447577772
absolute error = 3.6124222738484e-18
relative error = 8.8601909519632529597162034328973e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
memory used=3.8MB, alloc=2.9MB, time=0.17
x[1] = 1.125
y[1] (analytic) = 4.080216848918031245004667878777
y[1] (numeric) = 4.080216848918031248771372569335
absolute error = 3.7667046905580e-18
relative error = 9.2316286855117354351993146646345e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.126
y[1] (analytic) = 4.0832986063888715781264242722967
y[1] (numeric) = 4.0832986063888715820477164826947
absolute error = 3.9212922103980e-18
relative error = 9.6032462682562800719469316319850e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.127
y[1] (analytic) = 4.0863834471585752416788559167095
y[1] (numeric) = 4.0863834471585752457550412061526
absolute error = 4.0761852894431e-18
relative error = 9.9750435615077522255039597918349e-17 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.128
y[1] (analytic) = 4.0894713743119832624356990754214
y[1] (numeric) = 4.0894713743119832666670834597966
absolute error = 4.2313843843752e-18
relative error = 1.0347020426538851427313986751180e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.129
y[1] (analytic) = 4.0925623909370230511322458668527
y[1] (numeric) = 4.092562390937023055519135819337
absolute error = 4.3868899524843e-18
relative error = 1.0719176724584737319032992411240e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.13
y[1] (analytic) = 4.0956565001247114903930123270235
y[1] (numeric) = 4.0956565001247114949357147786922
absolute error = 4.5427024516687e-18
relative error = 1.1091512316841942425653662166188e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.131
y[1] (analytic) = 4.0987537049691580257488786188181
y[1] (numeric) = 4.0987537049691580304477009592546
absolute error = 4.6988223404365e-18
relative error = 1.1464027064470460351199989112851e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.132
y[1] (analytic) = 4.1018540085675677597467924053276
y[1] (numeric) = 4.1018540085675677646020424832336
absolute error = 4.8552500779060e-18
relative error = 1.1836720828593141600803456552490e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.133
y[1] (analytic) = 4.1049574140202445491551294972316
y[1] (numeric) = 4.104957414020244554167115621038
absolute error = 5.0119861238064e-18
relative error = 1.2209593470295821754614297222900e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.134
y[1] (analytic) = 4.1080639244305941052678089798371
y[1] (numeric) = 4.1080639244305941104368399183159
absolute error = 5.1690309384788e-18
relative error = 1.2582644850628178126334617297160e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.135
y[1] (analytic) = 4.1111735429051270973102631241492
y[1] (numeric) = 4.1111735429051271026366481070258
absolute error = 5.3263849828766e-18
relative error = 1.2955874830603121891141295762529e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.136
y[1] (analytic) = 4.1142862725534622589503654882003
y[1] (numeric) = 4.1142862725534622644344142067672
absolute error = 5.4840487185669e-18
relative error = 1.3329283271198622313691324327075e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.137
y[1] (analytic) = 4.1174021164883294979174237198279
y[1] (numeric) = 4.1174021164883295035594463275582
absolute error = 5.6420226077303e-18
relative error = 1.3702870033355635540889621303115e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.138
y[1] (analytic) = 4.120521077825573008732346680149
y[1] (numeric) = 4.1205210778255730145326537933115
absolute error = 5.8003071131625e-18
relative error = 1.4076634977980409953962170279038e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.139
y[1] (analytic) = 4.1236431596841543885520986181606
y[1] (numeric) = 4.1236431596841543945110013164357
absolute error = 5.9589026982751e-18
relative error = 1.4450577965944839813304655333575e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.14
y[1] (analytic) = 4.1267683651861557561315562411795
y[1] (numeric) = 4.126768365186155762249366068275
absolute error = 6.1178098270955e-18
relative error = 1.4824698858084635185151865524378e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.141
y[1] (analytic) = 4.1298966974567828739058876432372
y[1] (numeric) = 4.1298966974567828801829166075058
absolute error = 6.2770289642686e-18
relative error = 1.5198997515201857416947794991187e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.142
y[1] (analytic) = 4.1330281596243682731965751740702
y[1] (numeric) = 4.1330281596243682796331357491272
absolute error = 6.4365605750570e-18
relative error = 1.5573473798063812576368848367956e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.143
y[1] (analytic) = 4.1361627548203743825442074549888
y[1] (numeric) = 4.136162754820374389140612580331
absolute error = 6.5964051253422e-18
relative error = 1.5948127567404366383923583309844e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.144
y[1] (analytic) = 4.1393004861793966591711688746769
y[1] (numeric) = 4.1393004861793966659277319563017
absolute error = 6.7565630816248e-18
relative error = 1.6322958683922836073204863659985e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.145
y[1] (analytic) = 4.1424413568391667235773580278727
y[1] (numeric) = 4.1424413568391667304943929388988
absolute error = 6.9170349110261e-18
relative error = 1.6697967008286265703082555663499e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.146
y[1] (analytic) = 4.1455853699405554972720696929117
y[1] (numeric) = 4.1455853699405555043498907741996
absolute error = 7.0778210812879e-18
relative error = 1.7073152401127347922516231888900e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.147
y[1] (analytic) = 4.1487325286275763436451780802733
y[1] (numeric) = 4.1487325286275763508841001410473
absolute error = 7.2389220607740e-18
relative error = 1.7448514723046451580758896025216e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.148
y[1] (analytic) = 4.1518828360473882119807622235773
y[1] (numeric) = 4.151882836047388219381100542048
absolute error = 7.4003383184707e-18
relative error = 1.7824053834611230334470094676329e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.149
y[1] (analytic) = 4.1550362953502987846163175269177
y[1] (numeric) = 4.1550362953502987921783878509054
absolute error = 7.5620703239877e-18
relative error = 1.8199769596357194475505554388299e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.15
y[1] (analytic) = 4.1581929096897676272507006280068
y[1] (numeric) = 4.1581929096897676349748191755655
absolute error = 7.7241185475587e-18
relative error = 1.8575661868787557443298764241883e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.151
y[1] (analytic) = 4.1613526822224093424039578853379
y[1] (numeric) = 4.1613526822224093502904413453802
absolute error = 7.8864834600423e-18
relative error = 1.8951730512373802706522416957865e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.152
y[1] (analytic) = 4.1645156161079967260321909494573
y[1] (numeric) = 4.16451561610799673408135648238
absolute error = 8.0491655329227e-18
relative error = 1.9327975387555766566565615728400e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.153
y[1] (analytic) = 4.1676817145094639273006160334744
y[1] (numeric) = 4.167681714509463935512781271785
absolute error = 8.2121652383106e-18
relative error = 1.9704396354742199213926127719092e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.154
y[1] (analytic) = 4.1708509805929096115179766561321
y[1] (numeric) = 4.1708509805929096198934597050761
absolute error = 8.3754830489440e-18
relative error = 2.0080993274311082214410142796141e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.155
y[1] (analytic) = 4.1740234175276001262354727921153
y[1] (numeric) = 4.174023417527600134774592230304
absolute error = 8.5391194381887e-18
relative error = 2.0457766006609224557787671129525e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.156
y[1] (analytic) = 4.177199028485972670513372528788
y[1] (numeric) = 4.1771990284859726792164474088274
absolute error = 8.7030748800394e-18
relative error = 2.0834714411953295656526617139263e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.157
y[1] (analytic) = 4.1803778166436384673584754962368
y[1] (numeric) = 4.1803778166436384762258253453573
absolute error = 8.8673498491205e-18
relative error = 2.1211838350630134736640915930855e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.158
y[1] (analytic) = 4.1835597851793859393356005083486
y[1] (numeric) = 4.1835597851793859483675453290349
absolute error = 9.0319448206863e-18
relative error = 2.1589137682895623363801925154682e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.159
y[1] (analytic) = 4.1867449372751838873562730266726
y[1] (numeric) = 4.1867449372751838965531332972953
absolute error = 9.1968602706227e-18
relative error = 2.1966612268977144581132831594128e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.16
y[1] (analytic) = 4.1899332761161846726477912360218
y[1] (numeric) = 4.1899332761161846820098879114693
absolute error = 9.3620966754475e-18
relative error = 2.2344261969072688220433321882811e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.161
y[1] (analytic) = 4.1931248048907274019058527011435
y[1] (numeric) = 4.1931248048907274114335072134544
absolute error = 9.5276545123109e-18
relative error = 2.2722086643350435986280934141312e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.162
y[1] (analytic) = 4.1963195267903411156339267573512
y[1] (numeric) = 4.196319526790341125327461016348
absolute error = 9.6935342589968e-18
relative error = 2.3100086151950253594541888667588e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.163
y[1] (analytic) = 4.199517445009747979672560974756
y[1] (numeric) = 4.1995174450097479895322973686794
absolute error = 9.8597363939234e-18
relative error = 2.3478260354983507967142764553766e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.164
y[1] (analytic) = 4.2027185627468664799218132256705
y[1] (numeric) = 4.2027185627468664899480746218145
absolute error = 1.00262613961440e-17
relative error = 2.3856609112533359860334030368862e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.165
y[1] (analytic) = 4.2059228832028146202600040778825
y[1] (numeric) = 4.2059228832028146304531138232301
absolute error = 1.01931097453476e-17
relative error = 2.4235132284654578353746011048271e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=7.6MB, alloc=4.0MB, time=0.35
x[1] = 1.166
y[1] (analytic) = 4.2091304095819131236619874328181
y[1] (numeric) = 4.2091304095819131340222693546783
absolute error = 1.03602819218602e-17
relative error = 2.4613829731375017954624571543454e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.167
y[1] (analytic) = 4.2123411450916886365201405271318
y[1] (numeric) = 4.2123411450916886470479189337766
absolute error = 1.05277784066448e-17
relative error = 2.4992701312694001495380773743641e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.168
y[1] (analytic) = 4.2155550929428769361712776189791
y[1] (numeric) = 4.2155550929428769468668773002823
absolute error = 1.06955996813032e-17
relative error = 2.5371746888584979030889118599452e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.169
y[1] (analytic) = 4.2187722563494261416326948861554
y[1] (numeric) = 4.2187722563494261524964411142311
absolute error = 1.08637462280757e-17
relative error = 2.5750966318993195539740633008871e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.17
y[1] (analytic) = 4.2219926385284999275505572724101
y[1] (numeric) = 4.2219926385284999385827758022529
absolute error = 1.10322185298428e-17
relative error = 2.6130359463838105090625585047806e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.171
y[1] (analytic) = 4.2252162427004807413638412305939
y[1] (numeric) = 4.2252162427004807525648583007196
absolute error = 1.12010170701257e-17
relative error = 2.6509926183012932584912276592767e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.172
y[1] (analytic) = 4.2284430720889730236870505268483
y[1] (numeric) = 4.228443072088973035057192859935
absolute error = 1.13701423330867e-17
relative error = 2.6889666336383999704020615281992e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.173
y[1] (analytic) = 4.2316731299208064319149254888211
y[1] (numeric) = 4.2316731299208064434545202923518
absolute error = 1.15395948035307e-17
relative error = 2.7269579783792652085880545046026e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.174
y[1] (analytic) = 4.2349064194260390670523693028876
y[1] (numeric) = 4.2349064194260390787617442697931
absolute error = 1.17093749669055e-17
relative error = 2.7649666385054342786175788528426e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.175
y[1] (analytic) = 4.2381429438379607037728181905713
y[1] (numeric) = 4.2381429438379607156523014998739
absolute error = 1.18794833093026e-17
relative error = 2.8029925999958898385455996840049e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.176
y[1] (analytic) = 4.2413827063930960237082855228031
y[1] (numeric) = 4.2413827063930960357582058402615
absolute error = 1.20499203174584e-17
relative error = 2.8410358488271725660715099564170e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.177
y[1] (analytic) = 4.2446257103312078519743131623343
y[1] (numeric) = 4.2446257103312078641949996410889
absolute error = 1.22206864787546e-17
relative error = 2.8790963709733126682076495368878e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.178
y[1] (analytic) = 4.2478719588953003969330665595226
y[1] (numeric) = 4.2478719588953004093248488407419
absolute error = 1.23917822812193e-17
relative error = 2.9171741524059263613585812621180e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.179
y[1] (analytic) = 4.2511214553316224931978133648575
y[1] (numeric) = 4.2511214553316225057610215783849
absolute error = 1.25632082135274e-17
relative error = 2.9552691790941471152952847618748e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.18
y[1] (analytic) = 4.2543742028896708478820285629729
y[1] (numeric) = 4.2543742028896708606169933279749
absolute error = 1.27349647650020e-17
relative error = 2.9933814370047921325058894086213e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.181
y[1] (analytic) = 4.2576302048221932900963723775236
y[1] (numeric) = 4.2576302048221933030034248031382
absolute error = 1.29070524256146e-17
relative error = 3.0315109121022460853473406918293e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.182
y[1] (analytic) = 4.2608894643851920236967904441737
y[1] (numeric) = 4.2608894643851920367762621301599
absolute error = 1.30794716859862e-17
relative error = 3.0696575903485564770608248239765e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.183
y[1] (analytic) = 4.2641519848379268832869890000679
y[1] (numeric) = 4.2641519848379268965392120374562
absolute error = 1.32522230373883e-17
relative error = 3.1078214577035049818557487794841e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.184
y[1] (analytic) = 4.2674177694429185934785410925333
y[1] (numeric) = 4.2674177694429186069038480642768
absolute error = 1.34253069717435e-17
relative error = 3.1460025001245845910440190592699e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.185
y[1] (analytic) = 4.2706868214659520314118830673888
y[1] (numeric) = 4.2706868214659520450106070490147
absolute error = 1.35987239816259e-17
relative error = 3.1842007035669298996227758551133e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.186
y[1] (analytic) = 4.2739591441760794925414638581296
y[1] (numeric) = 4.2739591441760795063139384183924
absolute error = 1.37724745602628e-17
relative error = 3.2224160539835517474139686822591e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.187
y[1] (analytic) = 4.2772347408456239596883128614104
y[1] (numeric) = 4.2772347408456239736348720629453
absolute error = 1.39465592015349e-17
relative error = 3.2606485373252199557125877794878e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.188
y[1] (analytic) = 4.2805136147501823753632954516656
y[1] (numeric) = 4.2805136147501823894842738516427
absolute error = 1.41209783999771e-17
relative error = 3.2988981395404866378724152880926e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.189
y[1] (analytic) = 4.2837957691686289173643284583956
y[1] (numeric) = 4.2837957691686289316600611091754
absolute error = 1.42957326507798e-17
relative error = 3.3371648465758259879488720745564e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.19
y[1] (analytic) = 4.2870812073831182776508312036078
y[1] (numeric) = 4.2870812073831182921216536533967
absolute error = 1.44708224497889e-17
relative error = 3.3754486443754700560464650109268e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.191
y[1] (analytic) = 4.2903699326790889444986909741357
y[1] (numeric) = 4.2903699326790889591449392676432
absolute error = 1.46462482935075e-17
relative error = 3.4137495188816413797391287566528e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.192
y[1] (analytic) = 4.2936619483452664879390250840762
y[1] (numeric) = 4.2936619483452665027610357631723
absolute error = 1.48220106790961e-17
relative error = 3.4520674560344350596570034681229e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.193
y[1] (analytic) = 4.2969572576736668484840249663801
y[1] (numeric) = 4.2969572576736668634821350707539
absolute error = 1.49981101043738e-17
relative error = 3.4904024417719339643667662824111e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.194
y[1] (analytic) = 4.3002558639595996291431710197145
y[1] (numeric) = 4.3002558639595996443177180875333
absolute error = 1.51745470678188e-17
relative error = 3.5287544620301604892895992856452e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.195
y[1] (analytic) = 4.3035577705016713907331102270859
y[1] (numeric) = 4.3035577705016714060844322956555
absolute error = 1.53513220685696e-17
relative error = 3.5671235027431910578168118346997e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.196
y[1] (analytic) = 4.3068629806017889504844918563765
y[1] (numeric) = 4.3068629806017889660129274628018
absolute error = 1.55284356064253e-17
relative error = 3.6055095498430609910042068824885e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.197
y[1] (analytic) = 4.3101714975651626839490598499039
y[1] (numeric) = 4.3101714975651626996549480317508
absolute error = 1.57058881818469e-17
relative error = 3.6439125892599016880784931427575e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.198
y[1] (analytic) = 4.3134833247003098302103038103722
y[1] (numeric) = 4.3134833247003098460939841063303
absolute error = 1.58836802959581e-17
relative error = 3.6823326069219611238883315093511e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.199
y[1] (analytic) = 4.3167984653190578004009737941409
y[1] (numeric) = 4.3167984653190578164627862446866
absolute error = 1.60618124505457e-17
relative error = 3.7207695887555314536123067068993e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.2
y[1] (analytic) = 4.3201169227365474895307674296016
y[1] (numeric) = 4.3201169227365475057710525776624
absolute error = 1.62402851480608e-17
relative error = 3.7592235206850619940823917874224e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.201
y[1] (analytic) = 4.3234387002712365916275011886262
y[1] (numeric) = 4.3234387002712366080466000802456
absolute error = 1.64190988916194e-17
relative error = 3.7976943886331327695207664618995e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.202
y[1] (analytic) = 4.3267638012449029181950809525336
y[1] (numeric) = 4.3267638012449029347933351375371
absolute error = 1.65982541850035e-17
relative error = 3.8361821785205436014861297198811e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.203
y[1] (analytic) = 4.3300922289826477199915903308224
y[1] (numeric) = 4.3300922289826477367693418634844
absolute error = 1.67777515326620e-17
relative error = 3.8746868762663564623167946861554e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.204
y[1] (analytic) = 4.3334239868128990121308185110351
y[1] (numeric) = 4.3334239868128990290884099507458
absolute error = 1.69575914397107e-17
relative error = 3.9132084677877298070305647006718e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.205
y[1] (analytic) = 4.3367590780674149025105527415571
y[1] (numeric) = 4.3367590780674149196483271534915
absolute error = 1.71377744119344e-17
relative error = 3.9517469390002377635792946300129e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.206
y[1] (analytic) = 4.3400975060812869235709638759227
y[1] (numeric) = 4.3400975060812869408892648317094
absolute error = 1.73183009557867e-17
relative error = 3.9903022758176577712769402552685e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=11.4MB, alloc=4.1MB, time=0.54
x[1] = 1.207
y[1] (analytic) = 4.3434392741929433673864167372895
y[1] (numeric) = 4.3434392741929433848855883156807
absolute error = 1.74991715783912e-17
relative error = 4.0288744641520813844603441535850e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.208
y[1] (analytic) = 4.3467843857441526240940403951701
y[1] (numeric) = 4.3467843857441526417744271827125
absolute error = 1.76803867875424e-17
relative error = 4.0674634899139554101839414501718e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.209
y[1] (analytic) = 4.3501328440800265236623967832695
y[1] (numeric) = 4.3501328440800265415243438749761
absolute error = 1.78619470917066e-17
relative error = 4.1060693390121227168854948288276e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.21
y[1] (analytic) = 4.3534846525490236810035894273757
y[1] (numeric) = 4.3534846525490236990474424273982
absolute error = 1.80438530000225e-17
relative error = 4.1446919973537938047580145218984e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.211
y[1] (analytic) = 4.3568398145029528444321573956904
y[1] (numeric) = 4.3568398145029528626582624179925
absolute error = 1.82261050223021e-17
relative error = 4.1833314508445872248437938618581e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.212
y[1] (analytic) = 4.360198333296976247474102930773
y[1] (numeric) = 4.3601983332969762658828065998047
absolute error = 1.84087036690317e-17
relative error = 4.2219876853885926065536666714201e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.213
y[1] (analytic) = 4.363560212289612964029404572405
y[1] (numeric) = 4.3635602122896129826210540237775
absolute error = 1.85916494513725e-17
relative error = 4.2606606868883415856361073059208e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.214
y[1] (analytic) = 4.3669254548427422668913709341673
y[1] (numeric) = 4.366925454842742285666313815329
absolute error = 1.87749428811617e-17
relative error = 4.2993504412448932229894810577192e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.215
y[1] (analytic) = 4.3702940643216069896261936533644
y[1] (numeric) = 4.3702940643216070085847781242774
absolute error = 1.89585844709130e-17
relative error = 4.3380569343577815976719500428164e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.216
y[1] (analytic) = 4.3736660440948168918160613941278
y[1] (numeric) = 4.3736660440948169109586361279458
absolute error = 1.91425747338180e-17
relative error = 4.3767801521251692781995275479836e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.217
y[1] (analytic) = 4.3770413975343520276692001470946
y[1] (numeric) = 4.3770413975343520469961143308408
absolute error = 1.93269141837462e-17
relative error = 4.4155200804436800924779669832108e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.218
y[1] (analytic) = 4.3804201280155661180002084359801
y[1] (numeric) = 4.3804201280155661375118117712268
absolute error = 1.95116033352467e-17
relative error = 4.4542767052086206200541737089928e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.219
y[1] (analytic) = 4.3838022389171899255840594116627
y[1] (numeric) = 4.3838022389171899452807021152112
absolute error = 1.96966427035485e-17
relative error = 4.4930500123138811613427471666905e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.22
y[1] (analytic) = 4.3871877336213346338871451880633
y[1] (numeric) = 4.387187733621334653769177992625
absolute error = 1.98820328045617e-17
relative error = 4.5318399876520421653989644329959e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.221
y[1] (analytic) = 4.3905766155134952291787421511456
y[1] (numeric) = 4.3905766155134952492465163060235
absolute error = 2.00677741548779e-17
relative error = 4.5706466171142978148098780223519e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.222
y[1] (analytic) = 4.3939688879825538860262793527837
y[1] (numeric) = 4.3939688879825539062801466245554
absolute error = 2.02538672717717e-17
relative error = 4.6094698865906301649261685259100e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.223
y[1] (analytic) = 4.3973645544207833561777954850489
y[1] (numeric) = 4.3973645544207833766181081582496
absolute error = 2.04403126732007e-17
relative error = 4.6483097819696412210150219864083e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.224
y[1] (analytic) = 4.4007636182238503608349733176533
y[1] (numeric) = 4.4007636182238503814620841954606
absolute error = 2.06271108778073e-17
relative error = 4.6871662891387946697215123942115e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.225
y[1] (analytic) = 4.4041660827908189863201438718694
y[1] (numeric) = 4.404166082790819007134406276788
absolute error = 2.08142624049186e-17
relative error = 4.7260393939842249384863974764049e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.226
y[1] (analytic) = 4.4075719515241540831406559982103
y[1] (numeric) = 4.4075719515241541041424237727584
absolute error = 2.10017677745481e-17
relative error = 4.7649290823909553837681914853537e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.227
y[1] (analytic) = 4.4109812278297246684540104225264
y[1] (numeric) = 4.4109812278297246896436379299222
absolute error = 2.11896275073958e-17
relative error = 4.8038353402427525940158402202044e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.228
y[1] (analytic) = 4.4143939151168073319371607259328
y[1] (numeric) = 4.4143939151168073533150028507827
absolute error = 2.13778421248499e-17
relative error = 4.8427581534223436743029772804183e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.229
y[1] (analytic) = 4.4178100167980896450633871281557
y[1] (numeric) = 4.4178100167980896666297992771424
absolute error = 2.15664121489867e-17
relative error = 4.8816975078112249380812028963010e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.23
y[1] (analytic) = 4.4212295362896735737901523514522
y[1] (numeric) = 4.4212295362896735955454904540245
absolute error = 2.17553381025723e-17
relative error = 4.9206533892898784677217390066062e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.231
y[1] (analytic) = 4.4246524770110788946613522532473
y[1] (numeric) = 4.42465247701107891660597276231
absolute error = 2.19446205090627e-17
relative error = 4.9596257837376259162380865626849e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.232
y[1] (analytic) = 4.4280788423852466143273773300196
y[1] (numeric) = 4.4280788423852466364616372226252
absolute error = 2.21342598926056e-17
relative error = 4.9986146770328667556606146329553e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.233
y[1] (analytic) = 4.431508635838542392486404612786
y[1] (numeric) = 4.4315086358385424148106613908262
absolute error = 2.23242567780402e-17
relative error = 5.0376200550528639614392804032262e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.234
y[1] (analytic) = 4.4349418608007599682503428957595
y[1] (numeric) = 4.4349418608007599907649545866583
absolute error = 2.25146116908988e-17
relative error = 5.0766419036739364133165205372814e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.235
y[1] (analytic) = 4.4383785207051245899388576644125
y[1] (numeric) = 4.43837852070512461264418282182
absolute error = 2.27053251574075e-17
relative error = 5.1156802087714474813499465401814e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.236
y[1] (analytic) = 4.4418186189882964483049055172559
y[1] (numeric) = 4.4418186189882964712013032217428
absolute error = 2.28963977044869e-17
relative error = 5.1547349562197935185508368343238e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.237
y[1] (analytic) = 4.4452621590903741131952113071546
y[1] (numeric) = 4.4452621590903741362830411669075
absolute error = 2.30878298597529e-17
relative error = 5.1938061318924147566169161724863e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.238
y[1] (analytic) = 4.4487091444548979736491246629424
y[1] (numeric) = 4.4487091444548979969287468144604
absolute error = 2.32796221515180e-17
relative error = 5.2328937216619183970852032749991e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.239
y[1] (analytic) = 4.4521595785288536814392959904806
y[1] (numeric) = 4.4521595785288537049110710992722
absolute error = 2.34717751087916e-17
relative error = 5.2719977113999763738447425827957e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.24
y[1] (analytic) = 4.455613464762675598057615494122
y[1] (numeric) = 4.4556134647626756217219047554035
absolute error = 2.36642892612815e-17
relative error = 5.3111180869774927667872362813715e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.241
y[1] (analytic) = 4.4590708066102502451498622048078
y[1] (numeric) = 4.4590708066102502690070273442019
absolute error = 2.38571651393941e-17
relative error = 5.3502548342644787497406396785589e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.242
y[1] (analytic) = 4.4625316075289197584025134497329
y[1] (numeric) = 4.4625316075289197824529167239686
absolute error = 2.40504032742357e-17
relative error = 5.3894079391301744689026871934070e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.243
y[1] (analytic) = 4.4659958709794853448851686506773
y[1] (numeric) = 4.4659958709794853691291728482907
absolute error = 2.42440041976134e-17
relative error = 5.4285773874430806415914769657435e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.244
y[1] (analytic) = 4.4694636004262107438520447937159
y[1] (numeric) = 4.4694636004262107682900132357515
absolute error = 2.44379684420356e-17
relative error = 5.4677631650709003635712170852657e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.245
y[1] (analytic) = 4.4729347993368256910060043720902
y[1] (numeric) = 4.4729347993368257156383009128034
absolute error = 2.46322965407132e-17
relative error = 5.5069652578806375356843861738630e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.246
y[1] (analytic) = 4.476409471182529386228580066558
y[1] (numeric) = 4.4764094711825294110555690941183
absolute error = 2.48269890275603e-17
relative error = 5.5461836517385829876726153469647e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.247
y[1] (analytic) = 4.4798876194379939647794638935359
y[1] (numeric) = 4.4798876194379939898015103307313
absolute error = 2.50220464371954e-17
relative error = 5.5854183325104121277270510477995e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.248
y[1] (analytic) = 4.4833692475813679719689320208126
y[1] (numeric) = 4.4833692475813679971864013257542
absolute error = 2.52174693049416e-17
relative error = 5.6246692860610589418549271239886e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
memory used=15.2MB, alloc=4.1MB, time=0.74
x[1] = 1.249
y[1] (analytic) = 4.4868543590942798413066799235461
y[1] (numeric) = 4.4868543590942798667199380903744
absolute error = 2.54132581668283e-17
relative error = 5.6639364982549247406435403101370e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.25
y[1] (analytic) = 4.4903429574618413761305460296723
y[1] (numeric) = 4.4903429574618414017399595892637
absolute error = 2.56094135595914e-17
relative error = 5.7032199549557517344945295852954e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.251
y[1] (analytic) = 4.4938350461726512347186054837364
y[1] (numeric) = 4.493835046172651260524541504411
absolute error = 2.58059360206746e-17
relative error = 5.7425196420267418274543045292869e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.252
y[1] (analytic) = 4.4973306287187984188881191415326
y[1] (numeric) = 4.4973306287187984448909452297627
absolute error = 2.60028260882301e-17
relative error = 5.7818355453305412954275864302235e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.253
y[1] (analytic) = 4.5008297085958657660848263947917
y[1] (numeric) = 4.500829708595865792284910695911
absolute error = 2.62000843011193e-17
relative error = 5.8211676507292253853675507671244e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.254
y[1] (analytic) = 4.5043322893029334449660739154997
y[1] (numeric) = 4.5043322893029334713637851144139
absolute error = 2.63977111989142e-17
relative error = 5.8605159440844382419806635432712e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.255
y[1] (analytic) = 4.5078383743425824544812759032684
y[1] (numeric) = 4.5078383743425824810769832251662
absolute error = 2.65957073218978e-17
relative error = 5.8998804112573101955597024636497e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.256
y[1] (analytic) = 4.5113479672208981264532049165091
y[1] (numeric) = 4.5113479672208981532472781275743
absolute error = 2.67940732110652e-17
relative error = 5.9392610381085304484927373230069e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.257
y[1] (analytic) = 4.5148610714474736316636158689929
y[1] (numeric) = 4.5148610714474736586564252771172
absolute error = 2.69928094081243e-17
relative error = 5.9786578104983306754473264842780e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.258
y[1] (analytic) = 4.5183776905354134894467092777124
y[1] (numeric) = 4.5183776905354135166386257332096
absolute error = 2.71919164554972e-17
relative error = 6.0180707142866234715156688813868e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.259
y[1] (analytic) = 4.5218978280013370807939433558024
y[1] (numeric) = 4.5218978280013371081853382521227
absolute error = 2.73913948963203e-17
relative error = 6.0574997353328525125279698119531e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.26
y[1] (analytic) = 4.5254214873653821649737080556228
y[1] (numeric) = 4.5254214873653821925649533300685
absolute error = 2.75912452744457e-17
relative error = 6.0969448594961305286063807372053e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.261
y[1] (analytic) = 4.5289486721512083996693776819714
y[1] (numeric) = 4.5289486721512084274608458164135
absolute error = 2.77914681344421e-17
relative error = 6.1364060726352660810273299631719e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.262
y[1] (analytic) = 4.5324793858860008646392622137731
y[1] (numeric) = 4.5324793858860008926313262353686
absolute error = 2.79920640215955e-17
relative error = 6.1758833606087459353308054077853e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.263
y[1] (analytic) = 4.5360136321004735889019809944896
y[1] (numeric) = 4.5360136321004736170950144763997
absolute error = 2.81930334819101e-17
relative error = 6.2153767092747614554879230515866e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.264
y[1] (analytic) = 4.5395514143288730814507859769173
y[1] (numeric) = 4.5395514143288731098451630390268
absolute error = 2.83943770621095e-17
relative error = 6.2548861044913008077877544713993e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.265
y[1] (analytic) = 4.5430927361089818655003652369921
y[1] (numeric) = 4.5430927361089818940964605466291
absolute error = 2.85960953096370e-17
relative error = 6.2944115321160424775892097432149e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.266
y[1] (analytic) = 4.546637600982122016269661003697
y[1] (numeric) = 4.546637600982122045067849776354
absolute error = 2.87981887726570e-17
relative error = 6.3339529780064910672192217859101e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.267
y[1] (analytic) = 4.5501860124931587023042399881873
y[1] (numeric) = 4.5501860124931587313048979882431
absolute error = 2.90006580000558e-17
relative error = 6.3735104280199804429874646797931e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.268
y[1] (analytic) = 4.5537379741905037303417573347981
y[1] (numeric) = 4.5537379741905037595452608762404
absolute error = 2.92035035414423e-17
relative error = 6.4130838680136547531948206530724e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.269
y[1] (analytic) = 4.5572934896261190937240590596928
y[1] (numeric) = 4.557293489626119123130785006842
absolute error = 2.94067259471492e-17
relative error = 6.4526732838445590949347340917084e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.27
y[1] (analytic) = 4.5608525623555205243594713895519
y[1] (numeric) = 4.5608525623555205539697971577856
absolute error = 2.96103257682337e-17
relative error = 6.4922786613696199737013260893717e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.271
y[1] (analytic) = 4.5644151959377810482388289628871
y[1] (numeric) = 4.5644151959377810780531325193653
absolute error = 2.98143035564782e-17
relative error = 6.5318999864456256994210248301340e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.272
y[1] (analytic) = 4.5679813939355345445087974103041
y[1] (numeric) = 4.5679813939355345745274572746957
absolute error = 3.00186598643916e-17
relative error = 6.5715372449293380685279937316725e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.273
y[1] (analytic) = 4.5715511599149793081060493873352
y[1] (numeric) = 4.5715511599149793383294446325452
absolute error = 3.02233952452100e-17
relative error = 6.6111904226774721217335558547526e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.274
y[1] (analytic) = 4.5751244974458816159558566943127
y[1] (numeric) = 4.5751244974458816463843669472103
absolute error = 3.04285102528976e-17
relative error = 6.6508595055467195554594453794051e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.275
y[1] (analytic) = 4.578701410101579296738664682174
y[1] (numeric) = 4.5787014101015793273726701243218
absolute error = 3.06340054421478e-17
relative error = 6.6905444793938155484535998162832e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.276
y[1] (analytic) = 4.5822819014589853042282187110692
y[1] (numeric) = 4.5822819014589853350681000794528
absolute error = 3.08398813683836e-17
relative error = 6.7302453300754523569510897803225e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.277
y[1] (analytic) = 4.5858659750985912942048160001958
y[1] (numeric) = 4.5858659750985913252509545879549
absolute error = 3.10461385877591e-17
relative error = 6.7699620434484330258733604220717e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.278
y[1] (analytic) = 4.5894536346044712049472597824105
y[1] (numeric) = 4.5894536346044712362000374395706
absolute error = 3.12527776571601e-17
relative error = 6.8096946053696281217446037704218e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.279
y[1] (analytic) = 4.5930448835642848413070962558706
y[1] (numeric) = 4.5930448835642848727668953900757
absolute error = 3.14597991342051e-17
relative error = 6.8494430016960195994553185709351e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.28
y[1] (analytic) = 4.5966397255692814623687184072408
y[1] (numeric) = 4.5966397255692814940359219844868
absolute error = 3.16672035772460e-17
relative error = 6.8892072182846790413215965648641e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.281
y[1] (analytic) = 4.6002381642143033726989243668673
y[1] (numeric) = 4.6002381642143034045739159122366
absolute error = 3.18749915453693e-17
relative error = 6.9289872409928545310132374758621e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.282
y[1] (analytic) = 4.6038402030977895171895215457785
y[1] (numeric) = 4.6038402030977895492726851441752
absolute error = 3.20831635983967e-17
relative error = 6.9687830556779266366701774313802e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.283
y[1] (analytic) = 4.6074458458217790794965713974139
y[1] (numeric) = 4.6074458458217791117882916943005
absolute error = 3.22917202968866e-17
relative error = 7.0085946481975597786846288318473e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.284
y[1] (analytic) = 4.611055095991915084079873243628
y[1] (numeric) = 4.6110550959919151165805354457622
absolute error = 3.25006622021342e-17
relative error = 7.0484220044095491109862076794862e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.285
y[1] (analytic) = 4.6146679572174480018462892047514
y[1] (numeric) = 4.6146679572174480345562790809244
absolute error = 3.27099898761730e-17
relative error = 7.0882651101719713428205681456183e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.286
y[1] (analytic) = 4.6182844331112393594005158773358
y[1] (numeric) = 4.6182844331112393923202197591113
absolute error = 3.29197038817755e-17
relative error = 7.1281239513431614700040526306217e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.287
y[1] (analytic) = 4.6219045272897653519069120106541
y[1] (numeric) = 4.6219045272897653850367167931083
absolute error = 3.31298047824542e-17
relative error = 7.1679985137817543646949952812426e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.288
y[1] (analytic) = 4.6255282433731204595659950440859
y[1] (numeric) = 4.6255282433731204929062881865483
absolute error = 3.33402931424624e-17
relative error = 7.2078887833466827725209297436978e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.289
y[1] (analytic) = 4.6291555849850210677092229821847
y[1] (numeric) = 4.6291555849850211012603925089799
absolute error = 3.35511695267952e-17
relative error = 7.2477947458972183642335373903438e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.29
y[1] (analytic) = 4.6327865557528090905156817025115
y[1] (numeric) = 4.632786555752809124278116203702
absolute error = 3.37624345011905e-17
relative error = 7.2877163872930124350496259267855e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=19.0MB, alloc=4.1MB, time=0.93
x[1] = 1.291
y[1] (analytic) = 4.6364211593074555983543014132237
y[1] (numeric) = 4.6364211593074556323283900453535
absolute error = 3.39740886321298e-17
relative error = 7.3276536933940931161134001701104e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.292
y[1] (analytic) = 4.6400593992835644487552296029379
y[1] (numeric) = 4.6400593992835644829413620897769
absolute error = 3.41861324868390e-17
relative error = 7.3676066500608624388926982637498e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.293
y[1] (analytic) = 4.6437012793193759210139914545421
y[1] (numeric) = 4.6437012793193759554125580878317
absolute error = 3.43985666332896e-17
relative error = 7.4075752431541793914425459449492e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.294
y[1] (analytic) = 4.6473468030567703544320723274211
y[1] (numeric) = 4.6473468030567703890434639676206
absolute error = 3.46113916401995e-17
relative error = 7.4475594585353563530655698193789e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.295
y[1] (analytic) = 4.6509959741412717901975605489803
y[1] (numeric) = 4.6509959741412718250221686260142
absolute error = 3.48246080770339e-17
relative error = 7.4875592820661768854956549077937e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.296
y[1] (analytic) = 4.6546487962220516169094923964141
y[1] (numeric) = 4.6546487962220516519477089104203
absolute error = 3.50382165140062e-17
relative error = 7.5275746996089132793392505580534e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.297
y[1] (analytic) = 4.658305272951932219749544793368
y[1] (numeric) = 4.6583052729519322550017623154472
absolute error = 3.52522175220792e-17
relative error = 7.5676056970264082578228140727705e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.298
y[1] (analytic) = 4.6619654079873906333047248934913
y[1] (numeric) = 4.6619654079873906687713365664568
absolute error = 3.54666116729655e-17
relative error = 7.6076522601819845328716718579866e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.299
y[1] (analytic) = 4.665629204988562198044709373874
y[1] (numeric) = 4.6656292049885622337261089130028
absolute error = 3.56813995391288e-17
relative error = 7.6477143749395475250655260302218e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.3
y[1] (analytic) = 4.6692966676192442204574899160115
y[1] (numeric) = 4.6692966676192442563540716097965
absolute error = 3.58965816937850e-17
relative error = 7.6877920271636446052999833422691e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.301
y[1] (analytic) = 4.6729677995468996368469850102494
y[1] (numeric) = 4.672967799546899672959143721152
absolute error = 3.61121587109026e-17
relative error = 7.7278852027193740970688818496893e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.302
y[1] (analytic) = 4.6766426044426606807962818816229
y[1] (numeric) = 4.6766426044426607171244130468271
absolute error = 3.63281311652042e-17
relative error = 7.7679938874725297561673698740617e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.303
y[1] (analytic) = 4.6803210859813325543001760006409
y[1] (numeric) = 4.6803210859813325908446756328078
absolute error = 3.65444996321669e-17
relative error = 7.8081180672895093804764961436997e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.304
y[1] (analytic) = 4.684003247841397102570679311858
y[1] (numeric) = 4.6840032478413971393319439998817
absolute error = 3.67612646880237e-17
relative error = 7.8482577280374371797273346104386e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.305
y[1] (analytic) = 4.6876890937050164925191719860508
y[1] (numeric) = 4.6876890937050165294975988958148
absolute error = 3.69784269097640e-17
relative error = 7.8884128555840934131279335000586e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.306
y[1] (analytic) = 4.6913786272580368949188761784555
y[1] (numeric) = 4.6913786272580369321148630535904
absolute error = 3.71959868751349e-17
relative error = 7.9285834357980147205716988960665e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.307
y[1] (analytic) = 4.6950718521899921702513339558475
y[1] (numeric) = 4.6950718521899922076652791184897
absolute error = 3.74139451626422e-17
relative error = 7.9687694545485299203676140204619e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.308
y[1] (analytic) = 4.6987687721941075582405752392492
y[1] (numeric) = 4.6987687721941075958728775908002
absolute error = 3.76323023515510e-17
relative error = 8.0089708977057103449708796763126e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.309
y[1] (analytic) = 4.70246939096730337107866529674
y[1] (numeric) = 4.7024693909673034089297243186266
absolute error = 3.78510590218866e-17
relative error = 8.0491877511403840427501019157626e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.31
y[1] (analytic) = 4.7061737122101986903463250122245
y[1] (numeric) = 4.7061737122101987284165407666604
absolute error = 3.80702157544359e-17
relative error = 8.0894200007242559919739728167991e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.311
y[1] (analytic) = 4.7098817396271150676323208510871
y[1] (numeric) = 4.709881739627115105922093981835
absolute error = 3.82897731307479e-17
relative error = 8.1296676323298364950566723484293e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.312
y[1] (analytic) = 4.7135934769260802288553251424314
y[1] (numeric) = 4.7135934769260802673650568755663
absolute error = 3.85097317331349e-17
relative error = 8.1699306318305182520882847807181e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.313
y[1] (analytic) = 4.7173089278188317822919510000733
y[1] (numeric) = 4.7173089278188318210220431447467
absolute error = 3.87300921446734e-17
relative error = 8.2102089851005893097280067708939e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.314
y[1] (analytic) = 4.721028096020820930314669910632
y[1] (numeric) = 4.7210280960208209692655248598369
absolute error = 3.89508549492049e-17
relative error = 8.2505026780152246013407431179332e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.315
y[1] (analytic) = 4.724750985251216184843323726945
y[1] (numeric) = 4.724750985251216224015344458282
absolute error = 3.91720207313370e-17
relative error = 8.2908116964505408566761303213951e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.316
y[1] (analytic) = 4.7284775992329070865139465186297
y[1] (numeric) = 4.7284775992329071259075365950742
absolute error = 3.93935900764445e-17
relative error = 8.3311360262836510861446289066255e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.317
y[1] (analytic) = 4.7322079416925079275686154489233
y[1] (numeric) = 4.732207941692507967184179019593
absolute error = 3.96155635706697e-17
relative error = 8.3714756533925495867338101366079e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.318
y[1] (analytic) = 4.7359420163603614784700535679605
y[1] (numeric) = 4.7359420163603615183079953688847
absolute error = 3.98379418009242e-17
relative error = 8.4118305636563140517641900569140e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.319
y[1] (analytic) = 4.7396798269705427182447111374053
y[1] (numeric) = 4.7396798269705427583054364922946
absolute error = 4.00607253548893e-17
relative error = 8.4522007429550111800700515166376e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.32
y[1] (analytic) = 4.7434213772608625685580558298259
y[1] (numeric) = 4.7434213772608626088419706508431
absolute error = 4.02839148210172e-17
relative error = 8.4925861771697712185191033854668e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.321
y[1] (analytic) = 4.7471666709728716315258058784167
y[1] (numeric) = 4.7471666709728716720333166669485
absolute error = 4.05075107885318e-17
relative error = 8.5329868521827777239868198009202e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.322
y[1] (analytic) = 4.7509157118518639312648439886101
y[1] (numeric) = 4.7509157118518639719963578360398
absolute error = 4.07315138474297e-17
relative error = 8.5734027538772993031880047477073e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.323
y[1] (analytic) = 4.7546685036468806591875535628052
y[1] (numeric) = 4.7546685036468807001434781512864
absolute error = 4.09559245884812e-17
relative error = 8.6138338681377210345650456134483e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.324
y[1] (analytic) = 4.7584250501107139230433225328607
y[1] (numeric) = 4.758425050110713964224066136092
absolute error = 4.11807436032313e-17
relative error = 8.6542801808495755733427110883820e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.325
y[1] (analytic) = 4.7621853549999104997109638421691
y[1] (numeric) = 4.7621853549999105411169353261695
absolute error = 4.14059714840004e-17
relative error = 8.6947416778995109445699571545009e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.326
y[1] (analytic) = 4.7659494220747755917458053700446
y[1] (numeric) = 4.7659494220747756333774141939302
absolute error = 4.16316088238856e-17
relative error = 8.7352183451753842131333251686503e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.327
y[1] (analytic) = 4.7697172550993765876852058458285
y[1] (numeric) = 4.76971725509937662954286206259
absolute error = 4.18576562167615e-17
relative error = 8.7757101685662497134609551423585e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.328
y[1] (analytic) = 4.7734888578415468261162570585405
y[1] (numeric) = 4.7734888578415468682003713158218
absolute error = 4.20841142572813e-17
relative error = 8.8162171339624100127153956775309e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.329
y[1] (analytic) = 4.777264234072889363509436430093
y[1] (numeric) = 4.7772642340728894058204199709703
absolute error = 4.23109835408773e-17
relative error = 8.8567392272553408681635633285706e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.33
y[1] (analytic) = 4.7810433875687807458219777860331
y[1] (numeric) = 4.7810433875687807883602424497956
absolute error = 4.25382646637625e-17
relative error = 8.8972764343378464458793694129669e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.331
y[1] (analytic) = 4.7848263221083747838747319274995
y[1] (numeric) = 4.7848263221083748266406901504306
absolute error = 4.27659582229311e-17
relative error = 8.9378287411039837407652282220689e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.332
y[1] (analytic) = 4.7886130414746063325062923815678
y[1] (numeric) = 4.7886130414746063755003571977277
absolute error = 4.29940648161599e-17
relative error = 8.9783961334491751302305762822134e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.333
y[1] (analytic) = 4.792403549454195073508165484426
y[1] (numeric) = 4.7924035494541951167307505264346
absolute error = 4.32225850420086e-17
relative error = 9.0189785972700906939096209088158e-16 %
memory used=22.8MB, alloc=4.1MB, time=1.11
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.334
y[1] (analytic) = 4.7961978498376493023447677328647
y[1] (numeric) = 4.7961978498376493457962872326861
absolute error = 4.34515194998214e-17
relative error = 9.0595761184648019687706256256679e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.335
y[1] (analytic) = 4.7999959464192697186620371243952
y[1] (numeric) = 4.7999959464192697623429059141231
absolute error = 4.36808687897279e-17
relative error = 9.1001886829327889709712091094514e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.336
y[1] (analytic) = 4.8037978429971532205884489949236
y[1] (numeric) = 4.803797842997153264499082507567
absolute error = 4.39106335126434e-17
relative error = 9.1408162765748221115517336563655e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.337
y[1] (analytic) = 4.8076035433731967028322306553107
y[1] (numeric) = 4.8076035433731967469730449255818
absolute error = 4.41408142702711e-17
relative error = 9.1814588852932397085594865768353e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.338
y[1] (analytic) = 4.811413051353100858578572924352
y[1] (numeric) = 4.8114130513531009029499845894537
absolute error = 4.43714116651017e-17
relative error = 9.2221164949916836287242337819836e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.339
y[1] (analytic) = 4.8152263707463739851906404557028
y[1] (numeric) = 4.8152263707463740297930667561182
absolute error = 4.46024263004154e-17
relative error = 9.2627890915753344305888832760809e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.34
y[1] (analytic) = 4.8190435053663357937181865600786
y[1] (numeric) = 4.819043505366335838552045340361
absolute error = 4.48338587802824e-17
relative error = 9.3034766609508339545633448705178e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.341
y[1] (analytic) = 4.8228644590301212222175820316614
y[1] (numeric) = 4.8228644590301212672832917412255
absolute error = 4.50657097095641e-17
relative error = 9.3441791890263532496687217719215e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.342
y[1] (analytic) = 4.8266892355586842528870712990595
y[1] (numeric) = 4.8266892355586842981850509929732
absolute error = 4.52979796939137e-17
relative error = 9.3848966617115356961922412157446e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.343
y[1] (analytic) = 4.8305178387768017330210730363942
y[1] (numeric) = 4.8305178387768017785517423761718
absolute error = 4.55306693397776e-17
relative error = 9.4256290649176058394172951312899e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.344
y[1] (analytic) = 4.8343502725130771997873461891328
y[1] (numeric) = 4.8343502725130772455511254435294
absolute error = 4.57637792543966e-17
relative error = 9.4663763845574361626393563126105e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.345
y[1] (analytic) = 4.8381865405999447088308461921537
y[1] (numeric) = 4.8381865405999447548281562379595
absolute error = 4.59973100458058e-17
relative error = 9.5071386065453446730645603407911e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.346
y[1] (analytic) = 4.8420266468736726667080999842164
y[1] (numeric) = 4.8420266468736727129393623070531
absolute error = 4.62312623228367e-17
relative error = 9.5479157167973476315730050496362e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.347
y[1] (analytic) = 4.8458705951743676671559322535332
y[1] (numeric) = 4.8458705951743677136215689486509
absolute error = 4.64656366951177e-17
relative error = 9.5887077012310807294878278987527e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.348
y[1] (analytic) = 4.8497183893459783311983791834874
y[1] (numeric) = 4.8497183893459783778988129565627
absolute error = 4.67004337730753e-17
relative error = 9.6295145457658648037440525591433e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.349
y[1] (analytic) = 4.853570033236299151095629805732
y[1] (numeric) = 4.8535700332362991980312839736667
absolute error = 4.69356541679347e-17
relative error = 9.6703362363226474446438982023267e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.35
y[1] (analytic) = 4.8574255306969743381388389099302
y[1] (numeric) = 4.8574255306969743853101374016514
absolute error = 4.71712984917212e-17
relative error = 9.7111727588241094030455767070491e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.351
y[1] (analytic) = 4.8612848855835016742946593052721
y[1] (numeric) = 4.861284885583501721702026662533
absolute error = 4.74073673572609e-17
relative error = 9.7520240991946263215878303424062e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.352
y[1] (analytic) = 4.8651481017552363677033450786199
y[1] (numeric) = 4.8651481017552364153472064568019
absolute error = 4.76438613781820e-17
relative error = 9.7928902433603537988754433946409e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.353
y[1] (analytic) = 4.8690151830753949120342813477067
y[1] (numeric) = 4.8690151830753949599150625166221
absolute error = 4.78807811689154e-17
relative error = 9.8337711772491681070048632131168e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.354
y[1] (analytic) = 4.8728861334110589497027998652402
y[1] (numeric) = 4.8728861334110589978209272099362
absolute error = 4.81181273446960e-17
relative error = 9.8746668867907506676086694206206e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.355
y[1] (analytic) = 4.8767609566331791389521436910487
y[1] (numeric) = 4.8767609566331791873080442126123
absolute error = 4.83559005215636e-17
relative error = 9.9155773579165899281574304190571e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.356
y[1] (analytic) = 4.8806396566165790248044480145565
y[1] (numeric) = 4.8806396566165790733985493309203
absolute error = 4.85941013163638e-17
relative error = 9.9565025765599830529430242456973e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.357
y[1] (analytic) = 4.884522237239958913884608078892
y[1] (numeric) = 4.8845222372399589627173384256411
absolute error = 4.88327303467491e-17
relative error = 9.9974425286560783752656498865522e-16 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.358
y[1] (analytic) = 4.888408702385899753120909030819
y[1] (numeric) = 4.888408702385899802192697261999
absolute error = 4.90717882311800e-17
relative error = 1.0038397200141917470699979456559e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.359
y[1] (analytic) = 4.892299055940867012326296397445
y[1] (numeric) = 4.8922990559408670616375719863709
absolute error = 4.93112755889259e-17
relative error = 1.0079366576956435972125475275172e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.36
y[1] (analytic) = 4.8961933017952145706641697713002
y[1] (numeric) = 4.896193301795214620215362811366
absolute error = 4.95511930400658e-17
relative error = 1.0120350645040423355383641160583e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.361
y[1] (analytic) = 4.9000914438431886070025861699043
y[1] (numeric) = 4.9000914438431886567941273753941
absolute error = 4.97915412054898e-17
relative error = 1.0161349390336646001709210392951e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.362
y[1] (analytic) = 4.9039934859829314941607634243494
y[1] (numeric) = 4.9039934859829315441930841312491
absolute error = 5.00323207068997e-17
relative error = 1.0202362798789785971792612914292e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.363
y[1] (analytic) = 4.9078994321164856970517778437259
y[1] (numeric) = 4.9078994321164857473253100105364
absolute error = 5.02735321668105e-17
relative error = 1.0243390856346563271617718635594e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.364
y[1] (analytic) = 4.9118092861497976747253542984159
y[1] (numeric) = 4.9118092861497977252405305069666
absolute error = 5.05151762085507e-17
relative error = 1.0284433548955613047493030443921e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.365
y[1] (analytic) = 4.9157230519927217863146507653665
y[1] (numeric) = 4.9157230519927218370719042216304
absolute error = 5.07572534562639e-17
relative error = 1.0325490862567627646103584474431e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.366
y[1] (analytic) = 4.9196407335590242008909432824553
y[1] (numeric) = 4.919640733559024251890707817365
absolute error = 5.09997645349097e-17
relative error = 1.0366562783135355531290167669367e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.367
y[1] (analytic) = 4.9235623347663868112301211669584
y[1] (numeric) = 4.9235623347663868624728312372229
absolute error = 5.12427100702645e-17
relative error = 1.0407649296613579716114325351942e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.368
y[1] (analytic) = 4.9274878595364111514949062649416
y[1] (numeric) = 4.9274878595364112029809969538639
absolute error = 5.14860906889223e-17
relative error = 1.0448750388959096118632486625631e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.369
y[1] (analytic) = 4.9314173117946223188367139141204
y[1] (numeric) = 4.9314173117946223705666209324171
absolute error = 5.17299070182967e-17
relative error = 1.0489866046130935179770050589800e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.37
y[1] (analytic) = 4.9353506954704728989210772223787
y[1] (numeric) = 4.9353506954704729508952369089992
absolute error = 5.19741596866205e-17
relative error = 1.0530996254090095954936233244593e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.371
y[1] (analytic) = 4.9392880144973468953805601876939
y[1] (numeric) = 4.9392880144973469475994095106419
absolute error = 5.22188493229480e-17
relative error = 1.0572140998799827933403312343866e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.372
y[1] (analytic) = 4.9432292728125636631990891127129
y[1] (numeric) = 4.9432292728125637156630656698681
absolute error = 5.24639765571552e-17
relative error = 1.0613300266225486507647454909801e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.373
y[1] (analytic) = 4.9471744743573818460316356986353
y[1] (numeric) = 4.9471744743573818987411777185764
absolute error = 5.27095420199411e-17
relative error = 1.0654474042334611301653945413974e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.374
y[1] (analytic) = 4.9511236230770033174631891384162
y[1] (numeric) = 4.951123623077003370418735481245
absolute error = 5.29555463428288e-17
relative error = 1.0695662313096963549485083550391e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.375
y[1] (analytic) = 4.9550767229205771262109584685895
y[1] (numeric) = 4.9550767229205771794129486267557
absolute error = 5.32019901581662e-17
relative error = 1.0736865064484482388691062111786e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
memory used=26.7MB, alloc=4.1MB, time=1.30
x[1] = 1.376
y[1] (analytic) = 4.9590337778412034452737503822416
y[1] (numeric) = 4.9590337778412034987226244813691
absolute error = 5.34488740991275e-17
relative error = 1.0778082282471402503322995405273e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.377
y[1] (analytic) = 4.9629947917959375250324716528437
y[1] (numeric) = 4.9629947917959375787286704525576
absolute error = 5.36961987997139e-17
relative error = 1.0819313953034209829714218569914e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.378
y[1] (analytic) = 4.966959768745793650305709269774
y[1] (numeric) = 4.9669597687457937042496741645284
absolute error = 5.39439648947544e-17
relative error = 1.0860560062151617425157196179881e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.379
y[1] (analytic) = 4.9709287126557491013643453414388
y[1] (numeric) = 4.9709287126557491555565183613461
absolute error = 5.41921730199073e-17
relative error = 1.0901820595804682089165668928458e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.38
y[1] (analytic) = 4.9749016274947481189091677809396
y[1] (numeric) = 4.9749016274947481733499915926006
absolute error = 5.44408238116610e-17
relative error = 1.0943095539976779538148078575285e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.381
y[1] (analytic) = 4.9788785172357058730154417522248
y[1] (numeric) = 4.9788785172357059277053596595601
absolute error = 5.46899179073353e-17
relative error = 1.0984384880653679940383230163742e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.382
y[1] (analytic) = 4.982859385855512436048410821631
y[1] (numeric) = 4.9828593858555124909878667667125
absolute error = 5.49394559450815e-17
relative error = 1.1025688603823382080735127314453e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.383
y[1] (analytic) = 4.9868442373350367595537007306426
y[1] (numeric) = 4.9868442373350368147431392945273
absolute error = 5.51894385638847e-17
relative error = 1.1067006695476389297696943662402e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.384
y[1] (analytic) = 4.9908330756591306551266026806085
y[1] (numeric) = 4.9908330756591307105664690841726
absolute error = 5.54398664035641e-17
relative error = 1.1108339141605583180965239694745e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.385
y[1] (analytic) = 4.9948259048166327792642169990288
y[1] (numeric) = 4.9948259048166328349549571038027
absolute error = 5.56907401047739e-17
relative error = 1.1149685928206217814258742041072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.386
y[1] (analytic) = 4.9988227288003726222044420398869
y[1] (numeric) = 4.9988227288003726781465023488918
absolute error = 5.59420603090049e-17
relative error = 1.1191047041276053895376427926083e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.387
y[1] (analytic) = 5.0028235516071745007557971573507
y[1] (numeric) = 5.0028235516071745569496248159356
absolute error = 5.61938276585849e-17
relative error = 1.1232422466815252164873573751959e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.388
y[1] (analytic) = 5.0068283772378615551220725829952
y[1] (numeric) = 5.0068283772378616115681153796757
absolute error = 5.64460427966805e-17
relative error = 1.1273812190826546779423555518733e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.389
y[1] (analytic) = 5.010837209697259749725803031533
y[1] (numeric) = 5.0108372096972598064245093988302
absolute error = 5.66987063672972e-17
relative error = 1.1315216199315078404649927680328e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.39
y[1] (analytic) = 5.0148500529942018780345658588566
y[1] (numeric) = 5.0148500529942019349863848741378
absolute error = 5.69518190152812e-17
relative error = 1.1356634478288566916762799495358e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.391
y[1] (analytic) = 5.0188669111415315713941085990267
y[1] (numeric) = 5.0188669111415316285994899853467
absolute error = 5.72053813863200e-17
relative error = 1.1398067013757243993332020519599e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.392
y[1] (analytic) = 5.0228877881561073118723147136667
y[1] (numeric) = 5.0228877881561073693317088406104
absolute error = 5.74593941269437e-17
relative error = 1.1439513791733925204073491181721e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.393
y[1] (analytic) = 5.026912688058806449118020398064
y[1] (numeric) = 5.02691268805880650683187828259
absolute error = 5.77138578845260e-17
relative error = 1.1480974798234021891510198532758e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.394
y[1] (analytic) = 5.0309416148745292212386993031302
y[1] (numeric) = 5.0309416148745292792074726104151
absolute error = 5.79687733072849e-17
relative error = 1.1522450019275493177663653000803e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.395
y[1] (analytic) = 5.0349745726322027797010360512387
y[1] (numeric) = 5.0349745726322028379251770955231
absolute error = 5.82241410442844e-17
relative error = 1.1563939440878996626079058912845e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.396
y[1] (analytic) = 5.0390115653647852182584134468501
y[1] (numeric) = 5.039011565364785276738375192285
absolute error = 5.84799617454349e-17
relative error = 1.1605443049067780007041960943152e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.397
y[1] (analytic) = 5.0430525971092696059093423097474
y[1] (numeric) = 5.0430525971092696646455783712418
absolute error = 5.87362360614944e-17
relative error = 1.1646960829867732029937978942771e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.398
y[1] (analytic) = 5.0470976719066880238908668896466
y[1] (numeric) = 5.0470976719066880828838315337166
absolute error = 5.89929646440700e-17
relative error = 1.1688492769307492085729026844437e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.399
y[1] (analytic) = 5.0511467938021156067109828559262
y[1] (numeric) = 5.0511467938021156659611310015446
absolute error = 5.92501481456184e-17
relative error = 1.1730038853418361300106236969960e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.4
y[1] (analytic) = 5.0551999668446745872241088952286
y[1] (numeric) = 5.0551999668446746467318961146757
absolute error = 5.95077872194471e-17
relative error = 1.1771599068234352297839733683713e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.401
y[1] (analytic) = 5.0592571950875383457536569927423
y[1] (numeric) = 5.0592571950875384055195395124578
absolute error = 5.97658825197155e-17
relative error = 1.1813173399792218775009536767645e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.402
y[1] (analytic) = 5.063318482587935463265750520074
y[1] (numeric) = 5.0633184825879355232901852215101
absolute error = 6.00244347014361e-17
relative error = 1.1854761834131504491276192960058e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.403
y[1] (analytic) = 5.0673838334071537785981433037646
y[1] (numeric) = 5.0673838334071538388815877242399
absolute error = 6.02834444204753e-17
relative error = 1.1896364357294512902225472000027e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.404
y[1] (analytic) = 5.071453251610544449748396903708
y[1] (numeric) = 5.0714532516105445102913092372624
absolute error = 6.05429123335544e-17
relative error = 1.1937980955326316185838277519326e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.405
y[1] (analytic) = 5.0755267412675260192253773899867
y[1] (numeric) = 5.0755267412675260800282164882377
absolute error = 6.08028390982510e-17
relative error = 1.1979611614274842846890825616210e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.406
y[1] (analytic) = 5.0796043064515884834681369699611
y[1] (numeric) = 5.079604306451588544531362342961
absolute error = 6.10632253729999e-17
relative error = 1.2021256320190866278272512732624e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.407
y[1] (analytic) = 5.0836859512402973663362498848331
y[1] (numeric) = 5.0836859512402974276603217019271
absolute error = 6.13240718170940e-17
relative error = 1.2062915059127993188057901568960e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.408
y[1] (analytic) = 5.0877716797152977966756760663581
y[1] (numeric) = 5.0877716797152978582610551570436
absolute error = 6.15853790906855e-17
relative error = 1.2104587817142710858022091605070e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.409
y[1] (analytic) = 5.091861495962318589964230119911
y[1] (numeric) = 5.0918614959623186518113779746978
absolute error = 6.18471478547868e-17
relative error = 1.2146274580294375067751670253383e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.41
y[1] (analytic) = 5.0959554040711763340407372797126
y[1] (numeric) = 5.0959554040711763961501160509846
absolute error = 6.21093787712720e-17
relative error = 1.2187975334645315627707368822769e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.411
y[1] (analytic) = 5.100053408135779478921962065716
y[1] (numeric) = 5.1000534081357795412940345685935
absolute error = 6.23720725028775e-17
relative error = 1.2229690066260764745196569838443e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.412
y[1] (analytic) = 5.1041555122541324307113994594197
y[1] (numeric) = 5.1041555122541324933466291726227
absolute error = 6.26352297132030e-17
relative error = 1.2271418761208863912439610049905e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.413
y[1] (analytic) = 5.1082617205283396496040225077407
y[1] (numeric) = 5.1082617205283397125028735744539
absolute error = 6.28988510667132e-17
relative error = 1.2313161405560807604326943066608e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.414
y[1] (analytic) = 5.1123720370646097519910843600381
y[1] (numeric) = 5.1123720370646098151540215887762
absolute error = 6.31629372287381e-17
relative error = 1.2354917985390712247394627250425e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.415
y[1] (analytic) = 5.1164864659732596166690768434283
y[1] (numeric) = 5.116486465973259680096565708903
absolute error = 6.34274888654747e-17
relative error = 1.2396688486775759254430992864598e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.416
y[1] (analytic) = 5.1206050113687184951569517856954
y[1] (numeric) = 5.1206050113687185588494584296829
absolute error = 6.36925066439875e-17
relative error = 1.2438472895796102831219044910021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.417
y[1] (analytic) = 5.1247276773695321261257154033581
y[1] (numeric) = 5.1247276773695321900837066355683
absolute error = 6.39579912322102e-17
relative error = 1.2480271198535012195025524383663e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.1MB, time=1.50
x[1] = 1.418
y[1] (analytic) = 5.1288544680983668539445101848329
y[1] (numeric) = 5.128854468098366918168453483779
absolute error = 6.42239432989461e-17
relative error = 1.2522083381078759447649129006098e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.419
y[1] (analytic) = 5.1329853876820137513473028151164
y[1] (numeric) = 5.132985387682013815837666328986
absolute error = 6.44903635138696e-17
relative error = 1.2563909429516722097457151621412e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.42
y[1] (analytic) = 5.1371204402513927462243008090194
y[1] (numeric) = 5.1371204402513928109815533565468
absolute error = 6.47572525475274e-17
relative error = 1.2605749329941426496461680193913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.421
y[1] (analytic) = 5.1412596299415567525422246447136
y[1] (numeric) = 5.1412596299415568175668357160525
absolute error = 6.50246110713389e-17
relative error = 1.2647603068448435271081038713754e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.422
y[1] (analytic) = 5.1454029608916958053975663182059
y[1] (numeric) = 5.1454029608916958706900060758041
absolute error = 6.52924397575982e-17
relative error = 1.2689470631136546060816184040244e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.423
y[1] (analytic) = 5.1495504372451412002069693723453
y[1] (numeric) = 5.1495504372451412657677086518196
absolute error = 6.55607392794743e-17
relative error = 1.2731352004107639559654175764272e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.424
y[1] (analytic) = 5.1537020631493696360388695910856
y[1] (numeric) = 5.1537020631493697018683799020985
absolute error = 6.58295103110129e-17
relative error = 1.2773247173466838554160467497057e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.425
y[1] (analytic) = 5.1578578427560073630905396909911
y[1] (numeric) = 5.157857842756007429189293218128
absolute error = 6.60987535271369e-17
relative error = 1.2815156125322413957701594216108e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.426
y[1] (analytic) = 5.1620177802208343343146854873748
y[1] (numeric) = 5.1620177802208344006831550910228
absolute error = 6.63684696036480e-17
relative error = 1.2857078845785904199628588845481e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.427
y[1] (analytic) = 5.1661818797037883611997451620123
y[1] (numeric) = 5.1661818797037884278384043792395
absolute error = 6.66386592172272e-17
relative error = 1.2899015320972020920629050227120e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.428
y[1] (analytic) = 5.1703501453689692737080474130754
y[1] (numeric) = 5.1703501453689693406173704585118
absolute error = 6.69093230454364e-17
relative error = 1.2940965536998767681087620597820e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.429
y[1] (analytic) = 5.1745225813846430843759884257915
y[1] (numeric) = 5.1745225813846431515564501925109
absolute error = 6.71804617667194e-17
relative error = 1.2982929479987441948817284102252e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.43
y[1] (analytic) = 5.1786991919232461565803917643529
y[1] (numeric) = 5.1786991919232462240324678247555
absolute error = 6.74520760604026e-17
relative error = 1.3024907136062578952524780111988e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.431
y[1] (analytic) = 5.1828799811613893769752194517818
y[1] (numeric) = 5.1828799811613894446993860584783
absolute error = 6.77241666066965e-17
relative error = 1.3066898491352049966268022226154e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.432
y[1] (analytic) = 5.1870649532798623321028066748111
y[1] (numeric) = 5.187064953279862400099540761508
absolute error = 6.79967340866969e-17
relative error = 1.3108903531987102087523709139356e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.433
y[1] (analytic) = 5.1912541124636374891837967253638
y[1] (numeric) = 5.1912541124636375574535759077491
absolute error = 6.82697791823853e-17
relative error = 1.3150922244102243521669681330053e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.434
y[1] (analytic) = 5.1954474629018743810899569689131
y[1] (numeric) = 5.1954474629018744496332595455439
absolute error = 6.85433025766308e-17
relative error = 1.3192954613835417940157257277116e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.435
y[1] (analytic) = 5.1996450087879237955040608128896
y[1] (numeric) = 5.1996450087879238643213657660801
absolute error = 6.88173049531905e-17
relative error = 1.3235000627327889318135001335520e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.436
y[1] (analytic) = 5.2038467543193319682710248353648
y[1] (numeric) = 5.203846754319332037362811832076
absolute error = 6.90917869967112e-17
relative error = 1.3277060270724376948264099256282e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.437
y[1] (analytic) = 5.2080527036978447809444944254994
y[1] (numeric) = 5.2080527036978448503112438182294
absolute error = 6.93667493927300e-17
relative error = 1.3319133530172978393392031532095e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.438
y[1] (analytic) = 5.2122628611294119625330754826903
y[1] (numeric) = 5.2122628611294120321752683103661
absolute error = 6.96421928276758e-17
relative error = 1.3361220391825265285149429198861e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.439
y[1] (analytic) = 5.2164772308241912954504139209989
y[1] (numeric) = 5.2164772308241913653685319098692
absolute error = 6.99181179888703e-17
relative error = 1.3403320841836282611748201144062e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.44
y[1] (analytic) = 5.2206958169965528256733289292909
y[1] (numeric) = 5.2206958169965528958678544938195
absolute error = 7.01945255645286e-17
relative error = 1.3445434866364471193607229402687e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.441
y[1] (analytic) = 5.2249186238650830771122101455705
y[1] (numeric) = 5.2249186238650831475836263893315
absolute error = 7.04714162437610e-17
relative error = 1.3487562451571820006056991007913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.442
y[1] (analytic) = 5.2291456556525892701978931162592
y[1] (numeric) = 5.229145655652589340946683832833
absolute error = 7.07487907165738e-17
relative error = 1.3529703583623826330836659017471e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.443
y[1] (analytic) = 5.2333769165861035446892316276445
y[1] (numeric) = 5.233376916586103615715881301515
absolute error = 7.10266496738705e-17
relative error = 1.3571858248689532334923318905833e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.444
y[1] (analytic) = 5.2376124108968871867055897174241
y[1] (numeric) = 5.2376124108968872580105835248766
absolute error = 7.13049938074525e-17
relative error = 1.3614026432941465810530182771324e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.445
y[1] (analytic) = 5.2418521428204348599884803991883
y[1] (numeric) = 5.2418521428204349315723042092092
absolute error = 7.15838238100209e-17
relative error = 1.3656208122555790853704967200299e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.446
y[1] (analytic) = 5.2460961165964788413965823618339
y[1] (numeric) = 5.2460961165964789132597227370109
absolute error = 7.18631403751770e-17
relative error = 1.3698403303712209810457583495630e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.447
y[1] (analytic) = 5.2503443364689932606383701392776
y[1] (numeric) = 5.2503443364689933327813143367013
absolute error = 7.21429441974237e-17
relative error = 1.3740611962594036916609659141716e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.448
y[1] (analytic) = 5.2545968066861983442465974834531
y[1] (numeric) = 5.2545968066861984166698334556196
absolute error = 7.24232359721665e-17
relative error = 1.3782834085388195257769707862275e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.449
y[1] (analytic) = 5.2588535315005646637988779154288
y[1] (numeric) = 5.2588535315005647365028943111436
absolute error = 7.27040163957148e-17
relative error = 1.3825069658285270591329645750371e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.45
y[1] (analytic) = 5.2631145151688173883886106755809
y[1] (numeric) = 5.2631145151688174613738968408637
absolute error = 7.29852861652828e-17
relative error = 1.3867318667479488707002508399163e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.451
y[1] (analytic) = 5.2673797619519405413505045441019
y[1] (numeric) = 5.2673797619519406146175505230925
absolute error = 7.32670459789906e-17
relative error = 1.3909581099168730666825860649565e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.452
y[1] (analytic) = 5.271649276115181261244956257723
y[1] (numeric) = 5.2716492761151813347942527935885
absolute error = 7.35492965358655e-17
relative error = 1.3951856939554585710074257864074e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.453
y[1] (analytic) = 5.2759230619280540671055445073843
y[1] (numeric) = 5.2759230619280541409375830432274
absolute error = 7.38320385358431e-17
relative error = 1.3994146174842365792939686706639e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.454
y[1] (analytic) = 5.280201123664345127953904764702
y[1] (numeric) = 5.2802011236643452020691774444702
absolute error = 7.41152726797682e-17
relative error = 1.4036448791241081979476051772975e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.455
y[1] (analytic) = 5.2844834656021165365862544524633
y[1] (numeric) = 5.2844834656021166109852541218592
absolute error = 7.43989996693959e-17
relative error = 1.4078764774963458593069217646016e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.456
y[1] (analytic) = 5.2887700920237105876358422460295
y[1] (numeric) = 5.2887700920237106623190624534229
absolute error = 7.46832202073934e-17
relative error = 1.4121094112226079454341704741042e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.457
y[1] (analytic) = 5.2930610072157540599155995684554
y[1] (numeric) = 5.2930610072157541348835345657954
absolute error = 7.49679349973400e-17
relative error = 1.4163436789249193139020534702426e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.458
y[1] (analytic) = 5.2973562154691625030452766223299
y[1] (numeric) = 5.2973562154691625782984213660591
absolute error = 7.52531447437292e-17
relative error = 1.4205792792256915404704796925671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.459
y[1] (analytic) = 5.3016557210791445283673495858346
y[1] (numeric) = 5.301655721079144603906199737804
absolute error = 7.55388501519694e-17
relative error = 1.4248162107477166363874154315021e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=34.3MB, alloc=4.2MB, time=1.69
x[1] = 1.46
y[1] (analytic) = 5.3059595283452061041559898892827
y[1] (numeric) = 5.3059595283452061799810418176676
absolute error = 7.58250519283849e-17
relative error = 1.4290544721141664300034920874366e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.461
y[1] (analytic) = 5.3102676415711548551233907814661
y[1] (numeric) = 5.3102676415711549312351415616835
absolute error = 7.61117507802174e-17
relative error = 1.4332940619486013469087461962596e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.462
y[1] (analytic) = 5.3145800650651043662277506924963
y[1] (numeric) = 5.3145800650651044426266981081231
absolute error = 7.63989474156268e-17
relative error = 1.4375349788749659558040965107277e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.463
y[1] (analytic) = 5.3188968031394784907872172014803
y[1] (numeric) = 5.3188968031394785674738597451727
absolute error = 7.66866425436924e-17
relative error = 1.4417772215175920361039083925402e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.464
y[1] (analytic) = 5.3232178601110156629040997233343
y[1] (numeric) = 5.3232178601110157398789365977485
absolute error = 7.69748368744142e-17
relative error = 1.4460207885012034888971141812452e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.465
y[1] (analytic) = 5.327543240300773214203663339308
y[1] (numeric) = 5.3275432403007732914671944580219
absolute error = 7.72635311187139e-17
relative error = 1.4502656784509155725675652387646e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.466
y[1] (analytic) = 5.3318729480341316948918205103728
y[1] (numeric) = 5.3318729480341317724445464988089
absolute error = 7.75527259884361e-17
relative error = 1.4545118899922378727982885421287e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.467
y[1] (analytic) = 5.3362069876407991991360417315254
y[1] (numeric) = 5.3362069876407992769784639278748
absolute error = 7.78424221963494e-17
relative error = 1.4587594217510753637506444747485e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.468
y[1] (analytic) = 5.3405453634548156947738105082782
y[1] (numeric) = 5.3405453634548157729064309644255
absolute error = 7.81326204561473e-17
relative error = 1.4630082723537256987343388020201e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.469
y[1] (analytic) = 5.3448880798145573573529523641522
y[1] (numeric) = 5.3448880798145574357762738466019
absolute error = 7.84233214824497e-17
relative error = 1.4672584404268877193475205137633e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.47
y[1] (analytic) = 5.3492351410627409085081719198621
y[1] (numeric) = 5.3492351410627409872226979106662
absolute error = 7.87145259908041e-17
relative error = 1.4715099245976642944610370389413e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.471
y[1] (analytic) = 5.3535865515464279586781364210939
y[1] (numeric) = 5.3535865515464280376843711187801
absolute error = 7.90062346976862e-17
relative error = 1.4757627234935539174228118788186e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.472
y[1] (analytic) = 5.3579423156170293541674484323179
y[1] (numeric) = 5.3579423156170294334658967528194
absolute error = 7.92984483205015e-17
relative error = 1.4800168357424609875974147525893e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.473
y[1] (analytic) = 5.3623024376303095285578547589738
y[1] (numeric) = 5.3623024376303096081490223365603
absolute error = 7.95911675775865e-17
relative error = 1.4842722599726985618295715558813e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.474
y[1] (analytic) = 5.3666669219463908584730430095994
y[1] (numeric) = 5.3666669219463909383574361978089
absolute error = 7.98843931882095e-17
relative error = 1.4885289948129836185033709954295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.475
y[1] (analytic) = 5.3710357729297580237013815630615
y[1] (numeric) = 5.3710357729297581038795074356334
absolute error = 8.01781258725719e-17
relative error = 1.4927870388924416333066876566536e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.476
y[1] (analytic) = 5.3754089949492623716809630639933
y[1] (numeric) = 5.3754089949492624521533294158027
absolute error = 8.04723663518094e-17
relative error = 1.4970463908406092517904912523041e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.477
y[1] (analytic) = 5.3797865923781262863513159318443
y[1] (numeric) = 5.3797865923781263671184312798375
absolute error = 8.07671153479932e-17
relative error = 1.5013070492874369282750704031732e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.478
y[1] (analytic) = 5.3841685695939475613761527356201
y[1] (numeric) = 5.384168569593947642438526319751
absolute error = 8.10623735841309e-17
relative error = 1.5055690128632859593379402187793e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.479
y[1] (analytic) = 5.3885549309787037777415286574228
y[1] (numeric) = 5.3885549309787038590996704415909
absolute error = 8.13581417841681e-17
relative error = 1.5098322801989385016092232121711e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.48
y[1] (analytic) = 5.3929456809187566857337876433172
y[1] (numeric) = 5.392945680918756767388208316306
absolute error = 8.16544206729888e-17
relative error = 1.5140968499255852686953823021981e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.481
y[1] (analytic) = 5.3973408238048565913016782198325
y[1] (numeric) = 5.3973408238048566732528891962499
absolute error = 8.19512109764174e-17
relative error = 1.5183627206748429116717470913765e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.482
y[1] (analytic) = 5.4017403640321467468070253385816
y[1] (numeric) = 5.4017403640321468290555387598011
absolute error = 8.22485134212195e-17
relative error = 1.5226298910787490789534516924033e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.483
y[1] (analytic) = 5.4061443060001677461683490000368
y[1] (numeric) = 5.4061443060001678287146777351395
absolute error = 8.25463287351027e-17
relative error = 1.5268983597697574794724116730296e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.484
y[1] (analytic) = 5.4105526541128619244018248004439
y[1] (numeric) = 5.4105526541128620072464824471623
absolute error = 8.28446576467184e-17
relative error = 1.5311681253807514316053810340455e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.485
y[1] (analytic) = 5.4149654127785777615639859432053
y[1] (numeric) = 5.4149654127785778447074868288677
absolute error = 8.31435008856624e-17
relative error = 1.5354391865450351643210346471256e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.486
y[1] (analytic) = 5.4193825864100742911005706577984
y[1] (numeric) = 5.4193825864100743745434298402749
absolute error = 8.34428591824765e-17
relative error = 1.5397115418963435922583322673953e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.487
y[1] (analytic) = 5.4238041794245255126059233754456
y[1] (numeric) = 5.4238041794245255963486566440951
absolute error = 8.37427332686495e-17
relative error = 1.5439851900688409598517091408192e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.488
y[1] (analytic) = 5.4282301962435248089973624213046
y[1] (numeric) = 5.4282301962435248930404862979227
absolute error = 8.40431238766181e-17
relative error = 1.5482601296971176289512829384607e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.489
y[1] (analytic) = 5.4326606412930893681089313979137
y[1] (numeric) = 5.4326606412930894524529631376823
absolute error = 8.43440317397686e-17
relative error = 1.5525363594162015870066132245938e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.49
y[1] (analytic) = 5.4370955190036646087089558540139
y[1] (numeric) = 5.4370955190036646933544134464514
absolute error = 8.46454575924375e-17
relative error = 1.5568138778615496466699034334093e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.491
y[1] (analytic) = 5.4415348338101286109458312566713
y[1] (numeric) = 5.4415348338101286958932334265844
absolute error = 8.49474021699131e-17
relative error = 1.5610926836690570446306075978486e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.492
y[1] (analytic) = 5.4459785901517965512264727128585
y[1] (numeric) = 5.4459785901517966364763389212949
absolute error = 8.52498662084364e-17
relative error = 1.5653727754750541190245617875441e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.493
y[1] (analytic) = 5.450426792472425141531861319313
y[1] (numeric) = 5.4504267924724252270847117645156
absolute error = 8.55528504452026e-17
relative error = 1.5696541519163139903934447001347e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.494
y[1] (analytic) = 5.4548794452202170731741264565905
y[1] (numeric) = 5.4548794452202171590304820749522
absolute error = 8.58563556183617e-17
relative error = 1.5739368116300436850409285957944e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.495
y[1] (analytic) = 5.4593365528478254649996077847639
y[1] (numeric) = 5.4593365528478255511599902517841
absolute error = 8.61603824670202e-17
relative error = 1.5782207532538954297464394253083e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.496
y[1] (analytic) = 5.4637981198123583160423451442017
y[1] (numeric) = 5.463798119812358402507276875444
absolute error = 8.64649317312423e-17
relative error = 1.5825059754259687190093289801192e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.497
y[1] (analytic) = 5.4682641505753829626324490152875
y[1] (numeric) = 5.4682641505753830494024531673379
absolute error = 8.67700041520504e-17
relative error = 1.5867924767847995498945822613557e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.498
y[1] (analytic) = 5.4727346496029305399638086458202
y[1] (numeric) = 5.4727346496029306270394091172474
absolute error = 8.70756004714272e-17
relative error = 1.5910802559693789243211355798308e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.499
y[1] (analytic) = 5.4772096213655004481255994141773
y[1] (numeric) = 5.4772096213655005355073208464934
absolute error = 8.73817214323161e-17
relative error = 1.5953693116191402019151195089689e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.5
y[1] (analytic) = 5.4816890703380648226020554601193
y[1] (numeric) = 5.4816890703380649102904232387422
absolute error = 8.76883677786229e-17
relative error = 1.5996596423739702089263476379302e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.501
y[1] (analytic) = 5.4861730010000730092449780833807
y[1] (numeric) = 5.4861730010000730972405183385975
absolute error = 8.79955402552168e-17
relative error = 1.6039512468742075122050063945274e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.502
y[1] (analytic) = 5.4906614178354560437234548829297
y[1] (numeric) = 5.4906614178354561320266944908611
absolute error = 8.83032396079314e-17
relative error = 1.6082441237606406803906263873962e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.2MB, time=1.88
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.503
y[1] (analytic) = 5.4951543253326311354552690869872
y[1] (numeric) = 5.4951543253326312240667356705535
absolute error = 8.86114665835663e-17
relative error = 1.6125382716745174511050384527616e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.504
y[1] (analytic) = 5.4996517279845061560244830055907
y[1] (numeric) = 5.4996517279845062449447049354785
absolute error = 8.89202219298878e-17
relative error = 1.6168336892575374672735487466287e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.505
y[1] (analytic) = 5.5041536302884841320896840236577
y[1] (numeric) = 5.5041536302884842213191904192883
absolute error = 8.92295063956306e-17
relative error = 1.6211303751518631958534360318798e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.506
y[1] (analytic) = 5.5086600367464677427873860431718
y[1] (numeric) = 5.5086600367464678323267067736701
absolute error = 8.95393207304983e-17
relative error = 1.6254283280001089878357277679811e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.507
y[1] (analytic) = 5.5131709518648638216350837782652
y[1] (numeric) = 5.5131709518648639114847494634305
absolute error = 8.98496656851653e-17
relative error = 1.6297275464453555642986085397767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.508
y[1] (analytic) = 5.5176863801545878629384618066287
y[1] (numeric) = 5.5176863801545879530990038179066
absolute error = 9.01605420112779e-17
relative error = 1.6340280291311499112414339361780e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.509
y[1] (analytic) = 5.5222063261310685327072647848338
y[1] (numeric) = 5.5222063261310686231792152462887
absolute error = 9.04719504614549e-17
relative error = 1.6383297747014960991407279794730e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.51
y[1] (analytic) = 5.5267307943142521840843397438116
y[1] (numeric) = 5.526730794314252274868231533101
absolute error = 9.07838917892894e-17
relative error = 1.6426327818008678388091110993537e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.511
y[1] (analytic) = 5.5312597892286073772923658939088
y[1] (numeric) = 5.5312597892286074683887326432585
absolute error = 9.10963667493497e-17
relative error = 1.6469370490742046830745084655573e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.512
y[1] (analytic) = 5.535793315403129404102791886626
y[1] (numeric) = 5.5357933154031294955121679838065
absolute error = 9.14093760971805e-17
relative error = 1.6512425751669136449043532547840e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.513
y[1] (analytic) = 5.5403313773713448168315050023532
y[1] (numeric) = 5.5403313773713449085544255916576
absolute error = 9.17229205893044e-17
relative error = 1.6555493587248762009617236797836e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.514
y[1] (analytic) = 5.5448739796713159618657612601491
y[1] (numeric) = 5.5448739796713160539027622433719
absolute error = 9.20370009832228e-17
relative error = 1.6598573983944444184520994061827e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.515
y[1] (analytic) = 5.5494211268456455177269099768721
y[1] (numeric) = 5.5494211268456456100785280142892
absolute error = 9.23516180374171e-17
relative error = 1.6641666928224424854118173591698e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.516
y[1] (analytic) = 5.5539728234414810376734508387651
y[1] (numeric) = 5.5539728234414811303402233501152
absolute error = 9.26667725113501e-17
relative error = 1.6684772406561718129711808477063e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.517
y[1] (analytic) = 5.5585290740105194968489660889309
y[1] (numeric) = 5.5585290740105195898314312543978
absolute error = 9.29824651654669e-17
relative error = 1.6727890405434070957886328439618e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.518
y[1] (analytic) = 5.5630898831090118439794749790081
y[1] (numeric) = 5.5630898831090119372781717402046
absolute error = 9.32986967611965e-17
relative error = 1.6771020911324049531816315331544e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.519
y[1] (analytic) = 5.5676552552977675576247621827822
y[1] (numeric) = 5.567655255297767651240230243735
absolute error = 9.36154680609528e-17
relative error = 1.6814163910719017296411751046840e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.52
y[1] (analytic) = 5.5722251951421592069882364234397
y[1] (numeric) = 5.5722251951421593009210162515752
absolute error = 9.39327798281355e-17
relative error = 1.6857319390111094898696818636840e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.521
y[1] (analytic) = 5.5767997072121270172898801247029
y[1] (numeric) = 5.576799707212127111540512951835
absolute error = 9.42506328271321e-17
relative error = 1.6900487335997317364417494754216e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.522
y[1] (analytic) = 5.5813787960821834397068554591782
y[1] (numeric) = 5.5813787960821835342758832824963
absolute error = 9.45690278233181e-17
relative error = 1.6943667734879467783805573666736e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.523
y[1] (analytic) = 5.5859624663314177258863367349008
y[1] (numeric) = 5.58596246633141782077430231796
absolute error = 9.48879655830592e-17
relative error = 1.6986860573264269638373986416962e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.524
y[1] (analytic) = 5.5905507225435005070351436332935
y[1] (numeric) = 5.5905507225435006022425905070053
absolute error = 9.52074468737118e-17
relative error = 1.7030065837663273879941041801751e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.525
y[1] (analytic) = 5.5951435693066883775907543885512
y[1] (numeric) = 5.5951435693066884731182268521759
absolute error = 9.55274724636247e-17
relative error = 1.7073283514592960818940249764946e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.526
y[1] (analytic) = 5.5997410112138284834782825798487
y[1] (numeric) = 5.5997410112138285793263257019884
absolute error = 9.58480431221397e-17
relative error = 1.7116513590574644855926536048522e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.527
y[1] (analytic) = 5.6043430528623631149580057937283
y[1] (numeric) = 5.604343052862363211127165413322
absolute error = 9.61691596195937e-17
relative error = 1.7159756052134647113490381254236e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.528
y[1] (analytic) = 5.6089496988543343040680390045818
y[1] (numeric) = 5.6089496988543344005588617319009
absolute error = 9.64908227273191e-17
relative error = 1.7203010885804163913006730695519e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.529
y[1] (analytic) = 5.6135609537963884266667501162807
y[1] (numeric) = 5.613560953796388523479783333926
absolute error = 9.68130332176453e-17
relative error = 1.7246278078119331634076456874231e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.53
y[1] (analytic) = 5.6181768222997808090795197077546
y[1] (numeric) = 5.6181768222997809062153115716549
absolute error = 9.71357918639003e-17
relative error = 1.7289557615621308835580481918629e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.531
y[1] (analytic) = 5.6227973089803803393544516296622
y[1] (numeric) = 5.6227973089803804368135510700735
absolute error = 9.74590994404113e-17
relative error = 1.7332849484856179905544101151754e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.532
y[1] (analytic) = 5.6274224184586740831316457082485
y[1] (numeric) = 5.6274224184586741809146024307548
absolute error = 9.77829567225063e-17
relative error = 1.7376153672375036667447984987508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.533
y[1] (analytic) = 5.6320521553597719041306484260459
y[1] (numeric) = 5.6320521553597720022380129125613
absolute error = 9.81073644865154e-17
relative error = 1.7419470164734006098685822026581e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.534
y[1] (analytic) = 5.6366865243134110892607020672563
y[1] (numeric) = 5.6366865243134111876930255770279
absolute error = 9.84323235097716e-17
relative error = 1.7462798948494188987830218662200e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.535
y[1] (analytic) = 5.6413255299539609783584174384459
y[1] (numeric) = 5.6413255299539610771162520090585
absolute error = 9.87578345706126e-17
relative error = 1.7506140010221775937612161641686e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.536
y[1] (analytic) = 5.6459691769204275985574999026145
y[1] (numeric) = 5.6459691769204276976413983509962
absolute error = 9.90838984483817e-17
relative error = 1.7549493336488003170139074925100e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.537
y[1] (analytic) = 5.6506174698564583032951630967493
y[1] (numeric) = 5.6506174698564584027056790201781
absolute error = 9.94105159234288e-17
relative error = 1.7592858913869126026396118523317e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.538
y[1] (analytic) = 5.6552704134103464159598693396639
y[1] (numeric) = 5.6552704134103465156975571167761
absolute error = 9.97376877771122e-17
relative error = 1.7636236728946533836994255894328e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.539
y[1] (analytic) = 5.6599280122350358781850403782506
y[1] (numeric) = 5.6599280122350359782504551700501
absolute error = 1.000654147917995e-16
relative error = 1.7679626768306704992863306084427e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.54
y[1] (analytic) = 5.6645902709881259027933867662438
y[1] (numeric) = 5.6645902709881260031870845171126
absolute error = 1.003936977508688e-16
relative error = 1.7723029018541214976669543046392e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.541
y[1] (analytic) = 5.6692571943318756313965088202109
y[1] (numeric) = 5.6692571943318757321190462589209
absolute error = 1.007225374387100e-16
relative error = 1.7766443466246761772326989826978e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.542
y[1] (analytic) = 5.6739287869332087966544267527608
y[1] (numeric) = 5.673928786933208897706361393487
absolute error = 1.010519346407262e-16
relative error = 1.7809870098025208552071213410913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.543
y[1] (analytic) = 5.6786050534637183891997022428884
y[1] (numeric) = 5.678605053463718490581592386223
absolute error = 1.013818901433346e-16
relative error = 1.7853308900483537881073883280391e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.544
y[1] (analytic) = 5.6832859985996713292308183679645
y[1] (numeric) = 5.6832859985996714309432231019328
absolute error = 1.017124047339683e-16
relative error = 1.7896759860233964285126011968016e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=41.9MB, alloc=4.2MB, time=2.07
x[1] = 1.545
y[1] (analytic) = 5.6879716270220131427794894911426
y[1] (numeric) = 5.6879716270220132448229686922195
absolute error = 1.020434792010769e-16
relative error = 1.7940222963893835068597456079856e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.546
y[1] (analytic) = 5.6926619434163726426565773718797
y[1] (numeric) = 5.6926619434163727450316917060077
absolute error = 1.023751143341280e-16
relative error = 1.7983698198085689497709337774015e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.547
y[1] (analytic) = 5.6973569524730666140812944458789
y[1] (numeric) = 5.6973569524730667167886053694876
absolute error = 1.027073109236087e-16
relative error = 1.8027185549437317469083241066982e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.548
y[1] (analytic) = 5.7020566588871045049983799040469
y[1] (numeric) = 5.7020566588871046080384496650734
absolute error = 1.030400697610265e-16
relative error = 1.8070685004581712440085139100951e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.549
y[1] (analytic) = 5.7067610673581931210879388880337
y[1] (numeric) = 5.7067610673581932244613305269445
absolute error = 1.033733916389108e-16
relative error = 1.8114196550157129506767703340983e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.55
y[1] (analytic) = 5.7114701825907413254726398125845
y[1] (numeric) = 5.7114701825907414291799171633984
absolute error = 1.037072773508139e-16
relative error = 1.8157720172807055428229611940490e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.551
y[1] (analytic) = 5.7161840092938647431269695222932
y[1] (numeric) = 5.7161840092938648471686972136056
absolute error = 1.040417276913124e-16
relative error = 1.8201255859180248552133995395839e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.552
y[1] (analytic) = 5.7209025521813904699932506924041
y[1] (numeric) = 5.7209025521813905743699941484128
absolute error = 1.043767434560087e-16
relative error = 1.8244803595930795798809397838188e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.553
y[1] (analytic) = 5.725625815971861786809130590073
y[1] (numeric) = 5.7256258159718618915214560316046
absolute error = 1.047123254415316e-16
relative error = 1.8288363369718011951099043370515e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.554
y[1] (analytic) = 5.7303538053885428776512550239667
y[1] (numeric) = 5.7303538053885429826997294695051
absolute error = 1.050484744455384e-16
relative error = 1.8331935167206600981807493529531e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.555
y[1] (analytic) = 5.7350865251594235531998460262716
y[1] (numeric) = 5.735086525159423658585037292987
absolute error = 1.053851912667154e-16
relative error = 1.8375518975066537374186120017179e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.556
y[1] (analytic) = 5.7398239800172239787289065320789
y[1] (numeric) = 5.7398239800172240844513832368585
absolute error = 1.057224767047796e-16
relative error = 1.8419114779973156870016849267083e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.557
y[1] (analytic) = 5.7445661746993994068267800467483
y[1] (numeric) = 5.7445661746993995128871116072282
absolute error = 1.060603315604799e-16
relative error = 1.8462722568607159505080626435904e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 8.009e-16
Order of pole = 0.5
x[1] = 1.558
y[1] (analytic) = 5.7493131139481449148517980222023
y[1] (numeric) = 5.7493131139481450212505546578005
absolute error = 1.063987566355982e-16
relative error = 1.8506342327654595010666226068006e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.559
y[1] (analytic) = 5.7540648025104001471277523981938
y[1] (numeric) = 5.7540648025104002538655051311447
absolute error = 1.067377527329509e-16
relative error = 1.8549974043806917577850552882619e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.56
y[1] (analytic) = 5.758821245137854061883935504415
y[1] (numeric) = 5.7588212451378541689612561608049
absolute error = 1.070773206563899e-16
relative error = 1.8593617703760953301550081152115e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.561
y[1] (analytic) = 5.7635824465869496829444942638827
y[1] (numeric) = 5.7635824465869497903619554746869
absolute error = 1.074174612108042e-16
relative error = 1.8637273294218971661606779143148e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.562
y[1] (analytic) = 5.7683484116188888561718503873506
y[1] (numeric) = 5.7683484116188889639300255894714
absolute error = 1.077581752021208e-16
relative error = 1.8680940801888635071718294147989e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.563
y[1] (analytic) = 5.7731191449996370106689430025646
y[1] (numeric) = 5.7731191449996371187684064398709
absolute error = 1.080994634373063e-16
relative error = 1.8724620213483069703278328677553e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.564
y[1] (analytic) = 5.7778946514999279247450549210009
y[1] (numeric) = 5.7778946514999280331863816453688
absolute error = 1.084413267243679e-16
relative error = 1.8768311515720831887659311408443e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.565
y[1] (analytic) = 5.7826749358952684966499885083104
y[1] (numeric) = 5.7826749358952686054337543806653
absolute error = 1.087837658723549e-16
relative error = 1.8812014695325960923092772006992e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.566
y[1] (analytic) = 5.7874600029659435200813618930423
y[1] (numeric) = 5.7874600029659436292081435844021
absolute error = 1.091267816913598e-16
relative error = 1.8855729739027962277773770586263e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.567
y[1] (analytic) = 5.7922498574970204644698010213417
y[1] (numeric) = 5.7922498574970205739401760138616
absolute error = 1.094703749925199e-16
relative error = 1.8899456633561876970971318702546e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.568
y[1] (analytic) = 5.7970445042783542600468078432117
y[1] (numeric) = 5.7970445042783543698613544312296
absolute error = 1.098145465880179e-16
relative error = 1.8943195365668177880710524699098e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.569
y[1] (analytic) = 5.8018439481045920877000896986054
y[1] (numeric) = 5.8018439481045921978593869896895
absolute error = 1.101592972910841e-16
relative error = 1.8986945922092942112161682451457e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.57
y[1] (analytic) = 5.8066481937751781736211397590791
y[1] (numeric) = 5.8066481937751782841257676750759
absolute error = 1.105046279159968e-16
relative error = 1.9030708289587712293724751355674e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.571
y[1] (analytic) = 5.8114572460943585887498631729837
y[1] (numeric) = 5.8114572460943586996004024510679
absolute error = 1.108505392780842e-16
relative error = 1.9074482454909616443286951609474e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.572
y[1] (analytic) = 5.8162711098711860530210483592228
y[1] (numeric) = 5.8162711098711861642180805529482
absolute error = 1.111970321937254e-16
relative error = 1.9118268404821332273252307432212e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.573
y[1] (analytic) = 5.8210897899195247444174876964477
y[1] (numeric) = 5.8210897899195248559615951767995
absolute error = 1.115441074803518e-16
relative error = 1.9162066126091120159303741701601e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.574
y[1] (analytic) = 5.8259132910580551128345566612112
y[1] (numeric) = 5.8259132910580552247263226176596
absolute error = 1.118917659564484e-16
relative error = 1.9205875605492838551866571888139e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.575
y[1] (analytic) = 5.8307416181102786987610652800608
y[1] (numeric) = 5.8307416181102788110010737216158
absolute error = 1.122400084415550e-16
relative error = 1.9249696829805941931221414864331e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.576
y[1] (analytic) = 5.835574775904522956781200576824
y[1] (numeric) = 5.8355747759045230693700363330912
absolute error = 1.125888357562672e-16
relative error = 1.9293529785815444270678212820978e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.577
y[1] (analytic) = 5.8404127692739460839023835174292
y[1] (numeric) = 5.8404127692739461968406322396678
absolute error = 1.129382487222386e-16
relative error = 1.9337374460312087916682577983442e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.578
y[1] (analytic) = 5.8452556030565418527138687805241
y[1] (numeric) = 5.8452556030565419660021169427052
absolute error = 1.132882481621811e-16
relative error = 1.9381230840092186350268319704847e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.579
y[1] (analytic) = 5.8501032820951444493809205128911
y[1] (numeric) = 5.8501032820951445630197554127578
absolute error = 1.136388348998667e-16
relative error = 1.9425098911957723904651545980568e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.58
y[1] (analytic) = 5.8549558112374333164794020642401
y[1] (numeric) = 5.854955811237433430469411824369
absolute error = 1.139900097601289e-16
relative error = 1.9468978662716386439290333055706e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.581
y[1] (analytic) = 5.859813195335938000675622536373
y[1] (numeric) = 5.8598131953359381150173961052364
absolute error = 1.143417735688634e-16
relative error = 1.9512870079181472172878132137517e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.582
y[1] (analytic) = 5.8646754392480430052562878269677
y[1] (numeric) = 5.8646754392480431199504149799979
absolute error = 1.146941271530302e-16
relative error = 1.9556773148172041446062354498538e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.583
y[1] (analytic) = 5.8695425478359926475134086983399
y[1] (numeric) = 5.8695425478359927625604800389942
absolute error = 1.150470713406543e-16
relative error = 1.9600687856512826989436920072243e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.584
y[1] (analytic) = 5.8744145259668959209890232564936
y[1] (numeric) = 5.8744145259668960363896302173209
absolute error = 1.154006069608273e-16
relative error = 1.9644614191034297612711601546101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.585
y[1] (analytic) = 5.879291378512731362584596085589
y[1] (numeric) = 5.8792913785127314783393309292976
absolute error = 1.157547348437086e-16
relative error = 1.9688552138572653310443185900057e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.586
y[1] (analytic) = 5.8841731103503519245399611476319
y[1] (numeric) = 5.8841731103503520406494169681587
absolute error = 1.161094558205268e-16
relative error = 1.9732501685969854149707780017479e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=45.7MB, alloc=4.2MB, time=2.27
x[1] = 1.587
y[1] (analytic) = 5.8890597263614898512866804267341
y[1] (numeric) = 5.8890597263614899677514511503147
absolute error = 1.164647707235806e-16
relative error = 1.9776462820073563878845103562777e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.588
y[1] (analytic) = 5.8939512314327615611806951717089
y[1] (numeric) = 5.8939512314327616780013755579498
absolute error = 1.168206803862409e-16
relative error = 1.9820435527737297183234038108727e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.589
y[1] (analytic) = 5.8988476304556725331191514700612
y[1] (numeric) = 5.8988476304556726502963371130127
absolute error = 1.171771856429515e-16
relative error = 1.9864419795820328641493717174460e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.59
y[1] (analytic) = 5.9037489283266221980462867706038
y[1] (numeric) = 5.903748928326622315580574099834
absolute error = 1.175342873292302e-16
relative error = 1.9908415611187669655157610672744e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.591
y[1] (analytic) = 5.9086551299469088353532688609937
y[1] (numeric) = 5.9086551299469089532452551426649
absolute error = 1.178919862816712e-16
relative error = 1.9952422960710265276983306940376e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.592
y[1] (analytic) = 5.9135662402227344741768837004377
y[1] (numeric) = 5.9135662402227345924271670383827
absolute error = 1.182502833379450e-16
relative error = 1.9996441831264767069440081341738e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.593
y[1] (analytic) = 5.9184822640652097996019734066604
y[1] (numeric) = 5.9184822640652099182111527434612
absolute error = 1.186091793368008e-16
relative error = 2.0040472209733729265978982469731e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.594
y[1] (analytic) = 5.9234032063903590637725305999839
y[1] (numeric) = 5.9234032063903591827412057180513
absolute error = 1.189686751180674e-16
relative error = 2.0084514083005550489657439566867e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.595
y[1] (analytic) = 5.928329072119125001916360216022
y[1] (numeric) = 5.9283290721191251212451317386764
absolute error = 1.193287715226544e-16
relative error = 2.0128567437974466132229865170742e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.596
y[1] (analytic) = 5.9332598661773737532882248120596
y[1] (numeric) = 5.9332598661773738729776942046135
absolute error = 1.196894693925539e-16
relative error = 2.0172632261540624808033211581821e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.597
y[1] (analytic) = 5.9381955934958997870363943106745
y[1] (numeric) = 5.9381955934958999070871638815158
absolute error = 1.200507695708413e-16
relative error = 2.0216708540610012631514652217775e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.598
y[1] (analytic) = 5.9431362590104308329975260475596
y[1] (numeric) = 5.9431362590104309534101989492367
absolute error = 1.204126729016771e-16
relative error = 2.0260796262094545898883317493844e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 7.477e-16
Order of pole = 0.5
x[1] = 1.599
y[1] (analytic) = 5.948081867661632817424805918838
y[1] (numeric) = 5.9480818676616329381999861491464
absolute error = 1.207751802303084e-16
relative error = 2.0304895412912112636939087541616e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.6
y[1] (analytic) = 5.953032424395114803654286356424
y[1] (numeric) = 5.9530324243951149247925787594931
absolute error = 1.211382924030691e-16
relative error = 2.0349005979986395333239625654982e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.601
y[1] (analytic) = 5.9579879341614339377143617981767
y[1] (numeric) = 5.9579879341614340592163720655595
absolute error = 1.215020102673828e-16
relative error = 2.0393127950247147488210873457095e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.602
y[1] (analytic) = 5.9629484019161003988833272627379
y[1] (numeric) = 5.9629484019161005207496619345008
absolute error = 1.218663346717629e-16
relative error = 2.0437261310629998986846685981583e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.603
y[1] (analytic) = 5.9679138326195823551999705870222
y[1] (numeric) = 5.9679138326195824774312370528366
absolute error = 1.222312664658144e-16
relative error = 2.0481406048076547061466656068990e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.604
y[1] (analytic) = 5.972884231237310923932153837366
y[1] (numeric) = 5.9728842312373110465289603376013
absolute error = 1.225968065002353e-16
relative error = 2.0525562149534379596125667957221e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.605
y[1] (analytic) = 5.9778596027396851370083443633297
y[1] (numeric) = 5.9778596027396852599712999901475
absolute error = 1.229629556268178e-16
relative error = 2.0569729601957064621798354488974e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.606
y[1] (analytic) = 5.982839952102076911417060926098
y[1] (numeric) = 5.982839952102077034746775624548
absolute error = 1.233297146984500e-16
relative error = 2.0613908392304223199965579323072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.607
y[1] (analytic) = 5.9878252843048360245792053013396
y[1] (numeric) = 5.987825284304836148276289870456
absolute error = 1.236970845691164e-16
relative error = 2.0658098507541401299109024745123e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.608
y[1] (analytic) = 5.9928156043332950946982547292702
y[1] (numeric) = 5.9928156043332952187633208231703
absolute error = 1.240650660939001e-16
relative error = 2.0702299934640225747018064476948e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.609
y[1] (analytic) = 5.9978109171777745660932955625286
y[1] (numeric) = 5.9978109171777746905269556915124
absolute error = 1.244336601289838e-16
relative error = 2.0746512660578359094979889199085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.61
y[1] (analytic) = 6.0028112278335876995198834453142
y[1] (numeric) = 6.0028112278335878243227509769653
absolute error = 1.248028675316511e-16
relative error = 2.0790736672339504446319120561270e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.611
y[1] (analytic) = 6.0078165413010455674837203450615
y[1] (numeric) = 6.0078165413010456926564095053492
absolute error = 1.251726891602877e-16
relative error = 2.0834971956913393378488587255969e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.550e-16
Order of pole = 0.5
x[1] = 1.612
y[1] (analytic) = 6.0128268625854620545521437507452
y[1] (numeric) = 6.0128268625854621800952696251284
absolute error = 1.255431258743832e-16
relative error = 2.0879218501295873474759663924248e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.613
y[1] (analytic) = 6.0178421966971588626684283497218
y[1] (numeric) = 6.0178421966971589885826068842542
absolute error = 1.259141785345324e-16
relative error = 2.0923476292488912094573409476605e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.614
y[1] (analytic) = 6.0228625486514705214739054978273
y[1] (numeric) = 6.0228625486514706477597535002632
absolute error = 1.262858480024359e-16
relative error = 2.0967745317500483662685758457643e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.615
y[1] (analytic) = 6.0278879234687494036429108052661
y[1] (numeric) = 6.0278879234687495303010459461685
absolute error = 1.266581351409024e-16
relative error = 2.1012025563344739305938909788842e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.616
y[1] (analytic) = 6.0329183261743707452355751736583
y[1] (numeric) = 6.0329183261743708722666159875079
absolute error = 1.270310408138496e-16
relative error = 2.1056317017041943343859197656406e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.617
y[1] (analytic) = 6.0379537617987376710734796374546
y[1] (numeric) = 6.0379537617987377984780455237601
absolute error = 1.274045658863055e-16
relative error = 2.1100619665618476105133033949069e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.618
y[1] (analytic) = 6.0429942353772862251431993857913
y[1] (numeric) = 6.0429942353772863529219106102013
absolute error = 1.277787112244100e-16
relative error = 2.1144933496106886135453981488733e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.619
y[1] (analytic) = 6.0480397519504904060327673687502
y[1] (numeric) = 6.0480397519504905341862450641661
absolute error = 1.281534776954159e-16
relative error = 2.1189258495545842699444811657344e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.62
y[1] (analytic) = 6.053090316563867207406092924905
y[1] (numeric) = 6.0530903165638673359349590925957
absolute error = 1.285288661676907e-16
relative error = 2.1233594650980220444633925849980e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.621
y[1] (analytic) = 6.0581459342679816635203759049944
y[1] (numeric) = 6.0581459342679817924252534157122
absolute error = 1.289048775107178e-16
relative error = 2.1277941949461084362200085020346e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.622
y[1] (analytic) = 6.0632066101184518997915618095556
y[1] (numeric) = 6.0632066101184520290730744046532
absolute error = 1.292815125950976e-16
relative error = 2.1322300378045658089869075930998e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.623
y[1] (analytic) = 6.0682723491759541884128885063939
y[1] (numeric) = 6.0682723491759543180716607989431
absolute error = 1.296587722925492e-16
relative error = 2.1366669923797391008376469254141e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.624
y[1] (analytic) = 6.0733431565062280090315801468578
y[1] (numeric) = 6.0733431565062281390682376227694
absolute error = 1.300366574759116e-16
relative error = 2.1411050573785942435023157885833e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.625
y[1] (analytic) = 6.0784190371800811144887489580334
y[1] (numeric) = 6.0784190371800812449039179771786
absolute error = 1.304151690191452e-16
relative error = 2.1455442315087215010650479153216e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.626
y[1] (analytic) = 6.0834999962733946016275706511838
y[1] (numeric) = 6.0834999962733947324218784485168
absolute error = 1.307943077973330e-16
relative error = 2.1499845134783338364996268535325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.627
y[1] (analytic) = 6.0885860388671279871748042550302
y[1] (numeric) = 6.0885860388671281183488789417122
absolute error = 1.311740746866820e-16
relative error = 2.1544259019962685471185770830704e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.628
y[1] (analytic) = 6.0936771700473242887007322558178
y[1] (numeric) = 6.0936771700473244202552028203427
absolute error = 1.315544705645249e-16
relative error = 2.1588683957719937908643098437267e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.629
y[1] (analytic) = 6.0987733949051151106626020045313
y[1] (numeric) = 6.0987733949051152425980983138521
absolute error = 1.319354963093208e-16
relative error = 2.1633119935155986590164157802284e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.2MB, time=2.47
NO POLE
x[1] = 1.63
y[1] (analytic) = 6.1038747185367257355366544351225
y[1] (numeric) = 6.1038747185367258678538072357798
absolute error = 1.323171528006573e-16
relative error = 2.1677566939378062107174665430603e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.631
y[1] (analytic) = 6.1089811460434802200438312262063
y[1] (numeric) = 6.1089811460434803527432721454577
absolute error = 1.326994409192514e-16
relative error = 2.1722024957499667748205278354744e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.632
y[1] (analytic) = 6.1140926825318064964742566323543
y[1] (numeric) = 6.1140926825318066295566181793054
absolute error = 1.330823615469511e-16
relative error = 2.1766493976640627100286854650437e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.633
y[1] (analytic) = 6.1192093331132414791155953098944
y[1] (numeric) = 6.1192093331132416125815108766311
absolute error = 1.334659155667367e-16
relative error = 2.1810973983927082143687194675862e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.634
y[1] (analytic) = 6.124331102904436175790392565999
y[1] (numeric) = 6.1243311029044363096404964287212
absolute error = 1.338501038627222e-16
relative error = 2.1855464966491507441947824460268e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.635
y[1] (analytic) = 6.1294579970271608045075085688286
y[1] (numeric) = 6.1294579970271609387424358889853
absolute error = 1.342349273201567e-16
relative error = 2.1899966911472724018080351505990e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.636
y[1] (analytic) = 6.1345900206083099152327631705911
y[1] (numeric) = 6.1345900206083100498531499960168
absolute error = 1.346203868254257e-16
relative error = 2.1944479806015896617224208039824e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.637
y[1] (analytic) = 6.1397271787799075167839131145883
y[1] (numeric) = 6.139727178779907651790396380641
absolute error = 1.350064832660527e-16
relative error = 2.1989003637272579602021904221440e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.638
y[1] (analytic) = 6.1448694766791122088550885216543
y[1] (numeric) = 6.1448694766791123442483060523547
absolute error = 1.353932175307004e-16
relative error = 2.2033538392400697279423118910046e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.639
y[1] (analytic) = 6.15001691944822231917582068085
y[1] (numeric) = 6.1500169194482224549564111900221
absolute error = 1.357805905091721e-16
relative error = 2.2078084058564556602695661438926e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.64
y[1] (analytic) = 6.1551695122346810458097983038692
y[1] (numeric) = 6.1551695122346811819784013962822
absolute error = 1.361686030924130e-16
relative error = 2.2122640622934843319475962979671e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.641
y[1] (analytic) = 6.1603272601910816045984945423413
y[1] (numeric) = 6.1603272601910817411557507148533
absolute error = 1.365572561725120e-16
relative error = 2.2167208072688699059796693616003e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.642
y[1] (analytic) = 6.165490168475172381754812212087
y[1] (numeric) = 6.1654901684751725187013628547898
absolute error = 1.369465506427028e-16
relative error = 2.2211786395009684257703306451853e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.643
y[1] (analytic) = 6.170658242249862091611899818401
y[1] (numeric) = 6.170658242249862228948387215766
absolute error = 1.373364873973650e-16
relative error = 2.2256375577087741014228227803680e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.644
y[1] (analytic) = 6.1758314866832249395322961316073
y[1] (numeric) = 6.1758314866832250772593634636336
absolute error = 1.377270673320263e-16
relative error = 2.2300975606119334016102703444768e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.645
y[1] (analytic) = 6.1810099069485057899825662224634
y[1] (numeric) = 6.1810099069485059281008575658264
absolute error = 1.381182913433630e-16
relative error = 2.2345586469307315465950318115316e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.646
y[1] (analytic) = 6.1861935082241253397785970324779
y[1] (numeric) = 6.1861935082241254782887573616799
absolute error = 1.385101603292020e-16
relative error = 2.2390208153861032920957632321860e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.647
y[1] (analytic) = 6.19138229569368529650672572487
y[1] (numeric) = 6.1913822956936854354094009133922
absolute error = 1.389026751885222e-16
relative error = 2.2434840646996339435975210101002e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.648
y[1] (analytic) = 6.1965762745459735621258792377303
y[1] (numeric) = 6.1965762745459737014217160591857
absolute error = 1.392958368214554e-16
relative error = 2.2479483935935522720033221131587e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.649
y[1] (analytic) = 6.2017754499749694217559086419538
y[1] (numeric) = 6.201775449974969561445554771242
absolute error = 1.396896461292882e-16
relative error = 2.2524138007907395647288009777699e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.65
y[1] (analytic) = 6.2069798271798487376573070927123
y[1] (numeric) = 6.2069798271798488777414111071757
absolute error = 1.400841040144634e-16
relative error = 2.2568802850147305512898096398489e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.651
y[1] (analytic) = 6.2121894113649891484075053546177
y[1] (numeric) = 6.2121894113649892888867167351987
absolute error = 1.404792113805810e-16
relative error = 2.2613478449897078606324000096868e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.652
y[1] (analytic) = 6.2174042077399752732789440773031
y[1] (numeric) = 6.2174042077399754141539132097032
absolute error = 1.408749691324001e-16
relative error = 2.2658164794405109571841084788590e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.653
y[1] (analytic) = 6.22262422151960392182412719993
y[1] (numeric) = 6.22262422151960406309550537577
absolute error = 1.412713781758400e-16
relative error = 2.2702861870926321510108627441277e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.654
y[1] (analytic) = 6.2278494579238893086728660701076
y[1] (numeric) = 6.2278494579238894503413054880893
absolute error = 1.416684394179817e-16
relative error = 2.2747569666722190260968631054276e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.655
y[1] (analytic) = 6.2330799221780682735469290749028
y[1] (numeric) = 6.233079922178068415613082841972
absolute error = 1.420661537670692e-16
relative error = 2.2792288169060736230288827280681e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.656
y[1] (analytic) = 6.2383156195126055064973167990266
y[1] (numeric) = 6.2383156195126056489618389315379
absolute error = 1.424645221325113e-16
relative error = 2.2837017365216596160588573059519e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.657
y[1] (analytic) = 6.2435565551631987783693879479068
y[1] (numeric) = 6.2435565551631989212329333727895
absolute error = 1.428635454248827e-16
relative error = 2.2881757242470982177414398491965e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.658
y[1] (analytic) = 6.2488027343707841765010665012086
y[1] (numeric) = 6.248802734370784319764291057134
absolute error = 1.432632245559254e-16
relative error = 2.2926507788111688803031387200913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.659
y[1] (analytic) = 6.2540541623815413456593657954475
y[1] (numeric) = 6.2540541623815414893229262339977
absolute error = 1.436635604385502e-16
relative error = 2.2971268989433115676664078945904e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.66
y[1] (analytic) = 6.2593108444468987342204704726538
y[1] (numeric) = 6.259310844446898878285024459492
absolute error = 1.440645539868382e-16
relative error = 2.3016040833736289912339843230685e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.661
y[1] (analytic) = 6.2645727858235388455986224756095
y[1] (numeric) = 6.2645727858235389900648285916516
absolute error = 1.444662061160421e-16
relative error = 2.3060823308328856170214494166977e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.662
y[1] (analytic) = 6.2698399917734034949290625189798
y[1] (numeric) = 6.2698399917734036397975802615678
absolute error = 1.448685177425880e-16
relative error = 2.3105616400525146276152167000255e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.663
y[1] (analytic) = 6.2751124675636990710102837197202
y[1] (numeric) = 6.2751124675636992162817735037963
absolute error = 1.452714897840761e-16
relative error = 2.3150420097646072946067423362058e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.664
y[1] (analytic) = 6.2803902184669018035108593294496
y[1] (numeric) = 6.2803902184669019491859824887324
absolute error = 1.456751231592828e-16
relative error = 2.3195234387019246712648072599234e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.665
y[1] (analytic) = 6.2856732497607630354461117760574
y[1] (numeric) = 6.2856732497607631815255305642192
absolute error = 1.460794187881618e-16
relative error = 2.3240059255978932922173912540852e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.666
y[1] (analytic) = 6.2909615667283145009298954916526
y[1] (numeric) = 6.2909615667283146474142730834982
absolute error = 1.464843775918456e-16
relative error = 2.3284894691866072281657997479753e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.667
y[1] (analytic) = 6.2962551746578736082067712790772
y[1] (numeric) = 6.2962551746578737550967717717244
absolute error = 1.468900004926472e-16
relative error = 2.3329740682028332817850580909371e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.668
y[1] (analytic) = 6.3015540788430487279698552495994
y[1] (numeric) = 6.3015540788430488752661436636605
absolute error = 1.472962884140611e-16
relative error = 2.3374597213820050240641810774357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.669
y[1] (analytic) = 6.3068582845827444869696306500752
y[1] (numeric) = 6.3068582845827446346728729308401
absolute error = 1.477032422807649e-16
relative error = 2.3419464274602263491448591226700e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.67
y[1] (analytic) = 6.3121677971811670669190161888314
y[1] (numeric) = 6.3121677971811672150298792074525
absolute error = 1.481108630186211e-16
relative error = 2.3464341851742781547214728337867e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.671
y[1] (analytic) = 6.3174826219478295086999897657817
y[1] (numeric) = 6.3174826219478296572191413204597
absolute error = 1.485191515546780e-16
relative error = 2.3509229932616107175050253554019e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=53.4MB, alloc=4.2MB, time=2.66
x[1] = 1.672
y[1] (analytic) = 6.322802764197557021877071813839
y[1] (numeric) = 6.3228027641975571708051806310102
absolute error = 1.489281088171712e-16
relative error = 2.3554128504603455715152954009128e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.673
y[1] (analytic) = 6.3281282292504922995229777655511
y[1] (numeric) = 6.3281282292504924488607135010768
absolute error = 1.493377357355257e-16
relative error = 2.3599037555092868333262037052027e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.674
y[1] (analytic) = 6.3334590224321008383617544710559
y[1] (numeric) = 6.3334590224321009881097877114125
absolute error = 1.497480332403566e-16
relative error = 2.3643957071479103402214219984315e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.675
y[1] (analytic) = 6.3387951490731762642347207109341
y[1] (numeric) = 6.338795149073176414393722974405
absolute error = 1.501590022634709e-16
relative error = 2.3688887041163701714451689672136e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.676
y[1] (analytic) = 6.3441366145098456628945372703451
y[1] (numeric) = 6.3441366145098458134651810082138
absolute error = 1.505706437378687e-16
relative error = 2.3733827451554956538635691654231e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.677
y[1] (analytic) = 6.3494834240835749161327373689596
y[1] (numeric) = 6.3494834240835750671156959667047
absolute error = 1.509829585977451e-16
relative error = 2.3778778290067993820888918240734e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.678
y[1] (analytic) = 6.3548355831411740432460535746645
y[1] (numeric) = 6.3548355831411741946420013531558
absolute error = 1.513959477784913e-16
relative error = 2.3823739544124725840812523706182e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.679
y[1] (analytic) = 6.360193097034802547846882667812
y[1] (numeric) = 6.3601930970348026996564948845083
absolute error = 1.518096122166963e-16
relative error = 2.3868711201153899185834485859806e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.68
y[1] (analytic) = 6.3655559711219747700232352669232
y[1] (numeric) = 6.3655559711219749222471881170712
absolute error = 1.522239528501480e-16
relative error = 2.3913693248591047973615706827253e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.681
y[1] (analytic) = 6.370924210765565243853522376242
y[1] (numeric) = 6.370924210765565396492492994077
absolute error = 1.526389706178350e-16
relative error = 2.3958685673878556932270784222946e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.682
y[1] (analytic) = 6.3762978213338140602815363703721
y[1] (numeric) = 6.3762978213338142133362028303199
absolute error = 1.530546664599478e-16
relative error = 2.4003688464465629810791683071946e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.683
y[1] (analytic) = 6.3816768082003322353569892914251
y[1] (numeric) = 6.3816768082003323888280306093057
absolute error = 1.534710413178806e-16
relative error = 2.4048701607808351715180517568850e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.684
y[1] (analytic) = 6.3870611767441070838469766996656
y[1] (numeric) = 6.3870611767441072377350728338981
absolute error = 1.538880961342325e-16
relative error = 2.4093725091369656936451768900635e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.685
y[1] (analytic) = 6.3924509323495075982237406895646
y[1] (numeric) = 6.3924509323495077525295725423737
absolute error = 1.543058318528091e-16
relative error = 2.4138758902619359261410059936326e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.686
y[1] (analytic) = 6.3978460804062898330341110594726
y[1] (numeric) = 6.3978460804062899877583604780964
absolute error = 1.547242494186238e-16
relative error = 2.4183803029034134985817585033542e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.687
y[1] (analytic) = 6.4032466263096022946560090048022
y[1] (numeric) = 6.4032466263096024497993587827016
absolute error = 1.551433497778994e-16
relative error = 2.4228857458097552610818279634279e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.688
y[1] (analytic) = 6.4086525754599913364474030916731
y[1] (numeric) = 6.4086525754599914920105369697428
absolute error = 1.555631338780697e-16
relative error = 2.4273922177300102135251647545695e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.689
y[1] (analytic) = 6.4140639332634065592931126604252
y[1] (numeric) = 6.414063933263406715276715328206
absolute error = 1.559836026677808e-16
relative error = 2.4318997174139177173197202303773e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.69
y[1] (analytic) = 6.4194807051312062175548592062532
y[1] (numeric) = 6.4194807051312063739596163031456
absolute error = 1.564047570968924e-16
relative error = 2.4364082436119056907323789353144e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.691
y[1] (analytic) = 6.4249028964801626304299716874637
y[1] (numeric) = 6.4249028964801627872565698039436
absolute error = 1.568265981164799e-16
relative error = 2.4409177950751012394527888905295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.692
y[1] (analytic) = 6.4303305127324675987241571205134
y[1] (numeric) = 6.4303305127324677559732837993484
absolute error = 1.572491266788350e-16
relative error = 2.4454283705553178809244102534538e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.693
y[1] (analytic) = 6.435763559315737827043753235047
y[1] (numeric) = 6.4357635593157379847160969725151
absolute error = 1.576723437374681e-16
relative error = 2.4499399688050707765073515447242e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.694
y[1] (analytic) = 6.4412020416630203514128853816428
y[1] (numeric) = 6.4412020416630205095091356287518
absolute error = 1.580962502471090e-16
relative error = 2.4544525885775654684505861098828e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.695
y[1] (analytic) = 6.4466459652127979723209553098721
y[1] (numeric) = 6.4466459652127981308418024735811
absolute error = 1.585208471637090e-16
relative error = 2.4589662286267083650129575320980e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.696
y[1] (analytic) = 6.4520953354089946932058948646169
y[1] (numeric) = 6.4520953354089948521520303090588
absolute error = 1.589461354444419e-16
relative error = 2.4634808877071000982216033944493e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.697
y[1] (analytic) = 6.4575501577009811643786230843498
y[1] (numeric) = 6.4575501577009813237507391320556
absolute error = 1.593721160477058e-16
relative error = 2.4679965645740412782491759605461e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.698
y[1] (analytic) = 6.4630104375435801323941506262894
y[1] (numeric) = 6.4630104375435802921929405594139
absolute error = 1.597987899331245e-16
relative error = 2.4725132579835320039850678288955e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.699
y[1] (analytic) = 6.4684761803970718948747808899881
y[1] (numeric) = 6.4684761803970720551009389515372
absolute error = 1.602261580615491e-16
relative error = 2.4770309666922744423543642574619e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.7
y[1] (analytic) = 6.4739473917271997607908626630091
y[1] (numeric) = 6.4739473917271999214450840580682
absolute error = 1.606542213950591e-16
relative error = 2.4815496894576676456399311141911e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.701
y[1] (analytic) = 6.4794240770051755162045545698991
y[1] (numeric) = 6.4794240770051756772875354668636
absolute error = 1.610829808969645e-16
relative error = 2.4860694250378178028622757657136e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.702
y[1] (analytic) = 6.484906241707684895482067068678
y[1] (numeric) = 6.4849062417076850569945046004848
absolute error = 1.615124375318068e-16
relative error = 2.4905901721915314510564829986697e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.703
y[1] (analytic) = 6.490393891316893057979853207542
y[1] (numeric) = 6.4903938913168932199224454729028
absolute error = 1.619425922653608e-16
relative error = 2.4951119296783210211181656613449e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.704
y[1] (analytic) = 6.495887031320450070210224828429
y[1] (numeric) = 6.4958870313204502325836708930647
absolute error = 1.623734460646357e-16
relative error = 2.4996346962583995537597399220771e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.705
y[1] (analytic) = 6.5013856672114963934918763835174
y[1] (numeric) = 6.5013856672114965562968762813947
absolute error = 1.628049998978773e-16
relative error = 2.5041584706926923359700394385425e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.706
y[1] (analytic) = 6.5068898044886683770908040156412
y[1] (numeric) = 6.50688980448866854032805875021
absolute error = 1.632372547345688e-16
relative error = 2.5086832517428269370359774769680e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.707
y[1] (analytic) = 6.5123994486561037568571130439972
y[1] (numeric) = 6.5123994486561039205273245894299
absolute error = 1.636702115454327e-16
relative error = 2.5132090381711401601188550621650e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.708
y[1] (analytic) = 6.5179146052234471593632124924101
y[1] (numeric) = 6.5179146052234473234670837948424
absolute error = 1.641038713024323e-16
relative error = 2.5177358287406787958433081787438e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.709
y[1] (analytic) = 6.5234352797058556115489007988092
y[1] (numeric) = 6.5234352797058557760871357775822
absolute error = 1.645382349787730e-16
relative error = 2.5222636222151972803306394592599e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.71
y[1] (analytic) = 6.528961477624004055878852351461
y[1] (numeric) = 6.5289614776240042208521559003649
absolute error = 1.649733035489039e-16
relative error = 2.5267924173591599341586916751908e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.711
y[1] (analytic) = 6.5344932045040908710180200099042
y[1] (numeric) = 6.5344932045040910364270979984236
absolute error = 1.654090779885194e-16
relative error = 2.5313222129377431640914368802045e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.712
y[1] (analytic) = 6.5400304658778433980304742864492
y[1] (numeric) = 6.54003046587784356387603356101
absolute error = 1.658455592745608e-16
relative error = 2.5358530077168376277280923528711e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.713
y[1] (analytic) = 6.5455732672825234721072053875428
y[1] (numeric) = 6.5455732672825236383899537727603
absolute error = 1.662827483852175e-16
relative error = 2.5403848004630442502210266060255e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=57.2MB, alloc=4.2MB, time=2.85
x[1] = 1.714
y[1] (analytic) = 6.5511216142609329598284198432597
y[1] (numeric) = 6.5511216142609331265490661431885
absolute error = 1.667206462999288e-16
relative error = 2.5449175899436793940025590954333e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.715
y[1] (analytic) = 6.5566755123614193019658689876804
y[1] (numeric) = 6.5566755123614194691251229870656
absolute error = 1.671592539993852e-16
relative error = 2.5494513749267723504932908127508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.716
y[1] (analytic) = 6.562234967137881061830752092944
y[1] (numeric) = 6.5622349671378812294293245584743
absolute error = 1.675985724655303e-16
relative error = 2.5539861541810719617837291117613e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.717
y[1] (analytic) = 6.567799984149773479172742505344
y[1] (numeric) = 6.5677999841497736472113451869058
absolute error = 1.680386026815618e-16
relative error = 2.5585219264760394794525666951955e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.718
y[1] (analytic) = 6.573370568962114029635690682953
y[1] (numeric) = 6.5733705689621141981150363148864
absolute error = 1.684793456319334e-16
relative error = 2.5630586905818551252276691183354e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.719
y[1] (analytic) = 6.5789467271454879897755635909454
y[1] (numeric) = 6.5789467271454881586963658933017
absolute error = 1.689208023023563e-16
relative error = 2.5675964452694185122899034257913e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.72
y[1] (analytic) = 6.5845284642760540076461854730193
y[1] (numeric) = 6.58452846427605417700915915282
absolute error = 1.693629736798007e-16
relative error = 2.5721351893103490383488602969795e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.721
y[1] (analytic) = 6.5901157859355496789583505851238
y[1] (numeric) = 6.5901157859355498487642113376208
absolute error = 1.698058607524970e-16
relative error = 2.5766749214769816983469246540755e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.722
y[1] (analytic) = 6.5957086977112971288178840510681
y[1] (numeric) = 6.5957086977112972990673485610061
absolute error = 1.702494645099380e-16
relative error = 2.5812156405423780537259817409015e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.723
y[1] (analytic) = 6.6013072051962085990482325785396
y[1] (numeric) = 6.6013072051962087697420185214193
absolute error = 1.706937859428797e-16
relative error = 2.5857573452803159118851933824539e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.724
y[1] (analytic) = 6.6069113139887920411031723585858
y[1] (numeric) = 6.6069113139887922122419984019295
absolute error = 1.711388260433437e-16
relative error = 2.5903000344653032490087301241072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.725
y[1] (analytic) = 6.6125210296931567145752270617358
y[1] (numeric) = 6.6125210296931568861598128663536
absolute error = 1.715845858046178e-16
relative error = 2.5948437068725648148419687142932e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.726
y[1] (analytic) = 6.6181363579190187913053944396445
y[1] (numeric) = 6.6181363579190189633364606609025
absolute error = 1.720310662212580e-16
relative error = 2.5993883612780499333681130715614e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.727
y[1] (analytic) = 6.6237573042817069650997856424531
y[1] (numeric) = 6.6237573042817071375780539315434
absolute error = 1.724782682890903e-16
relative error = 2.6039339964584372182090350446622e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.728
y[1] (analytic) = 6.6293838744021680670587869689742
y[1] (numeric) = 6.6293838744021682399849799741859
absolute error = 1.729261930052117e-16
relative error = 2.6084806111911271702950024627902e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.729
y[1] (analytic) = 6.6350160739069726865243593793293
y[1] (numeric) = 6.6350160739069728598992007473215
absolute error = 1.733748413679922e-16
relative error = 2.6130282042542498584876601445996e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.73
y[1] (analytic) = 6.640653908428320797651096717808
y[1] (numeric) = 6.6406539084283209714753110948841
absolute error = 1.738242143770761e-16
relative error = 2.6175767744266619937309624464103e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.731
y[1] (analytic) = 6.6462973836040473916066692174754
y[1] (numeric) = 6.646297383604047565880982250859
absolute error = 1.742743130333836e-16
relative error = 2.6221263204879485055756286395006e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.732
y[1] (analytic) = 6.6519465050776281144072844874402
y[1] (numeric) = 6.6519465050776282891324228265527
absolute error = 1.747251383391125e-16
relative error = 2.6266768412184255876932869935386e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.733
y[1] (analytic) = 6.6576012784981849103938038187158
y[1] (numeric) = 6.6576012784981850855704951164551
absolute error = 1.751766912977393e-16
relative error = 2.6312283353991346892888445675922e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.734
y[1] (analytic) = 6.6632617095204916713541572852586
y[1] (numeric) = 6.6632617095204918469831301992801
absolute error = 1.756289729140215e-16
relative error = 2.6357808018118545199620564745838e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.735
y[1] (analytic) = 6.668927803804979891297706763072
y[1] (numeric) = 6.6689278038049800673796909570704
absolute error = 1.760819841939984e-16
relative error = 2.6403342392390904746922634614329e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.736
y[1] (analytic) = 6.6745995670177443268872116422082
y[1] (numeric) = 6.6745995670177445034229377872014
absolute error = 1.765357261449932e-16
relative error = 2.6448886464640835630936759317472e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.737
y[1] (analytic) = 6.6802770048305486635340576641065
y[1] (numeric) = 6.6802770048305488405242574397208
absolute error = 1.769901997756143e-16
relative error = 2.6494440222708072912412844152494e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.738
y[1] (analytic) = 6.6859601229208311871624149799684
y[1] (numeric) = 6.6859601229208313646078210757254
absolute error = 1.774454060957570e-16
relative error = 2.6540003654439705156169559085985e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.739
y[1] (analytic) = 6.6916489269717104616479971948011
y[1] (numeric) = 6.6916489269717106395493433114058
absolute error = 1.779013461166047e-16
relative error = 2.6585576747690127840595528283128e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.74
y[1] (analytic) = 6.6973434226719910119370988363601
y[1] (numeric) = 6.6973434226719911902951196869912
absolute error = 1.783580208506311e-16
relative error = 2.6631159490321146052922358231717e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.741
y[1] (analytic) = 6.7030436157161690128515943685033
y[1] (numeric) = 6.7030436157161691916670256801046
absolute error = 1.788154313116013e-16
relative error = 2.6676751870201912291604650788325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.742
y[1] (analytic) = 6.7087495118044379835855875544297
y[1] (numeric) = 6.7087495118044381628591660690031
absolute error = 1.792735785145734e-16
relative error = 2.6722353875208938849880753831240e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.743
y[1] (analytic) = 6.7144611166426944878994056669249
y[1] (numeric) = 6.7144611166426946676318691428252
absolute error = 1.797324634759003e-16
relative error = 2.6767965493226139657522750384360e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.744
y[1] (analytic) = 6.7201784359425438400166387400849
y[1] (numeric) = 6.7201784359425440202087259533161
absolute error = 1.801920872132312e-16
relative error = 2.6813586712144827002010385728894e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.745
y[1] (analytic) = 6.7259014754213058162299297600317
y[1] (numeric) = 6.7259014754213059968823805055446
absolute error = 1.806524507455129e-16
relative error = 2.6859217519863678264703781344187e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.746
y[1] (analytic) = 6.7316302408020203722212274008865
y[1] (numeric) = 6.7316302408020205533347824938782
absolute error = 1.811135550929917e-16
relative error = 2.6904857904288791692314203981904e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.747
y[1] (analytic) = 6.7373647378134533661022186267307
y[1] (numeric) = 6.7373647378134535476776199039456
absolute error = 1.815754012772149e-16
relative error = 2.6950507853333682247481006155916e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.748
y[1] (analytic) = 6.7431049721901022871806642004637
y[1] (numeric) = 6.743104972190102469218654521496
absolute error = 1.820379903210323e-16
relative error = 2.6996167354919277214051631363282e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.749
y[1] (analytic) = 6.7488509496722019904583658663702
y[1] (numeric) = 6.7488509496722021729596891149683
absolute error = 1.825013232485981e-16
relative error = 2.7041836396973970827623416826349e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.75
y[1] (analytic) = 6.7546026760057304368664997048427
y[1] (numeric) = 6.7546026760057306198319007902145
absolute error = 1.829654010853718e-16
relative error = 2.7087514967433530313191253108443e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.751
y[1] (analytic) = 6.7603601569424144392440558950701
y[1] (numeric) = 6.7603601569424146226742807531907
absolute error = 1.834302248581206e-16
relative error = 2.7133203054241224017228550765337e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.752
y[1] (analytic) = 6.7661233982397354140651308646117
y[1] (numeric) = 6.7661233982397355979609264595321
absolute error = 1.838957955949204e-16
relative error = 2.7178900645347741705486481384749e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.753
y[1] (analytic) = 6.7718924056609351389208235536275
y[1] (numeric) = 6.7718924056609353232829378787852
absolute error = 1.843621143251577e-16
relative error = 2.7224607728711247902462694956325e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.754
y[1] (analytic) = 6.7776671849750215157614932761416
y[1] (numeric) = 6.7776671849750217005906753556725
absolute error = 1.848291820795309e-16
relative error = 2.7270324292297346165060200767285e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.755
y[1] (analytic) = 6.7834477419567743399051424210758
y[1] (numeric) = 6.783447741956774525202142311128
absolute error = 1.852969998900522e-16
relative error = 2.7316050324079131721634580664896e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
memory used=61.0MB, alloc=4.2MB, time=3.04
x[1] = 1.756
y[1] (analytic) = 6.7892340823867510748176930019174
y[1] (numeric) = 6.7892340823867512605832617919667
absolute error = 1.857655687900493e-16
relative error = 2.7361785812037214115938785881772e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.757
y[1] (analytic) = 6.7950262120512926326709318357798
y[1] (numeric) = 6.7950262120512928189058216499463
absolute error = 1.862348898141665e-16
relative error = 2.7407530744159651167085527049482e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.758
y[1] (analytic) = 6.8008241367425291606839049102811
y[1] (numeric) = 6.8008241367425293473888689086477
absolute error = 1.867049639983666e-16
relative error = 2.7453285108442000631438268362452e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.759
y[1] (analytic) = 6.8066278622583858332535472801182
y[1] (numeric) = 6.8066278622583860204293396600509
absolute error = 1.871757923799327e-16
relative error = 2.7499048892887356640701751284694e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.76
y[1] (analytic) = 6.8124373944025886498803406244497
y[1] (numeric) = 6.812437394402588837527716621919
absolute error = 1.876473759974693e-16
relative error = 2.7544822085506282931633182389057e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.761
y[1] (analytic) = 6.8182527389846702388947963912265
y[1] (numeric) = 6.818252738984670427014512282131
absolute error = 1.881197158909045e-16
relative error = 2.7590604674316907479836586358303e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.762
y[1] (analytic) = 6.8240739018199756669905682554387
y[1] (numeric) = 6.8240739018199758555833813569298
absolute error = 1.885928131014911e-16
relative error = 2.7636396647344855186655092178357e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.763
y[1] (analytic) = 6.8299008887296682545700034248743
y[1] (numeric) = 6.8299008887296684436366720966827
absolute error = 1.890666686718084e-16
relative error = 2.7682197992623283131317573587311e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.764
y[1] (analytic) = 6.8357337055407353969079481394257
y[1] (numeric) = 6.8357337055407355864492317851896
absolute error = 1.895412836457639e-16
relative error = 2.7728008698192900744531800544154e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.765
y[1] (analytic) = 6.8415723580859943911396285282354
y[1] (numeric) = 6.8415723580859945811562875968303
absolute error = 1.900166590685949e-16
relative error = 2.7773828752101974992639065187607e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.766
y[1] (analytic) = 6.8474168522040982690784338130463
y[1] (numeric) = 6.8474168522040984595712297999161
absolute error = 1.904927959868698e-16
relative error = 2.7819658142406291453100089217989e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.767
y[1] (analytic) = 6.8532671937395416358694346760262
y[1] (numeric) = 6.8532671937395418268391301245166
absolute error = 1.909696954484904e-16
relative error = 2.7865496857169261235009089166589e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.768
y[1] (analytic) = 6.8591233885426665144844754460723
y[1] (numeric) = 6.859123388542666705931833948765
absolute error = 1.914473585026927e-16
relative error = 2.7911344884461808395299713831101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.769
y[1] (analytic) = 6.8649854424696681960646845991733
y[1] (numeric) = 6.8649854424696683879904707992225
absolute error = 1.919257862000492e-16
relative error = 2.7957202212362476160645601337667e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.77
y[1] (analytic) = 6.8708533613826010961162539158285
y[1] (numeric) = 6.8708533613826012885212335082986
absolute error = 1.924049795924701e-16
relative error = 2.8003068828957372238615879032387e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.771
y[1] (analytic) = 6.8767271511493846165653424917908
y[1] (numeric) = 6.8767271511493848094502822249957
absolute error = 1.928849397332049e-16
relative error = 2.8048944722340172304967858748395e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.772
y[1] (analytic) = 6.8826068176438090136779676575249
y[1] (numeric) = 6.8826068176438092070436353343695
absolute error = 1.933656676768446e-16
relative error = 2.8094829880612210378588703129414e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.773
y[1] (analytic) = 6.8884923667455412718507507267631
y[1] (numeric) = 6.8884923667455414656979152060856
absolute error = 1.938471644793225e-16
relative error = 2.8140724291882365224737581541932e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.774
y[1] (analytic) = 6.8943838043401309832783913653911
y[1] (numeric) = 6.8943838043401311776078225633076
absolute error = 1.943294311979165e-16
relative error = 2.8186627944267164636953569032583e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.775
y[1] (analytic) = 6.9002811363190162335037502486301
y[1] (numeric) = 6.9002811363190164283162191398806
absolute error = 1.948124688912505e-16
relative error = 2.8232540825890758483942946393371e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.776
y[1] (analytic) = 6.906184368579529492856425557088
y[1] (numeric) = 6.9061843685795296881527041763838
absolute error = 1.952962786192958e-16
relative error = 2.8278462924884891622456353490088e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.777
y[1] (analytic) = 6.9120935070249035137857147507459
y[1] (numeric) = 6.9120935070249037095665761941191
absolute error = 1.957808614433732e-16
relative error = 2.8324394229388977948882425651714e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.778
y[1] (analytic) = 6.9180085575642772340938589543353
y[1] (numeric) = 6.9180085575642774303600773804896
absolute error = 1.962662184261543e-16
relative error = 2.8370334727550058158972742599608e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.779
y[1] (analytic) = 6.9239295261127016860754731878399
y[1] (numeric) = 6.9239295261127018828278238195031
absolute error = 1.967523506316632e-16
relative error = 2.8416284407522815222147886441413e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.78
y[1] (analytic) = 6.9298564185911459115690715820469
y[1] (numeric) = 6.929856418591146108808330707325
absolute error = 1.972392591252781e-16
relative error = 2.8462243257469575073707174561714e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.781
y[1] (analytic) = 6.9357892409265028829266026311638
y[1] (numeric) = 6.9357892409265030806535476048972
absolute error = 1.977269449737334e-16
relative error = 2.8508211265560379120657602022413e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.782
y[1] (analytic) = 6.9417279990515954299069154525317
y[1] (numeric) = 6.9417279990515956281223246976523
absolute error = 1.982154092451206e-16
relative error = 2.8554188419972883234952639377905e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.783
y[1] (analytic) = 6.947672698905182172499083947393
y[1] (numeric) = 6.9476726989051823712037369562833
absolute error = 1.987046530088903e-16
relative error = 2.8600174708892415317856904562319e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.784
y[1] (analytic) = 6.9536233464319634596815216865335
y[1] (numeric) = 6.9536233464319636588761990223876
absolute error = 1.991946773358541e-16
relative error = 2.8646170120512017915115616289099e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.785
y[1] (analytic) = 6.9595799475825873141228262804083
y[1] (numeric) = 6.9595799475825875138083095785942
absolute error = 1.996854832981859e-16
relative error = 2.8692174643032404127704560985633e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.786
y[1] (analytic) = 6.9655425083136553828302979350911
y[1] (numeric) = 6.9655425083136555830073699045149
absolute error = 2.001770719694238e-16
relative error = 2.8738188264661999613196282720328e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.787
y[1] (analytic) = 6.9715110345877288937520828430617
y[1] (numeric) = 6.971511034587729094421527267533
absolute error = 2.006694444244713e-16
relative error = 2.8784210973616883689056151541766e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.788
y[1] (analytic) = 6.9774855323733346183388980114707
y[1] (numeric) = 6.9774855323733348195014997510705
absolute error = 2.011626017395998e-16
relative error = 2.8830242758120916777743187328479e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.789
y[1] (analytic) = 6.9834660076449708400713000901046
y[1] (numeric) = 6.9834660076449710417278450825539
absolute error = 2.016565449924493e-16
relative error = 2.8876283606405609171634858542648e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.79
y[1] (analytic) = 6.9894524663831133289584667268155
y[1] (numeric) = 6.9894524663831135311097419888462
absolute error = 2.021512752620307e-16
relative error = 2.8922333506710219113320348503511e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.791
y[1] (analytic) = 6.9954449145742213220144649496965
y[1] (numeric) = 6.9954449145742215246612585784237
absolute error = 2.026467936287272e-16
relative error = 2.8968392447281721442812586239906e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.792
y[1] (analytic) = 7.0014433582107435097179870527682
y[1] (numeric) = 7.0014433582107437128610882270645
absolute error = 2.031431011742963e-16
relative error = 2.9014460416374861827351735841480e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.793
y[1] (analytic) = 7.0074478032911240284615404454122
y[1] (numeric) = 7.007447803291124232101739427283
absolute error = 2.036401989818708e-16
relative error = 2.9060537402252067732198148546654e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.794
y[1] (analytic) = 7.0134582558198084589960839152395
y[1] (numeric) = 7.0134582558198086631341720512006
absolute error = 2.041380881359611e-16
relative error = 2.9106623393183544931423396763329e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.795
y[1] (analytic) = 7.0194747218072498308771087495312
y[1] (numeric) = 7.0194747218072500355138784719879
absolute error = 2.046367697224567e-16
relative error = 2.9152718377447259279074725476388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.796
y[1] (analytic) = 7.0254972072699146329181691618323
y[1] (numeric) = 7.0254972072699148380544139904601
absolute error = 2.051362448286278e-16
relative error = 2.9198822343328932531957312225463e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.797
y[1] (analytic) = 7.0315257182302888296578724777299
y[1] (numeric) = 7.0315257182302890352943870208569
absolute error = 2.056365145431270e-16
relative error = 2.9244935279122052139687666635019e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.798
y[1] (analytic) = 7.0375602607168838838463455473078
y[1] (numeric) = 7.0375602607168840899839255032988
absolute error = 2.061375799559910e-16
relative error = 2.9291057173127880708443514742672e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=3.24
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.799
y[1] (analytic) = 7.0436008407642427849571998712453
y[1] (numeric) = 7.0436008407642429915966420298874
absolute error = 2.066394421586421e-16
relative error = 2.9337188013655436745281407288787e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.8
y[1] (analytic) = 7.0496474644129460837310239530277
y[1] (numeric) = 7.0496474644129462908731261969179
absolute error = 2.071421022438902e-16
relative error = 2.9383327789021546150685441662964e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.801
y[1] (analytic) = 7.0557001377096179327564374212646
y[1] (numeric) = 7.0557001377096181404019987271988
absolute error = 2.076455613059342e-16
relative error = 2.9429476487550808132196564532784e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.802
y[1] (analytic) = 7.0617588667069321330947475036717
y[1] (numeric) = 7.0617588667069323412445679440358
absolute error = 2.081498204403641e-16
relative error = 2.9475634097575660141930505517929e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.803
y[1] (analytic) = 7.0678236574636181869542544778789
y[1] (numeric) = 7.067823657463618395609135222041
absolute error = 2.086548807441621e-16
relative error = 2.9521800607436300716798624242534e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.804
y[1] (analytic) = 7.0738945160444673564202587738724
y[1] (numeric) = 7.073894516044467565581002089577
absolute error = 2.091607433157046e-16
relative error = 2.9567976005480739666763024807330e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.805
y[1] (analytic) = 7.0799714485203387282468284585835
y[1] (numeric) = 7.0799714485203389379142377133475
absolute error = 2.096674092547640e-16
relative error = 2.9614160280064819479166539506147e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.806
y[1] (analytic) = 7.0860544609681652847163918948979
y[1] (numeric) = 7.0860544609681654948912715574082
absolute error = 2.101748796625103e-16
relative error = 2.9660353419552208110854743344994e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.807
y[1] (analytic) = 7.0921435594709599805732264351825
y[1] (numeric) = 7.0921435594709601912563820766952
absolute error = 2.106831556415127e-16
relative error = 2.9706555412314391539535239059065e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.808
y[1] (analytic) = 7.098238750117821826036920083326
y[1] (numeric) = 7.0982387501178220372291583790673
absolute error = 2.111922382957413e-16
relative error = 2.9752766246730680163605450735775e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.809
y[1] (analytic) = 7.1043400390039419759018891392612
y[1] (numeric) = 7.1043400390039421876040178698302
absolute error = 2.117021287305690e-16
relative error = 2.9798985911188243042885881489172e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.81
y[1] (analytic) = 7.1104474322306098247290409259947
y[1] (numeric) = 7.1104474322306100369418689787677
absolute error = 2.122128280527730e-16
relative error = 2.9845214394082085429526325889751e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.811
y[1] (analytic) = 7.1165609359052191081356767913138
y[1] (numeric) = 7.1165609359052193208600141618504
absolute error = 2.127243373705366e-16
relative error = 2.9891451683815068291254116774068e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.812
y[1] (analytic) = 7.122680556141274010189736674583
y[1] (numeric) = 7.1226805561412742234263944680338
absolute error = 2.132366577934508e-16
relative error = 2.9937697768797899376178844971386e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.813
y[1] (analytic) = 7.1288062990583952769144926333827
y[1] (numeric) = 7.128806299058395490664283065899
absolute error = 2.137497904325163e-16
relative error = 2.9983952637449180155195730810839e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.814
y[1] (analytic) = 7.1349381707823263359098048351939
y[1] (numeric) = 7.1349381707823265501735412353387
absolute error = 2.142637364001448e-16
relative error = 3.0030216278195354134722719287970e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.815
y[1] (analytic) = 7.1410761774449394220960596358944
y[1] (numeric) = 7.1410761774449396368745564460553
absolute error = 2.147784968101609e-16
relative error = 3.0076488679470739177395223786165e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.816
y[1] (analytic) = 7.147220325184241709586915489515
y[1] (numeric) = 7.1472203251842419248809882673189
absolute error = 2.152940727778039e-16
relative error = 3.0122769829717545385601314907095e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.817
y[1] (analytic) = 7.1533706201443814496969885625129
y[1] (numeric) = 7.1533706201443816655074539822423
absolute error = 2.158104654197294e-16
relative error = 3.0169059717385864654389850249964e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.818
y[1] (analytic) = 7.1595270684756541150906160607592
y[1] (numeric) = 7.1595270684756543314182919147702
absolute error = 2.163276758540110e-16
relative error = 3.0215358330933673965817021119434e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.819
y[1] (analytic) = 7.1656896763345085500778414185157
y[1] (numeric) = 7.165689676334508766923546618658
absolute error = 2.168457052001423e-16
relative error = 3.0261665658826880252625304256078e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.82
y[1] (analytic) = 7.1718584498835531270637716458996
y[1] (numeric) = 7.1718584498835533444283262249377
absolute error = 2.173645545790381e-16
relative error = 3.0307981689539253203297021704331e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.821
y[1] (analytic) = 7.1780333952915619091574632847049
y[1] (numeric) = 7.1780333952915621270416883977415
absolute error = 2.178842251130366e-16
relative error = 3.0354306411552497447178166186016e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.822
y[1] (analytic) = 7.1842145187334808189464995819814
y[1] (numeric) = 7.1842145187334810373512175078824
absolute error = 2.184047179259010e-16
relative error = 3.0400639813356240570599551863989e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.823
y[1] (analytic) = 7.1904018263904338134434276564624
y[1] (numeric) = 7.1904018263904340323694617992833
absolute error = 2.189260341428209e-16
relative error = 3.0446981883447993099044148557743e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.824
y[1] (analytic) = 7.1965953244497290652102306047914
y[1] (numeric) = 7.196595324449729284658405495206
absolute error = 2.194481748904146e-16
relative error = 3.0493332610333233464165004620865e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.825
y[1] (analytic) = 7.2027950191048651496670156725373
y[1] (numeric) = 7.2027950191048653696381569692677
absolute error = 2.199711412967304e-16
relative error = 3.0539691982525353416484323837857e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.826
y[1] (analytic) = 7.2090009165555372385911057991999
y[1] (numeric) = 7.2090009165555374590860402904484
absolute error = 2.204949344912485e-16
relative error = 3.0586059988545686667600559389076e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.827
y[1] (analytic) = 7.2152130230076432998127280368143
y[1] (numeric) = 7.215213023007643520832283641697
absolute error = 2.210195556048827e-16
relative error = 3.0632436616923509384089111333108e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.828
y[1] (analytic) = 7.2214313446732903031134985383596
y[1] (numeric) = 7.2214313446732905246585043083416
absolute error = 2.215450057699820e-16
relative error = 3.0678821856196026549563877348936e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.829
y[1] (analytic) = 7.2276558877708004323339100149724
y[1] (numeric) = 7.2276558877708006544051961353052
absolute error = 2.220712861203328e-16
relative error = 3.0725215694908441129941129437708e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.83
y[1] (analytic) = 7.2338866585247173036960337699729
y[1] (numeric) = 7.2338866585247175262944315611329
absolute error = 2.225983977911600e-16
relative error = 3.0771618121613870537486483033976e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.831
y[1] (analytic) = 7.2401236631658121903476546329209
y[1] (numeric) = 7.2401236631658124134739965520502
absolute error = 2.231263419191293e-16
relative error = 3.0818029124873428986983163724465e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.832
y[1] (analytic) = 7.2463669079310902531340633383577
y[1] (numeric) = 7.2463669079310904767891829807063
absolute error = 2.236551196423486e-16
relative error = 3.0864448693256184944286976930193e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.833
y[1] (analytic) = 7.2526163990637967776037371215442
y[1] (numeric) = 7.252616399063797001788469221914
absolute error = 2.241847321003698e-16
relative error = 3.0910876815339173664501884648134e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.834
y[1] (analytic) = 7.2588721428134234172541455373957
y[1] (numeric) = 7.2588721428134236419693259715866
absolute error = 2.247151804341909e-16
relative error = 3.0957313479707450711607883588918e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.835
y[1] (analytic) = 7.2651341454357144430239247489402
y[1] (numeric) = 7.2651341454357146682703905351974
absolute error = 2.252464657862572e-16
relative error = 3.1003758674954021039248716243735e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.836
y[1] (analytic) = 7.2714024131926729990376697779945
y[1] (numeric) = 7.2714024131926732248162590784578
absolute error = 2.257785893004633e-16
relative error = 3.1050212389679878174846347431094e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.837
y[1] (analytic) = 7.2776769523525673646096004633717
y[1] (numeric) = 7.2776769523525675909211525855268
absolute error = 2.263115521221551e-16
relative error = 3.1096674612494042918291752525910e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.838
y[1] (analytic) = 7.2839577691899372225123631308089
y[1] (numeric) = 7.28395776918993744935771852894
absolute error = 2.268453553981311e-16
relative error = 3.1143145332013505455476026615848e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.839
y[1] (analytic) = 7.2902448699855999335172362439372
y[1] (numeric) = 7.2902448699856001608972365205818
absolute error = 2.273800002766446e-16
relative error = 3.1189624536863290940034401219519e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.84
y[1] (analytic) = 7.2965382610266568172120145770248
y[1] (numeric) = 7.2965382610266570451275024844299
absolute error = 2.279154879074051e-16
relative error = 3.1236112215676414811340456583656e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=68.6MB, alloc=4.3MB, time=3.43
x[1] = 1.841
y[1] (analytic) = 7.3028379486064994391028527278992
y[1] (numeric) = 7.3028379486064996675546721694795
absolute error = 2.284518194415803e-16
relative error = 3.1282608357093920219321882193755e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.842
y[1] (analytic) = 7.3091439390248159040063550734161
y[1] (numeric) = 7.3091439390248161329953511052139
absolute error = 2.289889960317978e-16
relative error = 3.1329112949764873927246704787215e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.843
y[1] (analytic) = 7.3154562385875971557382055600903
y[1] (numeric) = 7.3154562385875973852652243922372
absolute error = 2.295270188321469e-16
relative error = 3.1375625982346375620990698339690e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.844
y[1] (analytic) = 7.3217748536071432831046370190424
y[1] (numeric) = 7.3217748536071435131705260172226
absolute error = 2.300658889981802e-16
relative error = 3.1422147443503539569841138370094e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.845
y[1] (analytic) = 7.3280997904020698322030459972565
y[1] (numeric) = 7.3280997904020700628086536841721
absolute error = 2.306056076869156e-16
relative error = 3.1468677321909530681967969777105e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.846
y[1] (analytic) = 7.3344310552973141250380654062898
y[1] (numeric) = 7.3344310552973143561842414631278
absolute error = 2.311461760568380e-16
relative error = 3.1515215606245559185591542457991e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.847
y[1] (analytic) = 7.3407686546241415844594136050335
y[1] (numeric) = 7.3407686546241418161470088729344
absolute error = 2.316875952679009e-16
relative error = 3.1561762285200861429978443180655e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.848
y[1] (analytic) = 7.3471125947201520654278448549001
y[1] (numeric) = 7.3471125947201522976577113364287
absolute error = 2.322298664815286e-16
relative error = 3.1608317347472762165419281152526e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.849
y[1] (analytic) = 7.3534628819292861926155324139173
y[1] (numeric) = 7.3534628819292864253885232745347
absolute error = 2.327729908606174e-16
relative error = 3.1654880781766600225069325112188e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.85
y[1] (analytic) = 7.3598195226018317043472218706367
y[1] (numeric) = 7.3598195226018319376641914401748
absolute error = 2.333169695695381e-16
relative error = 3.1701452576795830940679463109701e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.851
y[1] (analytic) = 7.3661825230944298028884986595428
y[1] (numeric) = 7.3661825230944300367503024336797
absolute error = 2.338618037741369e-16
relative error = 3.1748032721281910533515535518608e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.852
y[1] (analytic) = 7.3725518897700815110875200467554
y[1] (numeric) = 7.3725518897700817454950146884936
absolute error = 2.344074946417382e-16
relative error = 3.1794621203954438530612756202312e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.853
y[1] (analytic) = 7.3789276289981540353765682282906
y[1] (numeric) = 7.378927628998154270330611569436
absolute error = 2.349540433411454e-16
relative error = 3.1841218013551028115391751278773e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.854
y[1] (analytic) = 7.3853097471543871351397875429606
y[1] (numeric) = 7.385309747154387370641238585604
absolute error = 2.355014510426434e-16
relative error = 3.1887823138817407050016551295026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.855
y[1] (analytic) = 7.3916982506208994984534751681827
y[1] (numeric) = 7.3916982506208997345031940861828
absolute error = 2.360497189180001e-16
relative error = 3.1934436568507382501878976134012e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.856
y[1] (analytic) = 7.398093145786195124205301039518
y[1] (numeric) = 7.3980931457861953608041491799863
absolute error = 2.365988481404683e-16
relative error = 3.1981058291382859833456352065118e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.857
y[1] (analytic) = 7.4044944390451697105988391136926
y[1] (numeric) = 7.4044944390451699477476789984799
absolute error = 2.371488398847873e-16
relative error = 3.2027688296213820492074542721856e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.858
y[1] (analytic) = 7.4109021367991170500497984801639
y[1] (numeric) = 7.4109021367991172877494938073489
absolute error = 2.376996953271850e-16
relative error = 3.2074326571778367195486955117089e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.859
y[1] (analytic) = 7.417316245455735430480349217997
y[1] (numeric) = 7.4173162454557356687317648633765
absolute error = 2.382514156453795e-16
relative error = 3.2120973106862701186296285067014e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.86
y[1] (analytic) = 7.4237367714291340430179442929097
y[1] (numeric) = 7.4237367714291342818219463114907
absolute error = 2.388040020185810e-16
relative error = 3.2167627890261139727735027398882e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.861
y[1] (analytic) = 7.430163721139839396105045193843
y[1] (numeric) = 7.4301637211398396354625008213363
absolute error = 2.393574556274933e-16
relative error = 3.2214290910776079386620668884463e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.862
y[1] (analytic) = 7.4365971010148017360261654193154
y[1] (numeric) = 7.4365971010148019759379430736316
absolute error = 2.399117776543162e-16
relative error = 3.2260962157218080242236152021363e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.863
y[1] (analytic) = 7.4430369174874014738586523411422
y[1] (numeric) = 7.4430369174874017143256216238891
absolute error = 2.404669692827469e-16
relative error = 3.2307641618405815016904324960312e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.864
y[1] (analytic) = 7.4494831769974556188536343968346
y[1] (numeric) = 7.4494831769974558598766660948163
absolute error = 2.410230316979817e-16
relative error = 3.2354329283166058453323411305358e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.865
y[1] (analytic) = 7.4559358859912242182535669921635
y[1] (numeric) = 7.4559358859912244598335330788816
absolute error = 2.415799660867181e-16
relative error = 3.2401025140333730107532775226820e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.866
y[1] (analytic) = 7.4623950509214168035528169319699
y[1] (numeric) = 7.4623950509214170456905905691267
absolute error = 2.421377736371568e-16
relative error = 3.2447729178751923231076721577790e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.867
y[1] (analytic) = 7.4688606782471988432077316403445
y[1] (numeric) = 7.4688606782471990859041871793473
absolute error = 2.426964555390028e-16
relative error = 3.2494441387271812714135215973444e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.868
y[1] (analytic) = 7.4753327744341982018026458807814
y[1] (numeric) = 7.4753327744341984450586588642494
absolute error = 2.432560129834680e-16
relative error = 3.2541161754752763877628187751667e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.869
y[1] (analytic) = 7.4818113459545116056782851428534
y[1] (numeric) = 7.4818113459545118494947323061259
absolute error = 2.438164471632725e-16
relative error = 3.2587890270062266657253585240718e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.87
y[1] (analytic) = 7.4882963992867111150290313243491
y[1] (numeric) = 7.4882963992867113594067905969958
absolute error = 2.443777592726467e-16
relative error = 3.2634626922075976673237871413230e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.871
y[1] (analytic) = 7.4947879409158506024755228066778
y[1] (numeric) = 7.4947879409158508474154733140108
absolute error = 2.449399505073330e-16
relative error = 3.2681371699677702427311595880758e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.872
y[1] (analytic) = 7.501285977333472238119067496682
y[1] (numeric) = 7.5012859773334724836220895612697
absolute error = 2.455030220645877e-16
relative error = 3.2728124591759418938754358910462e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.873
y[1] (analytic) = 7.5077905150376129810843538898108
y[1] (numeric) = 7.5077905150376132271513290329936
absolute error = 2.460669751431828e-16
relative error = 3.2774885587221267700536791486090e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.874
y[1] (analytic) = 7.5143015605328110775569516979066
y[1] (numeric) = 7.5143015605328113241887626413144
absolute error = 2.466318109434078e-16
relative error = 3.2821654674971556345873646814310e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.875
y[1] (analytic) = 7.5208191203301125653221000796462
y[1] (numeric) = 7.5208191203301128125196307467179
absolute error = 2.471975306670717e-16
relative error = 3.2868431843926784619424104025295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.876
y[1] (analytic) = 7.5273432009470777848112880129684
y[1] (numeric) = 7.5273432009470780325754235304731
absolute error = 2.477641355175047e-16
relative error = 3.2915217083011630068685944900801e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.877
y[1] (analytic) = 7.5338738089077878966631378566094
y[1] (numeric) = 7.5338738089077881449947645561692
absolute error = 2.483316266995598e-16
relative error = 3.2962010381158920245920215290474e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.878
y[1] (analytic) = 7.5404109507428514058051096621729
y[1] (numeric) = 7.540410950742851654705115081788
absolute error = 2.489000054196151e-16
relative error = 3.3008811727309697597371904645484e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.879
y[1] (analytic) = 7.5469546329894106920625503189842
y[1] (numeric) = 7.5469546329894109415318232045597
absolute error = 2.494692728855755e-16
relative error = 3.3055621110413204222451012020295e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.88
y[1] (analytic) = 7.5535048621911485473016181413198
y[1] (numeric) = 7.5535048621911487973410484481943
absolute error = 2.500394303068745e-16
relative error = 3.3102438519426879659943273721676e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.881
y[1] (analytic) = 7.5600616448982947191126200414837
y[1] (numeric) = 7.5600616448982949697230989359595
absolute error = 2.506104788944758e-16
relative error = 3.3149263943316331939852176183066e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.882
y[1] (analytic) = 7.566624987667632461040304972611
y[1] (numeric) = 7.5666249876676327122227248334866
absolute error = 2.511824198608756e-16
relative error = 3.3196097371055401006254294053799e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.883
y[1] (analytic) = 7.5731948970625050893676638720398
y[1] (numeric) = 7.5731948970625053411229182921441
absolute error = 2.517552544201043e-16
relative error = 3.3242938791626142292318933295132e-15 %
h = 0.001
memory used=72.4MB, alloc=4.3MB, time=3.63
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.884
y[1] (analytic) = 7.5797713796528225464597928895968
y[1] (numeric) = 7.5797713796528227987887766773248
absolute error = 2.523289837877280e-16
relative error = 3.3289788194018783702958108407536e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.885
y[1] (analytic) = 7.5863544420150679706743832452064
y[1] (numeric) = 7.5863544420150682235779924260576
absolute error = 2.529036091808512e-16
relative error = 3.3336645567231840708426874002262e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.886
y[1] (analytic) = 7.5929440907323042728454076268625
y[1] (numeric) = 7.59294409073230452632453944498
absolute error = 2.534791318181175e-16
relative error = 3.3383510900271967144848237354984e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.887
y[1] (analytic) = 7.5995403323941807193465796131947
y[1] (numeric) = 7.5995403323941809734021325329072
absolute error = 2.540555529197125e-16
relative error = 3.3430384182154095990005462590269e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.888
y[1] (analytic) = 7.6061431735969395217411691846394
y[1] (numeric) = 7.6061431735969397763740428920045
absolute error = 2.546328737073651e-16
relative error = 3.3477265401901368758495601742228e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.889
y[1] (analytic) = 7.6127526209434224330247639735788
y[1] (numeric) = 7.6127526209434226882358593779284
absolute error = 2.552110954043496e-16
relative error = 3.3524154548545170058437194794276e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.89
y[1] (analytic) = 7.6193686810430773504675724967601
y[1] (numeric) = 7.6193686810430776062577917322474
absolute error = 2.557902192354873e-16
relative error = 3.3571051611125096053634919247562e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.891
y[1] (analytic) = 7.6259913605119649250628722128465
y[1] (numeric) = 7.6259913605119651814331186399953
absolute error = 2.563702464271488e-16
relative error = 3.3617956578689014588579941261087e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.892
y[1] (analytic) = 7.6326206659727651775882118541011
y[1] (numeric) = 7.6326206659727654345393900613566
absolute error = 2.569511782072555e-16
relative error = 3.3664869440293019894292020904345e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.893
y[1] (analytic) = 7.6392566040547841212859840939558
y[1] (numeric) = 7.6392566040547843788189998992374
absolute error = 2.575330158052816e-16
relative error = 3.3711790185001452688175367941740e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.894
y[1] (analytic) = 7.6458991813939603911699912315898
y[1] (numeric) = 7.6458991813939606492857516838457
absolute error = 2.581157604522559e-16
relative error = 3.3758718801886893718303516514408e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.895
y[1] (analytic) = 7.6525484046328718799646332006366
y[1] (numeric) = 7.6525484046328721386640465814007
absolute error = 2.586994133807641e-16
relative error = 3.3805655280030222385704879042223e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.896
y[1] (analytic) = 7.6592042804207423806833538417607
y[1] (numeric) = 7.6592042804207426399673296667106
absolute error = 2.592839758249499e-16
relative error = 3.3852599608520518093348295567657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.897
y[1] (analytic) = 7.6658668154134482358529880181017
y[1] (numeric) = 7.6658668154134484957224370386195
absolute error = 2.598694490205178e-16
relative error = 3.3899551776455183577542701974131e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.898
y[1] (analytic) = 7.6725360162735249933906587984906
y[1] (numeric) = 7.6725360162735252538464930032246
absolute error = 2.604558342047340e-16
relative error = 3.3946511772939819666487534248173e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.899
y[1] (analytic) = 7.6792118896701740691398805858861
y[1] (numeric) = 7.6792118896701743301830132023154
absolute error = 2.610431326164293e-16
relative error = 3.3993479587088360840631249511280e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.9
y[1] (analytic) = 7.6858944422792694160725307276929
y[1] (numeric) = 7.6858944422792696777038762236929
absolute error = 2.616313454960000e-16
relative error = 3.4040455208022949575556022627223e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.901
y[1] (analytic) = 7.6925836807833642001633588104863
y[1] (numeric) = 7.6925836807833644623838328958972
absolute error = 2.622204740854109e-16
relative error = 3.4087438624874084035444373564820e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.902
y[1] (analytic) = 7.6992796118716974829437095142116
y[1] (numeric) = 7.6992796118716977457542291424077
absolute error = 2.628105196281961e-16
relative error = 3.4134429826780478961134429455014e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.903
y[1] (analytic) = 7.7059822422402009107411415801352
y[1] (numeric) = 7.7059822422402011741426249495968
absolute error = 2.634014833694616e-16
relative error = 3.4181428802889160573167141597332e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.904
y[1] (analytic) = 7.7126915785915054106116321327263
y[1] (numeric) = 7.7126915785915056746049986886131
absolute error = 2.639933665558868e-16
relative error = 3.4228435542355418063357346277909e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.905
y[1] (analytic) = 7.7194076276349478929710622882295
y[1] (numeric) = 7.7194076276349481575572327239563
absolute error = 2.645861704357268e-16
relative error = 3.4275450034342858679052249165030e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.906
y[1] (analytic) = 7.7261303960865779609326866819739
y[1] (numeric) = 7.7261303960865782261125829407879
absolute error = 2.651798962588140e-16
relative error = 3.4322472268023371623259081540841e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.907
y[1] (analytic) = 7.7328598906691646263572962524467
y[1] (numeric) = 7.7328598906691648921318415290069
absolute error = 2.657745452765602e-16
relative error = 3.4369502232577156506640293944849e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.908
y[1] (analytic) = 7.7395961181122030326227903328538
y[1] (numeric) = 7.7395961181122032989929090748121
absolute error = 2.663701187419583e-16
relative error = 3.4416539917192699673234765790875e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.909
y[1] (analytic) = 7.7463390851519211841198808202997
y[1] (numeric) = 7.7463390851519214510864987298839
absolute error = 2.669666179095842e-16
relative error = 3.4463585311066776172570065616130e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.91
y[1] (analytic) = 7.7530887985312866824806579188518
y[1] (numeric) = 7.753088798531286950044701954451
absolute error = 2.675640440355992e-16
relative error = 3.4510638403404515916182290783799e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.911
y[1] (analytic) = 7.7598452650000134695467536856162
y[1] (numeric) = 7.7598452650000137377091520633674
absolute error = 2.681623983777512e-16
relative error = 3.4557699183419314550398467143958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.912
y[1] (analytic) = 7.7666084913145685770838463485505
y[1] (numeric) = 7.7666084913145688458455285439276
absolute error = 2.687616821953771e-16
relative error = 3.4604767640332899005538832013267e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.913
y[1] (analytic) = 7.7733784842381788832492551110796
y[1] (numeric) = 7.7733784842381791526111518604842
absolute error = 2.693618967494046e-16
relative error = 3.4651843763375315220263189997621e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.914
y[1] (analytic) = 7.780155250540837875819381911674
y[1] (numeric) = 7.7801552505408381457824252140282
absolute error = 2.699630433023542e-16
relative error = 3.4698927541784941339710462080639e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.915
y[1] (analytic) = 7.7869387969993124221837633663945
y[1] (numeric) = 7.7869387969993126927488864847353
absolute error = 2.705651231183408e-16
relative error = 3.4746018964808449179832784506999e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.916
y[1] (analytic) = 7.7937291303971495461125028890197
y[1] (numeric) = 7.7937291303971498172806403520957
absolute error = 2.711681374630760e-16
relative error = 3.4793118021700855411925608047132e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.917
y[1] (analytic) = 7.8005262575246832113038597567535
y[1] (numeric) = 7.8005262575246834830759473606235
absolute error = 2.717720876038700e-16
relative error = 3.4840224701725520904294367052239e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.918
y[1] (analytic) = 7.8073301851790411117187786696674
y[1] (numeric) = 7.8073301851790413840957534793006
absolute error = 2.723769748096332e-16
relative error = 3.4887338994154111344475787697099e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.919
y[1] (analytic) = 7.8141409201641514687091501389713
y[1] (numeric) = 7.8141409201641517416919504898498
absolute error = 2.729828003508785e-16
relative error = 3.4934460888266647350996156346268e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.92
y[1] (analytic) = 7.8209584692907498349465988329418
y[1] (numeric) = 7.8209584692907501085361643326649
absolute error = 2.735895654997231e-16
relative error = 3.4981590373351490095066316559076e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.921
y[1] (analytic) = 7.8277828393763859051586038098615
y[1] (numeric) = 7.8277828393763861793558753397519
absolute error = 2.741972715298904e-16
relative error = 3.5028727438705339474534299756034e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.922
y[1] (analytic) = 7.8346140372454303336787613746585
y[1] (numeric) = 7.8346140372454306084846810913704
absolute error = 2.748059197167119e-16
relative error = 3.5075872073633231999491623227802e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.923
y[1] (analytic) = 7.841452069729081558818008110076
y[1] (numeric) = 7.8414520697290818342335194472054
absolute error = 2.754155113371294e-16
relative error = 3.5123024267448576649163200330540e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.924
y[1] (analytic) = 7.8482969436653726340636284541646
y[1] (numeric) = 7.8482969436653729100896761238612
absolute error = 2.760260476696966e-16
relative error = 3.5170184009473113793359483605604e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.925
y[1] (analytic) = 7.8551486658991780661128780236733
y[1] (numeric) = 7.8551486658991783427504080182545
absolute error = 2.766375299945812e-16
relative error = 3.5217351289036937682745421898307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=3.83
NO POLE
x[1] = 1.926
y[1] (analytic) = 7.862007243282220659748060717533
y[1] (numeric) = 7.8620072432822209369980203111
absolute error = 2.772499595935670e-16
relative error = 3.5264526095478518523113925969658e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.927
y[1] (analytic) = 7.8688726826730783695599044760802
y[1] (numeric) = 7.8688726826730786474232422261357
absolute error = 2.778633377500555e-16
relative error = 3.5311708418144660593904934938181e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.928
y[1] (analytic) = 7.8757449909371911585260874199663
y[1] (numeric) = 7.8757449909371914370037531690347
absolute error = 2.784776657490684e-16
relative error = 3.5358898246390574561792557043528e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.929
y[1] (analytic) = 7.8826241749468678634517729478523
y[1] (numeric) = 7.8826241749468681425447178251012
absolute error = 2.790929448772489e-16
relative error = 3.5406095569579796883370060026112e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.93
y[1] (analytic) = 7.8895102415812930672790192339938
y[1] (numeric) = 7.889510241581293346988195656858
absolute error = 2.797091764228642e-16
relative error = 3.5453300377084261430853535340720e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.931
y[1] (analytic) = 7.8964031977265339782719354357008
y[1] (numeric) = 7.8964031977265342585982971115077
absolute error = 2.803263616758069e-16
relative error = 3.5500512658284231139886100159829e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.932
y[1] (analytic) = 7.9033030502755473160844637963994
y[1] (numeric) = 7.9033030502755475970289657239971
absolute error = 2.809445019275977e-16
relative error = 3.5547732402568394203684692444969e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.933
y[1] (analytic) = 7.9102098061281862047176737126536
y[1] (numeric) = 7.9102098061281864862812721840404
absolute error = 2.815635984713868e-16
relative error = 3.5594959599333795119552922900981e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.934
y[1] (analytic) = 7.9171234721912070723734607230139
y[1] (numeric) = 7.91712347219120735455711332497
absolute error = 2.821836526019561e-16
relative error = 3.5642194237985866842975578592019e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.935
y[1] (analytic) = 7.9240440553782765582115502729679
y[1] (numeric) = 7.9240440553782768410162158886889
absolute error = 2.828046656157210e-16
relative error = 3.5689436307938411994217858931607e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.936
y[1] (analytic) = 7.9309715626099784260167130135715
y[1] (numeric) = 7.9309715626099787094433518243041
absolute error = 2.834266388107326e-16
relative error = 3.5736685798613634298328081012203e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.937
y[1] (analytic) = 7.9379060008138204847831053015525
y[1] (numeric) = 7.9379060008138207688326787882319
absolute error = 2.840495734866794e-16
relative error = 3.5783942699442106571290862232658e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.938
y[1] (analytic) = 7.9448473769242415162226554858033
y[1] (numeric) = 7.944847376924241800896126430693
absolute error = 2.846734709448897e-16
relative error = 3.5831206999862826680732319013787e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.939
y[1] (analytic) = 7.9517956978826182092044234892275
y[1] (numeric) = 7.9517956978826184945027559775605
absolute error = 2.852983324883330e-16
relative error = 3.5878478689323147155078440219375e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.94
y[1] (analytic) = 7.958750970637272101131868125876
y[1] (numeric) = 7.9587509706372723870560275474986
absolute error = 2.859241594216226e-16
relative error = 3.5925757757278855637980138142026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.941
y[1] (analytic) = 7.9657132021434765262649635312202
y[1] (numeric) = 7.9657132021434768128159165822372
absolute error = 2.865509530510170e-16
relative error = 3.5973044193194103974719587487837e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.942
y[1] (analytic) = 7.9726823993634635709941130282566
y[1] (numeric) = 7.972682399363463858172827712679
absolute error = 2.871787146844224e-16
relative error = 3.6020337986541475340035897013187e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.943
y[1] (analytic) = 7.9796585692664310360728157039367
y[1] (numeric) = 7.9796585692664313238802613353309
absolute error = 2.878074456313942e-16
relative error = 3.6067639126801925394352763956966e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.944
y[1] (analytic) = 7.9866417188285494058160479291685
y[1] (numeric) = 7.9866417188285496942531951323081
absolute error = 2.884371472031396e-16
relative error = 3.6114947603464861176845329614131e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.945
y[1] (analytic) = 7.9936318550329688242713290213531
y[1] (numeric) = 7.9936318550329691133391497338721
absolute error = 2.890678207125190e-16
relative error = 3.6162263406028069163877343524323e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.946
y[1] (analytic) = 8.0006289848698260783694472211019
y[1] (numeric) = 8.0006289848698263680689146951501
absolute error = 2.896994674740482e-16
relative error = 3.6209586523997743394727558693100e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.947
y[1] (analytic) = 8.007633115336251588061829134443
y[1] (numeric) = 8.0076331153362518783939179383436
absolute error = 2.903320888039006e-16
relative error = 3.6256916946888513148167989212699e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.948
y[1] (analytic) = 8.014644253436376403451542778469
y[1] (numeric) = 8.0146442534363766944172287983781
absolute error = 2.909656860199091e-16
relative error = 3.6304254664223432740257558330227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.949
y[1] (analytic) = 8.0216624061813392089249313620124
y[1] (numeric) = 8.02166240618133950052519180358
absolute error = 2.916002604415676e-16
relative error = 3.6351599665533921208189059663227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.95
y[1] (analytic) = 8.0286875805892933342908819335644
y[1] (numeric) = 8.0286875805892936265266953235984
absolute error = 2.922358133900340e-16
relative error = 3.6398951940359888838316430594808e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.951
y[1] (analytic) = 8.0357197836854137729347400362931
y[1] (numeric) = 8.0357197836854140658070862244244
absolute error = 2.928723461881313e-16
relative error = 3.6446311478249626283681749082387e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.952
y[1] (analytic) = 8.0427590225019042069938885246578
y[1] (numeric) = 8.0427590225019045005037486850078
absolute error = 2.935098601603500e-16
relative error = 3.6493678268759855596258840890386e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.953
y[1] (analytic) = 8.0498053040780040395620157187845
y[1] (numeric) = 8.0498053040780043337103723516348
absolute error = 2.941483566328503e-16
relative error = 3.6541052301455755843537797903747e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.954
y[1] (analytic) = 8.0568586354599954339291051014579
y[1] (numeric) = 8.0568586354599957287169420349215
absolute error = 2.947878369334636e-16
relative error = 3.6588433565910901404944730122892e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.955
y[1] (analytic) = 8.0639190237012103598641857983045
y[1] (numeric) = 8.0639190237012106552924881899995
absolute error = 2.954283023916950e-16
relative error = 3.6635822051707324298016085551627e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.956
y[1] (analytic) = 8.0709864758620376469478901245053
y[1] (numeric) = 8.0709864758620379430176444632304
absolute error = 2.960697543387251e-16
relative error = 3.6683217748435489143805260919706e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.957
y[1] (analytic) = 8.0780609990099300449618715311838
y[1] (numeric) = 8.0780609990099303416740656385958
absolute error = 2.967121941074120e-16
relative error = 3.6730620645694292718414122109175e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.958
y[1] (analytic) = 8.0851426002194112913421433414748
y[1] (numeric) = 8.0851426002194115886977663737682
absolute error = 2.973556230322934e-16
relative error = 3.6778030733091075571608527023428e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.959
y[1] (analytic) = 8.0922312865720831857034057302022
y[1] (numeric) = 8.0922312865720834837034481797907
absolute error = 2.980000424495885e-16
relative error = 3.6825448000241608565544732832747e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.96
y[1] (analytic) = 8.099327065156632671441435472082
y[1] (numeric) = 8.0993270651566329700868891692822
absolute error = 2.986454536972002e-16
relative error = 3.6872872436770116220329401431856e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.961
y[1] (analytic) = 8.1064299430688389244206200614307
y[1] (numeric) = 8.106429943068839223712478176148
absolute error = 2.992918581147173e-16
relative error = 3.6920304032309299632854860290004e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.962
y[1] (analytic) = 8.1135399274115804487537248915043
y[1] (numeric) = 8.1135399274115807486929819349201
absolute error = 2.999392570434158e-16
relative error = 3.6967742776500248045015352535424e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.963
y[1] (analytic) = 8.1206570252948421796809892738246
y[1] (numeric) = 8.1206570252948424802686411000866
absolute error = 3.005876518262620e-16
relative error = 3.7015188658992572229028425888213e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.964
y[1] (analytic) = 8.1277812438357225935556541771839
y[1] (numeric) = 8.1277812438357228947926979850972
absolute error = 3.012370438079133e-16
relative error = 3.7062641669444253887381376660803e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.965
y[1] (analytic) = 8.1349125901584408249430316724443
y[1] (numeric) = 8.1349125901584411268304660071659
absolute error = 3.018874343347216e-16
relative error = 3.7110101797521815149273873277977e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.966
y[1] (analytic) = 8.1420510713943437908402331827983
y[1] (numeric) = 8.1420510713943440933790579375327
absolute error = 3.025388247547344e-16
relative error = 3.7157569032900204387474846903537e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.967
y[1] (analytic) = 8.1491966946819133220236807598096
y[1] (numeric) = 8.1491966946819136252148971775064
absolute error = 3.031912164176968e-16
relative error = 3.7205043365262792770032818388559e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=80.1MB, alloc=4.3MB, time=4.02
x[1] = 1.968
y[1] (analytic) = 8.1563494671667733015315327333406
y[1] (numeric) = 8.1563494671667736053761434083947
absolute error = 3.038446106750541e-16
relative error = 3.7252524784301444087613515551197e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.969
y[1] (analytic) = 8.1635093960016968102881622183876
y[1] (numeric) = 8.1635093960016971147871710983413
absolute error = 3.044990088799537e-16
relative error = 3.7300013279716498161021825040132e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.97
y[1] (analytic) = 8.1706764883466132798778341038975
y[1] (numeric) = 8.1706764883466135850322464911444
absolute error = 3.051544123872469e-16
relative error = 3.7347508841216741791194445076360e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.971
y[1] (analytic) = 8.1778507513686156524747332978382
y[1] (numeric) = 8.1778507513686159582855558513293
absolute error = 3.058108225534911e-16
relative error = 3.7395011458519428468830677099244e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.972
y[1] (analytic) = 8.1850321922419675479365041591486
y[1] (numeric) = 8.1850321922419678544047448961005
absolute error = 3.064682407369519e-16
relative error = 3.7442521121350285457216452856318e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.973
y[1] (analytic) = 8.1922208181481104380684682107047
y[1] (numeric) = 8.19222081814811074519513650831
absolute error = 3.071266682976053e-16
relative error = 3.7490037819443532738445622504348e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.974
y[1] (analytic) = 8.1994166362756708280656943981172
y[1] (numeric) = 8.1994166362756711358518009952564
absolute error = 3.077861065971392e-16
relative error = 3.7537561542541816181714092958093e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.975
y[1] (analytic) = 8.2066196538204674451401033370288
y[1] (numeric) = 8.2066196538204677535866603359849
absolute error = 3.084465569989561e-16
relative error = 3.7585092280396286980371921713417e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.976
y[1] (analytic) = 8.2138298779855184343397941766155
y[1] (numeric) = 8.2138298779855187434478150447905
absolute error = 3.091080208681750e-16
relative error = 3.7632630022766582968014196707153e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.977
y[1] (analytic) = 8.2210473159810485615677898992182
y[1] (numeric) = 8.2210473159810488713382894708513
absolute error = 3.097704995716331e-16
relative error = 3.7680174759420785398149395599541e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.978
y[1] (analytic) = 8.228271975024496423807404075449
y[1] (numeric) = 8.2282719750244967342413985533375
absolute error = 3.104339944778885e-16
relative error = 3.7727726480135497176836182501898e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.979
y[1] (analytic) = 8.2355038623405216665614393007418
y[1] (numeric) = 8.2355038623405219776599462579634
absolute error = 3.110985069572216e-16
relative error = 3.7775285174695762523519410160474e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.98
y[1] (analytic) = 8.2427429851610122085124347531447
y[1] (numeric) = 8.2427429851610125202764731347826
absolute error = 3.117640383816379e-16
relative error = 3.7822850832895156593938027363414e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.981
y[1] (analytic) = 8.2499893507250914734111875332068
y[1] (numeric) = 8.249989350725091785841777658076
absolute error = 3.124305901248692e-16
relative error = 3.7870423444535680384350562066047e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.982
y[1] (analytic) = 8.2572429662791256292007796750797
y[1] (numeric) = 8.2572429662791259422989432374563
absolute error = 3.130981635623766e-16
relative error = 3.7918002999427873872101784505419e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.983
y[1] (analytic) = 8.2645038390767308343833499534677
y[1] (numeric) = 8.2645038390767311481501100248197
absolute error = 3.137667600713520e-16
relative error = 3.7965589487390746753911305014075e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.984
y[1] (analytic) = 8.2717719763787804916368568537996
y[1] (numeric) = 8.2717719763787808060732378845199
absolute error = 3.144363810307203e-16
relative error = 3.8013182898251793866073856871304e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.985
y[1] (analytic) = 8.2790473854534125086890863229911
y[1] (numeric) = 8.2790473854534128237961141441327
absolute error = 3.151070278211416e-16
relative error = 3.8060783221847010215742455440153e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 1.986
y[1] (analytic) = 8.2863300735760365664561651754097
y[1] (numeric) = 8.286330073576036882234867000423
absolute error = 3.157787018250133e-16
relative error = 3.8108390448020893556933635603428e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.987
y[1] (analytic) = 8.2936200480293413944528482931621
y[1] (numeric) = 8.293620048029341710904252719634
absolute error = 3.164514044264719e-16
relative error = 3.8156004566626410472290535499299e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 1.988
y[1] (analytic) = 8.3009173161033020534818550315964
y[1] (numeric) = 8.3009173161033023706069920429919
absolute error = 3.171251370113955e-16
relative error = 3.8203625567525046653340591273377e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.989
y[1] (analytic) = 8.3082218850951872256095375199637
y[1] (numeric) = 8.3082218850951875434094384873694
absolute error = 3.177999009674057e-16
relative error = 3.8251253440586784389774788431109e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.99
y[1] (analytic) = 8.315533762309566511435170833514
y[1] (numeric) = 8.3155337623095668299108685173836
absolute error = 3.184756976838696e-16
relative error = 3.8298888175690091894260521931478e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.991
y[1] (analytic) = 8.3228529550583177346611623069249
y[1] (numeric) = 8.322852955058318053813690858827
absolute error = 3.191525285519021e-16
relative error = 3.8346529762721948420164202962971e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.992
y[1] (analytic) = 8.330179470660634253971484559881
y[1] (numeric) = 8.330179470660634573801879524249
absolute error = 3.198303949643680e-16
relative error = 3.8394178191577844928899080276551e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.993
y[1] (analytic) = 8.3375133164430322822256441138471
y[1] (numeric) = 8.3375133164430326027349424297311
absolute error = 3.205092983158840e-16
relative error = 3.8441833452161772450565362152411e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.994
y[1] (analytic) = 8.3448544997393582129755047946128
y[1] (numeric) = 8.3448544997393585341647447974334
absolute error = 3.211892400028206e-16
relative error = 3.8489495534386198213252699223072e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.995
y[1] (analytic) = 8.3522030278907959543122924380423
y[1] (numeric) = 8.3522030278907962761825138613473
absolute error = 3.218702214233050e-16
relative error = 3.8537164428172161317926335658273e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 1.996
y[1] (analytic) = 8.3595589082458742700511147466471
y[1] (numeric) = 8.3595589082458745926033587238692
absolute error = 3.225522439772221e-16
relative error = 3.8584840123449140314331041545877e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.997
y[1] (analytic) = 8.3669221481604741282603374821105
y[1] (numeric) = 8.3669221481604744514956465483279
absolute error = 3.232353090662174e-16
relative error = 3.8632522610155148250297496968645e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 1.998
y[1] (analytic) = 8.3742927549978360571431655237545
y[1] (numeric) = 8.3742927549978363810625836174537
absolute error = 3.239194180936992e-16
relative error = 3.8680211878236743321041772495398e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.999
y[1] (analytic) = 8.381670736128567508278784675143
y[1] (numeric) = 8.381670736128567832883357139983
absolute error = 3.246045724648400e-16
relative error = 3.8727907917648943705556898753026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 2
y[1] (analytic) = 8.389056098930650227230427460575
y[1] (numeric) = 8.3890560989306505525212010471543
absolute error = 3.252907735865793e-16
relative error = 3.8775610718355309426369749936272e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.001
y[1] (analytic) = 8.3964488507894476315277335201503
y[1] (numeric) = 8.3964488507894479575057563877758
absolute error = 3.259780228676255e-16
relative error = 3.8823320270327916279100179289500e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.002
y[1] (analytic) = 8.4038489990977121960307825863808
y[1] (numeric) = 8.4038489990977125226971043048389
absolute error = 3.266663217184581e-16
relative error = 3.8871036563547365286897742645539e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.003
y[1] (analytic) = 8.4112565512555928456831854069972
y[1] (numeric) = 8.4112565512555931730388569583268
absolute error = 3.273556715513296e-16
relative error = 3.8918759588002756127851059656079e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.004
y[1] (analytic) = 8.4186715146706423556616253676573
y[1] (numeric) = 8.4186715146706426837076991479251
absolute error = 3.280460737802678e-16
relative error = 3.8966489333691707905422546022695e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 2.005
y[1] (analytic) = 8.4260938967578247589292509647144
y[1] (numeric) = 8.4260938967578250876667807857925
absolute error = 3.287375298210781e-16
relative error = 3.9014225790620379498487818095301e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.006
y[1] (analytic) = 8.4335237049395227612003266820562
y[1] (numeric) = 8.4335237049395230906303677734015
absolute error = 3.294300410913453e-16
relative error = 3.9061968948803430205583587575683e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.007
y[1] (analytic) = 8.4409609466455451633235572372817
y[1] (numeric) = 8.4409609466455454934471662477176
absolute error = 3.301236090104359e-16
relative error = 3.9109718798264039520748215522582e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.008
y[1] (analytic) = 8.4484056293131342910915075811601
y[1] (numeric) = 8.4484056293131346219097425806605
absolute error = 3.308182349995004e-16
relative error = 3.9157475329033926493766574789153e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.009
y[1] (analytic) = 8.45585776038697343248354846041
y[1] (numeric) = 8.4558577603869737639974689418855
absolute error = 3.315139204814755e-16
relative error = 3.9205238531153356850489797483242e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.01
y[1] (analytic) = 8.4633173473191942823497647873654
y[1] (numeric) = 8.463317347319194614560431668451
absolute error = 3.322106668810856e-16
relative error = 3.9253008394671067053796213508686e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=4.22
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.011
y[1] (analytic) = 8.4707843975693843945432715010551
y[1] (numeric) = 8.470784397569384727451747125901
absolute error = 3.329084756248459e-16
relative error = 3.9300784909644377338665345686169e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.012
y[1] (analytic) = 8.4782589186045946415083890526353
y[1] (numeric) = 8.4782589186045949751157371936989
absolute error = 3.336073481410636e-16
relative error = 3.9348568066139079735543433611085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.013
y[1] (analytic) = 8.4857409178993466813321381039696
y[1] (numeric) = 8.4857409178993470156394239638104
absolute error = 3.343072858598408e-16
relative error = 3.9396357854229526709367641390214e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.014
y[1] (analytic) = 8.4932304029356404322665204914752
y[1] (numeric) = 8.4932304029356407672748107045519
absolute error = 3.350082902130767e-16
relative error = 3.9444154263998636599573199500764e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.015
y[1] (analytic) = 8.5007273812029615547290609781395
y[1] (numeric) = 8.5007273812029618904394236126082
absolute error = 3.357103626344687e-16
relative error = 3.9491957285537769317864634107164e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.016
y[1] (analytic) = 8.5082318601982889407890917948697
y[1] (numeric) = 8.5082318601982892772025963543858
absolute error = 3.364135045595161e-16
relative error = 3.9539766908946907977255962493481e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.017
y[1] (analytic) = 8.5157438474261022111472694580876
y[1] (numeric) = 8.5157438474261025482649868836085
absolute error = 3.371177174255209e-16
relative error = 3.9587583124334498702629276054775e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.018
y[1] (analytic) = 8.5232633503983892196158208437081
y[1] (numeric) = 8.5232633503983895574388235152992
absolute error = 3.378230026715911e-16
relative error = 3.9635405921817584290135867785747e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.019
y[1] (analytic) = 8.5307903766346535651070229983754
y[1] (numeric) = 8.5307903766346539036363847370173
absolute error = 3.385293617386419e-16
relative error = 3.9683235291521690679890048901730e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.02
y[1] (analytic) = 8.5383249336619221111374286770603
y[1] (numeric) = 8.5383249336619224503742247464589
absolute error = 3.392367960693986e-16
relative error = 3.9731071223580912818129661200102e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.021
y[1] (analytic) = 8.5458670290147525128553571118729
y[1] (numeric) = 8.5458670290147528528006642202712
absolute error = 3.399453071083983e-16
relative error = 3.9778913708137859333424055665785e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.022
y[1] (analytic) = 8.5534166702352407515991770402068
y[1] (numeric) = 8.5534166702352410922540733421993
absolute error = 3.406548963019925e-16
relative error = 3.9826762735343702413175628843114e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.023
y[1] (analytic) = 8.560973864873028676993916551128
y[1] (numeric) = 8.5609738648730290183594816494768
absolute error = 3.413655650983488e-16
relative error = 3.9874618295358121974517229846442e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.024
y[1] (analytic) = 8.568538620485311556593741847244
y[1] (numeric) = 8.5685386204853118986710567946977
absolute error = 3.420773149474537e-16
relative error = 3.9922480378349378193559469223802e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.025
y[1] (analytic) = 8.5761109446368456330778545651639
y[1] (numeric) = 8.5761109446368459758680018662779
absolute error = 3.427901473011140e-16
relative error = 3.9970348974494220092845320986472e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.026
y[1] (analytic) = 8.5836908448999556890073648510743
y[1] (numeric) = 8.583690844899956032511428464034
absolute error = 3.435040636129597e-16
relative error = 4.0018224073977969048654618767562e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.027
y[1] (analytic) = 8.5912783288545426191507049489356
y[1] (numeric) = 8.5912783288545429633697702873816
absolute error = 3.442190653384460e-16
relative error = 4.0066105666994496784990856421265e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.028
y[1] (analytic) = 8.5988734040880910103851556273436
y[1] (numeric) = 8.5988734040880913553203095621987
absolute error = 3.449351539348551e-16
relative error = 4.0113993743746179910678167184050e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.029
y[1] (analytic) = 8.6064760781956767291820653472129
y[1] (numeric) = 8.6064760781956770748343962085122
absolute error = 3.456523308612993e-16
relative error = 4.0161888294444005431971842634843e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.03
y[1] (analytic) = 8.6140863587799745166833496561362
y[1] (numeric) = 8.6140863587799748630539472348582
absolute error = 3.463705975787220e-16
relative error = 4.0209789309307431605102746990685e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.031
y[1] (analytic) = 8.6217042534512655913768658865487
y[1] (numeric) = 8.6217042534512659384668214364495
absolute error = 3.470899555499008e-16
relative error = 4.0257696778564492782277595186508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.032
y[1] (analytic) = 8.6293297698274452593782658337085
y[1] (numeric) = 8.629329769827445607188672073158
absolute error = 3.478104062394495e-16
relative error = 4.0305610692451775915690450130568e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 2.033
y[1] (analytic) = 8.6369629155340305323269366959782
y[1] (numeric) = 8.6369629155340308808588878097983
absolute error = 3.485319511138201e-16
relative error = 4.0353531041214396870753347631270e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.034
y[1] (analytic) = 8.6446036982041677529036481739842
y[1] (numeric) = 8.6446036982041681021582398152895
absolute error = 3.492545916413053e-16
relative error = 4.0401457815106034389300036335359e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.035
y[1] (analytic) = 8.6522521254786402279775312469364
y[1] (numeric) = 8.6522521254786405779558605389769
absolute error = 3.499783292920405e-16
relative error = 4.0449391004388905769214046397198e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.036
y[1] (analytic) = 8.6599082050058758693900217737226
y[1] (numeric) = 8.6599082050058762200931873117286
absolute error = 3.507031655380060e-16
relative error = 4.0497330599333765452396476366061e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.037
y[1] (analytic) = 8.667571944441954842383409703358
y[1] (numeric) = 8.6675719444419551938125115563875
absolute error = 3.514291018530295e-16
relative error = 4.0545276590219937916580804803390e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.038
y[1] (analytic) = 8.675243351450617221681642323977
y[1] (numeric) = 8.6752433514506175738377820367651
absolute error = 3.521561397127881e-16
relative error = 4.0593228967335292441833036922449e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 5.712e-16
Order of pole = 0.5
x[1] = 2.039
y[1] (analytic) = 8.6829224337032706552310376318083
y[1] (numeric) = 8.6829224337032710081153182266187
absolute error = 3.528842805948104e-16
relative error = 4.0641187720976229211709398933648e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.04
y[1] (analytic) = 8.6906091988789980356085715614843
y[1] (numeric) = 8.6906091988789983892220975399633
absolute error = 3.536135259784790e-16
relative error = 4.0689152841447711198967036329122e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.041
y[1] (analytic) = 8.6983036546645651791054104866132
y[1] (numeric) = 8.6983036546645655334492878316459
absolute error = 3.543438773450327e-16
relative error = 4.0737124319063261076705376500132e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.042
y[1] (analytic) = 8.7060058087544285124933680747845
y[1] (numeric) = 8.706005808754428867568704252353
absolute error = 3.550753361775685e-16
relative error = 4.0785102144144934856848266871598e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.043
y[1] (analytic) = 8.7137156688507427674819732641065
y[1] (numeric) = 8.7137156688507431232898772251506
absolute error = 3.558079039610441e-16
relative error = 4.0833086307023352732873758197486e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 3.874e-16
Order of pole = 0.5
x[1] = 2.044
y[1] (analytic) = 8.7214332426633686828738438189841
y[1] (numeric) = 8.721433242663369039415426001264
absolute error = 3.565415821822799e-16
relative error = 4.0881076798037672112473333427256e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.045
y[1] (analytic) = 8.7291585379098807144260676211528
y[1] (numeric) = 8.7291585379098810717024399511143
absolute error = 3.572763723299615e-16
relative error = 4.0929073607535617755865072943847e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.046
y[1] (analytic) = 8.7368915623155747524253015579929
y[1] (numeric) = 8.7368915623155751104375774526347
absolute error = 3.580122758946418e-16
relative error = 4.0977076725873465654571196624767e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.047
y[1] (analytic) = 8.7446323236134758469843055838652
y[1] (numeric) = 8.7446323236134762057335999526084
absolute error = 3.587492943687432e-16
relative error = 4.1025086143416038114260661444893e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.048
y[1] (analytic) = 8.7523808295443459410676372516468
y[1] (numeric) = 8.7523808295443463005550664982067
absolute error = 3.594874292465599e-16
relative error = 4.1073101850536709972107028562823e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.049
y[1] (analytic) = 8.7601370878566916112542397408051
y[1] (numeric) = 8.7601370878566919714809217650653
absolute error = 3.602266820242602e-16
relative error = 4.1121123837617414463980569318585e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.05
y[1] (analytic) = 8.7679011063067718162446641452442
y[1] (numeric) = 8.7679011063067721772117183451329
absolute error = 3.609670541998887e-16
relative error = 4.1169152095048637337875228255086e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.051
y[1] (analytic) = 8.7756728926586056531206745287905
y[1] (numeric) = 8.775672892658606014829221802159
absolute error = 3.617085472733685e-16
relative error = 4.1217186613229410681046761259226e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.052
y[1] (analytic) = 8.78345245468398012136499200857
y[1] (numeric) = 8.7834524546839804838161547550736
absolute error = 3.624511627465036e-16
relative error = 4.1265227382567329232419114388765e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
memory used=87.7MB, alloc=4.3MB, time=4.41
x[1] = 2.053
y[1] (analytic) = 8.7912398001624578946489418866673
y[1] (numeric) = 8.7912398001624582578438440096486
absolute error = 3.631949021229813e-16
relative error = 4.1313274393478566290613689158721e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.054
y[1] (analytic) = 8.7990349368813851003957756183625
y[1] (numeric) = 8.7990349368813854643355425267362
absolute error = 3.639397669083737e-16
relative error = 4.1361327636387786935444414713657e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.055
y[1] (analytic) = 8.8068378726358991071274471809142
y[1] (numeric) = 8.8068378726358994718132057910554
absolute error = 3.646857586101412e-16
relative error = 4.1409387101728288488619534058336e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.056
y[1] (analytic) = 8.8146486152289363196026311903167
y[1] (numeric) = 8.8146486152289366850355099279502
absolute error = 3.654328787376335e-16
relative error = 4.1457452779941856291506889554022e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.057
y[1] (analytic) = 8.8224671724712399817537779046958
y[1] (numeric) = 8.8224671724712403479349067067886
absolute error = 3.661811288020928e-16
relative error = 4.1505524661478869293756292912560e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.058
y[1] (analytic) = 8.8302935521813679874310080520517
y[1] (numeric) = 8.8302935521813683543615183687075
absolute error = 3.669305103166558e-16
relative error = 4.1553602736798268867009832537806e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.059
y[1] (analytic) = 8.8381277621857006989606582268924
y[1] (numeric) = 8.838127762185701066641683023248
absolute error = 3.676810247963556e-16
relative error = 4.1601686996367516150739259467227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.06
y[1] (analytic) = 8.8459698103184487735262954149556
y[1] (numeric) = 8.8459698103184491419589691730801
absolute error = 3.684326737581245e-16
relative error = 4.1649777430662651047365749409149e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.061
y[1] (analytic) = 8.8538197044216609973800270276853
y[1] (numeric) = 8.8538197044216613665654857484816
absolute error = 3.691854587207963e-16
relative error = 4.1697874030168294112329770330539e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.062
y[1] (analytic) = 8.8616774523452321278919406584271
y[1] (numeric) = 8.8616774523452324978313218635349
absolute error = 3.699393812051078e-16
relative error = 4.1745976785377557838409186684168e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.063
y[1] (analytic) = 8.8695430619469107434455156104334
y[1] (numeric) = 8.8695430619469111141399583441355
absolute error = 3.706944427337021e-16
relative error = 4.1794085686792161034268871442509e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.064
y[1] (analytic) = 8.8774165410923071011868560927463
y[1] (numeric) = 8.8774165410923074726375009238768
absolute error = 3.714506448311305e-16
relative error = 4.1842200724922384572356842626920e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.065
y[1] (analytic) = 8.8852978976549010026356038338452
y[1] (numeric) = 8.8852978976549013748435928576997
absolute error = 3.722079890238545e-16
relative error = 4.1890321890287038306749844624914e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.066
y[1] (analytic) = 8.8931871395160496671653957246274
y[1] (numeric) = 8.8931871395160500401318725648757
absolute error = 3.729664768402483e-16
relative error = 4.1938449173413484070238579301019e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.067
y[1] (analytic) = 8.9010842745649956133617399718343
y[1] (numeric) = 8.9010842745649959870878497824358
absolute error = 3.737261098106015e-16
relative error = 4.1986582564837680698810581461714e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.068
y[1] (analytic) = 8.9089893106988745482651921204591
y[1] (numeric) = 8.9089893106988749227520815875797
absolute error = 3.744868894671206e-16
relative error = 4.2034722055104093801217752081580e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.069
y[1] (analytic) = 8.916902255822723264507720188966
y[1] (numeric) = 8.916902255822723639756537532898
absolute error = 3.752488173439320e-16
relative error = 4.2082867634765773908293135271889e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.07
y[1] (analytic) = 8.9248231178494875453501560543463
y[1] (numeric) = 8.9248231178494879213620510314303
absolute error = 3.760118949770840e-16
relative error = 4.2131019294384321839609339416365e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.071
y[1] (analytic) = 8.9327519047000300776286381251207
y[1] (numeric) = 8.93275190470003045440476202967
absolute error = 3.767761239045493e-16
relative error = 4.2179177024529909907728056108190e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.072
y[1] (analytic) = 8.9406886243031383726179582493907
y[1] (numeric) = 8.9406886243031387501594639156176
absolute error = 3.775415056662269e-16
relative error = 4.2227340815781235580262859932824e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.073
y[1] (analytic) = 8.9486332845955326948197337219447
y[1] (numeric) = 8.9486332845955330731277755258897
absolute error = 3.783080418039450e-16
relative error = 4.2275510658725586816943115106513e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.074
y[1] (analytic) = 8.956585893521873998683333179253
y[1] (numeric) = 8.9565858935218743777590670407156
absolute error = 3.790757338614626e-16
relative error = 4.2323686543958761593744731484389e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.075
y[1] (analytic) = 8.9645464590347718732674931039377
y[1] (numeric) = 8.9645464590347722531120764884104
absolute error = 3.798445833844727e-16
relative error = 4.2371868462085166015394230294720e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.076
y[1] (analytic) = 8.9725149890947924948505696009972
y[1] (numeric) = 8.9725149890947928754651615216012
absolute error = 3.806145919206040e-16
relative error = 4.2420056403717744407525081002232e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.077
y[1] (analytic) = 8.9804914916704665874973780566995
y[1] (numeric) = 8.9804914916704669688831390761226
absolute error = 3.813857610194231e-16
relative error = 4.2468250359477965135850103081896e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.078
y[1] (analytic) = 8.988475974738297391590581247646
y[1] (numeric) = 8.9884759747382977737486734800834
absolute error = 3.821580922324374e-16
relative error = 4.2516450319995884057425251053378e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.079
y[1] (analytic) = 8.9964684462827686403345944320602
y[1] (numeric) = 8.9964684462827690232661815451573
absolute error = 3.829315871130971e-16
relative error = 4.2564656275910107273503745384174e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.08
y[1] (analytic) = 9.0044689142963525442399839278696
y[1] (numeric) = 9.0044689142963529279462311446672
absolute error = 3.837062472167976e-16
relative error = 4.2612868217867798181425509029254e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.081
y[1] (analytic) = 9.012477386779517783596343662645
y[1] (numeric) = 9.0124773867795181680784177635267
absolute error = 3.844820741008817e-16
relative error = 4.2661086136524661975894536997694e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.082
y[1] (analytic) = 9.0204938717407375089416421689402
y[1] (numeric) = 9.0204938717407378942007114935823
absolute error = 3.852590693246421e-16
relative error = 4.2709310022544963168711600673387e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.083
y[1] (analytic) = 9.0285183771964973495360404950448
y[1] (numeric) = 9.0285183771964977355732749443686
absolute error = 3.860372344493238e-16
relative error = 4.2757539866601531617343377154745e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.084
y[1] (analytic) = 9.0365509111713034298481895056373
y[1] (numeric) = 9.0365509111713038166647605437635
absolute error = 3.868165710381262e-16
relative error = 4.2805775659375735000740570817997e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.085
y[1] (analytic) = 9.0445914816976903940620230593014
y[1] (numeric) = 9.0445914816976907816591037155071
absolute error = 3.875970806562057e-16
relative error = 4.2854017391557506401315755990553e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.086
y[1] (analytic) = 9.0526400968162294386120715703696
y[1] (numeric) = 9.0526400968162298269908364410474
absolute error = 3.883787648706778e-16
relative error = 4.2902265053845316185197156554152e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.087
y[1] (analytic) = 9.0606967645755363527553284910755
y[1] (numeric) = 9.0606967645755367419169537416952
absolute error = 3.891616252506197e-16
relative error = 4.2950518636946198893313081836597e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.088
y[1] (analytic) = 9.0687614930322795671877102865517
y[1] (numeric) = 9.0687614930322799571333736536244
absolute error = 3.899456633670727e-16
relative error = 4.2998778131575757612915794052200e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.089
y[1] (analytic) = 9.0768342902511882107131585198053
y[1] (numeric) = 9.0768342902511886014440393128494
absolute error = 3.907308807930441e-16
relative error = 4.3047043528458112917647542148915e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.09
y[1] (analytic) = 9.0849151643050601749734407164419
y[1] (numeric) = 9.084915164305060566490719819952
absolute error = 3.915172791035101e-16
relative error = 4.3095314818325961829640478694897e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.091
y[1] (analytic) = 9.0930041232747701872467147396134
y[1] (numeric) = 9.0930041232747705795515746150313
absolute error = 3.923048598754179e-16
relative error = 4.3143591991920548164683167869644e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.092
y[1] (analytic) = 9.1011011752492778913229294744258
y[1] (numeric) = 9.1011011752492782844165541621137
absolute error = 3.930936246876879e-16
relative error = 4.3191875039991643699944629271163e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.093
y[1] (analytic) = 9.1092063283256359364641426978806
y[1] (numeric) = 9.1092063283256363303477178190972
absolute error = 3.938835751212166e-16
relative error = 4.3240163953297605964404593673305e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.094
y[1] (analytic) = 9.1173195906089980744578450953426
y[1] (numeric) = 9.1173195906089984691325578542211
absolute error = 3.946747127588785e-16
relative error = 4.3288458722605325716314552034425e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
memory used=91.5MB, alloc=4.3MB, time=4.60
x[1] = 2.095
y[1] (analytic) = 9.1254409702126272647713874775325
y[1] (numeric) = 9.125440970212627660238426663061
absolute error = 3.954670391855285e-16
relative error = 4.3336759338690229169030328378482e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.096
y[1] (analytic) = 9.1335704752579037878156163531466
y[1] (numeric) = 9.1335704752579041840761723411513
absolute error = 3.962605559880047e-16
relative error = 4.3385065792336323676040473909380e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.097
y[1] (analytic) = 9.1417081138743333663258311214164
y[1] (numeric) = 9.1417081138743337633810958765465
absolute error = 3.970552647551301e-16
relative error = 4.3433378074336122520800413735124e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 4.939e-16
Order of pole = 0.5
x[1] = 2.098
y[1] (analytic) = 9.1498538941995552948681842662402
y[1] (numeric) = 9.149853894199555692719351343956
absolute error = 3.978511670777158e-16
relative error = 4.3481696175490733721035212253524e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Complex estimate of poles used
Radius of convergence = 2.602e-16
Order of pole = 0.5
x[1] = 2.099
y[1] (analytic) = 9.1580078243793505774796540589666
y[1] (numeric) = 9.1580078243793509761279186075291
absolute error = 3.986482645485625e-16
relative error = 4.3530020086609762405291830840030e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 2.1
y[1] (analytic) = 9.1661699125676500734497274104786
y[1] (numeric) = 9.1661699125676504728962861729424
absolute error = 3.994465587624638e-16
relative error = 4.3578349798511409760571879365164e-15 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = y - 1.0;
Iterations = 1000
Total Elapsed Time = 4 Seconds
Elapsed Time(since restart) = 4 Seconds
Expected Time Remaining = 13 Seconds
Optimized Time Remaining = 13 Seconds
Time to Timeout = 14 Minutes 55 Seconds
Percent Done = 25.67 %
> quit
memory used=92.1MB, alloc=4.3MB, time=4.63